Indicators of Crime and Criminal Justice: Quantitative Studies

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U.S. Department of Justice Bureau of Justice Statistics

Indicators of crime and criminal justice: Quantitative studies

NCJ-62349, June 1980

Edited by STEPHEN E. FIENBERG Department of Statistics and Department of Social Science Carnegie-Mellon University ALBERT J. REISS, JR. Department of Sociology Yale University

PROPERTY OF National Crimina! Justice Aelerence Service (PdCJRS) Box 6003 Wockville, hPiD 20849-66'00

For sale by the Superintendent of Doculuents, U.S. Government Prilltiug OWce, Wasliington, D.C. 20402 U.S; Department of Justice Bureau of Justice Statistics Harry A. Sum,Ph. D. Director

The Social Science Research Council is a private nonprofit organization formed for the purpose of advancing research in the social sciences. It emphasizes the planning, appraisal, and stimulation of research that offers promise of increasing knowledge in social science or of increasing its usefulness to society. It is also concerned with the develoument of better research methods. irnpro;ement of the quality and accessibil- ity of materials for research by social scientists, and augmentation of resources and facilities for their research. The Council's Center for Coordination of Research on Social Indicators was established in September 1972, under a grant from the Division of Social Sciences, Na- tional Science Foundation (grant number GS-34219; currently SOC-77-21686). The Center's purpose is to ahance the contribution of social science research to the development of a broad range of indicators of social change, in response to current and anticipated demands from both research and policy communities.

Library of Congress Cataloging in Publication Data Main entry under title: Indicators of crime and criminal justice. Based on research initiated during the Workshop in Criminal Justice Statistics, held in the summer of 1975 by the Social Science Research Council. "NCJ-62349." Includes bibliographical references. Supt of Docs. no.: J 29.2:1n2 1. Criminal statistics-Addresses, essays, lectures. I. Fienberg, Stephen E. 11. Reiss, Albert J. 111. Workshop in Criminal Justice Statistics, 1975. 1V. Social Science Research Council. HV6018.152 364 80-607926

This project was supported by Grant No. 75-SS-99- 6017, awarded to the Social Science Research Council by the Statistics Division, National Criminal Justice Information and Statistics Service, Law Enforcement Assistance Administration(n0w Bureau of Justice Sta- tistics), U.S. Department of Justice, under the Omnibus Crime Control and Safe Streets Act of 1968, as amended. The project,entitlednWorkshopandFellow- ship in Criminal Justice Statistics," was directed forthe Social Science Research Council by David Seidman and monitored by Paul D. White of BJS. Points of view or opinions stated in this document are those of the author(s) and do not necessarily represent the official position or policies of the U.S. Department ofJustice. LEAA authorizes any person to reproduce, publish, translate, or otherwise useallor any part of the material in this publication, with the exception of those items indicating that they are copyrighted by or reprinted by permission from any other source. Preface The topics on which they focused were the One of the most pleasing outcomes of'the treatment of data in victimization surveys; workshop (at least to us) has been the con- The Social Science Research Council's measurement and experimental design in tinuing work of the participants and faculty Center for Coordination of Research on the study of police effectiveness; the sen- on methodological problems in criminal Social Indicators, organized in 1972, has tencing process; decisionmaking by the justice research. They have been intimately had an ongoing interest in promotingqual- U.S. Board of Parole; the deterrent effect involved in such activities as: (a) the ity research in the area of criminal justice of capital punishment; and the problem of National Academy of Sciencies-National statistics, especially at a national level. To designing a model of the criminal justice Research Council's Committee on Law this end, the Center's Advisory and Plan- system. Enforcement and Criminal Justiceand that ning Committee created in 1973 a special Committee's Panels on Deterrence and The papers in the present volume are a Incapacitation, and on Rehabilitation, (b) Subcommittee on Criminal Justice Sta- direct outgrowth of research initiated tistics, whose focus has been on under- the NAS-NRC Committee on National during or as a result of the workshop activ- Statistics and that Committee's Panel on standing and measuring aspects of crime ities. Earlier drafts of many of the papers and the criminal justice system. the National Crime Survey, (c) the Ameri- were presented and discussed at a work- can Statistical Association's Committee on The present volume can be traced back to a shop reunion which took the form of a con- Law and Criminal Justice Statistics, and meeting of the members of the Subcommit- ference held in the fall of 1977, again (d) SSRC's Advisory and Planning Com- tee with staff at the Law Enforcement sponsored by LEAA. The first paper in this mittee on Social Indicators. They have also Assistance Administration (LEAA) to dis- volume reports on the highlights of that initiated new research projects on a wide cuss research projects of mutual interest. conference, and provides an overview to variety of problems in the area. This con- The two of us (Stephen E. Fienberg and the frontiers of quantitative research in this tinued activity is perhaps the best indicator Albert J. Reiss, Jr.) were convinced that an area. The remaining sections of the volume of the success of the Workshop. upgrading of the quality of research in the are organized in large part around the criminal justice area could be affected research produced by the six working Almost as pleasing are the many profes- through the recruitment of statisticians and groups from 'the workshop. sional collaborations and personal friend- other quantitative social scientists to work ships that developed among those who The faculty of the workshop consisted of took part in the Workshop. These go far on interesting statistical modelling and Albert D. Biderman, Bureau of Social analysis projects in the area. We therefore beyond the work reported on in this Science Research (Washington, D.C.); volume. proposed to hold a workshop focussing on Alfred ~lumxn,Carnegie-Mellon Univer- the methodological and theoretical prob- sity; John Clark, University of Minnesota; We acknowledge with thanks the contribu- lems involved in the measurement af crime ~ichaelJ. Hindelang, State University of tions of David Seidman of the Social and its effects on society. New York at Albany; Albert J. Reiss, Jr., Science Research Council, and of Elaine Thus it was that in the summer of 1975, the Yale University; Richard Sparks, Rutgers Javonovich, his assistant, who staffed the Social Science Research Council, with University; and Leslie T. Wilkins, State Workshop; and of the staff and director of funding from LEAA* (now the Bureau of University of New York at Albany. the Council's Center for Social Indicators for their support and interest. Special Justice Statistics), organized a month-long The social scientist participants in the Workshop in Criminal Justice Statistics. thanks are due to Nancy McManus of the workshop were David W. Britt, Florida Social Science Research Council, who The workshop brought together three Atlantic University (currently at Nova Uni- groups: a faculty composed of seven worked closely with us in structuring the versity); William B. Fairley, Harvard Uni- volume, extracting manuscripts from experts in criminal justice; seven partici- versity (currently a private consultant); pants who were young academic statis- authors, and copyediting the entire volume. Stephen E. Fienberg, University of Minne- Ms. McManus was responsible for seeing ticians, sociologists, and psychologists; sota; Gary G. Koch, University of North and six government professionals. the manuscript through to completion, and Carolina; Kinley Larntz, University of we are indebted to her for her assistance. The workshop's program of activities Minnesota; Colin Loftin, Brown Univer- started with a series of lectures and semi- sity (currently at the University of Michi- STEPHENE. RENBERG nars and concluded with the organization gan); and Howard Wainer, University of ALBERT J. REISS,JR. of the faculty and the participants into six Chicago (currently at the Bureau of Social working groups. Among the topics covered Science Research). at the plenary meetings were conceptions Government professionals participating in of the criminal justice system, data sources, the workshop were Ken Brimmer, Mimi research approaches, methodological and Cantwell, Linda Murphy, Tom Petersik, substantive problems, and theoretical and J. Frederick Shenk, all of the U.S. issues. The intensive interchange at these Bureau of the Census; and Cynthia sessions sparked a high degree of interest in Turnure, Minnesota Governor's Commis- the six working groups, each of which then sion on Crime Prevention and Control. undertook a concentrated exploration of a problem area in criminal justice research.

'Grant No. 7533-994017. Abstract The quantitative study of criminal justice is a rapidly expanding field, involving the application of relatively sophisticated statistical methods and probabilistic models. This volume brings together some of the products of a workshop in criminal justice statistics sponsored by the Social Science Research Council and the Law Enforce- ment Assistance Administration (now the Bureau of Justice Statistics) during the summer of 1975. An introductory essay describes the highlights of a followup conference held in October 1977, at which workshop participants described some of their subsequent research. This essay provides an overview of the volume and of the frontiers of quantitative research in this area. The remaining papers consist of detailed versions of conference presentations, as well as reports on other related research in such diverse areas as: macro models for criminal justice planning; the deterrent effects of punishment on crime; effects of plea-bargaining on case disposition; criminal victimization and models for its analysis; victim proneness; parole decisionmaking, and police patrol experiments. Contents Preface, iii Abstract, iv David Seidman Current research in criminal justice statistics: Report of a conference, 1

Crime rates and victimization Albert J. Reiss, Jr. Understanding changes in crime rates, I1 Richard F. Sparks Criminal opportunities and crime rates, 18 Albert D. Biderman Notes on measurement by crime victimization surveys, 29 Stephen E. Fienberg Victimization and the National Crime survey Problems of design and analysis, 33 Albert J. Reiss. Jr. Victim proneness in repeat victimization by type of crime, 4 1 Stephen E. Fienberg Statistical modelling in the analysis of repeat victimization, 54

Sentencing and parole decisionmaking Richard Perline Quantitative approaches to the study of parole, 59 Howard Wainer Kinley Lurntz Linear logistic models for the parole decisionmaking problem, 63 David W. Britt The effects of plea bargaining on the disposition of personal Kinley Larntz and property crimes: A research note, 70 The deterrent effects of punishment Colin-Loftin Alternative estimates of the impact of certainty and severity of punishment on levels of homicide in American states, 75 Stephen S. Brier Recent econometric modelling of crime and punishment: Stephen E. Fienberg Support for the deterrence hypothesis?, 82 Criminal justice planning Awed Blumstein A prolegomenon for a macro model for criminal justice Gary G. Koch planning: JUSSIM 111, 99 Stephen E. Fienberg Redesigning the Kansas City Preventive Patrol Kinley Larntz Experiment, 109 Albert J. Reiss, Jr. Current research in criminal justice statistics: Report of a conference* DAVIDSEIDMAN** Social Science Research Council Washington, D. C.

The quantitative study of crime and crimi- discussions do not represent the full range Sparks presented one version of this distri- nal justice is a rapidly developing field of of research in criminal justice carried out bution, based on his London victimization research. While perhaps most of this devel- by workshop participants since the sum- survey. (See Sparks, Table 1.)' What is at opment can be attributed at least indirectly mer of 1975, but focus on the three areas of issue here is the sense in which the overall to the apparent rise in crime beginning in research discussed above and emphasize victimization rate characterizes the risk of the 196OYs,advances in particular areas can research supported by the Law Enforce- victimization for individuals in the group. be traced to more proximate causes. The ment Assistance Administration grant to If it is assumed that the overall rate repre- creation of major new data bases is perhaps the Social Science Research Council which sents the risk faced by individuals, then the the most obvious stimulus to quantitative made the workshop possible. distribution of individuals by number of victimizations ought to fit a Poisson distri- research, and here the invention and insti- This report draws upon both the written tutionalization of victimization surveys bution. The last column of Sparks's table conference papers and the discussions to shows the expected number of individuals have been particularly notable. There has present highlights of the conference in the been, within the criminal justice system by number of victimizations for a Poisson the three mainareas considered. It does not process. The standard finding emerges: itself, increased self-awareness, and this pretend to capture the full richness of the has stimulated attempts to rationalize the "the numbers reporting no victimization at presentations, and the reader should turn all, and the numbers reporting several inci- decisionmaking process .within the system. to the conference papers for the complete The basis of rationalization, in a number of dents, are both greater than would be pre- picture. Together, the report and the dicted by a Poisson distribution" (Sparks). instances, has been quantitative study of papers provide an overview of current the. actual operations of the system, research on the frontiers of the quantitative This result is a starting point for specula- combined with attempts to develop predic- study of crime and criminal justice and an tion and investigation. Sparks, for exam- tion methods which would allow for new assessment of current problems and ple, points out that slightly more compli- approaches to decision making. Finally, directions for future research. cated models fit the data better. In particu- there has been increasing questioning of lar, models based on either "contagion" or the effects of the criminal justice system on heterogeneity of victim proneness in the offenders, on the crime rate, and on society Victimization studies population work reasonably well. Unfor- as a whole; this questioning has led to MOSTPUBLISHED reports of victimization tunately, the two models cannot be dif- attempts to analyze quantitatively what surveys amount to little more than calcula- ferentiated in cross-sectional data, which those effects are, in ways which may tions of "victimization rates" for popula- points to the importance of exploiting the provide guidance for criminaljustice policy tions and subpopulations for particular longitudinal features of NCS. Sparks finds in the future. time periods. While these calculations may the contagion notion an implausible These three areas of research were intensely be useful, they leave unresolved certain explanation of the data, and this discussion studied at the Social Science Research conceptual issues, contribute little to an will pursue the victim proneness direction. Council's Workshop in Criminal Justice understanding of crime and victimization, If the explanation of the lack of fit of the' Statistics during the summer of 1975. Sub- and fail to exploit the full potential of the Poisson model is that individuals differ in sequent to the workshop, participants surveys (in particular, the longitudinal their victim proneness, a logical next step is carried out research in these areas and features of the National Crime Panel to sort out individuals by their degrees of others. The conference held in October Survey are underexploited). Several work- victim proneness, and see if the Poisson 1977 provided an opportunity for presen- shop participants have been studying vic- model fits within subgroups of the popula- tation of research results and for discussion timization surveys in ways which probe tion. Sparks tried this with his London of research plans. The presentations and more deeply into the structures and processes underlying the data. The primary 'Cltat~onsw~thoutdates refer to papers and other mate- *A report to the Bureau of Justice Statistics by the rials which served as the basis for conference presenta- Social Science Research Council, 605 Third Avenue, focus has been on problems related to mul- tions. Other citations are to materials included in the New Y ork, NY 10016, pursuant to Order Numbers- tiple and series victimization and the inter- l~stof references at the end of th~sreport. 0073-J-LEAA. This report is based upon working actions of survey design features and papers presented at the conference. The quotations and materials discussed will therefore not neces- resulting data. Considerable time at the sarily coincide with the versions of the papers conference was devoted to presentation published in this volume. and discussion of this work. **In September 1978 David Seidman left the Social Science Research Council forthe Rand Corporation, A useful introduction to problems of mul- Washington. D.C. tiple victimization is a well-known finding concerning the distribution of individuals by number of reported victimizations within the reference period. Richard data. but could not find any combination which, as a result of the random process, Second, the matrix depends upon the time of attributes, such as age, sex, race, or was not victimized in the reference period. sequence of victimizations. NCS incident social class, which could be used to cate- reports record the month of nonseries vic- gorize individuals to produce subgroups The plausibility of an absolutely immune group declines when a time perspective timizations. Victimizations of a household within which the Poisson model ade- within a month, however, lack the informa- quately fit the data. As he notes, it is not longer than the reference period of a single cross-sectional survey is adopted. This tion required to establish the time sequence. surprising that these simple demographic The timing of series victimizations presents variables would be insufficient. begins to suggest the importance of exploiting the over-time features of the Na- a more complicated problem, as the NCS It is possible that the observed pattern tional Crime Panel Survey. There are, of records only the month of occurrence of actually results from measurement prob- course, other reasons for relying upon lon- the first incident in the series (and if the lems in the surveys. One such measurement gitudinal files of the NCS for analysis of series began before the reference period, problem has to do with series incidents. multiple and series victimimtion. For one the date recorded is the first month of the Typically the number of incidents in a thing, the large number of incidents avail- reference period). Reiss therefore had to series is estimated by the victims, and there able in such files allows disaggregation to impose an arbitrary time order so as to appears to be a tendency to overestimate crime-specific victimization. For another, establish a sequence for all reported victim- the number-a phenomenon common to a repeated interviews can be used to build izations. He did this by randomly assigning number of different areas of investigation. long sequences of victimization experience, dates within months to events, with series For a variety of reasons, incorporation of which allow, among other things, investi- treated as single events. The error intro- series victimizations into the distributions gation of the stability of patterns. Finally, duced into the ordering by this random here considered is difficult, and their exclu- longitudinal files allow investigation of the procedure is likely to be relatively small for sion may substantially affect the shape of time between victimizations, which may be nonseries incidents, as incidents occurring the distribution. Some indication of the important to an understanding of multiple in different months are unaffected. The effect can be obtained by examining such victimization. errors introduced by treating series victim- questions as whether series victims also izations as single incidents and then placing report other victimizations, but this exami- Albert J. Reiss, Jr., has constructed what them (at a randomly selected date) in the nation is difficult in a small cross-sectional we believe to be the only extant working month the series begins (or the first month survey. Another measurement problem is longitudinal file of NCS data. He presented of the reference period) are harder to assess nonreporting. It may be, for example, that some results of analysis of this file to the because of the general paucity of informa- most nonreporting is by people who have conference. These results concerned the tion about series victimizations. However, been victims only once. Since the depar- relatively limited question of whether in Reiss has found that those who report tures from the Poisson distribution are repeated victimization of a given unit there series victimizations are highly unlikely to largely in the zero and one victimization is a propensity for repeated victimization report other victimizations, so that the groups, this would account for much of the by the same type of crime, or whether re- primary effect of his treatment of series vic- lack of fit. Accounting for that pattern of peated victimization is random as to crime timizations is likely to be a reduction in the nonreporting, however, is difficult. type. While the question is limited, it ap- proportion of cases in a crime switch' pears central to an understanding of victim matrix which fall on the diagonal of the If the deviation from the Poisson distribu- proneness and multiple victimization. matrix (since events within a series are in tion appears to be mainly a matter of too theory all of the same kind). The signifi- many people reporting no victimizations, it The analytical tool Reiss used is a crime switch matrix consisting of pairs of victjmi- cance of this will become clear as the results seems reasonable to fit a Poisson distribu- are discussed. tion to the distribution of those reporting zations, where a preceding victimization by at least one victimization, and then project type of crime is compared with a following A preliminary examination of the data backwards to estimate the number "be- victimization by type of crime. (Reiss's "Victim Proneness") enables one longing" in the zero victimization group The construction of such a matrix presents to compare the distributions of victimi.za- under Poisson assumptions. The 'excess" a number of questions and problems. First, tion incidents by type of crime where both actually found in that category might then what is the unit at risk? Confining his anal- incidents occurring in sequences and single be thought of as drawn from a population ysis to households as units, Reiss notes that victimizations are included with equivalent distributions not including singli victimi- somehow lacking vulnerability to crime. victimization of individuals within house- The source of this immunity to crime-or holds may symbolically represent victimizations. It is apparent that the distributions at least to certain kinds of crime-is not zation of the household. (Similarly, are substantially similar, which leads Reiss immediately obvious. Presumably it has individuals may not sharply distinguish to conclude that "multiple or repeat house- something to do with residential location household victimization from personal vic- hold victims are on the whole no more or life style. Of course, while a model pos- timization when the focus is on personal prone to victimization by certain types of tulating an immune group and a group victimizations. Because of the choice of crime than are all victims." If multiple subject to Poisson process may fit thedata, focusing on households, Reiss's analysis is victimization reflects victim proneness, it isolating the immune group for analysis unaffected by this problem.) It follows that nevertheless seems not to reflect proneness may not be possible, since there is no obvi- if the household is the unit of analysis, a re- to particular types of crime. ous way to separate it from the group searcher may either limit the analysis to household victimizations or include as well victimizations of individuals within the household. Reiss examined the data both ways. Reiss's crime switch matrix further exposes experience at the prior location. (That is, sketch of this approach is contained in sec- the structure of multiple victimization. As information is obtained which, depending tion 5 of his "Victimization and the Na- is perhaps clearer from a chi-squared upon the time of the move, may relate to tional Crime Survey: Problems of Design analysis of the matrix, the major element of the new resident's prior residence, but there and Analysis." He expanded upon these structure in the matrix is the heaping of is, in the recorded data, no way to distiil- ideas in a presentation at ehe conference. incidents along the diagonal. The implica- guish between victimization at the old location is that "the chances that a household In Fienberg's view, analysis of questions of tion and victimization at the new one.) The multiple victimization depends upon mod- or one or more of its members will be second question cannot be addressed at all, els for the occurrence of victimizations successively victimized by the same type of because no attempt is made to follow crime are greater than one would expect movers to their new residential locations. It over time. Without necessarily suggesting given the chances all households and their might be possible to approach the problem that it represents the true underlying struc- members have of being victimized by that relatively cheaply by adding to interviews ture, Fienberg proposes modelling victimi- type of crime." The analysis continues by with new residents a set of questions de- zation as a particular form of stochastic examining whether the frequency of signed to elicit retrospective information point process, a semi-Markov process. particular pairs depends upon which about victimization experiences, though (The Poisson process, discussed above, is a special case of the semi-Markov process.) element of the pair occurs first. For recall decay problems would be a substan- example, is the sequence assault-personal Such a process has two main features. tial obstacle to obtaining reliable infor- First, the probability that one is next vic- larceny more or less frequent than the mation. sequence personal larceny-assault? Reiss's timized by a crime of type j depends only Table 4 strongly suggests that the order Also important to questions of victim and upon the crime type of which one was last a within pairs makes no difference; that the location proneness is the character of the victim. That is, the transition from victimi- structure is symmetrical with respect to neighborhood of the interview location. zation state to victimization state is gov- order of occurrence. Reiss has merged certain neighborhood erned by a matrix of probabilities resem- characteristics onto his victimization tape, bling Reiss's crime switch matrix. Second, Reiss's paper merely establishes these ele- but what is perhaps the most important the interval between victimizations is ran- ments of structure. Conference partici- neighborhood characteristic for these pur- dom, though the distribution of time pants offered some speculative explana- poses, the neighborhood crime rate, is between victimizations depends upon the tions. Some possible explanations turn on unavailable. current victimization state. A convenient methodological artifacts: reporting defini- feature of semi-Markov processes is that, tions, response bias, interviewing tech- Some questions about these patterns of for many purposes, the transition matrix niques, and the like. More substantive multiple victimization relate to the length and the time interval distributions can be explanations focused on the characteristics of time in panel for respondents. The Reiss studied separately. The model is based on of locations, patterns of communication, data set contains a high proportion of re- continuous time, while victimization data and the elusive concept of victim proneness. spondents interviewed only a small number collection is one month at a time. Integrat- of times. It seems likely thatthe proporiion It was noted that, because the NCS is a sur- ing these two different approaches presents of single victimizations would decline as, modelling,problems. vey of household locations, there is in the sample "ages." It is also possible that theory the opportunity to explore victim some of the concentration on the diagonal Fienberg also notes that the hierarchical proneness and location proneness by of the crime switch matrix would decline, structure of the victimization surveys (in- examining over time (1) victimization ex- the pattern of victimization followed by dividuals within families, families within periences at locations where there is a victimization of the same kind declining as households, households within locations, change in individuals, and (2) victimization time between victimizations increases. locations within neighborhoods) compli- experiences of individuals who move out of Reiss in other work is examining time be- cates the modelling approach. These adqed a survey location. The importance of this tween victimizations, but results of that complications will not be discussed here. kind of examination is suggested by the re- work were not presented at the conference. A fundamental question is whether the lationship between being victimized and process is time homogeneous, or whether moving. Reiss pointed out that both series Stephen Fienberg has been developing models for analysis of victimizationdata in there are shifts in the process related to, victims and other multiple victims are say, time in panel or other causes. To an- highly likely to move. The questions which their full longitudinal structure, with particular attention to problems of multiple swer this question and others relating to need to be answered are whether the high time between events, Fienberg proposes a rate of victimization continues with a new victimization and various time-related effects in the data, such as the effects of research approach along the following household at the surveyed location and lines. In order to obtain the required long whether the high rate of victimization con- month of collection, time lag to reference month, and time in panel. A preliminary records, he begins with a subfile of respon- tinues for the mover at a new location. dents with full 3%year records. Assume we While in theory the survey design might start by considering the household as the permit the first question to be addressed, in unit of interest. Then there are 42 months practice it does not, because the records do in which an incident of victimization may not carefully distinguish between new and be reported. As a first step, consider only old tesidents in continuing locations and whether the household has or has not been because, in the case of new residents, no victimized within a given month, ignoring information is sought about victimization differences among types of crime and multiple victimization within a month. (Note that the NCS treatment of series victimiza- or starts with completely aged cohorts: the have bearing well beyond questions of mul- tion causes difficulties here.) Then there are same records are included. And starting in tiple victimization. The overriding problem 242 possible time sequence patterns, a either place one might compare different is that longitudinal analysis is required, number far too large for analysis. In prac- cohorts at similar points in their "life cy- while the attention of LEAA and the Bu- tice, the number of patterns found would cles" in the panel to investigate stationarity reau of the Census has been directed almost probably be much smaller; Fienbergguesses of victimization apart from the question of entirely to cross-sectional analysis. Related that about 20 patterns would account for time homogeneity Fienberg discussed. The to this are several problems resulting from 95 percent of the records. It would then be question separating the two approaches, selective attrition of panels, largely caused possible to examine the time patterns for then, is how long a record is necessary to by residential mobility and changes in shifts associated with time in panel. As a investigate time homogeneity. That, how- family composition. Alteration in survey next step, households could be scored each ever, cannot be answered a priori. In the design is required to (1) provide informa- month according to whether there has been absence of adequate prior investigations, tion about the continuity of respondents household victimization, personal victimi- the only way to know whether it is within household locations, and (2) allow zation, or no victimization, and the same necessary to use Fienberg's approach as investigation of patterns of movers, pre- kind of analysis could be done. The analy- compared with relying upon shorter and post-move. records is to compare findings based on the sis would then continue, examining finer Conferees commented upon the Census longest possible records with those based grain structure at each step. The informa- Bureau's "Description of Activities," a on shorter ones. tion on time sequencing of victimizations proposed research agenda for fiscal years generated in this way feeds back into the The discussion of the two possible starting 1978 through 1982. This Description treats models of generation of multiple victimiza- points for the investigation Fienberg pro- the matters mentioned in the previous tion which are at the heart of the investiga- posed pointed once again to the problem of paragraph, and it is worth quoting the tion. The discovery of time heterogeneity in panel attrition. It has already been noted entire treatment: long records would likely allow for various that those with high victimization are rela- transformations inducing homogeneity. In 3. Quesrionnaire design research tively likely to move from the household Research on the most effective questionnaire addition to casting light on the underlying location and therefore be lost to the panel. processes, such transformations would design will focus on the following areas: There are at least three different reasons for ... provide important information about the this. First, high victimization and house- d. A method of identifying respondents so interpretation of aggregate victimization hold propensity to move may independ- they can be traced across time. rates in cross-sectional analysis. The prob- ently be related to other causal variables, ... lem of the ill-fitting Poisson can be ad- such as low income. Second, it seems plau- 12. Conceptual issues regarding NCS dressed, and records sorted in ways allow- sible that some households may move . . . ing examination of victim proneness. because of high victimization. Presumably b. Mover/Nonmover Study (including a Several of the conferees questioned whether in .such cases the household has decided comparison of in-migrants with out-migrants). it was wise to begin with a subfile of those there is location proneness. Third, the 13. Analyrical issues with 3% years of data, suggesting instead young are relatively likely to leave the ... household, going off to college or setting a. Longitudinal studies. An exploration of starting with an entering cohort and ex- techniques and difficulties of exploiting NCS amining it over a six-month period. Reiss up their own households. Since the young crime features to do longitudinal analyses. suggested that there will be sufficient mul- have relatively high victimization rates, tiple victimization within a six-month this process will reduce the victimization It is noteworthy that mention of the longi- period to allow the kind of analysis rates for the household considered as a col- tudinal features of the design and their im- Fienberg had proposed for the longer lection of individuals. Either starting point portance for analysis does not appear until records. The suggested advantages of the for the Fienberg investigation will, pro- the final page of the document. It was the entering cohort approach are that it avoids vided it ultimately deals with complete long clear sense of the conferees both that the gaps in records (which Fienberg had noted records, lead to an examination of a limited placement of that brief discussion at the as a complication facing his approach) and subset of the original panels, and the vic- end indicated the priority attached to lon- it significantly reduces problems associated timization experience of the movers is gitudinal analysis by those responsible for with panel attrition. And, of course, the likely to differ systematically from the ex- NCS, and that such low priority was totally number of possible patterns is substantially perience of those who remain. Further- inappropriate. smaller with 12 months than with 42 more, if, as is sometimes the case, it is im- months. possible to tell from the data records Decisionmaking whether the occupants of a household have Fienberg's answer was that time hetero- changed from interview to interview, some Considerable attention at the workshop geneity was more likely to be discoverable of the "complete" long records will actually had been given to aspects of decision- with the longer records. The conferees then be spliced records of more than one house- making in parole and sentencing. Several suggested starting with entering cohorts hold (in the nonlocational sense). Given the of the workshop participants continued re- and "aging" them. It is clear that if they are likelihood that the victimization experi- search in this area and presented results to aged far enough, with movers deleted, it ences of the various households comprising the conference. makes no difference whether one starts the spliced record will systematically differ, with entering cohorts and works forward The Salient Factor Score system used by these "completed" records will provide the Federal Board of Parole approaches misleading information. the parole prediction problem by assigning While the presentations and discussion at scores for each individual on nine categori- the conference focused on questions of cal variables and adding the scores (equally multiple victimization, they pointed to several important problems in the design and analysis of victimization surveys which weighted) to produce a single Salient Fac- squared statistics for each. In addition, he The group of individuals with predicted tor Score, which is used to predict parole computed the likelihood ratio chi-squared probabilities above the cutpoint will pre- outcome. Herbert Solomon (1976) reana- for an equally weighted model ("Burgess sumably include some parole failures and lyzed the data earlier used to develop the scale," the salient factor method). While some parole successes. The group below Salient Factor Score system. He showed models which include the interaction term the cutpoint wil! also include some suc- that, for a subset of four predictor varia- do better than models which do not, cesses and some failures. The difference bles, logit models, which weight the varia- differences in goodness of fit among the between the proportion of all successes bles unequally, can achieve better prediction various models without the interaction who fall above the cutpoint and the pro- than the equal weighting of the Salient term are exceedingly small. That is, it does portion of all failures who fall above the Factor Score system, in the sense of fitting not seem to matter much whether one uses cutpoint is a measure of the ability of the the observed proportion of successes. (In four or eight variables (presumably because model to discriminate properly. As the cut- part, no doubt, this better prediction of high collinearity among the variables). point is varied, this difference is likely to occurs because Solomon's method pro- Nor does it seem to matter much whether change, and the proportion of the whole duces a larger number of prediction cate- one uses the equal weights of the salient group falling above the cutpoint will surely gories than the Salient Factor system, factor method or a more sophisticated change. For each of the models Larntz given the same number of predictor weighting scheme. varied the cutoff point and examined the variables.) Kinley Larntz felt that analysis Larntz then removed the restriction of the key difference. These results are presented could be pushed further (or at least beyond analysis to categorical variables. Several of as a series of graphs. To facilitate compari- the published description of Solomon's the categorical variables of the first analy- son across models, Larntz graphed the dif- work) and that it would be useful to ap- sis were produced by categorizing measured ferences not as functions of the cutoff proach a different data base with the same scales, and Larntz therefore restored the point, but rather of the proportion of the general questions. He described his work original scales. Removing the restriction total sample below the cutoff point. on this problem at the conference. called for changing the analysis technique It is to be expected that the logistic models The State of Minnesota had undertaken a to logistic regression, and Larntz applied will perform relatively well in this test, be- parole project similar to the federal effort, this technique to seven variables which are cause the variables had initially been developing its own salient factor score sys- quite similar to the variables used in the selected on the basis of their performance tem on the basis of an extensive body of earlier analysis. See Larntz, for partial in the combined validation and construc- data concerning released prisoners. Larntz results. Once again, the number of variation samples. Performance of the logistic obtained data for about 1000 released pris- bles included in the model did not have a regressions near this level would, because oners from the State of Minnesota, the striking effect on goodness of fit. Indeed, a less preselection of variables was involved, data used in the development of the salient model containing only two variables, age at indicate that they are of a relatively high factor system, and reanalyzed it using mul- first conviction and number of previous quality. The high peak associated with a tivariate log-linear methods. (Tables and parole failures, performed nearly as well as logistic regression based on only two graphs from Larntz's analysis are in his a seven-variable model. Larntz tested inter- variables is therefore particularly striking. "Linear Logistic Models for the Parole actions, but did not include any in the Decisionmaking Problem.") reported models because they seemed to In principle, analysis of this kind could be have little effect. It is striking that even the used to select an optimal cutpoint value. Larntz begins with a logit analysis using the seven-variable model does not represent an However, that selection depends upon eight categorical variables of the salient enormous increase in goodness of fit overa criteria for optimality, and it is not entirely factor scores applied to 485 cases selected model using no variables except a constant clear what those criteria should be. Maxi- from the full file (this reduced sample is the term. It is difficult to compare the logistic mum separation is obviously an attractive "construction sample"). This analysis par- regressions with the logit models in terms candidate. However, one might want to, allels that of Solomon, except for the larger of goodness of fit, since the variables used say, sacrifice some degree of separation for number of variables. In addition, Larntz in the logit models were selected by the a larger proportion of the total sample tested for two-factor interactions (which Minnesota parole project precisely because below the cutpoint. Solomon does not report having done). they produced a salient factor score which Larntz next asked whether the effects of Only an age at first conviction-burglary seemed to "work" well for the data Larntz interaction seemed to have much effect, preselection of variables distorted the was using. The variables used in the logistic results, so that the estimated probabilities with those first convicted at higher ages regressions were somewhat less preselected. more likely to be parole failures if qhe were in fact not very good estimates. He instant offense is burglary, while whether The point of parole prediction models, of tested this possibility by taking the esti- the instant offense is burglary matters little course, is not to fit observed probabilities mated probabilities from each model and for those first convicted at age 19 or of parole failure for categories of potential using them to generate a binomial random younger. Larntz estimated models using parolees. It is rather to provide predictions variable (success or failure) for each indi- the full eight variables, the,eight variables of success or failure which may serve as the vidual. He then repeated the cutpoint and with the one interaction, a subset of four basis for parole decisions. The important difference analysis for each model, using variables (equivalent to the Solomon question, therefore, is how well the model model), and four variables with the is able to separate parole successes from interaction, computing three kinds of chi- parole failures. Larntz turned to the other half of the data set, the validation sample, for an approach to this question. The logic is roughly as follows. For each individual in the sample, the model will generate a prediction of success. The analyst then chooses a cutpoint on the probability scale. the generated outcome scores rather than a difficult thing to do. It is therefore not than the probability model would suggest. the actual outcomes. Graphs for three surprising that it appears difficult to im- Furthermore, even if they are expected to models are presented in Larntz. The first prove upon Larntz's two-variable logistic happen, they cause difficulty for the esti- two graphs are for logistic models. It is regression model. mation of individual probity, particularly clear that in both czses the curve has shifted if the item is far from the individual's pro- upwards, which suggests that the distribu- Wainer in fact told the conferees that he bity, because information about individual tion of estimated probabilities is too spread had given up hope of accurately predicting probity decreases with distance of the item out. Application of these models to a new recidivism (or parole failure), and in his from the individual probity while its in- data set should reveal considerable shrink- work on what appeared to be the parole fluence on the estimate of probity in- age. There is noticeably less upward prediction problem was actually address- creases. The problem, then, is how to ing a different question. From the perspec- shifting for the one logistic regression reduce or eliminate the effects of these tive of his analytic approach, events (or the model included, indicating that the esti- errors in estimating probity. mated probabilities are reasonably good. variables involved in parole prediction) are And it should be emphasized that the viewed much like items in a test, and each The statisticians at the conference discussed logistic regression involved here has only event is characterized by its "rarity" ("dif- this estimation problem at some length, two predictor variables. The conclusion is ficulty" in the testing context). Recidivism, providing Wainer with some useful sugges- that a very simple model, involving only or parole failure, is viewed simply as an tions, but not reaching a clear solution. two variables, performs quite satisfacto- event with a certain amount of rarity. In- While predictions of success are important dividuals in the testing context are char- rily-at least in comparison with the other in modern methods of parole decisionmak- models tested. It is obvious, however, that acterized by their level of ability, which, in ing, they are not the sole basis for the there remains considerable error in predic- the parole context, Wainer refers to as decision. The Federal probation guidelines tion. "probity." The statistical methods yield combine salient factor scores (i.e., predic- estimates both of the rarity of events and of tions) with offense characteristics ("seri- Howard Wainer has also worked on the the probity of individuals. ousness'') to produce "average total time parole prediction problem, using data from Wainer wants to beable todescribe institu- served before release. " Wainer applied the Federal parole system. Since his tions, say in the criminal justice system, by two-way table decomposition methods to attempts to improve upon the predictive the characteristics of the individuals enter- the matrix showing the midpoints of rec- performance of the salient factor system by ing them. Then, if one saw that recidivism ommended sentence intervals for each use of alternative estimation procedures among the products of some institution combination of salient factor score and had earlier been considered by most of the were declining, one could ask whether the offense characteristic category in the conferees, they were not discussed exten- decline resulted from a change in the nature salient factor system. His results indicate sively at the conference. But it is worth of the institutional population or from that "the existing parole policy corresponds mentioning that, by using psychometric something else, such as a new program closely to a multiplicative model in which methods applied to the variables used in seriousness of offense seems to count the Federal salient factor scores, Wainer which had been instituted. In other words, almost three times as much as offender was able to improve on the salient factor one would want to examine recidivism of the institutional population controlling for characteristics among adults" (Perline and score predictions. However, as with Wainer). The relativeIy small effect of the Larntz's various models, the improvement the probity of the population. The focus, then, .is shifted from prediction of salient factor scores (that is, the measure of in predictive power was relatively small, offender characteristics or of probability of and the resulting predictions are not very individual behavior to system characteristics. recidivism) suggests either that the inac- accurate. As Wainer and Perline have writ- curacy of the predictions of recidivism is ten, "our results are at least as good with Having introduced this perspective to the taken into account in decisonmaking, or this approach as with any other, but still conferees, Wainer presented a problem for that characteristics of the offense are leave a great deal to be desired." their consideration. In estimating rarity considered more important in determining The conferees were in general agreement as and probity, he has found occasional item- time served. Wainer suggests that the two to why none of the approaches leads to very person interactions, or instances in which dimensions of the guideline scheme, salient good prediction of parole success or particular item-person combinations are factor scores and offense characteristics, failure. Leaving aside such common prob- badly fit by the model. The analogy in the correspond to two schools of thought on testing context is to those occasions on lems of prediction as, say, the influence of incarceration, rehabilitation, and retribu- which an individual with low ability never- chance events on behavior, there is the tion. It could be argued, then, that his theless gets a difficult item right, or an in- problem that the parole prediction prob- finding concerning the relative importance dividual with a high ability misses an easy lem is considered only in the context of a of the two factors indicates the relative highly homogeneous population represent- item. Because of the probabilistic nature of importance of the two views of the purpose ing a very small and extreme portion of the the event-person combinations, some of incarceration in parole decisionmaking. distribution of behavioral characteristics. "errors" of this kind are bound to happen. The prison population is itself extremely However, they seem to happen more often Before parole boards can consider the de- restricted in its range of variation, and precision to release a prisoner, there must be a sumably an extreme portion of the prison decision to incarcerate the individual in the population is seen as "obviously" unsuit- first place. David Britt and Kinley Larntz able for parole, so the parole data base is have investigated judicial sentencing decisions, using a sample of 200 cases from the even more restricted. As Leslie Wilkins put 1 it, parole prediction is an attempt to predict Denver, Colorado, courts, originally col- far out in the tail of a distribution, which is lected under the auspices of the State Courts Sentencing Project and provided by Deterrence because it is reasonable to suppose that im- Leslie Wilkins. After elimination of cases The problem of estimating the deterrent prisonment decisions are influenced by because of inadequate data or because they effect of criminal sanctions occupied con- such factors as prison crowding. If impris- involved "victimless crimes," 138 cases siderable time at the workshop and consid- onment rates and crime rates are simulta- were analyzed to determine the major fac- erable effort by workshop participants neously determined, as this suggests, then tors used by judges in reaching thedecision since then. The major work on deterrence simultaneous equations models may be- of whether or not to incarcerate an individ- since the workshop has been that of the Na- come appropriate. Estimation of simulta- ual convicted of a criminal offense. Logit tional Research Council's Panel on Re- neous equations models requires appropri- models were used in the analysis. search on Deterrent and Incapacitative ate identification restrictions, that is, Effects (1978). The panel was chaired by variables which influence sanctions but not In brief summary, the results indicate that crimes, or variables which influence crime dispositions of crimes against property workshop participant Alfred Blumstein and included two other workshop partici- but not sanction risk. The choice of identi- appear related to variation in the serious- fying restrictions is a difficult problem, ness of the crime and the offender's previ- pants, Gary Koch and Albert J. Reiss, Jr. Daniel Nagin, staff to the panel, spent sev- which, in the panel's view, has not been ous record in a straightforward way. "As adequately resolved. the crime becomes more serious and the eral weeks at the workshop, and Brian offender's previous record becomes poorer, Forst, co-author of one of the panel's com- In sum, a deterrent effect is not clearly the chances of the individual's being incar- missioned papers, reported on his research demonstrated in existing studies. This brief cerated increase." (Britt and Larntz). to the workshop. It is appropriate, there- presentation sparked considerable discus- Furthermore, seriousness of offense does fore, that the conference discussion of de- sion among the conferees. A number of not seem to lead to incarceration for those terrence began with a brief statement by them argued that treatment of the simul- with a good prior record. For crimes Blumstein summarizing the panel's work. taneity problem involves far more than against persons, seriousness of offense did Blumstein noted that the panel had focused choosing appropriate identifying restric- not play a large role in incarceration, pre- on general deterrence, where the issue is the tions and separating deterrence and inca- sumably because nearly all the offenses association between crime rates and sanc- pacitation. The argument is that the rela- involved were relatively serious ones. A tions. Virtually all the research on this issue tionship between imprisonment and crime two-variable model using the nature of the has found, after controlling for other rates is more complicated than the aggre- plea and whether the charge was reduced determinants of crime, a negative associa- gate statistical models suggest. The ways in best fit the data. No characteristics of the tion between crime and sanctions. Whether which adaptation to the pressures of offender affected the chances of being there is a causal relationship is a more diffi- changing crime rates affects prisons over jailed once these two variables were taken cult question. The panel considered three time, and the related question of how into account. principal aspects of this question: changes in prisons affect crime rates, have not been studied to any substantial extent. The contrast between sentencing decisions, 1. Single equation models typically use, on The composition of prison populations at least as they appear to be made in Den- the left-hand side of the equation, a frac- may shift, the social environment of the ver, and parole decisions under modern tion in which crime is the numerator, while prisons may change (arguably making pris- guideline systems is worth noting. The the sanction risk on the right-hand side of ons more-or less-attractive places to parole decision system explicitly builds in a the equation is a fraction with crime in the be), the symbolic meaning of imprison- variety of characteristics of the individual denominator. If there is error in the meas- ment may change as prisons become polit- in determining release. The sentencing urement of crime, it will generate a negative icized, and so forth. Further, it is decisions incorporate no individual char- association between crime rate and sanc- reasonable to expect that the effects of acteristics (but for prior record in the case tion risk, even in the absence of a deterrent imprisonment on crime rates depend upon of property offenses) in determining when effect. Without good estimates of the mag- prison release rates and the character of the to incarcerate. nitude of the error, therefore, it is difficult prisoners released. At the very least, dis- Several qualifications should be intro- to know what to make of the association entangling these factors requires disaggre- duced. First, the sentencing study did not found in the data. gation of the available data by offense-a investigate length of sentence. Second, in- recommendation with which the panel 2. Imprisonment is typically the sanction dividual characteristics may be incorpo- agrees and which is followed in a number of used in deterrence studies. However, while rated into prior events in the criminal jus- the studies. Whether modifications to the risk of imprisonment may have a deter- tice system: the Denver data concern only account for the other problems and ques- rent effect, the fact of imprisonment may convicted individuals. Individual charac- tions can be built into the kind of aggregate affect crime rates through kcapacitation of teristics may play a far larger role in the analysis common in the study of deterrence active criminals. An estimated effect of im- decisions to arrest, prosecute, and convict. is another matter. In any event, the requi- prisonment, therefore, may combine both A full investigation of the various factors site data are not available to do so now deterrent and incapacitative effects in un- determining outcomes in the criminal even if in principle it can bedone. The ques- known proportions. justice process would have to begin at a tion of whether valid conclusions about the much earlier stage than the sentencing 3. A negative association between crime deterrent effect of sanctions can be reached stage. It seems likely that the development and sanction may result from deterrence of through the use of aggregate models which of OBTS data will make such investigations crime by sanction, but it may also result do not include these complex problems was easier to conduct in the future. from the inhibition of sanction by rising not resolved in conference discussion. crime rates. This is particularly a problem in studies which, like most published studies of deterrence, rely on cross- sectional data at the state level. It is also a particular problem to the extent that studies rely on the sanction of imprisonment, Discussion then turned to the problem of In objecting to Blumstein's hypothetical A strong theme of much of the discussion estimating deterrent effects in single equa- experiment, conferees noted that by fixing of this problem was that the specification tion models. Blumstein had noted that if values of C and using them in the model to of deterrence models common in the litera- crime is measured with error in the stand- generate values of C/ N, the experimenter ture may not allow thedetermination of de- ard models for the problem, estimates of would in effect be generating simply values terrence effects. Considerable complexity deterrent effects are biased. The standard of the reciprocal of N. This suggested to must be added to the models. The "crime model would take the following form: some of the conferees that the problem was rate" needs to be decomposed. It might be incorrectly formulated. As one conferee viewed as a function of a distribution of in- said, "You cannot fix Cand then talkabout dividual rates of offending. As Reiss has Where C = number of crimes generating crime rates." written, "there are three general kinds of N = population Another approach to the question formu- change that affect the incidence of crime in I = number of sanctions lates the basic equation in terms not of the a population. They are changes in the e = random error term quantities actually used in the standard prevalence of offenders in a population, A = parameter to be estimated approaches, but rather in conceptual changes in individual incidence of offending, and inferactions between prevalence Estimates of A are biased if Cis measured terms. Thus "crime rate,"or something like and incidence rates" ("Understanding with error. Blumstein added, however, that it, is seen as a function of "sanction risk," if C is measured without error, then un- among other things. Call the coefficient of Changes in Crime Rates''). In effect, theleft- biased estimates of A are possible. The "sanction risk" B. Then the standard equa- hand side of the deterrence equation must statement generated considerable contro- tion is seen as a particular realization of the consider all of these. Both prevalence of versy, less because conferees believed it to conceptual model, using proxies for the offenders and individual rates of offending be false (it is not clear that any of them felt conceptual variables. Then there are two may be influenced by the criminal justice it was false, when properly qualified) than separate questions which can be asked of system in a number of ways, and these because its implications for the study of de- the estimation. First, is the estimate of A would need to be considered on the right- terrence are problematic. In other words, unbiased? That question, which has hand side. In addition to the general presuming an unbiased estimate of A, is apparently preoccupied the literature, deterrent effect of imprisonment, one that estimate a measure of the deterrent appears to have the answer Blumstein sug- should consider the incapacitation effect, effect of criminal sanctions? The question gested: if C is measured without error, an the effects of differential release rates, and can be approached through two hypotheti- unbiased estimate of A is possible. The other complications. In the opinion of cal experiments, the first proposed by second question, however, concerns the some of the conferees, unless decomposi- Blumstein and the second by other con- relationship between A and B. And it tions of this sort are essayed, it will be impossible to disentangle the various effects ferees. would appear that the particular structure of the variables used in the estimation- of sanctions and therefore impossible to Blumstein's experiment is roughly this. that is, the presence in the denominator of estimate a deterrent effect. Analysis along Pick a value for A. Generate data for Iand the sanction risk variable of the numerator these lines, however, is not a short-term C, without error. (These may be real or of the crime rate variable-means that A is project. The data simply do not now exist hypothetical data.) Generate a random not an unbiased estimate of B. to implement it. variable e. Then use the equation to generate values of C/ N. Label I/ C "imprison- If the answer to the second question sug- There remains the possibility that, short of ment rate" and C/ N (as generated by the gested above is correct, it immediately implementing the more complex model model) "crime rate." Give these variables to raises another problem. How does one esti- described above, one can consider esti- a statistician and ask him to estimate A. mate B? Colin Loftin, drawing upon his mates derived from the standard deter- The statistician should be able to produce own deterrence research, suggests using rence model as measures of the aggregate an unbiased estimate of (the known value sanctions rather than sanction risk as the effect of sanction risk, without worrying of) A. The structure of the model suggests explanatory variable. He noted that the too much about what proportion, if any, of that A is a measure of the effect of the im- deterrence research has generally found the aggregate effect is actually deterrence. prisonment rate on the crime rate. that measures of theseverity of punishment Taking that approach raises the question of have less of an effect on crime rates than do whether the findings of deterrence research The second experiment uses a random measures of the certainty of punishment. can be accepted, subject to this rather sub- number generator to produce values for C, Severity measures, unlike certainty ("risk") stantial limitation. I, and N. Then the two variables C/ N and measures, do not share a common element Stephen Fienberg has taken a close look at I/C are formed. The correlation between with crime rate measures. Loftin has used them is calculated. Given the construction some of the deterrence studies, and the number of executions as a sanction of the variables, there should be a negative results he reported to the conference sug- variable in his capital punishment research. correlation, even though number of crimes, gest that estimates of the deterrent effects This removes the common term, but it number of incarcerations, and population of sanctions should be treated with some leaves somewhat open the question of the are random numbers. In other words, caution. (Fienberg subsequently supplied a underlying behavioral model. Blumstein's statistician, given "crime rate" written version of his report, Brier and and "incarceration rate" and asked to esti- Fienberg, "Recent Econometric Modelling mate (the unknown value of) A, will pro- of Crime and Punishment: Support for the duce an estimated negative value. Since the Deterrence Hypothesis?".) data are purely random, it is difficult to see Fienberg first examined lsaac Ehrlich's why A should be considered a measure of (1973) well-known analysis of 1960 data the deterrent effect of incarceration. from 47 states and the reanalysis of these data done by Vandaele (1978) for the Na- tional Academy panel. Fienberg first notes the well-known shortcomings of Uniform Brian Forst (1976) attempted to replicate This reinforces the argument of other Crime Re~ortsdata as measures of the Ehrlich's study using 1970 data. There are analysts that the relationship among the variables ;equired by Ehrlich's supply of differences in some of the variables used by variables has changed over time, so that it offenses function and suggests that it Forst and Ehrlich, and Forst did not follow is misleading to compute the deterrent would be appropriate to use statisticai EhriichS specifications. in particular, effect based on the entire series. Second, methods designed for the "errors in varia- Forst used more sociodemographic vari- analysis of residuals points to 1934 as an bles" problem and for multiple indicators ables than Ehrlich. Further, Forst analyzed outlier in the data. Deleting that one of unobservable variables. Ehrlich's 1960 only the aggregate crime rate, while Ehrlich observation has a substantial impact on the data were unavailable and published re- used rates for individual crimes. Forst's reestimated coefficients. In the original scale ports do not fully specify the simultaneous sults differ strikingly from those of Ehrlich, of the variables, the coefficient of the equations model actually used, so it was as he found the coefficients of the deter- execution variable is negative but not not possible to replicate the Ehrlich analy- rence variables insignificant. It is, of statistically significant. In a logarithmic sis. Vandaele had reanalyzed the Ehrlich course, possible that these differences are specification, the estimated coefficient is data and concluded that inferences about to be explained by a change in patterns of positive. The data for 1934 show a small deterrence are not sensitive to changes in criminal behavior over a 10-year period, value for the murder rate and a high value the specification of the model. Using the but it is not clear what would explain such for the execution variable (number of data reported by Vandaele, Fienberg was a change. The extra sociodemographic executions for murder in year t + 1 divided able to duplicate the results. However, he variables may also explain the difference. by the number of convictions in year t). questions the conclusion that inferences Fienberg obtained most of the Forst data Fienberg suggests that the 1934 data are are not sensitive to changes in specifica- and reanalyzed it. He was able to duplicate "suspect." Whatever the explanation, the tion, noting that Vandaele's published re- Forst's results quite closely. However, one fact that a single observation has such a sults for murder, rape, and assault do seem key variable, a measure of income disper- substantial effect on the estimates reduces sensitive to the choice of specification. This sion, could not be obtained from Forst, confidence in the findings generally. is no small problem, because the correct and Fienberg therefore used several Ehrlich's specification of the "murder sup- specification cannot be. determined by different measures of income dispersion. ply" function is linear in logarithms, with analysis of the data themselves. He discovered that the choice of a measure one major exception. Time, used as a sur- One of the kev variables in the analvsis is had substantial effects on most of the rogate for improvements in medical tech- probability of incarceration, measured by estimated coefficients. That is, the model is nology, enters the transformed equation the ratio of the number of commitments to extremely sensitive to minor differences in (that is, the equation after converting to the number of offenses. Vandaele had the definition of a single variable. Since linearity in the logarithms) untransformed. noted that for several states this ratio is there are no strong grounds for preferring The reason for treating time differently greater than one, which, of course, is the one definition to another, this suggests from all the other variables is not clear. upper limit for probabilities. This is not extreme caution in accepting the results of Fienberg reestimated the murder supply necessarily an indication of error in the the analysis of deterrence effects. function using a fully logarithmic specification (that is, using logT instead of T). The data, because there are a number of plausi- One of the most widely discussed deter- effect was to change the sign of the coef- ble and reasonable explanations for ratios rence studies is Ehrlich's (1975) longitudi- ficient of the execution variable. Fienberg greater than one. It does, however, suggest nal study of the deterrent effect of capital then tried various other transformations of that the ratio may not be a reasonable meas- punishment. Ehrlich's data could not be ure of the perceived probability of incar- obtained, and Fienberg therefore reana- time and discovered that by this means he could change the results of the estimation ceration. Vandaele reestimated the equa- lyzed the closely related data of Bowers and almost at will. This might not be a great tions deleting states with ratios greater Pierce. While Fienberg discusses a number problem if there were some logical defense than one and found little change in the of methodological problems which raise for the choice of any particular transforma- results. Fienberg argues that to treat the questions about Ehrlich's specifications data in this way is to assume that, while and conclusions, only two aspects of the re- tion, but none is apparent. Stated in very strong form, the appropriate conclusion ratios greater than one may be bad data, analysis will be discussed here. there is nothing wrong with ratios less than would appear to be that longitudinal anal- one. However, Fienberg continues, the fact The Ehrlich data cover the years 1933-1969, ysis of the Ehrlich capital punishment data that the underlying process produces prob- and, because of the use of lags, analysis is can produce virtually any conclusion about ability estimates greater than one suggests limited to 1934-1969. Other analysts have the deterrent effect of capital punishment, that there is something very wrong in the noted that if the years 1963-1969 are depending upon the arbitrary choice of a process as a whole, and therefore that there deleted, the coefficient of the probability of scale for time. execution variable loses statistical signifi- is no more reason to accept ratios less than The final paragraph of the Brier-Fienberg cance. To this Fienberg adds two points. one than to accept those greater than one. paper baldly presents their overall conclu- First, by redesigning aspects of the analy- Using an analogy, he suggests that if a com- sions: "We can find no reliable empirical sis, so that the model was recursive, not puter program computes 100 correlations, support in the existing literature either for simultaneous, he was able to analyze resid- and 5 of them have values greater than 1.O, or against the deterrence hypothesis. uals, and these analyses show that the wisdom may dictate throwing out all 100 Moreover, we believe that little will come observations for 1963-1969 are discrepant. values, and not just the 5 impermissible from further attempts to model the effects ones. The impermissible values serve as evi- of punishment on crime using the type of dence that none of the values are to be data we have described in this paper." This trusted. Fienberg's logic strongly suggests reinforces the lessons suggested above: a the conclusion that no deterrence studies reformulation of the problem must precede relying upon such data can be accepted as any advances in the study of deterrence. providing reliable evidence of a deterrent effect. Conference participants Conference papers and other materials Ehrlich, lsaac (1975) . Alfred Blumstein Brier, Stephen S. and Stephen E. Fienberg "The deterrent effect of capital punishment: A Urban Systems Institute Recent econometric modelling of crime and question of life and death." American Economic Carnegie-Mellon University punishment: Support for the deterrence hypothesis? Review 65:397-417. David W. Britt Ehrlich, lsaac (1973) Criminal Justice Program Fienberg, Stephen E. "Participation in illegitimate activities: A Nova University Victimization and the National Crime Survey: Problems of design and analysis theoretical and empirical investigation." Journal Stephen E. Fienberg of Political Economy 81521-565. Department of Statistics Larntz, Kinley and David W. Britt Forst, Brian E. (1976) and Department of Social Science The effects of plea bargaining on the disposi- "Participation in illegitimate activities: Fur- Carnegie-Mellon University tion of person and property crimes: A research note ther empirical findings." Policy Analysis 2477- Kinley Larntz 492. Department of Applied Statistics Larntz, Kinley National Research Council (1978) University of Minnesota Linear logistic models for the parole decisionmaking problem Deterrence and incapacitation. (Panel on Re- Colin Loftin search on Deterrent and lncapacitative Effects.) Department of Sociology and Loftin, Colin Edited by Alfred Blumstein, Jacqueline Cohen, Center for Research on Social Organization Alternative estimates of the impact of cer- and Daniel Nagin. Washington, D.C.: National University of Michigan tainty and severity of punishment on levels of Academy of Sciences. homicide in American states Albert J. Reiss, Jr. Solomon, Herbert (1976) Department of Sociology Reiss, Albert J., Jr. "Parole outcome." Journal of Research in Yale University Understanding changes in crime rates Crime and Delinquency, July, 107-126. Richard F. Sparks Reiss, Albert J., Jr. Vandaele, Walter (1978) School of Criminal Justice Victim proneness by type of crime victimiza- "Participation in illegitimate activities: Ehr- Rutgers University tion over time lich revisited." In National Research Council, Deterrence and incapacitation, Washington, Howard Wainer Sparks, Richard F. D.C.: National Academy of Sciences. Bureau of Social Science Research Criminal opportunities and crime rates Washington, D.C. Wainer, Howard and Richard Perline Leslie T. Wilkins Quantitative approaches to the study of School of Criminal Justice parole SUNY at Albany

Guests Charles R. Kindermann Bureau of Justice Statistics U.S. Department of Justice Paul D. White Bureau of Justice Statistics U.S. Department of Justice

staff David Seidman Social Science Research Council Center for Coordination of Research on Social Indicators Criine rates and victimization

Understanding changes in crime rates ALBERT3. REISS,JR . Department of Sociology Yale University

Much of the empirical research in crimi- the offenders acdount for only a single Changes in the prevalence nology is based on. explaining changes in crime event (even though the police under- of offenders crime rates and much of the research evalu- stand that multiple arrests for a single ating law enforcement or criminal justice incident clear osly that incident, barring Any change in the prevalence of offenders programs depends upon measuring changes admissions by the offenders to other crime in a population comes about as a conse- in crime rates. The choice of measures of events). quence of changes in replacement rates for crime is much debated and their validity or a population of offenders. Changes in entry Likewise, where there is more than one or exit from a population of offenders orof reliability critically reported. Yet the rela- offender and more than one criminal act in tionship among measures of crime, e.g., be- age at onset and desistance from a popula- an event, different offenders may commit tion affect replacement rates. We may iden- tween crime incident rates and aggregate different acts in that event. While these dif- rates of individual offending, is not well ar- tify several sources of change in replace- ferences may be reflected in different ment rates. ticulated. This stems in part from a lack of charges or indictments for offenders in- understanding of the nature of crime volved in a common event, they will not be First, it has long been understood that events, of the criteria for selecting measures reflected in measures that assign each changes in the size ofbirth cohorts or of co- based on such events, and of the sources of offender the same crime incident classi- horts at .risk in the population affect the change in measures of crime. This paper fication. prevalence of offenders in a population if attempts to clarify some of these problems the probabilities of age at onset and desis- in the measurement of crime using exam- We shall not pursue here other implications tance and individual rates of offending ples primarily from research on deterrence of multiple offenses, offenders, and victims remain constant. Even when the prevalence and incapacitation. in crime events since we shall have occasion rate for a cohort remains constant, any in- to draw the reader's attention to some of crease or decrease in the size of birth them in presenting a simple model for un- Understanding crime events cohorts affects the prevalence of offenders derstanding changes in crime rates. in a total population after the cohort Any occurrence of crime is a complex Understanding changes reaches the age- of onset of offending. event. Scanting most elements in the occur- in crime incident rates rence of crime events, the three critical ones Second, while it is understood that changes for measuring crime are that an event may Whether a crime event is classified as a sin- in length of offending career may have an comprise one or more criminal acts, one or gle incident or as multiple incidents, there effect on the crime rate, it is not generally more offenders, and one or more victims. are three kinds of change that affect the appreciated that both changes in age at Of less critical significance are variation in incidence of crime in a population. They onset and at desistance can affect the re- duration of events in time and the number are changes in the prevalence of offenders placement rate of offenders in a population of settings involved in the criminal activity. in a population, in individual incidence of and, therefore, the prevalence of offenders offending, and in interactions between in a population. Now it is commonly understood that when prevalence and incidence rates. Assuming a crime event is counted as a single crime Third, changes in the number, size, degree no changes in individual incidence of act or incident, the number of victims and of openness, composition, and territory of offending (or interactions), for example, an of offenders on the average exceed the social networks may affect the prevalence aggregate crime incident rate may change number of crime incidents since some of offenders in a population, since these solely due to changes in the prevalence of events involve more than one victim changes affect the potential for recruitment offenders in a population. Correlatively, if and/or more than one offender. But what of offenders to offending groups. Both the prevalence rate remains constant, often is overlooked is that when there is changes in market networks for the goods changes in the individual incidence of more than one offender for any incident, and services of crime as well as changes in offending will affect the aggregate-- - crime formal and informal social networks mav incidence rate. Because the prevalence rate affect recruitment. and the individual incidence of offending may vary independently, their rates of change may be negatively as well as positively correlated. These changes are not necessarily inde- on the number and selected characteristics Unfortunatqy, we do not know how many pendent one of another. Changes in social of offenders in crime incidents reported by dfferent offenders are involved in these networks, for example, can affect changes victims. For crimes against persons, the crime incidents reported during a 6-month in the age at onset or desistance from of- number of offenders is usually reported; period. Nonetheless, when we view these fending. It also is possible that beyond a for most crimes against property, offenders crime incidents in Table 2 from the per- certain point changes in the prevalence rate are not known. Table 1 provides informa- spective of an offending population, we see may increase both the number and size of tion' on the size of offending groups for that only 30 percent of all offenders in these social networks, a phenomenon sometimes selected types of crime incidents while crime incidents were lone offenders. Again, observed in gang delinquency and orga- Table 2 has information on the distribution there is considerable variation with only 10 nized crime. The relationship of processes of offenders by size of offending group for percent of all offenders who commit a seri- of recruitment to the number and size of the same types of crime. ous assault with a weapon followed by theft social networks is not well understood. Although there is considerable variation in being lone offenders but 58 percent of all the individual or group contribution to offenders who commit a rape with no theft Changes in individual offending in crime incidents reported by being lone offenders. There is, on the aver- offending rates victims in Table 1, almost two of every age, 2.1 offenders for each crime incident three reported incidents involved only a against a person. There is considerable Any change in individual incidence of single offender. For crimes against the per- variation in this average with 2.9 offenders offending likewise affects the crime inci- socnthe proportion of incidents committed on the average for incidents of serious dence rate. We may think of three major by a single offender ranged from only 30 assault with a weapon followed by theft to types of change that affect individual rates 1.4 offenders for a rape with no theft. of offending in a population. percent of all serious assaults with a weapon followed by theft to 82 percent of First, changes in opportunities to commit all attempted rapes with no theft from the crime events can change individual rates of victim. offending. Assuming an offender, his or her probability of offending is some function of both opportunities and intervening opportunities to commit criminal acts. The opportunity to commit motor vehicle theft, for example, may increase both as the ratio of motor vehicles to the population increases and as the ease of a successful attempt increases. Second, changes in the size or structure of an offending group or network can alter Table 1. the group and, therefore, an individual member's rate of offending. There is plausible evidence that on the average an individ- ~otai incidents ual's rate of offending is greater as a mem- Type of crime offenders ber of an offending group than as a lone offender. Any reduction in the ratio of known individual to group offending, therefore, Rape w/theft 30 should increase, on the average, individual Rape, no theft 112 rates of offending. Att. rape, w/theft 39 Att. rape, no theft 316 Robbery, w/weapon 752 Third, changes in the size and composition Robbery, no weapon 596 of crime networks should affect an individ- Att. robbery, w/weapon 432 ual's rate of offending. Substantial changes Att. robbery, no weapon 584 Ser. assault, theft, weapon 519 in markets for illegal goods or services, for Ser. assault, theft, no weapon 71 example, can affect the individual offender Ser. assault, weapon, no theft 1,339 Ser. assault, no weapon, no theft 244 as anagent of supply, assuming elasticity of Minor assault, theft 485 victims in the population. Minor assault, no theft 1,947 kt.assault, w/weapon, no theft 3,289 Att. assault, no weapon, no theft 5,940 Purse snatch, no force 249 Implications for research on deterrence Att. purse snatch, no force 202 and incapacitation Pocket picking 441 Burglary, forced entry, something taken 95 Little is known about the distribution of Burglary, forced entry, 0 taken, damage 126 Burglary, forced entry, 0 taken, 0 damage 44 individual rates of offending or changes in Burglary, unlawful entry, 0 force 588 individual rates of offending during an Burglary, att. forced entry 374 Larceny, $250+ 120 offender's career. In particular, almost Larceny, $1 00-$249 208 nothing is known about the mix of individ- Larceny, $50-$99 279 ual and group offenses in an individual's Larceny, $25-$49 302 Larceny, $1 0-$24 454 rate of offending. The National Crime Sur- Larceny, under $10 749 vey of crime victims provides information Larceny, $ unknown 103 Att. larceny 842 Car theft 74 Att. car theft 120 Theft, other vehicle 14 Att. theft, other vehicle 26

Total 22,107 Percent 10e.O Given the limitations in these data that we tion by high-rate lone offending persons or individual's crime rate, then it would be do not know how many different offenders unless high-rate offending persons who more reasonable to assume that on the are involved in the reported incidents (we commit group offenses have a substantial average incapacitation would avert only would assume that minor assaults without mix of individual offenses, a substantial one-half a crime for each person crime in theft would involve fewer different offend- number of offenders must be removed the individual's rate of offending. i3ut this ers than rape, for example) nor the mix of from a population to affect substantially would be a reasonable estimate only if we individual and group offenses in an indi- the crime rate. also assumed that for group offenses the re- vidual's rate of offending, we cannot esti- Research on the effects on the crime rate of placement rate for incapacitated members mate with any precision what on the aver- incapacitating offenders generally makes a is 0 and that there are no deterrent effects age any offender contributes to crime simple presumption that each offense in an on the other group offenders as a incidents. We can say, however, that if an individual's rate of offending is a single consequence of incapacitating one of its offender were involved in a group incident, offender offense. Thus, it is assumed that members. it is not certain whether removing that the number of,crimes averted by incapaci- If we are reasonably correct in the fore- offender from that population of offenders tating an offender is equal to the individ- going argument, some more general infer- would have averted that incident. We can ual's rate of offending. Clearly that is not ences can be drawn. In investigating the also say that where offenders are largely generally the case when an individual com- effects of incapacitation on the crime rate, involved in group incidents, unless there is mits an offense as a member of an offend- it is assumed that incapacitation effects can a deterrent effect on co-offenders in the ing group. Were we to assume that ouresti- be separated from, and investigated apart event, it is unlikely that any crimes are mate of 2.1 offenders per crime against the from, deterrent effects. Clearly that is not averted by removing any single member of person holds for the person offenses in an the offender -.grow. We mav also infer that the case where group offending is involved. unless offenses committed lone offend- Whenever an individual is involved in ky group offenses, unless incapacitation of ers are committed in substantial propor- that member has a deterrent effect on the

Percent distribution of incidents by size of offending group for selected types of crime incidents: All National Crime Survey incidents reporting offender information, July 1, 1972, to December 31, 1975

Percent of incidents by size of offending group Total percent 1 2 3 4 5 6-10 11-14 15-19 20t

70.0 13.3 10.0 6.7 100.0 79.5 11.6 4.5 1.8 1.8 0.9 100.1 64.1 17.9 10.2 2.6 2.6 2.6 100.0 81.9 5.7 3.8 2.9 1.6 3.5 0.6 100.0 36.8 35.2 16.2 3.9 2.8 4.1 0.3 0.5 0.1 99.9 44.8 23.7 15.3 6.0 4.2 5.4 0.3 0.2 0.2 100.1 54.6 24.1 11.1 4.9 1.4 3.2 0.7 100.0 49.7 22.8 12.7 5.6 3.4 4.1 0.9 0.4 0.5 100.1 30.0 28.9 18.9 10.2 5.6 4.4 1 .O 0.5 0.5 100.0 39.4 24.0 19.7 11.3 1.4 2.8 1.4 100.0 59.7 12.6 9.1 6.1 3.1 5.8 1.4 0.7 1.5 100.0 74.2 10.7 5.3 2.9 0.8 4.5 0.4 1.2 100.0 44.3 23.5 18.8 b.6 1.6 5.4 0.4 0.4 100.0 70.8 10.1 7.3 4.0 2.4 3.9 1.1 0.4 0.2 100.2 67.2 12.4 7.6 4.1 2.7 4.2 0.7 0.4 0.8 100.1 . 70.6 11.0 6.7 4.0 2.6 3.9 0.5 0.3 0.4 100.0 61.9 25.3 0.9 2.8 0.8 0.4 100.1 61.4 24.3 8.9 3.5 1.5 0.5 100.1 65.1 21.8 8.9 2.7 1.6 100.1 52.6 30.5 10.5 4.2 2.1 99.9 68.3 22.2 5.6 1.6 1.6 0.8 100.1 61.4 25.0 11.4 0.2 100.0 72.8 17.4 6.6 1.7 0.5 1 .O 100.0 66.0 18.7 9.6 2.7 1.1 1.3 0.5 99.9 60.0 25.0 9.2 2.5 0.8 1.7 0.8 100.0 70.7 19.2 6.7 1.9 1.5 100.0 66.7 19.0 5.7 4.7 2.1 1.4 0.4 100.0 75.2 14.9 7.0 1 .O 1.7 0.3 100.1 71.1 16.3 6.6 3.8 0.9 1.1 0.2 100.0 73.3 16.4 6.4 2.0 1.1 0.7 0.1 100.0 68.9 19.4 5.8 4.9 1 .O 100.0 56.5 23.8 11.1 5.8 1.2 1.4 0.2 100.0 71.6 17.6 6.8 4.1 100.1 45.0 30.0 17.5 2.5 3.3 1.7 100.0 78.6 7.1 7.1 7.1 99.9 53.9 30.8 15.3 100.0 14.21 0 3,505 1,932 925 51 7 749 120 61 88 64.3 15.9 8.7 4.2 2.3 3.4 0.5 0.3 0.4 other offenders involved with him, the groups with fairly open boundaries in a The effect of incapacitation on replace- effect of his incapacitation could easily be larger social network, then replacement ment rates is undoubtedly complex not zero crimes averted, as the co-offenders follows somewhat the principles of replace- only for the reasons already mentioned but could continue to account for the same ment in a vacancy chain (White 1970). A because replacement occurs over a period number of crime incidents. if, however, the vacated position in a high offending group of time. Replacement is not always an incapacitation of an offender has a deter- is more likely to be filled by marginal immediate response to vacancy. All other rent effect on co-offenders, incapacitation offenders than by new offenders. Recruit- things being equal, the longer a vacancy may contribute substantially to reducing ment of new entrants to an offending popu- exists, the more likely any vacancy is to be the crime rate. Any model of the effects of lation thus is unlikely to occur by direct filled by processes of internal shifts into incapacitation on the crime rate should re- replacement in high offending groups but vacancies with a final closure by recruit- flect deterrent effects on the network of indirectly in a chain of replacement; such ment from outside. Unless there are deter- offenders as well. direct effects on replacement will depend rent effects or substantial discontinuities in Models of the effect of incapacitation on very much on the structure and extent of social networks that affect recruitment the crime rate assume that decreasing the social networks. One might expect that net- levels, one would expect replacement to be prevalence rate of offenders in a popula- works are more extensive and open in high fairly high. population density areas and areas where tion has a corresponding effect on the Nonetheless, one way that any organiza- crime rates are high. Thus one might expect crime rate. There are several reasons why tion may close off a vacancy is to vacate the this may be a weak assumption. higher replacement rates in large cities than in;ural areas. Similarly, replacement may position. Thus, it is possible that the effect The models generally ignore replacement be higher in young than older age groups rates of incapacitated offenders. The size of since the boundaries of the former are more an incapaciktion effect depends upon the permeable and fluid. size of the group, the fluidity of its boundaries, and the rate of replacement. To measure the rate of replacement is difficult, since much depends upon the age of the offender, the mix of offenses, the group contribution to an individual's rate of offending, the structure of social networks, and any other factors that affect changes in replacement rates. If we assume that individuals are inducted into criminal careers Table la: largely in co-offending and that offending networks are reasonably large, we would expect high replacement rates. Indeed, - since within any offending group, or within Type of crime Not a network of any reasonably large size, say known ten or more, any individual offender is Rape. w/theft quite likely to be linked with different Rape, no theft 1.8 offenders in different offenses, it is possible Att. rape, w/theft Att. rape, no theft 0.9 that this condition of relatively free substi- Robbery, w/weapon 2.2 tution of group members in committing Robbery, no weapon 4.6 any given group offense may work against Att. robbery, w/weapon 1.4 replacement if any member is selectively Att. robbery, no weapon 2.5 Ser. assault, theft, weapon 4.2 withdrawn, i.e., the group is simply re- Ser. assault, theft, no weapon 12.3 duced in size. But it also is possible that Ser. assault, weapon, no theft 4.6 ease of substitution in offending may gen- Ser. assault, no weapon, no theft 2.4 Minor assault, theft 2.6 erate recruitment and actually increase Minor assault, no theft 1.3 group size. Att. assault. w/wea~on.no theft 5.2 Att. assault; no weapon, no theft 2.4 Just how replacement takes place is qot Purse snatch. no force 20.7 well understood. It seems unlikely that any Att. purse snatch, no force 3.3 high offending group recruits directly from Pocket picking 56.5 the nonoffending population and thereby Burglary, forced entry, something taken 98.0 Burglary, forced entry, 0 taken, damage 88.3 increases the prevalence rate of offenders in Burglary, forced entry, 0 taken, 0 damage 86.8 a population. Rather, if one thinks of Burglary, unlawful entry, 0 force 93.4 Buralarv.- .. att. forced entrv 91.6- ..- Larceny, $25O+ 95.7 Larcenv. $1 00-249 96.7 ~arceny;$50-99 Larcenv, $25-49 Larceny, $1 0-24 Larceny, under $10 Larcenv, $ unknown Att. larcenv - - Car theft Att. car theft Theft, other vehicle An. theft, other vehicle Total number

Percent 80.4

0.0 = less than half of one percent of incapacitation on a group or network tion may lead to quicker replacement than The proposed model assumes then that in- may be to reduce its size. But it is well to short-term incapacitation. capacitation can increase both the prev- bear in mind that unless a group is at maxi- ' alence rate, through a complex process of mum productivity, the same amount of We have noted that current models of the recruitment to offending groups which work may be accomplished by a smaller effect of incapacitation on the crime rate actwlly increases the offending proportion number of members in a smaller number of assume that reducing the prevalence of of a population, and individual rates of positions. Reductions in prevalence of offenders in a population reduces the crime oflending. Indeed, if the effect of incapaci- offenders in a population can always be rate. We have proposed a more robust tating a member of an offending group in- offset by an increase in individual rates of model, one where incapacitation can increases the recruitment effort of all remain- offending. From a sociometric perspective, crease as well as decrease the crime rate. It ing members, the replacement rate might if the probability that any member of a also should be apparent that incapacitation be greater than one, and the offending group of a given size will be selected into a can reduce the crime rate only under the group might increase in size. Assuming subset of offenders for a given offense is conditions of less than total replacement in that the supply of crime victims for a popu- one in "n" incidents, then the elimination of offending groups and no increase in the in- lation of offenders is elastic, an increase in any member may only increase his proba- dividual rates of offending of those who re- group size can increase the group offending bility of being selected, which in turn in- main in the population. rate. The ~roblemis undoubtedlv more creases somewhat his individual rate of complex since it depends upon both aggre- offending. It is also possible that replace- gate effects of recruitment in a population ment is related to the length of incapacita- of offenders and reallocation of offending tion of one of its members since the likeli- groups whose rates of aggregate offending hood ofereturn declines with the length of vary. expected absence. Long-term incapacita-

Percent distribution of number of reported offenders by type of crime for all National Crime Survey incidents: July 1, 1972, to December 31,1975

Number of offenders Offense Percent total reporting

1 2 3 4 5 6-10 11-15 16-20 21+ Percent Number Offenden 70.0 13.3 10.0 6.7 100.0 30 100.0 78.1 11.4 4.4 1.7 1.7 0.9 - 100.0 114 98.2 64.1 18.0 10.3 2.6 2.6 2.6 - 100.1 39 100.0 81.2 5.6 3.8 2.8 1.6 3.5 0.6 100.0 319 99.1 36.0 34.5 15.9 3.8 2.7 4.0 0.3 0.5 0.1 100.0 769 97.8 42.7 22.6 14.6 5.8 4.0 5.1 0.3 0.2 0.2 100.1 625 9 5.4 53.9 23.7 11.0 4.8 1.4 3.2 0.7 100.1 438 98.6 48.4 22.2 12.3 5.5 3.3 4.0 0.8 0.3 0.5 100.1. . 599 97.5 28.5 27.6 18.0 9.7 5.3 4.2 0.9 0.6 0.6 100.0 544 95.8 34.6 21.0 17.3 9.9 1.2 2.5 - 1.2 100.0 81 87.7 57.0 12.1 8.7 5.8 3.0 5.5 1.3 0.6 1.4 100.0 1,403 95.4 72.4 10.4 5.2 2.8 0.8 4.4 0.4 1.2 100.0 250 97.6 43.2 22.9 18.3 5.4 1.6 5.2 - 0.4 0.4 100.0 498 97.4. 69.9 9.9 7.2 4.0 2.3 3.8 1.I 0.4 0.1 100.0 1,972 9g.7 63.8 11.7 7.2 3.9 2.6 4.0 0.6 0.4 0.7 100.1 3,468 94.8 68.9 10.7 6.5 3.9 2.6 3.8 0.5 0.3 0.4 100.0 6,087 97.6 49.0 20.1 7.0 2.2 0.6 0.3 - 99.9 314 79.3 59.3 23.4 8.6 3.5 1.4 0.5 - 100.0 209 96.7 28.3 9.5 3.9 1.2 0.7 100.1 1,014 43.5 1.O 0.6 0.2 0.1 0.0 99.9 4,952 2.0 8.0 2.6 0.7 0.2 0.2 0.1 100.1 1,077 11.7 8.1 3.3 1.5 0.3 100.0 333 13.2 4.7 1.1 0.4 0.1 0.0 0.1 0.0 99.8 9,073 6.6 5.5 1.6 0.8 0.2 0.1 0.1 0.0 99.8 4,457 8.5 2.6 1.1 0.4 0.1 0.0 0.1 0.0 100.0 2,796 4.3 2.3 0.6 0.2 0.1 0.0 - 99.9 6,374 3.3 2.3 0.7 0.2 0.2 0.1 0.1 0.0 100.1 8,057 3.5 '2.3 0.5 0.2 0.0 0.1 0.0 - 100.0 9,700 3.1 2.3 0.5 0.2 0.1 0.0 0.0 0.0 99.8 13,806 3.3 2.4 0.6 0.2 0.1 0.0 0.0 0.0 99.9 22,368 3.4 3.3 0.9 0.3 0.2 0.0 - 99.8 2,129 4.9 10.2 4.3 2.0 1.0 0.2 0.3 0.0 99.8 4,667 18.2 2.4 0.6 0.3 0.1 0.0 - 99.9 2,192 3.5 4.0 2.7 1.6 0.2 0.3 0.2 - 99.8 1,344 9.2 3.0 0.3 0.3 0.3 - 99.8 369 4.1 11.3 6.5 3.2 100.0 124 21.O 14,210 3,505 1,932 926 517 749 120 61 88 11 2,591 12.6 3.1 1.7 0.8 0.5 0.7 0.1 0.1 0.1 100.1 19.6 There is also a complex relationship be- would have a greater deterrent effecton the result is fragmentation of the original tween the mix of individual and group propensity of less frequently involved of- group and its members' selective recruit- offenses in an individual's rates of offend- fenders to commit crime than would the in- ment to other groups where their individual ing and membership in offendinggroups. It capacitation of less frequently involved of- offending rates might increase; or the re- does not seem reasonable to assume chat if fenders on the propensity of the most maining members might become two or an individual commits an offense at some involved offenders. more nuclei aro~ndwhich new offending times alone and other times as a member of groups form. In either case, there is a an offending group that the lone offense is It is conceivable that the selective incapaci- potential for increasing both the preva- entirely independent of the group. There is tation of offenders who are disproportion- lence rate and individual rates of offending. some reason to believe that in the early ately involved in the offenses of a group Whether these alternative possibilities stages of a person's criminal career, most of might not have a substantial effect on the occur and with what frequency, or whether the offenses any offender commits are remaining members. Several conditions the deterrent effect on remaining members group offenses. Later criminal careers, by might offset the expected effect of incapac- is the most likely result, requiresinvestiga- comparison, appear to have a larger pro- itation. One is that the remaining members tion. portion of individual offenses. Just how recruit additional members (Hoekema groups affect the propensity of persons to 1973). A second is that the group reallo- It is well to bear in mind that replacement is offend alone is not known. What is known cates members of offending positions a continuous process in many different is that among young offenders, the continu- within the offending group. Short and kinds of groups, including offending ous lone offender is uncommon, but just Strodtbeck (1965) note that vacancies in groups. The American population is fairly how common he is at later ages is not the gang leadership position commonly are known. filled by reallocation. Another possible Models for measuring the effect of incapacitation on the crime rate usually assume that individual rates of offendingare a constant-a tenuous assumption. Where variation is assumed, it is postulated that the distribution of individual rates of offending is such that a relatively small proportion of individualsmake a disproportionate contribution to the crime rate. If, however, individuals with high rates of offending account disproportionately for group of- Table 2. fenses, then their contribution to the overall crime rate is substantially reduced. Correlatively, if high offending individuals Total are disproportionately lone offenders, or if Type of crime number offenses with a single offender contribute offenders disproportionately to higher offender rates, then their contribution to the overall Rape, w/theft 48 crime rate is substantially greater. The Rape, no theft 156 Att. rape, w/theft 68 effect of selective incapacitation of offend- Att. rape, no theft 513 ers with high rates of offendingthen may be Robbery, w/weapon 1,780 particularly sensitive to the mix of individ- Robbery, no weapon 1,429 Att. robbery, w/weapon 861 ual and group offenses in individual and Att. robbery, no weapon 1,382 group offending rates. Ser. assault, theft, weapon 1,488 Similarly, from the perspective of a group Ser. assault, theft, no weapon 179 Ser. assault, weapon, no theft 3,537 offending rate, if certain offenders are dis- Ser. assault, no weapon, no theft 480 . proportionately involved in most group Minor assault, theft 1,164 Minor assault, no theft 3,860 offenses, their incapacitation may have a Att. assault, w/weapon, no theft 6,996 substantial effect on the group offending Att. assault, no weapon, no theft 11,676 rate. This would be the case particularly if Purse snatch, no force 392 Att. purse snatch, no force 327 such high-rate offending persons are less Pocket picking 679 easily replaced, and their incapacitation Burglary, forced entry, something taken 164 Burglary, forced entry, 0 taken, damage 189 Burglary, forced entry, 0 taken, 0 damage 68 Burglary, unlawful entry, 0 force 876 Burglary, att. forced entry 625 Larceny, $250+ 212 Larceny, 100-249 310 Larceny, 50-99 474 Larceny, 25-49 425 Larceny, 10-24 705 Larceny, under 10 1,095 Larceny, $ unknown 157 Att. larceny 1,530 Car theft 114 Att. car theft 238 Theft, other vehicle 24 Att. theft, other vehicle 42 Total 44,263 Percent, incidents against persons only Percent, all incidents mobile and transient. Turnover rates in the Codicil References membership of schools and communities Hoekema, A. J. (1973) are very high where crime rates are high Readers will be quick to detect weaknesses in the proposed model for understanding Rechtsnormen en Sociale Feiren: Theorie en and offenders are disproportionately con- Empirie rond de Kleine Haven diefstal. Rotter- centrated. This suggests that peer group changes in the crime rate and its implica- dam. tien for conclusions about the effects of structures are far from static. There is con- Short, James F. and Fred L. Strodtbeck (1965) tinual recruitment and replacement of deterrence and incapacitation on the crime rate. Some will be quick to note that the Group process andgang delinquency. Chicago: members. Just how substantial replace- University of Chicago Press. structure of social networks and groups is ment of members is for offending groups White, Harrison (1970) because of residential mobility is not less formal than the argument supposes. Others will argue that human behavior is Chains of opportunity. Cambridge: Harvard known, but it is possible that transiency University Press. itself has an effect on the prevalence rate of less rational than the argument assumes. offenders in a population. The effects of Still others will suggest that the burden of recruitment and replacement on offending evidence hardly warrants a model which may be greater for young than for older assumes human intervention to reduce persons and greater for closed than for crime rates may actually increase them. open social networks or groups. And so it may be. Beneath the argument, however, lies a presumption that offending groups may not be all that different from other kinds of groups in a society. And the proposed model provides a basis for examining whether incapacitation may increase as well as decrease crime rates.

J Percent distribution of estimated numJber of offenders by type of crime and mean number of offenders per incident for all National Crime Survey incidents where number of offenders was reported. July 1, 1972, to December 31, 1975

Percent of offenders for each size of offending group Number Total Number offenders of percent per 1 2 3 4 5 6-10 11-15 16-20 21+ incidents

43.7 16.7 18.8 20.8 100.0 30 1.6 57.1 16.7 9.6 5.1 6.4 5.1 100.0 112 1.4 36.8 20.6 17.5 5.9 7.4 11.8 100.1 39 1.7 50.5 7.0 7.0 7.0 4.9 18.3 5.3 100.0 316 1.6 15.6 29.8 20.6 6.5 5.9 14.8 1.5 4.2 1.2 100.1 7 58 2.3 18.7 19.7 19.1 10.1 8.7 19.0 1.9 1.3 1.5 100.0 603 2.4 27.4 24.2 16.7 9.8 3.5 13.8 4.6 100.0 434 2.0 21.0 19.2 16.1 9.6 7.2 14.8 4.9 2.7 4.6 100.1 59 1 2.3 10.4 20.2 19.8 14.3 9.8 13.2 4.6 3.7 4.2 100.2 51 9 2.9 15.7 19.0 23.5 17.9 2.8 9.5 11.7 100.1 7 1 2.3 22.6 9.6 10.4 9.2 5.9 18.5 7.3 4.7 11.9 100.1 1,339 2.6 37.7 10.8 8.1 5.8 2.1 19.6 2.7 13.1 99.9 244 2.0 18.5 19.6 23.5 9.3 3.4 19.0 3.2 3.6 100.1 485 2.4 35.7 10.2 11.0 8.1 6.0 16.7 7.4 3.3 1.6 100.0 1,958 2.0 31.6 11.6 10.7 7.7 6.4 16.8 4.2 3.4 7.5 99.9 3,319 2.1 35.9 11.2 10.2 8.1 6.7 16.8 3.6 3.0 4.5 100.0 5,991 1.9 39.3 32.1 16.8 7.1 2.6 2.0 99.9 250 1.6 37.9 30.0 16.5 8.6 4.6 2.4 100.0 202 1.6 42.3 28.2 17.2 7.1 5.2 100.0 443 1.5 30.5 35.4 18.3 9.8 6.1 100.1 95 1.7 45.5 29.6 11.1 4.2 5.3 4.2 99.9 126 1.5 39.7 32.4 22.1 5.9 100.1 45 1.5 48.9 23.3 13.4 4.6 1.7 5.8 2.4 100.1 59 5 1.5 39.5 22.4 17.3 6.4 3.2 6.9 4.3 100.0 379 1.6 34.0 28.3 15.6 5.7 2.4 8.0 6.1 100.1 120 1.8 47.4 25.8 13.5 5.2 8.1 100.0 21 0 1.5 39.2 22.4 10.1 11.0 6.3 17.2 100.0 281 1.7 53.4 21.2 14.8 2.8 5.9 1.9 3.8 100.0 303 1.4 45.8 21.0 12.8 9.6 2.8 6.1 1.8 99.9 460 1.5 50.1 22.5 13.1 5.5 3.7 3.9 1.2 100.0 753 1.5 45.2 25.5 11.5 12.7 5.1 100.0 104 1.5 31.1 26.1 18.2 12.8 3.3 6.7 1.8 100.0 851 1.8 46.5 22.8 13.2 10.5 7.0 100.0 76 1.5 22.7 30.3 26.5 5.1 8.4 7.1 100.1 124 1.9 45.8 8.3 12.5 33.3 99.9 15 1.6 33.3 38.1 28.6 100.0 26 1.6 14,210 7.01 0 5,796 3,700 2,585 6,366 1,620 1,128 1,848 22,303 30.2 14.2 12.7 8.5 6.3 16.1 4.1 3.0 4.9 100.0 2.1 32.1 15.8 13.1 8.4 5.8 14.4 3.7 2.5 4.2 100.0 2.0 Criminal opportunities and crime rates RICHARDF. SPARKS School of Criminal Justice Rutgers University

A statistic very commonly used by crimi- infrequently seen as an indication of in- It seems intuitively obvious that each of nologists is the crime rate-e.g., the creased depravity or decreased probity, or these four objectives requires the calcula- number of crimes known to the police per as a sign of a usually ill-defined "social tion of crime rates-that is, the number of 100,000 population. In recent years, with pathology." Somewhat similarly, Taylor, crimes committed in a given place and time the development of victimization survey- Walton, and Young (1975:42) have argued period must be standardized for the popu- ing, similar use has been made of the vic- that from a radical perspective crime sta- lation in that place at that time period. It timization rate-e.g., the number of vic- tistics can be used as an "examination of seems prima facie absurd to compare the timizations reported per 1,000 persons or the extent of compliance in industrial number of homicides in the United King- households. It is argued here that such society (in quite the same way . . . as it is dom with the number of homicides in the rates need very careful interpretation and possible to use statistics on strikes as an United States, given that the United States that for many purposes they may be ex- index of dissensus in direct class relations has about four times as large a resident tremely misleading. It is also argued that in at the work-place)." population as the United Kingdom; simi- the calculation of such rates it is generally larly, not much can be inferred from a com- 2. A second purpose for measuring crime desirable to take into account opportuni- parison of the number of thefts in the has been the evaluation of the effectiveness ties for committing illegal acts as well as the United States in 1933 with the number of of the machinery of social control. As is population of potential offenders at risk. thefts in the United States in 1977, given well-known, Bentham (1778) was one of that the U.S. resident population rose by the first to urge that accurate measurement over 70 percent in that time period. Purposes for which crime rates of crime was a necessary adjunct for the Whether our concern is with social moral- are calculated legislator; he urged the collection of sta- ity, social control, the assessment of risk or tistics on convictions and prisoners as "a The purpose of this paper is to consider the testing of theory, it is necessary to kind of political barometer, by which the some conceptual and statistical properties control for variations in crime which are effects of every legislative operation rela- of crime and/ or victimization rates. Before due to differences in the numbers of per- tive to the subject may be indicated and doing that, however, it is necessary to sons able to commit crimes; criminological made palpable." review briefly the reasons why such rates theories, for example, are theories about are used as measures of criminal behavior 3. A third reason for measuring crime is the causes of crime,-and not about popula- or its consequences and, more generally, the estimation of the risk of becoming a tion growth. Similarly, we would not con- why it has been thought important to victim. This concern is present, though clude that people were becoming more measure crime or victimization in particu- often implicit, in contemporary efforts to dishonest, social control less effective, or lar times or places. There appear to be four develop "social indicatorsV(cf.Bauer 1964, life moredangerous, without standardizing main reasons: esp. chap. 2). As victimization surveying for population size. 1. Historically, the first purpose for col- has developed over the past decade, the assessment of risk has become increasingly letting statistics on crime and criminals The calculation of crime appears to have been the measurement of prominent; indeed' it appears have been and victimization rates the health,. of nations, cities, etc. one of the main objectives of the National The names given by the earliest demog- Crime Surveys (NCS) now being conducted A simple rate, like a crime or victimization raphers and statisticians to their measures by the Census Bureau for the Law Enforce- rate, is a function of only two elements: (I) ment Assistance Administration (see Penick a number of acts, events, situations, etc., of crime-Moralstatistik, statistique mo: and Owens 1976:143-45). which occur in a given place and time rule-give a sufficient indication of this period; and (2) a number of persons or objective; if the numbers of crimes orcrim- 4. Finally, the measurement of crime has other elements present in the same place inals increased, then in some sense the been a necessary preliminary to the devel- moral "health" of the nation was growing bpment and testing of criminological worse. Something of this concern appears theories. Typically the testing of such to linger on In popular InterPretatlons of theories has involved comparisons of crime crime statistics: a rising crime rate is not rates in different places or types of place (for example, cities versus suburbs), or over time, or attempts at correlating changes in candidate independent or explanatory variables with changes in crime rates. and time period. Thus a crime rate R is Crime and victimization rates raise a ing as within-group descriptions of experi- typically defined by number of well-known problems of meas- ence or risk. For example, if every white urement. Typically we are interested in the male aged 21 on his last birthday had an numbers of crimes which are actually approximately equal chance of contracting committed; but statistical series like the smallpox by his 22nd birthday, an age- where C = number of crimes committed, Uniform Crime Reports of course give only specific rate of infection of smallpox would P = number of persons available the numbers of crimes "known to the give an accurate measure of risk to each to commit crimes, police." Similarly, victimization surveys individual, though of course it would not k = a number chosen either to aim to measure the numbers of victimiza- describe any individual's actual experience give a convenient rate or a tions which actually occur; what they get (since either he catches smallpox or hedoes convenient base (e.g., 100,000 instead is the number of victimizations not). The same thing is true for phenomena persons). correctly recalled by survey respondents, like crime or victimization, which can in- Thus a rate R.has a natural verbal transla- reported to interviewers, etc. Each rate volve the same individual more than once tion: "For every k persons, R, crimes were thus has, in its numerator, a "dark figure" in any noninfinitesimal time period. If committed." of incidents which are not counted. Similar every member of a given subgroup were to A victimization rate R, is typically defined problems can also occur with the denomi- commit or suffer (say) exactly two crimes in a similar fashion, but with two differ- nators of these rates, through underenu- per year, then the resulting rate would ences. First, the numerator of the right- meration in a census; typically, however, necessarily reflect each individual's exper- hand side contains the number of victimi- these are much less serious. Having noted iencce in that year. Though this is of course zations rather than the number of crimes; these problems of measurement, I shall unlikely to happen, a crime rate would still depending on the definitions of these two from now on ignore them; my interest is in not be too misleading, provided that the things, and the "counting rules" used for the interpretation of crime and/ or victim- within-group variance were small, relative each, they need not be identical.' Second, ization rates, and not with the accuracy of to the subgroup mean(i.e., in proportion as the denominator is typically the number of the counts of incidents or persons which the coefficient of variation approached persons, organizations, etc. capable of they may involve. zero). Finally, even if the within-group being viclirns. Thus the current NCS The first of these problems of interpreta- variance were considerable, the rate might surveys, for example, compute commercial tion is a purely statistical one. It is obvious not be too misleading, provided the victimization rates to a base of (nongovern- that a rate defined as in (I) is a kind of aver- distribution were approximately normal mental) recognizable businesses; no ac- age; it is in fact a function of the arithmetic (or more generally were symmetrical about count is taken of the population of persons mean number of crimes committed per its mean). able to rob or burgle those businesses. (See, person. But such an average, taken over the It seems clear that this is generally not the e.g., National Criminal Justice Informa- whole of a population, clearly need not rep- case, however, either for crimes committed tion and Statistics Service 1976: 123.) resent the experience of any individual or or victimizations experienced. Data from a Rates of this kind measure the incidenceof subgroup within that population. A death number of studies to date strongly suggest crime or victimization, since their numera- rate for the whole of a population-some- that the frequency distributions of crime- tors contain (essentially) numbers of times called a "crude" death rate-may related events are typically extemely events. But analogous rates can be conceal considerable variations in the in- skewed, with the majority of the population constructed which measure the prevalence cidence of death in various subgroups of having no crimes or victimizations in a of crime-committing or being a victim; for that population. For this reason it is cus- given time period, and at the other extreme such rates the numerator is usually the tomary to calculate separate rates for sub- a small proportion of the population number of persons (organizations, etc.) groups whose experience is known to be having a great many. It follows that a crime who had committed one or more crimes, or different; e.g., age-specific or race-sex- or victimization incidence rate will be an been a victim on one or more occasions, in specific rates, or rates associated with dif- extremely misleading descriptor of the a given time period. Since a single offender ferent causes of death as well as withdiffer- group's experience, or of the risk of crime may commit more than one offense in a ent populations. (Cf. Reiss 1967:22-23.) or victimization. Such rates make possible between-group given time period, or a person or organiza- This point can be illustrated with data comparisons; for instance, of the risk of tion may be a victim on more than one taken from a victimization survey which I dying of heart disease at age 15 compared occasion, incidence and prevalence rates conducted in three Inner London areas in with the risk at age 75. Moreover, if the are not necessarily identical. (Compare 1973 (see Sparks, Genn, and Dodd 1977, subgroups used to calculate such "specific" death rates, where the number of deaths is chap. 4). Table 1 gives the numbers of re- rates are reasonably homogeneous with re- necessarily identical with the number of spondents reporting 0, 1,2, incidents of spect to the phenomenon being measured, . . . persons who die.)2 victimization of various types as havinge the resulting rates will not be very mislead- lForadiscussion ofthedefinitionsand "countingmies" happened within the survey reference used in the Unform Crime Reports, and their relation period (approximately the calendar year to those used in the National Crime Surveys, see 1972), together with sample victimization Hindelang (197639-97). rates per person. It will be seen that for two 'In the case of phenomena which have some temporal of the three areas, and for the sample as a duration (e.g., diseases), a further distinction is some- whole, the total victimization rate is in times drawn between "point-prevalence" rates and "period-prevalence" rates. Crime and victimization excess of 1.0 per person. A naive interpre- prevalence ratesare of the latter type, i.e.. they give the tation of these rates might suggest that percent of the population at risk who were criminals or victims within a time period such as a year. Table 1. Distribution of victimization incidents in three Inner London areas in 1972, and expected numbers based on Poisson distribution (all three areas) I Area I Number of incidents Brixton Hackney Kensington Total numbers I (A= 1.07) i I Number Percent Number Percent Number percent Number percent I

None 201 56 104 58 93 51 298 55 187 1 40 22 40 22 40 22 120 22 200 2 13 7 11 6 32 17 56 10 107 3 14 8 18 10 8 4 40 7 38 4 6 3 2 1 3 2 11 2 10 5 2 1 3 2 1 1 6 1 2 6+ 6 3 1 1 7 4 14 3 1 I Totals 182 100 179 100 184 100 545 100 Total numbers of incidents: 208 151 223 582 - Mean Numbers - of incidents: 1.14 .84 1.21 1.07 everyone in the sample was a victim at least assumptions of "contagion" or increasing, such a measure completely masks the ex- once in the year; or, alternatively, that the probability of victimization (Coleman treme cases of multiple victimization which risk of victimization in those areas was i964:299-305) or of heterogeneity of occur; if this is to be avoided, then the full about 100 percent, i.e., virtual certainty; "proneness" to victimization (Greenwood frequency distribution must be presented.3 yet, as the table shows, over half of the re- and Yule 1920) give a somewhat better fit spondents in each area reported no to data like those of Table 1; so does the Opportunities skew distribution first described by Yule incidents at all. and rates (1924) and discussed by Simon (1957: 145- Similar findings have emerged from a 64), which is based on slightly different The concept of opportunity is familiar in number of other victimization surveys assumptions. Using the London survey criminology, chiefly through the work of done in recent years (see, e.g., Aromaa data an attempt was made to identify em- Merton (1938) and Cloward and Ohlin 1971, 1974; Wolf and Hauge 1975; Rey- pirically (following a suggestion in Cole- (1960).4 Though seldom explicitly referred nolds 1973). The same general picture man 1964:378-80) subgroups of the sample to, the concept has also played a part in appears to be emerging from the NCS with different mean rates of victimization, many less elaborate attempts to explain surve.ys. In the commercial victimization for whom the distributions of incidents variations in crime rates over time or place. survey conducted in Houston, Texas, for could be adequately described by separate Thus, for example, it has often been noted example, the aggregate rate for robbery simple Poisson processes. Unfortunately, that there are well-marked seasonal varia- and burglary was 1.278 incidents per estab- this attempt was unsuccessful. No set of tions in observed patterns of crime, with lishment; yet nearly 60 percent of the busi- criteria-based on attributes such as age, crimes of violence typically being more nesses surveyed reported no incidents at all sex, race, or social class, either singly or in common in the summer months and crimes as having occurred within the I-year refer- combination-was found by which the such as burglary being more common in ence period (see Penick and Owens sample could be subdivided into groups in the winter: a common explanation for such 1976: 127-30; Hindelang 1976:22). In the which the frequency distribution of multi- findings is that social interaction is greater case of the NCS surveys this problem is ple victimization was no greater than in the summer, thus providing greater especially serious, since in LEAA's pub- would be expected by chance. (See Sparks, opportunity for interpersonal violence, lished reports to date on these surveys, the Genn, and Dodd 1964: 166-67; for a similar victimization rate is virtually the only sta- analysis with no better result, see Aromaa 'Though the evidence is much less complete, it appears tistic used. that the committing of crimes is distributed inasimilar 1973.) fashion. Carr-Hill (1971) found that convictions for Given a skewed distribution of the kind In summary, in the present state of our crimes of violence among adult males in England and disclosed by Table 1, the victimization rate Wales displayed a distribution not unlike that of Table I: knowledge, even specific subgroup rates most of the population had no convictions, while a might still have some readily interpretable are apt to be extremely misleading as de- small proportion had many. As with victimizat~on,a meaning in terms of victimization experi- scriptors of theexperience of, or the risk of, crime rate based on such a distribution would be ex- ence and/or risk, if the occurrence of mul- victimization. A prevalence measure- tremely misleading: it would greatly overstate the in- tiple victimization were approximately volvement in crime of the majority, while, of course, such as the percentage who are victimized understating the activity of the "crime-prone" random, i.e., if it more or less conformed to on one or more occasions in a given time minority. a Poisson distribution with the overall period-is somewhat less misleading. But 4Though it is interesting to note that, in general, both mean as a transition rate. As the right-hand Merton and Cloward and Ohlin tended to regard le- column of Table 1 shows, however, this is gitimate and illegitimate opportunities as alternatives, not the case: the numbers reporting no vic- and thus mutually exclusive: either one obtained a legitimate job or he joined the rackets. But-at least in timization at all, and the numbers report- Western industrial societies-the major opportunities ing several incidents, are both greater than for illegitimate gain open to most people involve theft would be predicted by a Poisson distribu- of some kind from their places of employment: thus tion. Compound distributions-based on legitimate and illegitimate opportunity structures are intimately connected. For a study of blue-collar theft illustrating this point, see Horning (1964). whereas longer hours of darkness in the It follows that, for any of the four objectives situation. Such models assume that crime- winter months provide greater opportunity of measurement mentioned earlier, oppor- proneness is not uniform in the population;, for undetected entry into others' property. tunities for crime need to be taken into and while the evidence for this proposition' account in calculating crime rates for com- More recently, a few researchers have is admittedly thin, the proposition itself is parisons across time or place. Thus, if the explicitly considered the relations between intuitively reasonable. This point has been crime rate is to be used as an indicator of crime and opportunities for it. Before con- neglected in some recent attempts at mod- sidering these approaches, however, we social morality, probity, violence-prone- elling criminal behavior (see, for example, need to examine the relations between an ness, collective wickedness, etc., it is in Avi-Itzhak and Shinnar 1973; Shinnar opportunity for committing a crime, and effect being interpreted as an average 1975,1977). Shinnar does refer to the aver- the commission of crime itself. It is clear tendency in the population to behave in age number of crimes committed (which he that, as a matter of ordinary language, the certain illegal ways; but a person's actually designates by A) as a random variable; but existence of an opportunity for a crime to behaving in those ways presupposes that he since he deals constantly in theexpectation be committed is a logically necessary con- has the opportunity to do so. Suppose that of this variable, he often seems to assume dition of that crime's occurring. That is, if we associate with each person in the popu- that it is literally the same for every mem- we are prepared to assert that an opportun- lation a tendency to steal, assault others, ber of the population of "criminals." This ity to commit, e.g., a theft at a particular etc.; borrowing a bit of economists'jargon, assumption may suffice for the purpose of time and place did not exist, then we should we might speak of a propensity to steal, making overall estimates of the hcapacita- normally be compelled to say that no theft assault, defraud, etc. Such a propensity can tive effect of imprisonment: as Blumstein et did in fact take place. Thus it is a necessary be defined as the conditional probability al. (1978:69) have noted, most models of truth, and not merely a very well-confirmed that an individual .will steal, assault, etc., the incapacitative effect can be generalized hypothesis, that no motor cars were stolen given that he has the opportunity to do so. to incorporate distributions of parameters in the United States (or anywhere else) in The evidence discussed earlier suggests that such as A. (See also Greenberg 1975; Cohen the distribution of this propensity in the the year 1850; that no room air-conditioners 1978.) But the assumption of a homogene- population will be skewed rather than were stolen in the year 1900; that no color ous A or proneness seems mistaken, if what television sets were stolen in 1930; and that normal. The unconditional probability is wanted is to model individuals'criminal no credit-card frauds were committed in that an individual will steal, p(T), would careers (which is in fact important for some 1940. The opportunities for those crimes then be given by the product of this condi- incapacitative strategies, e.g., those aimed simply did not exist in those years. tional probability or propensity, and the at "high-risk" offenders). A further compli- probability p(0) that he has the necessary cation is that what may be called the "ve- The proposition that changes in opportuni- opportunity: locity" of individuals' criminal behavior ties to commit crime will lead to changes in probably varies; that is, A is probably not the numbers of crimes actually committed constant over time. For a discussion see appears to be a hypothesis-to involve a But p(0) = 0 by definition, when no op- Green (1978); and for a discussion of contingent matter of fact, and not a truth of portunities exist; thusp(T) will also neces- models which can be used to tackle such logic. But the matter is more complicated sarily be zero under those conditions. Thus problems, see Fienberg (1977); Bartholo- than that. Certainly it is not necessarily if the average (or marginal) propensity to mew (1973). true that if the amount of stealable prop- steal remains constant in a population be- erty increases, the number of thefts will, tween t~and t:, but opportunities for thefts The point being made here, however, is ceteris paribus, increase. However, a de- increase, the probability of theft (and that p(T) is itself a function not merely of crease in the quantum of stealable probably the numbers of thefts actually individuals' propensities to behave in cer- property, social interaction, etc., may of committed) will increase; but that is not an tain ways (i.e., p(TI 0), which is the "real" necessity lead to a decrease in thefts, indication that the population is becoming proneness at issue), but also of their oppor- assaults, etc., if it results in some individ- any more dishonest. In somewhat old- tunities to exercise those propensities. The uals who formerly had opportunities to fashioned language, we might describe social and spatial distributions of those op- commit these acts no longer having them. such a situation by saying that the number portunities need to be taken into account, in any full attempt to describe or explain Thus, suppose that in a time period 11 every of temptations had increased (so that some member of a population of N persons has who formerly had no such temptations criminal behavior. some opportunities to steal; a further in- available now had them); not that people A similar consideration applies if the crime crease in opportunities in that population were becoming any more susceptible to rate is to be used as a measure of the system may lead to more thefts, or it may not. Sup- such temptations as they had. of social control, or as a dependent variable pose at 12 the number of opportunities for The unconditional probability p(T) can in a criminological theory or its testing. In theft is reduced, so that k individuals are obviously serve as a transition rate in a each case, what the crime rate is supposed completely without opportunities (so that Poisson process leading to actual thefts. to measure is (approximately) the tendency thefts can only be committed .by N - k The numbers of thefts occurring would in of the population to behave in certain ille- members of the population); all other this case be a random variable depending in gal ways, under specified control arrange- things being equal, the number of the thefts part on "theft-proneness" and in part on ments (e.g., a particular set of penalties) or will necessarily decrease. Evidently if we chance factors; models such as those of specified social-structural or other condi- are comparing numbers of thefts com- Greenwood and Yule (1920) would fit this tions (e.g., a given level of unemployment, mitted at 11 and 12 we must take account of status integration, or relative deprivation). changes in opportunities between those Plainly variations in opportunities must be two periods; and this is so whether tl pre- controlled for, if changes in crime rates are cedes 12 or follows it. to be interpreted correctly: a sharp decrease in opportunities for crime, for example, could be expected to lead to a decrease in Wilkins (1964:55). criminal behavior independently of any Boggs noted correctly that a consequence changes in presumed causal factors or the of population-standardized crime rates social-control system, merely because it was the production of "spuriously high" was no longer possible for some people to crime rates for central business districts, where 0 = opportunities for the type of commit crimes which they would otherwise which contain relatively small resident crime in question, have committed. populations but large amounts of mer- k =a constant chosen to give a chandise, parked cars, and so on. Accord- convenient base or rate (e.g., Finally, variations in opportunity must be ingly, she constructed "crime-specific" numbers of cars stolen per 1,000 taken into account in assessing the risk of rates using denominators which could persons able to steal cars, per victimization. If, for example, the number reflect opportunities for the type of crime 1,000 cars available to steal. of cars in use doubles while the number of in question: a business-residential land-use (Note that R,* is defined as zero when 0 is ca,r thefts only goes up by fifty percent, then ratio for commercial burglary and robbery, zero, since in that case Cis necessarily zero the average risk of a car's being stolen has the amount of street space available for as well.) If we write RF1forthe opportunity- declined; similarly, if people cease to go out parking, in the case of car theft, and so on. standardized crime rate in tl,and RF2for the of their houses at night, their risk of being Rank correlations between these rates and similar rate in 12, then R? 1 < R*2 if (C2CI)< assaulted in the street at night obviously (0201);that is, the rate will decrease if the declines. rates standardized for population only, across 128 census tracts in St. Louis, were number of crimes fails to increase as One of the first researchers to take into very high for highway robbery, residential rapidly as the number of opportunities. It is account variations in opportunity was burglary, rape, homicide, and aggravated also evident that if 02= 01,then Sarah Boggs, in her study of urban crime assault; but they were low and in some patterns (1965). Boggs noted that cases negative for other offenses, e.g., T = Environmental opportunities for crime vary -.23 in the case of nonresidential daytime from neighborhood to neighborhood. Depend- burglary (Boggs 1965:901). ing on the activities pursued in different sections of the city, the availability of such targets as It is important to note, however, that that is, if opportunities remain unchanged safes, cash registers, dispensing machine, standardization for variations in oppor- between 12 and 11,they can be ignored in the people and their possessions varies in amount tunities for crime is not an alternative to calculation of crime rates. This is also true, and kind. These differing environmental oppor- standardization for the size of the popula- of course, for population. An opportunity- tunities should be reflected in the occurrence tion available to commit crimes (as Boggs's standardized crime rate thus uses in its rates [of crime]. (Boggs, 1965:899) analysis suggests). Instead, both the popu- denominator the elements of both crime lation of potential offenders, and the stock rates and victimization rates, as these are of available opportunities for crime, usually calculated. should be reflected in the denominator of a crime rate. Thus, an opportunity-standardized rate R,* would be defined by The effects of taking into account oppor- The effects of standardizing for opportuni- Similarly, using the data in Table 2, the tunities can be illustrated by considering ties can be quite striking. They may be numbers of thefts from cars can quite the data in Table 2, most of which are taken quickly illustrated by comparing correla- accurately be forecast from population and from Wilkins (196455). Column 2 of this tions between thefts from cars, and the the numbers of cars registered (R2= .93). table gives !he numbers of thefts from same thefts standardized for both popuia- As 1 shaii argue later, however, it is often motor cars reported to the police in Eng- tion and cars available (i.e., columns 2 and the case that neither the population at risk, land and Wales during the years 1938-61 5 of Table 2), and the (fictional) explana- nor the stock of opportunities, is of much (excluding 1939); column 3 gives the num- tory variable in the column headed "X". theoretical interest; what is wanted, then, is bers of cars registered in England and For the numbers of thefts and X, r = +.93; to exclude their effects, and examine varia- Wales during those same years. Column 4 for the number of thefts standardized for tions in crime that are "left over" after that contains the resident population of Eng- population and cars registered, and X, r = exclusion. Thus, for example, after estimat- land and Wales in 1938-61 (General Reg- -.21. Thus what at first sight seems a very ing the numbers of thefts from cars T', ister Office, 1964:Table 2). Column 5 is strong positive correlation (+.93) is turned using equation (3a), we may calculate the calculated from columns 2, 3, and 4, and into a moderate negative correlation (-.21), residual thefts T* = T - T', and use those represents the numbers of thefts per when changes in the population and the residuals as the dependent variable in sub- 100,000 population per 1,000 cars available stock of cars available are taken into sequent analyses. (The correlation between to steal; for convenience I have indexed this consideration. those residuals, and the fictitious explana- series so that 1938 = 100. The column tory variable in column X of Table 2, is headed "X" is also taken from Wilkins The effects of population and opportunities +.20.) It is to be noted that excluding the (196455); it is in fact the numbers of thefts may vary, of course, and may themselves effects of population and opportunities in from shops and stalls reported to the police be of interest. To illustrate the estimation this way does not have the same effect as in England and Wales in 1938-61. It is not of those effects, we may regress the num- controlling for changes in opportunities (in clear to me why these figures were given by bers of thefts in Table 2 on population and this case, changes in the numbers of cars) Wilkins, since he nowhere discusses them the numbers of cars. It might be argued by partial correlation. A partial correlation in the text of his book; they are, however, that the effects of population and oppor- r,,., is of course a correlation between the convenient for illustrative purposes. We tunities were additive; intuitively, how- residuals of the regression of x on z and may consider them to represent some can- ever, it seems more reasonable to assume those of the regression of y on z; the effect didate explanatory variable, e.g., average that they are multiplicative, so that of the control variable z is thus removed family income in pounds sterling. from both x and y. In the present case, however, we are removing the effects of Wilkins's own discussion of the data in where T' = estimated number of thefts, columns 2 and 3 of this table raises a population and opportunities from the C = the stock of cars, dependent variable only, in order to ex- number of questions. For one thing, he P = the population. considers the numbers of theftsfrom motor amine the residual variation in relation to This can be rewritten, after taking loga- some candidate independent variable or cars, rather than the numbers of thefts of rithms on both sides, as a motor cars;s for another thing, he uses the variables. (See, for a further discussion, numbers of thefts reported to the police, Mosteller and Tukey 1977:269-71.) Some rather than the (reported) theft rate per cases in which partial correlation and kin- which can be estimated using ordinary Least dred techniques may be appropriate, in the 100,000 persons, though as column 4 shows squares. A somewhat similar approach was the resident population of England and analysis of criminal opportunities, will be recently used by Felson and Cohen (1977) discussed in a later section of this paper. Wales increased about 12 percent over the in their analysis of burglary rates in the years 1938-61. inspection of the table will United States in the period 1950-72. Felson In a more recent paper, Gould (1969) show that the numbers of thefts reported and Cohen utilize what they call a "routine presented data similar to those given by rose by about 350 percent, in the same activity" approach to crime, based on the Wilkins, for thefts of cars and numbers of years; the theft rate per 100,000 persons of human ecology theories of Amos Hawley cars registered, in the United States in the course increased by somewhat less than (1950); they show that a substantial pro- years 1933-65. Gould also compared year- this. The number of cars available to steal- portion of the variation in burglary rates end amounts of cash on hand in banks with or to steal from-rose by over 200 percent, can be accounted for (corrected R2 = .986) the numbers of bank robberies and bur- however; the result is that the number of by a multiplicative combination of three glaries, during the years 1921-65. In each thefts from cars, standardized both for variables, namely the percent of the popu- case Gould, like Wilkins, compared the population and for cars, rose by only 29 lation aged 15-24; the proportion of "pri- numbers of thefts with his measures of percent. mary individual" households; and an opportunity, and took no account of changes in the population able to commit 'Wilkins has since informed me that reliable data for ingenious measure of the "inertia" of prop- thefts of cars were not available for the period in erty targets, viz. the weight of the lightest the two types of theft; in view of the fact question. television set advertised in current Sears & that the U.S. resident population increased Roebuck catalogues. (See also Cohen and by about 50 percent between 1933 and Felson 1978.) 1965, this is no small omission. (It might of course be appropriate to take into account 'changes in the age structure of the population, or to exclude the effect of some subgroup thought to be especially likely to be involved in the partic;lar kind of crime in question-as Felson and Cohen (1977) did in their analysis of burglary.) Gould does less unchanged. Similarly, the design of in the ratios 4. 10: 4. lo3: 4. lo6; on this not present, in his 1969 paper, data which most bank vaults deprives the majority of basis, he calculated that the probability of would permit the calculation of doubly the population of the opportunity to steal being killed by an acquaintance was some standardized rates of theft, or of residual the valuables in those vaults; professional 3,000 times greater than the probability of theft after the exclusion of population and bank burglars, equipped with explosives or being killed by a stranger and that the opportunity effects. But from his graphs of thermic lances, still have their opportuni- probability of being killed by a family the two time series (Gould 1969:53) it is ties available to them. In general, if preven- member was some 600,000 times greater. clear that both car theft and bank robbery/ tive measures are themselves of theoretical These "probabilities" assume, of course, burglary rates declined, relative to oppor- interest-if, for example, it is intended to that the numbers and types of contacts are tunities, up to about the middle 1940's; and assess their effects on the crime rate-then on average the same within each of these that, even without allowing for increases in those effects should be kept separate, and three groups, which is improbable to say the population, rates relative to opportuni- not excluded from crime rates in the way the least. Nonetheless, the general logic of ties remained virtually unchanged from the suggested in the preceding section. To the this approach seems to me correct; for the mid-1940's to the mid-1960's. (The correla- extent that one's interest is in other crimi- purpose of explaining the social, spatial, or tion between numbers of car thefts and cars nological factors, however, the opportu- temporal distribution of violent crime, as registered is +.97, for the years 1950-65; for nity-reducing effects of preventive or other well as for assessing the risk of it, some cash in banks and bank robberies/ burglar- social-control factors may best be removed account needs to be taken of the ies, the correlation is +.98 for the period from the crime rates in question, so the re- distribution of opportunities (i.e., interac- 1944-65.) sidual crime rates can be examined by tions between persons) which are a Still more recently, Mayhew et al. (1976) themselves. logically necessary condition of such victimization. analyzed car thefts and numbers of cars There still remain many difficulties of defi- registered, in London in the years 1961-74. nition. In the case of crimes of violence, In the case of crimes against property, the They noted that the parallel trend noted opportunities are presumably created by choice of an adequate base for calculating . earlier by Wilkins (for theftsfrom cars, and contacts or interactions between persons. an opportunity-standardized rate can also cars registered) did not continue, at least in As is well-known, in a population of N per- be problematic. One approach is simply to London, after 1961. Mayhew et al. were sons, the maximum possible number of use the stock of stealable goods; this is in mainly concerned with the effects of a pre- two-person contacts which can take place fact what was done by Wilkins, Gould, and ventive measure (steering column locks) in equals N(N - 1)/2; this was in fact the base Mayhew et al. in their studies of theft from, reducing opportunities for theft. Since used by Boggs (1965:900) in calculating her and of, cars. But for other types of theft, the 1970, steering column locks have been re- "crime-specific" rates of homicide and matter is less clear. Thus Gould (1969), in quired on all cars manufactured in or im- aggravated assault. However, this maxi- analyzing bank robberies and burglaries, ported into England; the result has clearly mum number is of potential contacts of any used data on amounts of cash and coin in been a decline since that date in the stock of kind (assuming-what is not off-hand banks. It might be argued, however, that what Mayhew et al. call "stealable" cars. clar-that the notion of a "contact"can be the number of banking offies is a better Yet they found that the number of thefts defined with reasonable precision). To be measure of opportunity than the amounts of cars has continued to rise sharply in even approximately satisfactory, standard- of cash which are contained in those bank- London, especially since 1970. If theft rates ization for opportunities for crimes of ing offices. (Data from the Statistical Ab- since that date were standardized for (de- violence would need to take into account stract [US. Department of Commerce, clining) opportunities in terms of the the nature and duration (and possibly the 19701 show that the amount of cash and numbers of unprotected cars, the increase frequency) of interactions between differ- coin in banks increased about five times in in theft rates would be much greater than is ent types of persons, e.g., across different the period studied by Guuld; the number of suggested by the data which Mayhew et al. types of communities or in given interper- banking offices increased by only about 70 present. sonal relationships. Thus some years ago percent.) Similarly, should one use the Svalastoga (1962) analyzed a small sample number of supermarkets and/ or depart- Defining and measuring of homicide cases in Denmark; he found, as ment stores as a base for shoplifting, or the opportunities for crime have most-other researchers on homicide, value of those stores' inventories? The that the majority involved family members answer would seem to be that it depends on What constitutes an opportunity for the and that strangers accounted for only 12 the purpose for which rates are being calcu- commission of a crime naturally depends percent of the cases studied. On the basis of lated. If the objective is the assessment of on the type of crime in question, and satis- a small survey of students, plus some ad- risk, then the number of institutions factory definition-both conceptual and mitted guesswork, Svalastoga estimated (stores, banks, etc.) would usually be more operational-can in some cases be very dif- that a Danish person might have contacts appropriate; if the objective is the explana- ficult. One problem, to which I see no with relatives, acquaintances, and strangers tion of observed patterns of theft, then the general solution, concerns the vagueness of stocks of available goods might be the borderline between difficulty and im- preferred. possibility, reflected by the Mayhew et al. In the case of thefts from individuals and/ or (1976) study just discussed. Steering-column locks may deprive amateur car thieves of households, the choice of an appropriate the opportunity to ply their trade; but they base is even more complicated. In some leave the opportunities open to profes- places, estimates are available for the sional car thieves (presumably) more or stocks of consumer goods owned by individuals and/ or unincorporated businesses (see, e.g., Roe 1971:70-71), where some estimated values for the United Kingdom in the years 1955-66 are given; these data one, and in two houses out of every three 1969,1970; Mansfieid, Gould, and Namen- are shown at written-down replacement could have had a choice of sets (or the wirth 1974) appear to treat changes in the cost, though if price-index changes are chance of a color set) to steal. Over the stocks of one type of property-cars-in taken into account an estimate of physical same period-and for exactly the same, precisely this way. Thus Gould (196954) stocks of goods coiild in principle be reason-the chance of any particular tele- writes that "the availability of property in- derived from them). In this country, data vision set's being stolen has almost cer- fluences the amount of theft against it," are available from the Statistical Abstract tainly decreased sharply. and he refers to this as a"causa1sequence." He goes on to speculate that "property and from a variety of trade publications, Until better data are available on the such as Merchandising Week, on most crime is not only related to the availability amounts and types of property stolen, it of property, but this relationship is it- types of durable consumergoods. Typically, does not seem worthwhile to estimate ... these data are for ~roduction,shipments, self structured by the relative scarcity or changes in opportunities for theft with abundance of the property being stolen." or sales of such godds, though estimates of greater precision or detail. Unfortunately, stocks can be derived from them if (Gould 196956)Healso notes that changes little such information is now available. in patterns of car theft, and in the availabil- assumptions are made about average life Since 1974, data have been collected (or average "stealable" life). Where figures ity of stealable cars, parallel an apparent (though not published) in supplementary change in the population of car thieves, for estimated stocks of such goods are returns from police forces under the Uni- available, they almost invariably disclose who (according to arrest data) are now form Crime Reporting program; these much more likely to be juvenile or adoles- massive increases over the past three returns, which have recently been made decades, usually far greater than the cent "joyriders" than they were in the more detailed, apply only to thefts reported 1930's or 1940's. (Gould also notes that increases in burglaries and larcenies to the police, and nothing is now known recorded in the Uniform Crime Reports. similar changes appear to have taken place about their validity. The same is true of the among bank robbers, with "professional" Thus, according to estimates based on similar data now being collected in the market research by a television network robbers having largely been replaced by National Crime Surveys. The Crime Inci- inept amateurs.) (NBC 1975), only 9 percent of all American dent forms (NCS-2 and NCS-4) used in households had a television set in 1950; by these surveys contain questi~ns'~ertainin~Gould suggests, then, that (at least so far as 1974 the figure was over 94 percent, with to the value (calculated in several different car theft is concerned) the period from the over two-thirds of those households having ways) of stolen or damaged property; but early 1930's to the early 1940's was "a color television and about two-thirds they are now coded so as to distinguish period of economic scarcity" (Gould having more than one set. (Similarly, trade only between thefts of cash, motor vehicles 1969%) in which car theft was mainly an sources estimate that the total number of and accessories, and "other" property. activity of "professional" thieves; and that radio sets in use in the United States Given more data on the types and amounts the years after about 1942wereUmarkedby increased by nearly 3% times in the period of property stolen, it would, in principle, be abundance," and the emergence of juvenile 1950-74.) Within the past few years, there possible to estimate the stocks of property "nonprofessional" thieves. Inspection of has evidently been an even more rapid from which those thefts occurred; if this the (graphed) data which Gould presents, increase in ownership of such things as were done, it would be possible to estimate however, suggests a rather different pic- stereo equipment, tape recorders and rates of theft relative to opportunities, ture. From his graph of car registrations cassette players, hand-held calculators, and either cross-sectionally or over time. and car thefts, it appears that: CB radios. The result has been to increase Car registrations rose in the years 193341, substantially the quantity of personal though the increase would admittedly be disposable property available to be stolen, Opportunities and criminological' explanations less if increases in population were taken and thus the opportunities for theft.6 In the into account. case of television sets, for example, the Thus far, this paper has been concerned Cars were possibly relatively scarce in figures just quoted mean that in 1950 a with the effects of variations in opportuni- the years 194145-there was a decline ,of burglar or thief had less than one chance in ties for crime-for example, changes in the about 16 percent, from about 35 million to ten of finding a television set in an Ameri- stock of personal disposable property, in about 30 million. can household chosen at random; by 1974 the case of theft-on the interpretation of Since 1945, the stock of cars registered he would have had difficulty in not finding the crime rate: it has been argued that, rose steadily, but the numbers of car thefts 6According to a recent newspaper account, moving given the purposes for which we commonly fell, until about 1950. companies estimate that the average household move measure crime, it is appropriate to stand- After 1950, the increase in car thefts involved 1,000cubic feet of goods 15 years ago; now the ardize crime rates for opportunities. I can roughly paralleled the increase in cars figure is about 2,000 feet. Not surprisingly, suburban- see no argument against this kind of stand- registered. ites are said to be "worse than city dwellers"in this respect. See "In age of accumulation, moving is a trial," ardization, which would not apply with New. York Times, March 19, 1978, p. R1. equal force to standardization for changes in the population available to commit crimes. It remains to be considered, in conclusion; whether opportunity factors also can or should figure as separate independent variables in an explanation of criminal behavior or variations in crime rates. Recent papers b.y Gould and his associates (Gould It is evident that none of these changes in demand for stolen vehicles, and the supply 1963.) In this case the number of thefts stocks of stealable cars, and of car thefts, in of available vehicles. The authors admit would be expected to fall, for two distinct any way necessitates the shift which that they are only able to carry out a partial reasons: first because demand for stolen appears to have taken place, from "profes- test of their model; in particular, they have cars fell, and secondly because of a de- sional" to "amateur" thieves; this change is no data on the relative magnitude of "pro- crease in opportunities. quite independent. Moreover, the relation fessional" and "amateur" demand for One case in which it may be useful to treat between cash and coin in banks, and num- stolen vehicles, nor on the shapes of the changes in opportunities independently is bers of bank robberies, is (as Gould respective demand curves. Their paper il- the case in which they function as an inter- [1969:56] puts it) "somewhat different"; to lustrates two ways in which an opportunity vening variable, helping to explain an the extent that there has been a somewhat factor-e.g., the supply of stealable goods- observed relationship between crime or similar shift in the population of robbers, may be incorporated into an explanatory victimization and some other variable. this is not paralleled by changes in the theory. But it is important to note that it is Thus, several victimization surveys have amounts of cash and coin available to steal. not opportunities as such-in the sense found a negative association between age Using the concepts outlined earlier in this described in this paper-that figure in such and victimization, especially for violent paper, we could in fact describe the situa- a theory. Instead, it is the relative scarcity crimes such as assault (Sparks, Genn, and tion relating to car theft in the following or abundance of goods, which may affect Dodd 1977:chap. 4; Aromaa 1971; Hinde- ways: participation in theft in, broadly speaking, lang 1976:111-14). A possible explanation In the years 193341, the numbers of cars one of two ways: (1) by affecting motiva- for this finding is that older people tend to registered rose fairly steadily, while the tion to steal (e.g., by making it easier to go out less often, especially at night; they numbers of thefts of cars declined; the rate obtain goods legitimately or conversely by are thus less at risk of (certain sorts of) vic- RT of car thefts standardized for opportu- increasing relative deprivation) and (2) by timization. (What is opportunity from the nities fell sharply. Quite probably this leading to changes in social control meas- offender's point of view, of course, is risk could have been because, though it was ures (in the broadest sense of that term, from the victim's.) If this factor is taken successively easier to steal a car (there were including measures for the protection of into account, the zero-order association more of them), it was also easier to obtain stealable property). Mansfield, Gould, and between age and victimization may dis- one legitimately. Namenwirth do mention both of these, but appear, or at least be reduced. In our Lon- In the years 194145, when no new cars they make no attempt to operationalize or don victimization survey, for example, the were manufactured and the stock of steal- measure either one. The first of these ex- zero-order y between age and victimization able cars declined, the numbers of thefts planations would seem to require (for was -.42; between age and the number of (and the theft rate R?) rose; because cars example) some evidence about the dislri- nights per week the respondent went out, became relatively scarce, the opportunities bution of stealable property, as well as the y = -.18; between nights out and victimi- for obtaining them legitimately also de- quantity of it; it might also require consid- zation, y = +.20. The partial y between age creased. eration of the value of that property since and victimization, controlling for nights In the years 1945-50, the numbers of cars (under certain conditions) an increase in out, was reduced to -.29. A reasonable in- (and thus of opportunities for car theft) supply relative to demand may lead to a terpetation of these findings is that a part of rose again; car thefts fell,so the car theft rate decrease in price. Thus, for example, if the older respondents' lower victimization RT fell even more sharply; again this could more cars are available, opportunities for rate was due simply to the fact that they have been because cars were more easy to car theft will (ceteris paribus) increase; but were less often at risk. A similar analysis is obtain legitimately. it should also be easier to obtain cars legiti- possible for some of the National Crime Finally, in the years 1951-65, the num- mately. In this case we should expect a de- Survey data, since the NCS-6 "attitude" bers of cars (and of opportunities for car crease in R?, such as that which occurred questionnaire administered to half of the theft) rose steadily; so did the numbers of in the years 1933-41 and 1945-50. The respondents in the city-level surveys con- thefts, so that the car theft rate R? re- second line of explanation might involve tains a question (Q.8a) asking "How often mained about unchanged. showing, for example, that when property do you go out in the evening for entertain- is relatively abundant people are less likely ment?"; so far as I know, however, these These temporal patterns areevidently com- to protect4t against theft, or to report thefts patible with many different combinations data have not been analyzed from this to the police. But an increase in the stock of point of view. bf professional and amateur car thieves goods-and thus in opportunities to and different participation rates of each. acquire those goods legitimately-can Another case in which variations in oppor- In a later paper, Mansfield, Gould, and occur together with an increase in protec- tunity need to be considered separately Namenwirth (1974) expand on Gould's tive measures; an example would be a law occurs when those variations are (hypothe- earlier work (and incidentally standardize requiring steering-column locks to be fitted sized to be) consequences of protective or both car ownership and car theft for to all cars. (As Mayhew et al. [I9761 point social-control measures in the broadest changes in population, as Gould had not). out, such a law was passed in Germany in sense of that term. In the case of steering- They attempt, using data from four coun- column locks on cars, for example, it tries, to test a model according to which would seem best to analyze thefts of cars thefts of cars (and, by implication, other with such locks separately from thefts of stealable property) are determined by the cars without them, taking into account the interaction of "professional" and "amateur" stocks of cars of each type; the hypothesis that locks were effective in preventing theft would predict that thefts of cars with locks would decrease (or increase less rapidly) relative to thefts of cars without them. In- tensive (and highly visible) police patrols, Conclusions anti-shoplifting devices, apartment-house Many of the ideas in this paper were developed security systems, burglar alarms, exact- It seems that there are some instances in which variations in opportunities to com- at the SSRC Workshop in 1975; earlier versions fare buses, and the like, may all beassumed of the paper were presented at the annual meet- to reduce some potential criminals' oppor- mit crime may be substantively important in the explanation of variations in crime ing of the American Society of Criminology in tunities for crime, by making the successful November 1977, and at a Workshop on Quanti- accomplishment of crimes more difficult rates, and so should be treated independ- tative Analysis of Crime and Criminal Justice, for the average person (or potential crimi- ently rather than being "netted out" of the sponsored by the Institute for Social Research, nal). To the extent that our theoretical crime rates themselves. In general, how- University of Michigan, in August 1978. 1 am and/or practical interests are focussed on ever, it seems to me that variations in grateful to many people for their comments on this kind of effect, we would not want to opportunities for crime are likely to be those earlier versions: in particular to Don Gott- rather obvious and uninteresting where the fredson, Andrew von Hirsch, David Seidman, remove the effects of variations in oppor- Howard Wainer, Colin Loftin, and Simon tunity from the dependent varilble (i.e., explanation of crime is concerned. It is seldom useful to point out that cars could not Singer. None of them is responsible for residual crime rates), but to treat them independ- errors. ently. If our interests lie elsewhere, how- be stolen before cars were invented; and it ever, we might well wish to remove those is not, in general, illuminating to point out effects, so as to see better the effects of that a man who never goes out of his house References other variables on variations in crime. will never get assaulted or robbed in the Aromaa, Kauko (1971) street. Arkipaivan Vakivaliaa Suomesia [Everyday Inevitably, there will be borderline cases. But though they may often be relatively triv- violence in Finland]. Helsinki: Kriminolginen The "inertia" measure used by Cohen and Tutkimoslaitos. Felson (1977), discussed earlier, is an ex- ial in themselves, variations in opportunity may nonetheless often obscure the effects Aromaa, Kauko (1973) ample. The fact that many durable con- "Victimization to violence: Some results of a sumer goods have become smaller and of more important theoretical variables. To avoid this, the procedure of standardiz- Finnish survey." Inrernarional Journalof Crimi- lighter (as measured by the weight of the nology and Peno1og.v 1:245. lightest television set advertised in current ing crime rates for opportunities, as out- Sears and Roebuck catalogues) can cer- lined in this paper, seems to me appropri- Aromaa, Kauko (1974) ate. This procedure is in fact analogous to The replicarion of a survey on vicrimizarion ro tainly be interpreted as increasing (the violence. Helsinki: Institute of Criminology. average man's) opportunities to steal. Are the "method of residues" proposed some we interested in the effect of rhar change on years ago b;y Coleman (1964: chap. 15). Avi-Itzhak, B., and R. Shinnar (1973) rates of theft? Or are we interested in varia- Coleman noted that a great deal of effort "Quantitative models of crime control." Jour- nal of Criminal JusrkP l(3): 185-217. tions in theft of durable consumer goods, had at one time gone into finding a "law of given that change in opportunities? Each of social gravity" to the effect that, say, the Bauer, Raymond A. (ed.) (1966) these questions requires a different measure amount of travel or other interaction Social indicaiors. Cambridge, Mass.: M.I.T. of theft-the former excluding, the latter between two cities is directly proportional Press. including, the effects of variation due to the to the product of their populations, and Bentham, Jeremy (1778) opportunity variable. inversely proportional to some function of "Observations of the Hard Labour Bill." the distance between them. Such a "law" Works (J. Bowring, ed.), vol. 4, 2841. Suppose, furthermore, that the use of has the unfortunate defect that it often does Blumstein, Alfred, Jacqueline Cohen, and transistors, printed circuits, etc., has made not fit the observed data on intercity travel Daniel Nagin (eds.) (1978) some kinds of goods smaller and easier to very well. But it also has the even more seri- Deterrence and incapacitation: Esrimaiing the steal (under average circumstances). Sup- ous defect that, where it does fit, it is utterly effects ofcriminal sancrions on crime rates. Re- pose, moreover, that (as is almost certainly uninteresting. By standardizing rates of port of the Panel on Deterrent and lncapacita- true) those same technological factors have travel for populations and distance, Cole- tive Effects, National Research Council. Wash- made those goods much cheaper (and thus man suggested, one could calculate for any ington, D.C.: National Academy of Sciences. generally easier to acquire legitimately). pair of cities a "residue" which would be the Boggs, Sarah L. (1965) Suppose, furthermore, that-as is also cer- difference between observed travel and "Urban crime patterns." American Sociologi- tainly true-the stocks of such goods avail- that expected on the basis of population cal Review, 30:899-908. able to steal have increased sharply at the and distance alone; examination of these Carr-Hill, Roy A. (1971) same time. In those circumstances, to treat residues might then reveal more interesting The violennr offender: Illusion or reali~y? prices, stocks, and "inertia" as separate effects which would otherwise be obscured. Oxford University Penal Research Unit, Occa- variables in an explanation of theft rates sional Paper No. I. Oxford: Basil Blackwell. The same approach may often be useful in will be likely to lead to severe problems of Cloward, Richard, and Lloyd Ohlin (1960) multicollinearity; but these will still be relation to crime and victimization. The Delinquency and opportunity. New York: present, even if any one or two of the three number of homicides in New York is Free Press. (say, stocks of goods and "inertia") are re- greater than the number of homicides in, moved, along with changes in the popula- say, New Orleans; but the homicide rare tion, in the calculation of crime rates. standardized for population is higher in New Orleans. The number of car thefts in the United States in 1965 is greatel than the number in 1945; but the car theft rare standardized for both population and the stock of stealable cars is smaller. Only by removing the sociologically trivial effects of population and opportunities can more interesting and important effects be seen. Cohen, Jacqueline (1978) Horning, Donald M. (1964) Reiss, Albert J., Jr. (1967) "The incapacitative effects of imprisonment: Blue-collar theff. Ph.D. dissertation, Indiana Studies in crime and law enforcement in major A critical review of the literature." In Alfred University. metropolitan areas. Vol. 1, section 1: Measure- ment of the nature and amount of crime. Presi- Blumstein, Jacqueline Cohen, and Daniel Nagin ~ ~ ~R ~~ L~~~~f ~ C.i ~~~ld,~ ~ ~ and~ ,J.~zvi , (eds.), Deterrence and incapacitation: Es!ima!- dent's Commission on Law Enforcement and Namenwirth (1976) Administration of Justice, Field Surveys Ill. ing the eflects of criminal sanctions on crime ..A socioeconomic model for the prediction of rates. Report of the Panel on Deterrent and In- societal rates of property theft.w~~~~~lF~~~~~ Washington, D.C.: U.S. Government Printing Office. capacitative Effects, National Research Council, 52:462-72. Washington, D.C.: National Academy of Reynolds, Paul Davidson, et al. (1973) Sciences. Mayhew, Bruce H., and Roger L. Levinger(l976) Victimization in a melropo/itan region: Com- "Size and density of interaction in human Cohen, Lawrence E., and Marcus Felson (1978) parison of a central city area and a suburban aggregates.w American Journal of Socio~ogy community. Minneapolis: Minnesota Center for "Social change and crime rate trends: A rou- 82:86-1 tine activity approach." Working Papers in Sociological Research (mimeo.). Mayhew, P., R. V. G. Clarke, A. Sturman, and Applied Social Statistics. Department ofSociol- Roe, A. R. (1971) " ogy, University of Illinoisat Urbana-Champaign. J. M. Hough (1976) The financial interdependence of the econ- Crime as opportunity. Home Office Research omy. London: Chapman and Hall. Coleman, James S. (1964) Study No. 34. London: Her Majesty's Stationery introduction to mathematical sociology. New Office. Shinnar, Reuel, and Benjamin Avi-ltzhak (1973) York: Free Press. "Quantitative models in crime control." Jour- Merton, Robert K. (1938) nal of Criminal Justice 1:7. Felson, Marcus, and Lawrence E. Cohen(1977) wSocial structure and anomie.,. In Social acts and community structure: * theory and structure (rev. ed. 1957), chap. 3, Shinnar, Reuel(1975) routine activity approach." Working Papers in New York: Free Press. "The incapacitative function of prison intern- Applied Social Statistics. Department of Sociol- ment: A quantitative approach." Department of ogy, University of Illinois at Urbana-Champaign, Mosteller, Frederick, and John W. Tukey (1977) Chemical Engineering, City University of New April 13, 1977 (mimeo.). Data analysis and regression. Reading, Mass.: York (mimeo.). Addison-Wesley. General Register Office (1964) Simon, Herbert A. (1957) ,961, ,~+~l~~dand wales. vol. 1: National Broadcasting Corporation (1975) Models of man: Social and rational. New census, "TV households, sets and per cent saturation." Age, marital conditioh, and general tables. York: John Wiley & Sons. London: Her Majesty's Stationery Office. NBC Research Estimates. TV Factbook, No. 44 (1974-75):69. Sparks, Richard F., Hazel G. Genn, and David Gould, Leroy C. (1969) J. Dodd (1977) changing structure of property crime in National Criminal Justice Information and Sta- Surveying victims: A study of the measure- an affluent society.w~~~~~l F~~~~~48:50-59. tistics Service, Law Enforcement Assistance ment of &iminal victimization, p~rceptionsof Administration (1976) Gould, Leroy C. (1970) crime, and attitude to criminal justice. London: Criminal victimization surveys in Chicago, John Wiley & Sons, Ltd. "Crime and its impact in an affluent society." ~~t~~it,bs~ ~,vew york,~ and~ phila- l ~ ~ , In Jack D. Douglas (ed.), Crime andjustice in delphia: A comparison of 1972 and 1974find- Taylor, Ian, Paul Walton, and Jock Young American society. Indianapolis: Bobbs-Merrill. ings. ~ ~crime survey~ i N~.~ SD- ~ (1975) ~ l Green, Gary (1978) NCS-C-6. Washington, D.C.: US. Government Critical criminology. London: Routledge and "Measuring the incapacitative effectivenessof Printing Office. Kegan Paul. fixed punishment." In James A. Cramer (ed.), penick, B~~~~~K. id^^^ and ~~~~i~~ E. B. U.S. Department of Commerce, Bureau of the Preventing crime, Sage Criminal Justice System owens1~1(eds,) (1976) Census (1970) Annuals, vol. 10, New York: Sage Publications. surveying crime. ~ ireport~ of~the Panell for Statistical abstract of the United States, 1970. Greenberg, David (1975) the Evaluation of Crime Surveys, Committee on Washington, D.C.: U.S. Government Printing "The incapacitative effect of imprisonment: National Statistics, Assembly of Mathematical Office. Some estimates." Law and Society Review and Physical Sciences, National Research Coun- Webb, Stephen D. (1972) 9541-80. cil. Washington, D.C.: National Academy of "Crime and the division of labor: Testing a Sciences. Greenwood, M., and G. Udny Yule (1920) Durkheimian model." American Journal of "An inquiry into the nature of frequency dis- Sociology 78:643-56. tributions representative of multiple happenings Svalastoga, Kaare (1956) with particular reference to the occurrence of "Homicide and social contact in Denmark." multiple attacks of disease or repeated acci- American Journal of Sociology 6237-4 1. dents." Journal of the Royal Statistical Society Wilkins, Leslie T. (1964) 83-255. Social deviance: Social policy, action, and Hawley, Amos (1950) research. London: Tavistock Publications. Human ecologj~: A theory of community Wolf, Preben, and Ragnar Hauge (1975) structure. New York: Ronald. "Criminal violence in three Scandinavian Hindelang, Michael J. (1976) countries." In Scandinavian studies in crimi- Criminal victimization in eight American nology, vol. 5, London: Tavistock Publications. cities: A descriptive analysis of common theft Yule, G. Udny (1924) and assault. Cambridge, Mass.: Ballinger Pub- "A mathematical theory of evolution, based lishing Co. on the conclusions of Dr. J. C. Wills, F.R.S." Philosophical Trans. B, 213:31. Notes on measurement by crime victimization surveys ALBERT D. BIDERMAN Bureau of Social Science Research Washington, D. C. *

The first part of this paper describes short- we are, in the design of the NCS, neglecting to be many incidents, each qualifying comings in victimization surveys in provid- almost totally gaining information on under the definition of a criminal victimi- ing data for the measurement of the preva- criminal victimization that is more readily zation used by the survey. To make a threat lence (rather than the incid.ence) of crime. approached as a condition than as an credible to the victim and to continue a The second part discusses the immunizing incident. We are also neglecting the state of terrorization, the terrorist must effects of victimization experiences to durable consequences, that is, the changes neither continually repeat his threat nor future experiences, and how the concept of in condition, produced by point-in-time demonstrate his willingness to carry it out immunization may be applied to the assess- incidents. In other words, NCS pursues an by actually inflicting violence. ment of risk of victimization. incidence, rather than prevalence, rationale. Among the kinds of victimization that may Albert J. Reiss, Jr. (1972) also illustrates a be conceived and measured in prevalence somewhat different type of continuing vic- The significance of measurements timization by the case of the tenant inhabit- of events and conditions rather than in incidence terms are various forms of continuing terrorization and ing a dwelling affected by building code Incidents and conditions. Among many extortion, for example, the worker who is violations. The "crime" of the landlord in failures of the National Crime Survey kept in line by union or company "goons," this instance is similarly a state, rather than (NCS) to derive the full potential of the school children who must regularly yield incident form of crime, that continues in victimization survey method that stem their lunch money to fellow student toughs, duration through time, so long as the con- from the carryover into its conception and the merchant subject to a shakedown dition of the structure remains uncorrected. design of Uniform Crime Reports (UCR) racket, the prostitute terrorized by her Bigamy has the same continuing character rationales is its emphasis on crimes as pimp, or the spouse or sexual partner kept and involves a victimization where the big- incidents occurring at points in time. The from separating from a hated relationship amist keeps a partner ignorant of the other. survey method is more effective as a tool for by fear of violence. Such victimization states are subject to in- gaining respondents' reports of their cidence measurement with regard to points current states than of recalled events in To some degree, victimization surveys of entering or leaving the state, but preva- even very recent and brief periods of their yield information about these kinds of situ- lence measures are applicable to the obser- life histories. To a considerable degree, the ations through tabulations of what are vation of such victimization in a population. significance of crime from a disaggregated, called "series victimizations." In the NCS these are defined as three or more similar The series form of incident may also be an individual-oriented perspective (as opposed indicator of a condition of victim prone- to a collective perspective) resides in incidents of victimization mentioned by a respondent, but which, because of fre- ness, that is, a person vulnerable to offenses durable consequences of victimization, of a similar character by different offenders rather than events of ephemeral conse- quency and/or similarity, the respondent on frequent occasions. Among such condi- quences for the individual. While we must cannot individually date in time or differ- entiate descriptively from one another. tions mentioned in victimization survey re- work toward developing elaborate proce- sults are the shopkeeper in a high-crime dures for stimulatipg recall in order to (Were each incident of a series counted as area or the resident of a highly burglary- provide a survey instrument that will not one, they would form a very appreciable prone dwelling unit or the person who is grossly undercount even UCR Index portion of all personal victimizations in the forced to park his automobile where it is crimes (conventionally labeled "serious"), National Crime Survey; I would hazard a minimum of 20 percent of the total number regularly subject to vandalization. of incidents.) Thus, the terrorized spouse may be identifiable in a victimization survey through repeated incidents of spouse beating, and the terrorized school child by repeated incidents of robbery. It is not necessary for a durable condition of victimization to exist, however, for there While the NCS utilized the panel technique circumstances, indicators from the data of The discussion earlier showed that"trivia1" primarily to institute a control on "tele- compensation would, of course, no longer crimes can be significant, however. One scoping," the value of the panel feature be of individual concern, since the costs significance they can have is when they are probably will reside more in the elucidatiqi? would be sccialized by perfect compensa- not isolated events but rather are associated of those forms of victimization best char- tion. The social costs also would greatly with a status of the person making him vul- acterized in terms of prevalence, rather exceed the aggregate value of individual nerable to continuing or repeated victimiza- than incidence, measures. As indicated harms because of the expense of operating tion. Public victim compensation systems, earlier, because inquiry can be made of cur- the compensation system.) like private casualty insurance systems, are rent conditions of victimization, recall exclusively incident oriented and would be problems are avoided. Conditions are In current (as well as in conceivable) reality, blind to such cases, .bowever. Compensa- more accessible to survey detection than we deal with limited systems of compensation would also not deal with such costs to past events. In addition, their very duration tion. ~heoreticali~,victimization surveys the victim as anxiety and the effects on or frequency in the individual life space would be needed primarily to measure the behavior proceeding from anxiety. Private makes the former more significant for indi- gaps, in scope and degree, between the casualty insurance does have one form of viduals than are the many incidents with actual occurrence of harms and the reach interest in victim vulnerability, multiple highly ephemeral consequences for indi- of the system of compensation. In actual- victimization, and the hazards of local viduals with which victimization surveys ity, however, the systems of social compen- social environments-its interest in avoid- have been preoccupied. Finally, as Reiss sation are terribly poor at generating good, ing insuring anyone who might fall within a has pointed out, such victimizations usually comprehensive statistics. In the United high risk class. present a much higher potential for effec- States, the factors of decentralization and tive system intervention than is the case the mixture of public and private systems A similar rationale applies to agencies for with point-in-time incidents. make social and casualty insurance data social control. The victimization survey close to useless for the purposes of social should be necessary for data only with re- Another facet of victimization subject to a indicators of the "output" type. These de- gard to instances of failures of (transgres- prevalence, rather than incidence measure- fects of agency data place an additional sions against) social controls which result ment rationale, is the durable consequence burden on the victimization survey-that in people being victimized by events that of a point-in-time crime event. This is the is, the survey is the only means currently control systems aim to prevent, but which rationale 1employed in my feasibility study available for gaining data on harms dealt go totally unnoticed by these systems. In of injury-produced handicaps and pain with by systems of compensation, even actuality, the survey is useful precisely be- prevalence among A randomly sampled though, with only modest perfections of cause it helps compensate for the imperfec- population. (Biderman 1975) the statistical operations of such institutions of control agencies as recorders and Ideal control and compensation models. tions, such phenomena should be revealed processors of information on their own Elsewhere; I have discussed ideal models of with far greater scope and accuracy by data transactions. society which can be posited by taking from transactions of the systems them- Individualistic and reductionistic conlra- current ideas of crime control and victim selves. dictions. The recall problems of the victim- compensation to their logical extremes. Two aspects of our earlier discussion bear ization survey point to two contradictions The "perfect" condition from which the on victimization surveys as a source of in using the victimization survey for social victimization survey can be seen as measur- guidance for victim compensation systems. indicators, where one seeks indicators ing departures is one in which social life is Data from the NCS havealready been used which have the value standard of concrete so regulated that no one ever harms any to estimate the costs of operatingcrirnevic- harm to specific individuals. other. To perfect a social order that is less- tim compensation systems. The orientation First, the relatively trivial and ephemeral than-perfect in this regard, a perfect com- of casualty compensation, with an excep- pensation system can be posited; that is, consequences of most individual incidents tion which will be discussed shortly, is en- of victimization which the surveys (and one in which any victim of harm receives tirely toward specific incidents of idss. To compensation (from the doer of harm or other offense statistics) seek to measure are be administered economically, a crime precisely a major source of the recall diffi- from the state) that makes him "whole" compensation system would have to oper- again. culty that affects survey data and that ate with a lower limit of liability, since by makes expensive, brief-reference-period, Our data problems can perhaps be under- far the largest proportion of all incidents large sample panel techniques necessary stood in this way: we are able to construct entail losses that are too minor to be worth for their conduct. As was pointed out, were intellectual models of social welfare that the costs of processing them. The bulk of the survey oriented solely to victimizations are much more integrated, comprehensive, the data gathered by a victimization survey having serious and lasting consequences to and logical than are any institutions or would fall below a reasonable threshold individuals, many of its methodological social welfare we can actually bring into and therefore prove to be irrelevant to a problems would be greatly alleviated. being. If we had (or could possibly have) feasible system of compensation. Surveys restricted in this way could becon- the ideal welfare state with a perfect system ducted far more economically and reliably of comprehensive social insurance, all than those which attempt to bring into harms befalling individuals would be re- their scope even just those incidents that corded and measured as part of the process qualify as "serious" by being in the set used of social compensation (or state-enforced by Uniform Crime Reports for a "Crime recompense by offenders). (Under these Index," or which are felonious or indicta- ble under law. An early finding of the victimization survey method was that the bulk- of such incidents entailed relatively minor misses most of the significance of most There is an explanation for an immunizing effects on the health or economic well- crime to the individual. effect of intersvecies victimization that is captured in everyday speech by the phrase, being of victims, relative, that is, to a host There is a second contradiction in the indi- "Once bitten, twice shy." There may be of other common hazards of daily life. vidualistic, disaggregated orientation to They nonethe!ess were clearly seri~usfrom some virtue, however, in exploring the victimization indicators which the vrob- application of a medical analogy to crimi- the standpoint of the offense given to legal, lems of recall also bring to our attentibn. It moral, and social norms. Aggregates of nal victimization. Considering such an is implicit in an assumption about motiva- analogy suggests some additional signifi- such incidents, furthermore, are of greater tion inherent in the survey approach. Co- interest. For vulnerable individuals re- cant elements of immunization that are not operation with a public survey by a re- suggested by the folk wisdom we have peated victimization can be of major con- spondent makes little rational sense from cited. Indeed, it is questionable whether sequence as can be the fear of repeated the standpoint of individual self-interest victimization. The former-repeated vic- avoidance behavior is a good analogy to for most respondents. For a few, partici- the concept of immunization in medicine. timization-directs attention, not to indi- pating in a lengthy interview on the subject Learning, or even unconscious avoidance, vidual incidents, but rather to a pattern of of victimization may be a welcome intellec- as a result of slight negative reinforcements vulnerability to victimization over spans of tual and social diversion in lives otherwise does indeed produce less vulnerablility to individual lives. While the latter-that is barren of such experiences, but to most re- more szvere perils from the same harmful fears which may lead to costly alterations spondents, presumably, the survey consti- agency or class of agencies as was the of people's life patterns-can result from a tutes an intrusion into a preferred round of single and even minor incident of victimi- source of the original insult. For it to fit the activities. Cooperation with a survey does zation, they arise when one's victimization medical analogy better, however, the vic- make rational sense, however, as a civic is seen as related to a persisting condition timizing experience has to result in some act; a citizen duty. If an interview is of vulnerability specific to the individual or change in the subject that makes it less vul- couched solely in terms of private signifi- nerable to actual attacks by the criminal general to the community. For social indi- cance, what should motivate respondents to cators, particularly important are fears agent, rather than a behavioral change in recall and report in that interview events of resting on perceptions of the extent to the direction of avoiding that agent. Locks relatively small private significance? In- which norms and laws with regard to re- on doors, bars on windows, a burglar deed, is it not a contradiction in itself to spect for persons and their property do or alarm system and other so-called "target conduct surveys which depend upon a col- do not control the conduct of fellow in- hardening measures" as well as such steps lective sense and a civic regard, and which habitants of one's community. as training in self-defense measures, carry- are in themselves of value only in a collec- ing weapons on the part of individuals, and One way in which we may seek to avoid tive way, yet have these surveys guided by a criminal victimization is by individual various adjustments on the part of mer- rationale to which nothing makes sense but chants with regard to rearranging patterns action; that is, by being guarded in expos- private self-interest? ing one's property and one's person to of customer movement and merchandise others; by retreating, figuratively, into a display could all be illustrative here. Immunizing effect constricted life behind defensible walls. To Another form of immunization is the im- of exposure the extent that such guarded and constricted munization from exDosures which controls behavior becomes general and is success- Early observations in victimization surveys overreactive respon'ses of a self-defensive ful, indexes of offenses and victimization found empirical distributions of the num- sort. An analogy here can possibly be made would be kept down, but at vast costs in ber of persons (Ni) victimized a given to immunization from exposure to the real freedom and in the richness of life. number of times (VI]in a time interval in effects of allergies. Experience with some Another manner of protection is collective which N,, was lower for all Vi > I than forms of victimization: for example, petty means; that is, through a normative system would be expected on the basis of a theft or minor assaults, can develop the re- internalized by the processes of socializa- probability model that assumed an equal action, "It is not as bad as all that," and tion and reinforced by both private and or random distribution of risk among the actual exposures to crimes of low conse- public sanctioning of deviance from the entire population and given the mean in- quence may eliminate relatively incapaci- norms. It is upon these collective means, cidence for population. While refinements tating adjustments such as extreme fear rather than individual guardedness, that of the victimization survey method have and behavioral circumspection. Residents we are mostly dependent for organized life produced distributions of n's of victimiza- and merchants in areas of fairly pervasive in society. The role of crime counts as indi- tion having different shapes than this, and disorder may have such immunizing ex- cators of this social condition, of the vital- while there are many plausible post hoc posures against overreactive defense mech- ity of the normative order, is what has interpretations in terms of both phenomena anisms. elevated them as indexes to the major posi- and method for the distributions of As in the case of medicine, however, both multiple victimizations that are observed, tion as "social indicators" that they have analysis and treatment in criminology con- always occupied since men first sought nonetheless, the problem invites considera- front the problem that a given exposure quantitative measures of the state of their tion of a possible immunizing effect of can lead to the mobilization of either appro-. victimization.1 society. Indicators of the extent to which - priate or inappropriate defense reactions, people and organizations are guarded or IWe are concerned here only with "natural immuniza- depending upon complex relationships be- trusting in their relations with each other, tion." tween the individual and his exposure to or feel they must be, would serve this pur- the agent. pose as well as offense or victimization data do. To look for the significance of crime Thus far we have touched only on individual- exclusively in the concrete harm resulting level immunization. Two kinds of social or from a given event to a specific individual collective perspectives can also be taken. The first is the development of a population immunity. This takes place when a sufficient number of individuals reach a sufficiently high level of immunity so that the survival of the offending species is affected. Risk of victimization Determining which components of a com- It takes place only when the offending munity may be those most vulnerable pre- Consideration of the concept of immuniz- sents very different statistical problems if a agent is dependent for its survival on a ing victimization may also help guard population of hosts subject to immuniza- large proportion of all the victimization (in against tempting fallacies inherent in the the real world or in that time slice of It that tion. It requires the creation of a very high frequent tendency to equate incidence rates level of long lasting immunity of a very we can capture in our measurements) stems with "risk." large percentage of the population. This re- from many repeated victimizations of the moves the opportunities for the criminal "Risk," first of all, conveys a future, rather same individuals than it is where repeated agent to survive and reproduce so that it than a past, temporal implication. If there victimizations are rare or nonexistent (as in approaches extinction. Levels of immuni- is a high immunizing effect of exposure, the the case with homicide "risks"). The last zation in extent and efficacy below this verv individuals who contribute to inci- case is analogous to the fatal or usually level of population immunity can generate deice during any period of observation fatal disease. The only possible immuniz- increased vulnerability. may be precisely those who will be found to ing effect is one of population immuniza- have been at low risk during some later tion by selective elimination of the more Population immunities also develop by the period of observation (i.e., there will be few vulnerable. Rare multiple victimization differential survival of its more immune instances of repeated victimization). This can also be a function of extremely low members. This can occur with or without may be the case even with no change, or levels of relatively randomly distributed in- change in the prevalence of the-agentin the even some increase, in the total rate for the cidence. High multiple victimization can be territory of the community or the mean community or class to which the victimized found associated with either very high but virulence of the agent. An example of selec- individuals belong, provided only that the widely dispersed total incidence or with tive survival resulting in elevated popula- supply of those vulnerable to victimization highly concentrated (ncnrandom) inci- tion immunity would be decreased ecologi- is very large relative to the actual incidence dence. cal burglary and robbery incidence rates of victimization. occurring in a community as the most vul- If multiples are rare, then we have no nerable small business establishments fail Secondly, statistical risk inferred from an means for estimating a given individual's * because of crime losses. There may be no incidence rate for a population is expressed vulnerablility other than by categorically associated decrease in the prevalence of as a probability value for a member of that associating him with some class that has an offenders in the territory of that commu- population. Distributions of individual observed rate of incidence. (If multiples are nity (they may prey more outside its con- risk, in the sense of future vulnerzbility, rare because of fatality, we must use a sta- fines) and the offenders remaining may be can be very unevenly distributed among the tistical logic of nonreplacement.) If multi- more likely to use extreme measures in the population, however. If the concept of risk ples are common, however, and if we are offenses they do commit among the re- is to be associated with an incidence rate, capable of making sufficiently long-term maining "harder" targets. either there must be empirical and theoreti- observations of individuals, then we can cal grounds for assuming a high degree of state empirical vulnerability rates for indi- Another way in which the social analogy homogeneity of vulnerability among the viduals and observe the stability of predic- can be pursued is by regarding the commu- population or care must be taken to use tions of future victimization from observa- nity's defenses as the immunizing effects of words that suggest the "risk" of aggregates, tions of past victimization for each individ- exposure rather than individuals'. Most of rather than individuals; ual. If multiples are common because of the defensive adaptions to crime that are concentration, this may yield only slight This suggests additional difficulties with possible are collective ones taken at the improvement over "risk" estimates based the risk concept. If there is a high concen- community rather than the individual on-aggregate incidence for subclasses, pro- tration of victimization among some por- level. "Social defense" presumably requires viding the correlations of incidence with tion of a community, an inaccurately low prompt, effective immunizing reactions to the ciassifications available are very high. measure of incidence for the entire com- low levels of attack. If there is great dispersion, however, indi- munity may more accurately reflect the risk vidual measures will be required for accu- Most of the attention in criminology has rate for the large majority of the members racy, as they will also be if there are im- been given to the effects of measures of of the population (or the median or modal munizing effects of any great consequence. social defense. "Victimology," however, "risk") than would an incidence rate based concentrates its attention on the individual. on a more exhaustive measure of incidence. Some recent evaluation studies, for exam- There are good indications that this is References ple, in Portland, Oregon, have attempted indeed the case with rates based on victimi- to analyze the consequences of individial Biderman, Albert D. (1975) zation survey data in that small, but highly "Victimology and victimization surveys." In defensive measures for aggregate levels of vulnerable, components of the population 1. Drapkin and E. Viano (eds.) Victimology: A crime incidence. Such studies logically are most subject to underenumeration. For newfocus(vol. 111, Crimes, victims, and justice), present the statistical requirement for an aggregate risk level indicator most often Lexington, Mass.: Lexington Books. taking into account the effects of victimiza- most applicable by members of a commu- Reiss, Albert J., Jr. (1973) tion subsequent individual and popula- nity, that is, one descriptive of the "chances "Surveys of self-reported delicts." A paper tion vulnerability to victimization-a diffi- of my being victimized if the future resem- presented for the Symposium on Studies of cult and as yet untouched analytic problem. bles the past," an incidence rate that ne- Public Experience, Knowledge, and Opinion of glects the experience of both the most and Crime and Justice, Washington, D.C., March least vulnerable components of the com- 17-18, 1972, revised July 1973. munity would serve best. From the standpoint of social problem concerns, it may be only or mostly those who suffer frequent victimization and who benefit from no immunizing effects, who suffer appreciably at all. This is true where the effects of any one victimization are small, but repeated victimization may be costly or fatal. Victimization and the National Crime Survey: Problems of design and analysis

STEPHENE. FIENBERG Department of Statistics and Department of Social Science Carnegie-Mellon University .

1. Introduction (4) A set of city commercial surveys to of LEAA resources devoted to the statisti- parallel (3). cal analyses of NCS data was one of the Crime and its impact on society have long In this chapter we restrict our attention principal findings of the Panel for the been the subject of public interest and social Evaluation of Crime Surveys appointed by concern. While the study of crime has solely to the continuing national survey of household locations. the Committee on National Statistics proved profitable to social scientists over (Penick and Owens 1976, p. 3). This report the years, the limitations of police crime The NCS has been designed and executed contains considerably more detailed de- statistics (e.g., see Biderman and Reiss, for LEAA by the U.S. Bureau of the scriptions of the NCS survey and question- 1967) have always been viewed as being so Census and it includes personal interviews naire design than we provide here. It great as to make it virtually impossible to at six-month intervals with individuals in describes the developmental research be- measure criminality in a population. Hood up to 65,000 households. Given the mag- hind the design, and it suggests areas for and Sparks (1970) note that "Questions nitude of the NCS and the massive files of further investigation. The conclusions of about criminality, like those about sexual data collected since the initial field work the report overlap considerably with ours behavior, are especially liable to distorted began in mid-July of 1972, it is remarkable regarding the need for extensive ongoing and untruthful answers." Thus it was with that the NCS has received so little attention methodological research. great anticipation that the social science from professional statisticians outside of community heralded the adoption of the Bureau of the Census. Any assessment of the NCS must look survey research methods to find the victims closely at its objectives and determine to of crime, and to learn of their experiences. Central to an examination of victimization what extent they are being met. The pri- As a result of some small-scale attempts at and the concepts underlying the NCS is the mary purpose of the NCS as described victim surveys in the United States and notion of a crime or criminal incident and actually has several components: how it gets recorded by various criminal Great Britain, and after considerable (1) To measure the incidence of crime. justice agencies. The dictionary definition planning and preparation, the Law Enforce- (2) To measure the changes in crime of crime offers little in the way of a starting ment Assistance Administration (LEAA) rates over time. point. For example, a recent edition of the initiated a major new social statistics series (3) To characterize socioeconomic as- Random House Dictionary defines crime based on a national victimization survey. pects of criminal events and their victims. as The primary purpose of the national vic- an action or an instance of negligence that is Closely related to item (3) are the aims timization survey, as stated in a planning deemed injurious to the public welfare or morals (4) To identify high-risk subgroups in document developed by LEAA, is "to or to the interests of the state nnd that is legally the population and to estimate the rate of measure the annual change in crime in- prohibited. multiple victimization. cidents for a limited set of major crimes and To shed some light on this matter, Section (5) To provide a measure of victim risk. to characterize some of the socioeconomic 2 describes in detail a single criminal inci- aspects of both the reported events and dent, and notes how it would be recorded in From its inception, the NCS was viewed as their victims (Penick and Owens 1976, p. statistics gathered by the police and in the a multipurpose survey that would produce 220)." Henceforth, we refer to this survey NCS. not only the general-purpose victimization as the National Crime Survey (NCS), but rates already described, but also data for the reader should bear in mind that the Section 3 contains a brief summary of the policy-oriented problems; for example, focus of the N CS is upon victims and their survey and questionnaire design of the (6) To calibrate the Uniform Crime Re- experiences with crime, not on crime itself. NCS, and describes some aspects of its exe- ports data produced by the FBI. cution. Special attention is focused on the Actually the NCS consists* of four (7) To index changes in reporting panel structure of the survey design, with a behavior. separate surveys: rotation plan for households. The major (8) To measure the effectiveness of new (1) A continuing national survey of shortcomings of the design are then noted. criminal justice programs (the city surveys household locations. Sectipn 4 is brief and it summarizes the were initiated for exactly this reason). (2) A continuing national survey of published analyses from the NCS. The lack .commercial establishments. To determine if the NCS properly fulfills (3) A separate set of single or duplicated aims (1)-(4) special attention needs to be surveys of household locations in selected Copyright @ 1978 by Academic Press, Inc. All rights of cities. reproductionin any form reserved. ISBN:O-12-513350-2. Reprinted by permission, with minor changes, from 'Since this paper was prepared, all but the continuing Surve.rSoti1plinl: and Measurement (K.Namboodiri, ed.). national survey of households has been discontinued. focused on questions that utilize the longi- How one records crime is a function of Let us begin with the police record of the tudinal structure of the NCS. Section 5 one's perspective. A single criminal incident event as it is transmitted to the FBI for use outlines a number of substantive questions or social encounter can involve one or in its Uniform Crime Reports (UCR). In a regarding victimization and victim-survey more offenders, one or more victims or multiple offense situation, the police clas- methodology that in principle should be possibly no victims at all, and multiple vio- sify each offense, and then locate the of- answerable by analysis of NCS data. A lations of the law leading to multiple indict- fense that is highest on the list of what is major stumbling block to the successful ments of a single offender or several known as Part I Offenses (the ranking is completion of these analyses is the highly offenders who have participated in the criminal homicide, forcible rape, robbery, complex NCS survey structure, designed to event. There may even be mutual offending aggravated assault, burglary, larceny-theft, produce descriptive statistics rather than and victimization, for example, in cases of and motor vehicle theft). The highest offense is entered and the others are ignored. data-~ amenable~ to analvtical studies of in- assault. Thus a particular configuration of terrelationships and their changes over crimes aggregated over a given time period Multiple offenses need to be separated in time. Although the NCS is a rotating panel may well look dramatically different when time and place to lead to multiple entries in in form, the primary purposes of the panel viewed from the perspective of offense the UCR. The exeption to this rule involves structure are to get more stable rate com- rates as opposed to victimization rates, and crimes against the person (criminal homi- parisons from one period to the next, and neither set of ratesis likely to reveal the true cide, forcible rape, and aggravated assault) to bound the time frame under consider- nature of the criminal events that have where one offense is entered for each vic- ation. taken place. tim. Thus the UCR record will contain one offense of forcible rape (against the A single hypothetical example can illus- woman) and one offense of aggravated 2. Recording crime trate the comolexitv associated with crirni- assault (against the man). Had the youths nal incidents and tGe manner in which they only robbed but not assaulted the man, there Criminal incidents are events or social en- are recorded. A.young couple living in the counters involving one or more offenders would only be one offense entered. These household of the woman's parents in Stam- offenses would be recorded by the New and one or more victims, in one or more ford, Connecticut, go to New York City on locations for specific periods of time. The York City police, and 1 am unclear as to December 3 1 to celebrate New Year's Eve. which day (and thus which year) they will duration of a single criminal incident may They park their car in a lot on the east side be 10 minutes, an hour, a day, a week, or be attributed. The UCR record will also of Manhattan and have a leisurely dinner show that the offense(s) have been cleared even a month. Nonetheless, when put into a at a nearby restaurant. After dinner when larger timeframe a criminal event is quite (i.e., "resolved") by the arrest of the three they return to their car, they are accosted youths in New Jersey. Although this event profitably viewed as the realization of a by five young males just outside the park- point process distributed over time and led to one or two UCR offenses, it might ing lot and are taken into an adjacent alley- well lead to the prosecution of the five space, and we do so in Section 5. What way, at approximately 11:OO p.m. One of complicates the modeling of a large num- youths on up to a total of five counts of the youths threatens the couple with a re- rape, 10 counts of aggravated assault and ber of crimes is the interpenetrating social volver, and the other four take turns raping networks linking offenders and victims, robbery, and five counts of motor vehicle the woman. When the woman resists, one theft. both within a single incident and across of the youths assaults her with a knife, and several incidents, and giving rise to multi- then he also assaults the man. Following Suppose now that the couple's household is ple offending and multiple victimization. the acts of rape the youths take the chosen as part of the NCS so that the event Reiss (1980). describes some of the impact woman's purse and the man's wallet, and will also be recorded from the victim's per- of such networks and associated group they appear to flee. It is now about 1:00 spective. Both the man and the woman structures on crime rates with special atten- a.m., January I. The couple have to travel would be interviewed separately and the tion to the implications for measuring the several blocks to report the incident to the NCS would record two victimizations in effects of deterrence and incapacitation. police. When they finally return to the December: one for the woman "assaultive The stochastic structure of criminal social parking lot with a police officer at 3:00 violence with theft-rape,"one for the man networks and the resulting lack of in- a.m., they discover that their automobile is "assaultive violence with theft-serious dependence of criminal incidents also has missing. A week later three young males assault with weapon." Even if the man had potentially important implications for are stopped by the police in Newark, New only been robbed but not assaulted there both the design and analysis of victimiza- Jersey, driving the couple's car through a would still be two victimizations recorded tion surveys. It is for this reason that we red stoplight and they are arrested. (as compared with a single offense). More- discuss some first steps in the stochastic over, because of the separation of house- model of victimizations for individuals The incident just described involved five hold victimizations from individual vic- over time in Section 5. offenders, two victims, three arrests, and timizations, when the woman's father numerous offenses including forcible rape, robbery, aggravated assault, and moior vehicle theft. It spanned several hours (and two calendar years!) and took place in at least two locations. How would it be classified by various recording systems? reports the household victimizations, he 3. Design of the NCS For estimating various rates, a series of may well report the theft of the car sepa- a. Sample design weights and adjustment procedures are rately, and the month of victimization may applied to the raw data. The weighting probe given as Janwry, and thus it could go The NCS is a sample survey of households cedures are standard practice for surveys of into a separate calendar year. and their occupants, and as such it closely this sort and are basically designed to ad- resembles the Current Population Survey just for the differential probabilities of In summary, our single criminal incident (CPS), which is also conducted by the including various household locations in involving five offenders and two victims, Bureau of the Census, in almost all aspects. the survey, and to reduce bias and variance leads to one or two offenses recorded in In fact, descriptions of the designation of of sample estimators. The final adjustment New York and two or three victimizations housing units for the CPS (e.g., see involves the use of ratio estimation so that recorded in Connecticut. The perspectives Thompson and Shapiro 1973) are almost the distribution of individuals (or house- are clearly different, and so too are the identical to those for the NCS (e.g., see holds) in the sample is in accord with inde- records of the event. U.S. Department of Justice 1976a,b), the pendent estimates of the current popula- Because a large proportion of criminal in- major exceptions being the sample sizes, tion in each 72 age-sex-race categories. cidents is never reported to the police, the the interview schedules, and the panel and By reporting only adjusted rates, for both discrepancy between all criminal offenses rotation group structures. the NCS and the CPS, Census has removed and those reported to the police has been The structure of the NCS is that of a strati- from public scrutiny many of the actual described by Biderman and Reiss (1967) as fied multistage cluster sample. The first defects of the sample design when it is the "dark figure" of crime, and one of the stage consists of dividing the United States actually implemented. Since all aggregate original purposes of victimization surveys into approximately 2000 primary sampling counts have essentially the same totals for was"to bring more of the dark figure to sta- units (PSUs) comprising counties or various categories, we can never tell when a tistical light." Biderman and Reiss go on to groups of contiguous counties. The PSUs given sample is badly off the mark, nor in note: are then separated into 376 strata and one what directions. In exploring the dark figure of crime, the pri- PSU is selected from each stratum with Although the NCS is basically a sample of mary question is not how much of it becomes probability proportional to population revealed but rather what will be the selective household locations, at the same time it properties of any particular innovation for its size. Within each PSU so selected, a sys- yields both a sample of households or fami- illumination. As in many other problems of tematically chosen group of enumeration lies and a sample of individuals. Household scientific observation, the use ofapproaches and districts is selected, and then clusters of locations are of little substantive interest in apparatuses with different properties of error approximately four housing units each are the study of victimization. While the NCS has been a means of approaching truer approxi- chosen within each enumeration district. allows for the study of differential rates of mations of phenomena that are difficult to For 1973, this process led to the designa- measure. victimization by type of household location tion of about 80,000 housing units, and in- (e.g., house, apartment, rooming house, Any set of crime statistics, including those of the terviews were obtained from occupants of mobile home), not one of the 100 tables in survey, involves some evaluative institutional about 65,000. Most of the remainingdesig- processing of people's reports. Concepts, defini- the LEAA report for 1973 (U.S. Depart- nated housing units were vacant or other- ment of Justice 1976b) deals with such tions, quantitative models, and theories must be wise ineligible for inclusion in the NCS. adjusted to the fact that the data are not some information. The primary reason that the objectively observable universe of "criminal The basic sample is divided in six subsam- NCS is a sample of locations rather than acts," but rather those events defined, captured, ples or rotation groups of a little over households or individuals appears to be and processed as such by some institutional 10,000 households each. (Actually there because Census has available a detailed mechanism [pp. 14-1 51. are seven subsamples, but the data for the frame only for locations. Much controversy has centered on the newest one are not incorporated into the The NCS primarily measures victimization comparability of police statistics on offense reported rates. Rather these data are used while the CPS primarily measures employ- rates and NCS survey statistics on victimi- for bounding purposes, as described in Sec- ment and unemployment. Since both un- zation rates (e.g., see Biderman 1967; tion 3, a.) The occupants 12 years of age or employment and victimization are relatively Biderman and Reiss 1966; Penick and older are interviewed at six-month inter- rare phenomena, a naive person might Owens 1976, pp. 152-154; U.S. Depart- vals for a total of three years. Every six suggest that a sample design that has ment of Justice 1976b), but the utility (or months a new rotation group enters the proved successful for measuring unemploy- lack thereof) of the NCS data for such com- sample and the "oldest" existing rotation ment should, with only minor modifica- parisons should not obscure the richness of group from the previous sample is dropped. tions, do a good job of measuring information about victimization available Each rotation group is divided into six victimization. Such a suggestion is naive in the NCS. It is for this reason that the panels, with one panel being interviewed in because, among other things, it ignores the NCS data must be collected and organized each month of the six-month period. considemble knowledge we have available in a manner that will make it amenable to regarding crime and its physical as well as standard forms of statistical analysis. socioeconomic characteristics. In central Otherwise the rich veins of information on cities, crime rates vary dramatically from such topics as high-risk segments of the block to block, and a limited amount of population and multiple vicfimization, or fieldwork might lead to cluster boundaries the way that deviance is perceived and dealt that differ dramatically from those that with in various social contexts, may never be mined. would seem appropriate for unemployment. c. Reference period and bounding ' no bounding for the new household or for It may well be that the NCS sampling plan One of the most crucial prbblems in the its members as individuals. Murphy and is most sensible given budgetary constraints, design of a victimization survey is eliciting Cowan (1976) report that unbounded but an exploration of alternatives and accurate information on the time of households in returning rotation groups variants io the current plan should occurrence of criminal incidents. The comprise (for 1974-1975) 13.3 percent of probably be included in the research, problem has at least two components: the interviewed sample. In addition, only development, and evaluation program of about 95 percent of the interviews in the the Bureau of the Census. (1) Recall decay. The longer the time bounded households are themselves bounded lapse between a criminal incident and the due to considerable transience for house- b. Questionnaire design date of interview, the greater the probabil- holds in heavily urban areas. As a result, as The questionnaire administered every six ity that the event will not be reported to the few as 20 percent of the individuals over a months at each household consists of two interviewer. three-year period in a given set of house- Telescoping. Events occurring in one parts: a basic screen and crime incident (2) hold locations may produce complete vic- time period can be reported as occurring in reports. The basic screen includes house- timization records for the period. These a different one. The displacement of tele- hold location information, household or design characteristics drastically impair the scoped events can be forward or backward family information, the personal character- utility of the NCS data for longitudinal in time. istics of all of the individuals in the analysis of individual victimization profiles. household (who may change from interview It is especially difficult to model recall Considerable methodological interest is to interview), plus household or individual decay and telescoping, since such evidence centered on the differences in victimization screen questions on crime. The report of seems to point to differential rates ofdecay experience for migrants and nonmigrants. the Panel for the Evaluation of Crime and telescoping for different types of In addition to follow-up studies of out- Surveys (Penick and Owens 1976) gives a crimes, and for different types of respon- migrants (which are quite costly), it seems detailed critique of the basic screen, and we dents. Moreover, there can be no check on reasonable to do special analyses of the in- refer the interested reader to their discus- a crime that has never been reported, either migrants to the sample locations since their sion. For each crime incident detected by to the police or the NCS. Thus the only way the screen, a crime incident report data are already in the NCS (see Penick to get a handle on these two phenomena is and Owens 1976; Reiss 1977b). For every containing answers to almost 100 questions via a sample of crimes reported to the is completed. out-migrant household there is an in- police and the subsequent inclusion of vic- migrant one. Of course the current lack of tims of these reported crimes in a victim The questionnaire distinguishes between bounding for in-migrants would compli- survey. Such "reverse record checks" were individual identifiable incidents and series cate such analyses, but it should be feasible part of the pretests of the NCS survey in- of at least three similar incidents which the to do a special study of in-migrants where a strument (see U.S. Department of Justice respondent is unable to separate in time bounding period would be included along 1972, 1974). The problem with drawing in- and place of occurrence. For individual with additional interviews beyond the victimizations, the questionnaire records ferences from reverse record checks is that they are aimed at data which are missing standard three-year period for the house- the month in which the crime took place, hold location. but for series victimizations the respondent from the victimization survev. but which only needs to indicate the quarter(s) in are not missing at randome(see Rubin which the incidents took place (i.e., spring, 119761 for a discussion of the importance of 4. Published analyses summer, fall, winter), the number of inci- the missing at random assumption). of the NCS data dents (345-10, 1I+, or don't know), and A consideration of both recall decay and Not only does the formal responsibility for the details for the most recent event in the telescoping is necessary for the determina- the design and execution of the NCS lie series. We discuss the distinction between tion of the optimal reference period for a with the U.S. Bureau of the Census, but the single and series victimization in more de- victim survey. The NCS reference period is analysis of the collected data is also the re- tail in Section 4, where we note how the six months, and Census uses the first in-. sponsibility of a small staff of Census em- Bureau treats series victimizations and why terview and six-month period of ,a house- ployees. This analysis by LEAA and Cen- we believe series victimizations should be hold location for bounding, that is, estab- sus involves the periodic preparation of the topic of extensive and analytical inves- lishing a time frame to avoid duplication of two- and three-dimensional cross-tabula- tigation. What is unclear to us from pub- incidents in subsequent interviews. For a tions of estimated victimization rates and lished documents and various unpublished detailed study of theeffects of boundingon estimates of their standard errors. The memoranda is the extent to which series telescoping, see Murphy and Cowan cross-tabulations produced are basically victimization is a true phenomenon or an (1976). A major problem in the design of those requested in advance by professional artificial construct resulting from the NCS the NCS arises because the bounding pro- staff at LEAA, and not as a result of a more questionnaire design. cedures bound household locations, not detailed and complex statistical analysis. Not only does the NCS questionnaire households or individuals. If one household replaces another during the course of Suppose for simplicity that NCS employed solicit information on the details of an a simple random sample and that the data incident, the offender, and any resulting the three-year period during which a location is included in the NCS sample, there is (which are primarily categorical in nature) physical injury and how it was treated, but for any year were analyzed using some vari- it also inquires whether the incident was ant of loglinear model analysis for a k- reported to the police and if not, why not. dimensional cross-classification (e.g., see Bishop et al. 1975). Then one of the implications of finding a model that gives a good fit to the data would be that the k-dimensional table may be succinctly summarized by a series of tables of smaller dimension, while only 26.6 percent of all victimizations may well simplify the modelling process, from which the original table can be recon- not in series. Thus, series victimizations This is clearly the case if we are interested in structed with essentially zero information may have accounted for over one-third of the structure of individual reported victim- loss. Such analyses can thus provide a all crimes of violence. ization patterns over time. rationale for reporting certain cross-tabw We note that despite the panel structure of The Panel for the Evaluation of Crime Sur- lations and not others. This point is de- veys gives several suggestions for analytic scribed in more detail by Fienberg (1975). the survey, LEAA has yet to make use of research on the existing NCS data. One of Even though the NCS does not employ the full longitudinal structure of the data these suggestions deals with the relation- simple random sampling, the idea of care- base. The construction of a panel tape tracking individuals and households over ship between series victimization and mul- ful statistical analyses leading to the choice tiple victimization, a topic we discussed in of cross-tabulations to be published is one time was not deemed to be a central goal of Section 4. To investigate this relationship, which should be considered more seriously the NCS, and the preparation of such a tape was only belatedly arranged through a however, we need models for the occur- by LEAA and Census. contract with a group at a private univer- rence of victimizations over time, and we How many reports has LEAA published sity. It might beargued that the panel struc- propose one such model in siction 5b. A on the results of the NCS national house- ture of the NCS sample is intended to second suggestion deals with analyses to in- hold sample? As of December 1976*, handle certain technical problems and to vestigate under- and over-reporting of inci- several preliminary but only two final give more accurate year to year compari- dents as they relate to the month of incident reports had been released: a 162-page sons, and not for longitudinal analysis of and the month of interview. In Section 5a report on the 1973 survey (U.S. Depart- individual files. Thiscan be true only in this we take up some aspects that need to be ment of Justice 1976b), and a much briefer narrowest of senses because without a de- considered in such analyses. 73-page report comparing findings for tailed longitudinal analysis we can never a. Reporting biases and time-in-panel 1973 and 1974 (US. Department of Justice know whether the aggregate annual re- 1976a). Since both final reports also ported victimization rates are at all accu- For several characteristics on which data contain data on separate commercial rate. For example, Reiss (1977), reporting are collected in the Current Population surveys, the interested reader is left with on some preliminary longitudinal analyses, Survey, Bailar (1975) notes that there is a very slim pickings from what appeared to notes that highly victimized individuals are higher level for the first interview than for be a sumptuous meal. Moreover, these two much more likely to be out-migrants than succeeding ones, and so on. The effect of reports contain only weighted data or those with low victimization rates, and such variation is usually referred to as "ro- proportions. No raw counts are available. series victims are more likely to move than tation group bias," and there is reason to Thus it is almost impossible for the skilled nonseries victims. Moreover, a high per- expect such biases in the NCS data as well. statistician to do extensive secondary centage of individuals reporting series vic- In the NCS the rotation group bias prob- analysis of the published data. timizations in a given six-month period lem is compounded by several factors in- report no victimizations in the subsequent cluding the elapsed time between the inci- When preliminary versions of the 1973 re- six-month period. These observations call dent and the interview (recall that inter- port were distributed by LEAA, several in- into question the accuracy of the published views provide data for the preceding six- vestigators noted that series victimizations victimization rates. month period). were not included in the computation of any published rates or calculations. Thus What we would like to do is develop a all reported numbers and rates of victimi- 5. Modelling victimization model which compares the victimization zation may be severe underestimates. For rates for specific crimes for a series of refer- example, LEAA estimated for 1973 (U.S. To understand reported annual victimiza- ence months as a function of the number of Department of Justice 1976b) that there tion rates and the implications of changes interviews, the time-lag from incident to in- were approximately one million series vic- in the'm from one year to the next, we need terview, and other possibly relevant tem- timizations in the personal sector and just a detailed understanding of how victimiza- poral variables. We build up to this in over 20 million victimizations not in series. tion varies among individuals and sub- stages. A series consists of three or more victimiza- groups within the population. This detailed understanding will necessarily have to In Table 1 we show the list of panels being tions, and an average of five victimizations interviewed by month of collection for a per series is likely an underestimate for the come from the analysis of disaggregated data, and of individual victimization rec- full three-year collection cycle, where the NCS data. (Some calculations based on an months have been labeled from 31 to 66. unpublished tabulation suggest that the ords over time. Such analyses will be complicated by the complex structure of the Panels 1-6 form a subsample that was first average is in excess of six victimizations per interviewed in months 1-6 (we ignore the series.) This then means that at least 20 per- NCS sample design, but the effects of stratification and clustering on analyses will vary initial interview for bounding purposes cent of all victimizations in the personal here) and leaves the sample after the inter- sector have been excluded from the re- greatly from problem to problem. For many problems the use of unweighted data views in months 31-36. Note that the dif- ported calculations. This matter becomes ference between the month of collection even more serious when we note that, in and the number of a panel being inter- 1973,46.3 percent of all personal series vic- viewed equals the number of months the timizations involved crimes of violence- panel has been in the sample (time-in- *The final draft of this paper was completed then. panel). All three variables bear examination in terms of their effects on reported rates. The time-in-panel variable yields the rotation group bias information, while month of collection measures seasonality Table 1. An illustration of the NCS panel rotation structure and other unique temporal effects, and I panel number represents temporal charac- Panels being interviewed teristics and effects unique to those that entered the sample at the same time.,The formal identity linking these three variables is the same as that linking age, period, and cohort as described by Fienberg and Mason (1978), and any model using all three as independent variables needs to take into account the identification problem associated with the linear components of the effects. Since each interview collects data for the preceding six-month period, for each refi erence month there are a total of 36 distinct panels which provide data. For example, panels l,7, 13, 19,25, and 3 1 provide data with a one-month lag for month 30 during collection month 31; panels 2,8,14,20,26, and 32 provide data with a two-month lag during collection month 32; and so on. Thus the ensemble of 36 victimization rates for a given reference month can be modeled as a function of month of collection, time lag to reference month, panel number, and time in panel (as well as various additional independent variables such as education and race if we wisb to compare subgroups of the sample). Of course we need to model several reference months simultaneously if we are to use all of the independent variables at once. If we in addition use reference month as an independent variable, then we have an additional identification problem related to the identity involving reference month, collection month, and time-lag until interview. To analyze and model data using the variables just described, we need to know whether we can treat the data for different especially troublesome with any attemptto timization rate A, for crime type i, and that reference months from the same panel as model these phenomena is that we candeal the expeded number of victimizations the being independent. Moreover, it is unclear only with individual victimizations, and individual will experience for crime type i whether we should use rate as the response not series, even though the latter may make in a fixed period of time T is simply A,T. variate or counts of victimization (e.g., the up a sizeable proportion of the total This is, of course, the expected number if number of respondents with 0, 1,2 .. . vic- reported victimizations in a given period. we assume that victimizations follow a timizations), and whether we should use Poisson process. Since victimization is a weighted or unweighted data. b. A rnodelformultiplevictimizationsover rare event, in order to test the Poisson Models of the sort we have just described model we need to pool individuals into need to be explored carefully if we are to Most of the models that have been groups expected to have similar values of get a proper handle on such problems as proposed for victimization assume that A,. Those victimization studies that have 'rotation group bias and memory decay each individual has an "annual" vic- looked at victimization distributions for associated with recall. Modeline these fixed periods of time and for subgroups of phenomena separately (e.g., m ail& 1975; the population typically find that the Pois- Finkner and Nisselson, Chapter 5, 1978) son model gives a poor fit. This may be an when they in fact occur simultaneously artifact of the data collection procedure, it should only be the first step in an analysis, may be a result of not using a fine enough since it may lead to improper inferences disaggregation, or it may in fact be the unless there are order-of-magnitude differ- result of the inappropriateness of the Pois- ences in the sizes of their effects. What is son process. One more general structure for modeling time model. This problem resembles one Because the NCS is similar in sample victimization as a point process is the semi- explored by Singer and Spilerman (1974, design to many other large-scale social sur- Markov process, which includes the Pois- 1976a,b), who have used the semi-Markov veys such as the CPS, the Annual Housing son process as a special case. In this struc- process model of Eqs. (1) and (2) for inves- Survey, and the National Assessment of ture we view victimization as a point tigating ~ccupationaimobility. In their Education Progress, it shares with these process ( Y(r), t >0}, where Y(t) =j if the work they have placed special emphasis on other surveys various methodological individual were last a victim of crime typej. the embeddability of fragmentary multi- problems associated with data analysis and If the process is semi-Markov (see e.g., wave panel data into a class of continuous inference. For example, the weighting pro- Cinlar 1975), then it has transition proba- time Markov models, and the identifica- cedures used to get aggregate victimization bilities tion problem within that class of models. rates and estimates of standard errors are not necessarily appropriate for other ana- p,(t) = ~r{Y(t)= jl Y(0) = i}, (1) The use of this class of models in the con- lytical purposes. To solve these problems, text of the NCS is complicated by the fact where i and j run over the possible types of statisticians must develop variants of vari- that as few as 20 percent of all individuals crimes, say 1 < i, j < r. These transition ous multivariate techniques appropriate probabilities can be expressed directly in have full three-year records. Moreover, it is for the analysis of data from complex sur- terms of two sets of quantities: unclear whether we need to take into veys. At the same time they must work account the complexities of the sample toward the development of survey designs (1) A matrix of one-step transition design when we try to model the victimiza- that are especially amenable to classes of probabilities governin a discrete-time tion histories of individuals with common analytical purposes, or at least to specific Markov chain, M ={rn,$, which represent sociodemographic and geographic charac- forms of analysis. an individual's "victimization propensities" teristics. A final complication in the NCS given his current victimization state. data is the existence of series victimiza- Our evaluation of the NCS is well summa- tions, which illustrate a strong propensity rized by the following excerpt from the Re- for rapid and repeated victimization of a port of the Panel for the Evaluation of specific type. Analyses based on underlying Crime Surveys (Penick and Owens 1976): and depending on the last type of victimiza- continuous time models certainly should The panel has found much to commend, and tion. include both series and separate individual much to criticize, in the design and execution of The transition probabilities are the unique victimizations. the NCS to date. We have argued that a very solution of the system of equations great amount of methodological and developmental research must be done, and many changes 6. Discussion in existing procedures must be made, ifcertain of The two models described in the preceding the specific initial objectives of the surveys are to be accomplished. The panel also maintains, section have not been explored with the however, that those objectives themselves need NCS data, even in a preliminary form. further scrutiny and that a subtle but funda- They do, however, illustrate the problems mental change in the official concept of victimi- where i, j= I, 2, . . . ,r, involved in the analysis of data from the zation surveying is necessary if the potential NCS when the purpose of the analysis is to value of this relatively new research method is to provide estimates of aggregate victimization be fully realized [p. 1521. rates. While some have argued that model- and J(t) is the probability density corre- ing of this sort is unrelated to the primary sponding to the distribution function objectives of the NCS, we disagree. First, This article grew out of material discussed in the when the distributions F,(I) are ki- we believe that an understanding of the Workshop on Criminal Justice Statistics held in basic structure of the panel data produced Washington, D.C., July 1975, and sponsored by ponential, the process reduces to a time- the Social Science Research Council Center for homogeneous Markov one, and when, in by the NCS is crucial to a proper evalua- Coordination of Research on Social Indicators addition, the probabilities {m, do not tion of aggregate victimization rates. and the Law Enforcement Assistance Adminis- depend on i, that is, the rows are ho- Second, the detailed stochastic modeling of tration. The author is indebted to several of the mogeneous, we get a set of Poisson individual records is required to directly participants of the Workshop whose ideas and processes. meet one of the NCS objectives described suggestions inevitably have found their way into in the introduction of this chapter: to iden- this article. In particular, thanks are due to In order to use this general semi-Markov Albert D. Biderman, Kinley Larntz, Albert J. model for the NCS data, we need to see tify high-risk subgroups and to estimate the rate of multiple victimization. Third, a Reiss Jr., David Seidman, and Richard Sparks. how the one-month-at-a-time data collection framework of the NCS can be em- reading of various documents about the NCS makes clear that it is in fact a multi- bedded in the structure of the continuous purpose survey, and substantive issues and concerns need to be properly articulated so that the NCS design may be appropriately modified. References Fienberg, S. E., and W. Mason (1978) Singer, B., and S. Spilerman (1974) "Identification and estimation of age-period- Bailar, B. A. (1975) "Social mobility models for heterogeneous "The effects of rotation group bias on esti- cohort models in the analysis of discrete archival populations." In Sociological Methodology (K. mates from panel surveys." Journalofthe Amer- data." In Sociological methodology 1979 1973-74 (H. Costner, ed.), pp. 356-401, San Schuessler, ed.), pp. 1-67. San Francisco: 70:23-30. Francisco: Jossey-Bass. ican Statistical Association Jossey-Bass. A. Singer, B., and S. Spilerman (1976a) Biderman, D. (1967) Finkner, A., and H. Nisselson (1978) "Surveys of population samples for estimating "The representation of social processes by "Some statistical problems associated with crime incidence." The Annals of the American Markov models." American Journal of Sociol- Academy of Political and Social Science cross-sectional surveys." In Survey sanlpling ogy 82: 1-54. 374: 16-33. and measurement (K. Namboodiri, ed.), New Singer, B., and S. Spilerman (1976b) York Academic Press. "Some methodological issues in the analysis Biderman, A. D., and A. J. Reiss, Jr. (1967) Hood, R., and R. Sparks (1970) "On exploring the 'dark figure' of crime." The of longitudinal surveys." Annals of Economic Key issues in criminology. New York: and Social Measurement 5447474. Annals of the American Academy of Polirical McGraw-Hill. and Social Science 374: 1-15. Thompson, M. M., and G. Shapiro (1973) Murphy, L. R., and C. C. Cowan (1976) "The current population survey: An over- Bishop, Y. M. M., S. E. Fienberg, and P. W. "Effects of bounding on telescoping in the Holland (1975) view." Annals of Economic and Social Measure- National Crime Survey." American Statistical ment 2105-129. Discrete multivariate ana(tvsis: Theory and Association Proceedings ofrhe Social Sratirtics practice. Cambridge, Mass.: M.I.T. Press. Section, part 11, pp. 633-638. U.S. Department of Justice, Law Enforcement Cinlar, E. (1975) Assistance Administration (1972) Penick, B. K., and M. E. B. Owens (eds.) Sun Jose methods test of known crime vic- Introduction to stochastic processes. Engle- (1976) wood Cliffs, N.J.: Prentice-Hall. tims. Statist. Tech. Rep. No. 1. Washington, Surveying crime. Panel for the Evaluation of D.C.: U.S. Government Printing Office. Fienberg, S. E. (1975) Crime Surveys. Washington, D.C.: National "ferspective Canada as a social report." Academy of Science. U.S. Department of Justice, Law Enforcement Social Indicators Research 2: 153-174. Assistance Administration (1974) Reiss, A. J. (1980) Crimes and victims: A report on the Dayton- "Understanding changes in crime rates," this Sun Josepilot survey of victimization. Washing- volume. ton, D.C.: U.S. Government Printing Office. Reiss, A. J. (1977) U.S. Department of Justice, Law Enforcement Personal communication. Assistance Administration (1976a) Rubin, D. B. (1976) Criminal victimization in the United States: A -inference and missing data.- ~ i ~ comparison~ ~ of~ 1973~ andi 1974findingsk ~ (No. SD 6358 1-592. NCP-N-3). Washington, D.C.: U.S. Govern- ment Printing Office. U.S. Department of Justice, Law Enforcement Assistance Administration (1976b) Criminal victimization in the United States 1973 (No. SD NCP-N-4). Washington, D.C.: U.S. Government Printing Office. Victim proneness in repeat viciimizaPion by type of crime*

ALBERTJ. REISS, JR . Department of Sociology Yale University @

This paper explores whether victimization (3) Excluding proneness to repeat vic- selection of victims. Do offenders, for by crime is a random occurrence or timization by the same type of crime, any example, select victims for their vulnerabil- whether some households and persons in a crime occurs about as frequently with any ity to victimization? Similarly, while it is population are more vulnerableor prone to other type of crime over time as would be known that the risk of victimization varies victimization and repeat victimization than expected from the joint probability of their considerably across territorial space, among are others. To do so: a crime-switch matrix occurrence. Four symmetrical pairs of different social aggregates, and over time, is constructed for repeat victimizations and crimes occur less frequently than expected, there is too little information on repeat vic- that distribution is compared with one however: assault with personal larceny, timization and the behavior proneness of expected under a simple assumption of assault with household larceny, personal victims. random occurrence of repeat victimization larceny with burglary, and personal lar- by type of crime. Both households and ceny with household larceny. These are sig- There are two major related and competing their members are considered as units at nificant changers in a mover-stayer model. explanations for differences in the risk of victimization and repeat victimization: vic- risk. (4) The order of occurrence of a type of tim proneness and victim vulnerability. crime has no effect on the probability of The paper also explores the error structure The victim proneness explanation selects in a crime-switch matrix. The major types occurrence of a pair. (5) The probability of consesutive vic- personal, social, and behavior character- and sources of error are: istics of persons as potential victims and timization by the same type of crime varies (1) Errors in reporting month of occur- their relationship to offenders as explana- directly with the probability of occurrence rence of incidents and the absence of infor- tory variables while the victim vulnerabil- of that type of crime among all victims. mation on date of occurrence. ity explanation selects situations and char- (2) The absence of information on oc- acteristics of offenders, their networks, currence of series incidents so that their The problem behavior and relationships to potential occurrence may be ordered in time and in victims as explanatory variables. Considerable interest attaches to the relation to nonseries incidents. question of whether victimization by crime Simply put, victim proneness models (3) Multiple reporting from members of is a random occurrence or whether some explain high risk of victimization and re- a household. households and persons in a population are peat victimization by victim behavior and In examining observed switches in type of more vulnerable or prone to victimization relationships with potential offenders that crime in repeat victimization, the following and repeat victimization than are others. precipitates crimes or increases their vul- are noted: The question is not easily answered since nerability to potential offenders. The (1) Among repeat victims, given prior theoretically one would want to model the vulnerability models are more offender victimization by one of the most frequently distribution and behavior of both victims oriented, explaining repeat victimization in occurring crimes (assault, personal larceny and offenders. Too little information is terms of such factors as the offender's prior without contact, household larceny, and available at present to construct such a relationship with victims, selection of crim- burglary) the most likely next victimization model. There is too little information on inal opportunities, and the organization of is by the same type of crime; for repeat vic- the distribution of offenders in a popula- networks of offending. The considerable timization for the less frequently occurring tion and almost none on their networks or overlap of the models not only makes it dif- crimes (motor vehicle theft, robbery, purse- ficult to test them as competing explana- snatching/pocket-picking, and rape), the tions but argues for a more general model. most likely next victimization is the most A more precise general model, however, frequently occurring of all major crimes, depends upon yet to be acquired informa- personal larceny without contact. tion on the behavior of both victims and (2) Nonetheless, there is substantial offenders. household proneness to victimization by *This paper is based on research supported by LEAA the same type of crime. Grant #SS-99-6013. We can begin to answer our initial question Risk of victimization household, a not uncommon condition, it of whether victimization by crime is a ran- and victim proneness seems unlikely that the member distinguishes the household collectively from his dom occurrence or rather whether some The question of what unit is at risk in vic- persons or households in a population are or her individual membership in it. House- timization by any given type of crime or in hold and person crimes are probably ex- more prone (or vulnerable) to victimiza- repeat victimization by crime is not easily tion by crime by investigating the extent to perienced as personal victimizations in resolved. Among major types of crime single-person households. which repeat victimization within the U.S. measured in the NCS, a household is con- population conforms to a random model of sidered at risk for the offenses of burglary, Selection of the unit at risk in repeat vic- occurrence. The National Crime Survey household larceny, and auto theft while its timization then is no simple matter. From (NCS) makes it possible to examine repeat individual members are considered at risk one perspective the unit at risk is a house- ' victimization and the characteristics of for offenses against the person, viz., rape, hold and its members; from another, it is its repeat victims to determine whether certain robbery, assault, larceny with contact individual members. Yet in selecting either kinds of victims are more at risk than as the unit at risk, somewhat different others. This paper limits the examination (purse-snatching and pocket-picking), and personal larceny without contact. Yet, assumptions are possible. Selecting the to whether in repeat victimization of a where each member of the household may household as the unit at risk, one assump- household and its members, or of house- purchase and own an automobile from in- tion is that it is at risk only for household holds only, there is a propensity to repeat dividually earned income, an auto theft and not person victimizations. An equally victimization by the same type of crime. mav svmbolicallv represent more of a per- plausible assumption, however, is that the The answer to the question, by what type of sonal ihan a household crime. This m& be household as a collectivity is at risk so that crime is repeat victimization most likely to particularly the case where the household household and person victimizations of its occur, given victimization by a prior type member is a young person who has pur- members are regarded as household vic- of crime, is obtained by constructing a chased an automobile for his journey to timizations. Selecting the person as the unit crime-switch matrix for repeat victimiza- work and personal use. Larceny of a pay- at risk, one assumption is that each mem- tions and determining whether it conforms check from the principal wage-earner of a ber of the household experiences both to anexpected model of occurrence under a household, on the other hand, may sym- household and person crimes as personvic- simple assumption of random occurrence bolically represent a household rather than timizations so that household victimiza- of repeat victimization by type of crime. a personal Victimization. Similarly, an tions should attach to each member of the The crime-switch matrix consists of pairs assault that incapacitates the principal household. An equally plausible assump- of victimization where a preceding victimi- wage-earner may be regarded as a family or tion perhaps is that only the personvictimi- zation by type of crime is compared with a a househgld victimization rather than a zations should attach to the person as the following victimization by type of crime. single member's victimization. unit at risk. When the effect that victimization by a Many, though not all, households consist Each of these assumptions can be exam- previous type of crime has on the occur- of families who appear to regard any ined as the unit at risk for repeat victimiza- rence of the next type of crime is examined household crime as a victimization in tion. Refinements in the unit at risk are also in repeat victimization, the question arises which they share. On the averageanyadult possible, such as by size of household whether the order in which the prior event member of the household can report more (single-person, two-person, and three-or- occurs has an effect on the next reported accurately the crimes against the house- more-person households) or for their com- type of crime. For example, in sequential hold than the personal crimes against all position in terms of families and unrelated or repeat victimization by a pair of any two members of the household. The NCS thus individuals. The preliminary inquiry re- types of crime such as personal larceny and uses only a single member of the household ported in this paper is limited to examining robbery, is one as likely to be victimized by to respond to the Household Screen Ques- the household as the unit at risk. Crime a personal larceny following a robbery as tionnaire to obtain information on crimes switch matrices are constructed for the by a robbery following a personal larceny, against the household while it asks each household as the unit at risk using all given that the probability of occurrence of member the questions in the Individual offenses against the household and its either a robbery or a personal larceny re- Screen Questionnaire to obtain informa- members (Tables 2-5) and for the house- mains the same at both points in time? Or, tion on crimes against the person. Never- hold using only household crimes (Tables is one more prone to robbery following a theless, the NCS provides evidence that the 7-8). personal larceny than to a personallarceny household respondent does not always following a robbery? We shall answer this report all of the household crimes and question by investigating the degree of additional household crimes, particularly symmetry in paired victimizations by type burglary and motor vehicle theft, are re- of crime. ported by individual members in response to the Individual Screen Questionnaire or the Crime Incident Report (Dodge 1975). These matters of how information on personal and household crimes can most accurately be obtained aside, the evidence suggests that symbolically household members often experience a household crime as a personal as well as a household victimization. Where the household is a single-person Construction of the crime-switch ported as occurring is recorded; when that This procedure produces an unknown matrices and their error structure month lies outside the reference veriod for amount of error in ordering events within a which crime incidents are beini recalled, month since the order of events within a The crime-switch matrix is a cross-classifi- the series is recorded as beginning in the month is determined from the randomly cation of pairs of crimes in the order of sixth month of the reference period or that assigned dates of occurrence. their occurrence in a sequence ofvictimiza- farthest from the time of interview. The tions over time. The number of pairs (p)in Excluding all but one incident of a series seasons of the year during which the series a sequence of two or more victimizations is also produces errors of two types. First, ex- incidents took place also are recorded. one less than the number of victimizations cluding series reduces the diagonal cells in When more than one incident is reported a (n), i.e., p = (n -1). There were 57,407 pairs crime-switch matrix, i.e., the "stayers" in a of victimizations for households reporting taking place within the same month, they are not ordered by time of occurrence mover-stayer model. A substantial propor- sequences of two or more person and tion of all series victimizations would fall within the month. household victimizations and 16,884 pairs on the diagonal since on first reporting any of victimizations for households reporting These survey questionnaire procedures victimizations, 76 .percent of all persons two or more household-only victimizations. make it difficult to order victimizations and 71 percent of all households report All incidents fir households reporting two precisely. Where there is multiple victimi- only series victimization within the 6-7 or more victimizations between July I, zation, crime incidents can only be ordered month period. Not all cells of the diagonal 1972, and December 31, 1975, are included by month of occurrence and not within the would be affected equally since series vic- in our matrices. Since households and their month. Moreover, the incidents in a series timization varies by type of crime. Second, members were in sample for varying victimization cannot be ordered by time of in the remaining cases where both series lengths of time-from one to seven inter- occurrence. Where both series and non- and nonseries or two or more series victim- views-the probability of repeat victimiza- series victimization are reported, series and izations are reported, there are misclassifi- tion depends upon the length of time in nonseries incidents cannot be ordered by cations in preceding and following types of sample. This fact is not taken into account time of occuyrence. Given these survey crime in order of occurrence. Such errors in the construction of the matrices. Both limitations, a set of procedures was affect only the "changer" cells in a mover- bounded and unbounded incident data are adopted for this report that orders victimi- stayer model. On balance there is far more included. zations in time.' These procedures are of the first type than of the second type of described below. error since the number of events in a series Respondents initially define crime events is large relative to reporting of nonseries First, using a random number generator, a in response to stimulus items in the Basic events within the same reference period Screen Questionnaire. For each incident date of occurrence was assigned to each nonseries incident within the month of the and series only reporting predominates reported in the Basic Screen Questionnaire, over series and nonseries reporting within reference period for which it was reported. a Crime Incident Report is completed that the same reference period. Were all series Where there was more than one incident includes a large number of facts about the to be included, then, one would expect even reported within a given month, the assign- actual event. These facts are used to classify greater victim proneness (or stayer propen- ment .of the date of occurrence was inde- .events into particular types of crime vic- sity) in our observed model. timization. Although there undoubtedly pendent for each event. Table I presents the percent distribution by are some errors in respondent reporting, it Second, a series incident was treated as type of crime for all first and last reported is doubtful that they materially affect the only a single incident. The random number classification by type of crime. When such generator was used to assign a date of crime incidents where the household and its members reported one or more crime errors occur, they should produce more occurrence within the first reported month error in detailed types than in major types of occurrence of the series incident within incidents and the first and second incidents of a pair for all sequences of two or more of crime classifications. the reference period. The type of crime victimizations. First and last reported assigned to the series incident was that Reverse-record check studies show that crime incidents include the same crime reported for the most recent incident in the errors occur in month of reporting the inci- incident when only a single victimization is series since that is the only incident for dent. These errors can have an impact on reported but all ,first reported victimiza- which type of crime is reported. the ordering of events in time and thus tions also include the,first reported incident affect the order of types of crimes in a pair Third, merging all person and household in a sequence of victimizations and all last in the crime-switch matrix. The procedure series and nonseries incidents, the incidents reported incidents include the last incident followed by the NCS, however, reduces the were first ordered for each household and in a sequence. Where there are only two likelihood of these errors having a substan- then reordered for household incidents crime incidents in a sequence of victimiza- tial effect since Crime Incident Reports are only. The first ordering produced a house- tions, the first (preceding) and second (fol- taken in the order of occurrence of events, hold crime-switch matrix using all offenses lowing) incidents may be of the same or dif- beginning with the "first" incident. against the household and its members and ferent type of crime. In sequences of three The Crime lncident Report of the NCS the second a household crime-switch or more victimizations, however, the records only the month and not the date of matrix for offenses against the household second incident of a first pair becomes the reported occurrence of a nonseries victimi- only. first incident of the next pair in a crime- zation. For series incidents, the month in 'Other procedures may be adopted in later work. For switch matrix, and so on. Thus, all which the first incident in the series is re- example. for series incidents given the month of first incidents in a sequence other than the last reported occurrence of a series incident. the span of will appear as afirst incident in a pair and months (from seasonal data) for which they occur can all but thefirst incident in a sequence will be determined. Taking an estimate of the number of incidents in the series, we can then estimate an average appear as the second incident in a pair. time between series incidents. If we randomly assign dates of occurrence to these series incidents, they can then be merged with nonseries incidents. - Table 1. Percent of each type of crime by order of reporting victimizations of households and their members: AII household and person victimizations, July 1,1972, to December 31,1975 Order of reporting victimization

Reported as Reported as Reported as All reported Type of crime first incident ~ ~ ~ ~preceding n incidentr ~ following~ e incident~ of a aair of a pair I Number Percent Number Percent Number Percent Number Percent Number Percent Rape 63 0.1 67 0.1 77 0.1 81 0.1 144 0.1 Attempted rape 161 0.3 161 0.3 196 0.3 197 0.3 358 0.3 Serious assault 959 1.7 932 1.7 1,346 2.3 1,316 2.3 2,279 2.0 Minor assault 1,028 1.9 994 1.8 1,473 2.6 1,437 2.5 2,471 2.2 Attempted assault 3,646 6.6 3,775 6.9 5,767 10.1 5,892 10.3 9,558 8.5 Robbery 653 1.2 594 1.1 799 1.4 741 1.3 1,395 1.2 Attempted robbery 429 0.8 384 0.7 649 1.1 606 1.1 1,037 0.9 Purse snatch/pocket picking 752 1.4 715 1.3 610 1.1 573 1.0 1,328 1.2 Attempted purse snatch 120 0.2 115 0.2 93 0.2 87 0.1 209 0.2 Personal larceny, $50 and over 5,481 10.0 5,525 10.0 5,054 8.8 5,100 8.9 10,613 9.4 Personal larceny, under $50 14.71 2 26.7 14,658 26.6 15,999 27.9 15,941 27.8 30,732 27.3 Attempted personal larceny 1,428 2.6 1,483 2.7 1,463 2.6 1,517 2.6 2,954 2.6 Burglary, forced entry 3,357 6.1 3,331 6.1 3,026 5.3 2,995 5.2 6,362 5.7 Burglary, no force 4,646 8.4 4,689 8.5 4,375 7.6 4.41 7 7.7 9,074 8.1 Attempted burglary 2,300 4.2 2,257 4.1 2,194 3.8 2,153 3.8 4,458 4.0 Household larceny, $50 and over 3,350 6.1 3,307 6.0 3.31 1 5.8 3,269 5.7 6,621 5.9 Household larcany,under $50 8,997 16.4 9,046 16.4 8,234 14.3 8,271 14.4 17,286 15.3 Attempted household larceny 858 1.6 886 1.6 827 1.4 854 1.5 1,713 1.5 Motor vehicle theft 1,331 2.4 1,403 2.6 1,151 2.0 1,223 2.1 2,562 2.3 Attempted motor vehicle theft 730 1.3 704 1.3 763 1.3 737 1.3 1,469 1.3

, Total 55,001 100.0 55,026 100.0 57,407 100.0 57,407 100.0 11 2,623 100.0 *The entries for "Reported as first incident" and "Reported as following incident of a pair" do not always sum to the Total, "All reported incidents." for each tvpe of crime; there are 21 5 incidents for which month of occurrence is unreDorted.

Table 2a.

Purse Type of crime Att. Serious Minor Att. Att. snatch, "reported as Rape rape assault assault assault robbery pocket preceding incident picking

Rape 6 3 8 1 5 2 2 1 Attempted rape 1 16 6 9 21 1 6 2 Serious assault 2 11 119 75 21 2 37 19 18 Minor assault 4 8 83 152 244 22 20 21 Attempted assault 11 29 199 228 1,685 59 81 37 Robbery 2 4 50 30 76 89 27 23 Attempted robbery 1 5 30 21 72 27 54 12 Purse snatchlpocket picking 1 2 21 19 47 26 9 46 Attempted purse snatch 3 2 10 2 3 1 Personal larceny, $SO+ 7 15 110 99 401 61 44 44 Personal larceny, under $50 16 33 238 292 1,314 126 136 144 Attempted personal larceny 1 3 25 34 115 22 24 15 Burglary, forced entry 7 17 90 59 199 42 25 27 Burglary, no forcible entry 9 11 85 107 31 9 45 34 41 Attempted burglary 8 46 46 166 30 15 23 Household larceny, $50+ 4 8 62 61 238 43 24 30 Household larceny, under $50 7 18 89 154 554 75 49 64 Attempted household larceny 1 4 11 8 74 4 11 3 Motor vehicle theft 1 1 29 24 78 20 11 16 Attempted motor vehicle theft 1 12 16 62 8 12 5

Total number 81 197 1,316 1,437 5,892 741 606 57 3 One would expect, therefore, considerable persons reporting single victimizations. NCS survey procedures separate the re- similarity in the type of crime distributions Actual burglaries fit the opposite pattern, porting and classification of household and for the first and second incidents in pairs of being less common among repeat than all person incidents. Whenever a single event crime incidents since they can differ only in victims. In the aggregate, crimes against of victimization involves both a household the distributions for first and last incidents the household occur only somewhai less and a person crime, e.g., a barglary fob in a sequence of victimizations. Any selec- frequently among repeat than among all lowed by a rape, they are reported as two tive influence in proneness to type of crime victims while the opposite is the case for separate incidents. Our procedure will err for multiple or repeat victimization of a crimes against household members, i.e., in assigning them as separate events in household and its members will be re- crimes against persons. time. Moreover, NCS procedures take a separate incident report from each member flected largely in differences between the The degree to which there are switches in distribution for all first reported incidents of the household who was "robbed, victimization by type of crime for a house- harmed, or threatened" in the same event. and that for the first incident of a pair or hold and its members in multiple or repeat the distribution for last reported incidents Since these incidents are identified only by victimization depends in part upon the sys- month of occurrence, our procedure again and that for the last incident of a pair or in tem of classification for crime incidents. differences with the distribution for all re- will err in assigning them as separate events The procedure followed was to classify ported victimizations. in time. Although members to a common each crime event by the most serious event can be classified in a separatedetailed What is most apparent in Table 1 is the offense reported. A rape with theft, for criine category, e.g., an assault on one and striking similarity in the distributions by example, was classified only as a rape and an attempted assault on the others, in gen- type of crime for all first and last reported not as two separate incidents of a rape and eral such events will contribute dispropor- and all preceding and following incidents theft. Sequences of incidents that occur tionally to the diagonal cells of the crime- of a pair with that for all reported incidents. within the same crime event are thus ex- switch matrix. Relative to the aggregate of Although this similarity is determined to cluded from the crime-switch matrix. all multiple victimization over time, these some degree by the relative frequency of events are relatively uncommon so that the types of crime among all victimizations, it amount of error should be small. These is apparent that multiple or repeat victims sources of error could be eliminated were of households aregenerally no more or less NCS procedures to clearly separate inci- prone to victimization by certain types of dents that occur in the same event in time crime than are all victims. There are some from those that do not and also identify exceptions. Assaulp, particularly attempted members of the household to a common assaults, occur more frequently among event. repeat than among all victims and by de- duction they occur less commonly among

Number of crime incident pairs of preceding and following detailed major types of crime reported by a household and its members: All households reporting two or more victimizations while in survey, July 1, 1972, to December 31, 1975

Type of crime reported as following inciderit

Per- House- Per- House- hold Att. Att. sonal Att'per- Bur- Bur- Att. house- motor Total purse sonal larceny sonal glary, glary,no bur- larceny hold larceny under vehicle vehicle number Inat* $50+ S50 larceny force force glary la;;: u;~larceny theft theft

7 16 5 2 4 2 9 1 3 77 3 11 43 5 7 8 13 7 27 2 5 3 196 2 100 233 26 78 92 53 68 145 16 32 8 1,346 4 93 315 30 64 83 32 82 163 16 25 12 1,473 3 371 1,244 141 196 301 184 230 557 72 87 52 5,767 1 76 130 21 41 54 23 41 78 5 15 13 799 55 156 21 26 37 16 27 63 7 13 6 649 4 48 141 22 38 42 26 30 48 8 17 15 61 0 10 9 18 5 4 4 1 3 10 2 6 93 9 859 1,385 173 231 337 159 317 544 55 133 7 1 5,054 13 1,428 7,067 474 436 960 363 637 1,749 158 247 168 15,999 4 156 446 149 53 72 47 68 142 19 35 33 1,463 4 212 450 53 666 237 198 183 394 53 79 31 3,026 7 354 917 74 258 993 134 253 550 58 88 38 4,375 151 395 43 192 172 360 116 327 39 33 32 2,194 4 350 636 65 179 261 121 475 552 68 82 48 3,311 14 544 1,779 133 378 597 297 555 2,526 171 149 81 8,234 2 65 161 24 33 49 47 62 164 73 16 15 827 2 134 253 25 74 76 48 74 127 8 122 28 1,151 1 77 156 33 36 40 27 39 96 23 36 83 763 87 5,100 15,941 1,517 2,995 4,417 2,153 3,269 8,271 854 1,223 737 57,407 i

> The crime-switch matrix in Tables 2-5 pre- matrix. The reader is cautioned, in any most likely events. The other major crimes sents shifts in type of crime for repeat or case, against interpreting the ordering of against persons or households occur much multiple victimization of households re- personal crime incidents as applying to the less frequently: motor vehicle theft (3 per- porting two or more victimizationsbetween same person. cent); robbery (2 percent); purse-snatching July 1, 1972, and December 31, 1975. The or pocket-picking (l percent); and the least frequent, rape (0.4 percent). Yet, amongre- matrix is presented in two different ways. Observed switches in type of crime Table 2 presents the frequency distribution peat victims, given prior victimization by in repeat victimization one of the most frequently occurring for the crime-switch matrix. Table 3 dis- of a household and its members plays the percent of each type of crime that crimes (assault, personal larceny without follows a preceding reported type of crime There is considerable mutliple and repeat contact, household larceny, and burglary). in a sequence of eight major types of crimes victimization by crime. The longer the time the most likely next victimization is by the against households and persons. interval for which victimization is meas- same type of crime. Roughly a third of all - -- -... - - --- ured, the greater the propensity to repeat assaults and of all burglaries, 38 percent of The reader sho~ldbear in mind that these .victimization. all household larcenies and 54 percent of all reports of victimization are for a household personal larcenies are preceded and fol- and its members. Where crimes against Given the distribution of all reported vic- lowed by reports of victimization by that persons are involved, the two incidents in a tim incidents or of that for repeat victims same type of crime (Tables 2 and 3). In re- only (Table l), the most likely victimiza- pair might be for the same or for different peat victimization for the less frequently members of the same household. Thus, a tion by a major type of crime is a personal occurring crimes (motor vehicle theft, rob- larceny (39 percent) with household lar- robbery followed by robbery could be re- bery, purse-snatching or pocket-picking, ported for the same or for different mem- ceny (22 percent), burglary (17 percent) and assault (15 percent) among the next and rape), the most likely next victimiza- bers of the same household. Unfortunately, tion is the most frequently occurring crime we are unable to distinguish victims within of personal larceny without contact. the same household to a common event, Roughly 3 in 10 of these less frequently e.g., an assault, and our procedure for occurring crimes are followed by a per- ordering events will treat them as separate sonal larceny (Table 2). victimizations occurring at different, though closely related, points in time. There is, therefore, a conf9unding of some preceding and following events in the crime-switch

Table 2b.

Purse Type of crime Att. Serious Minor Att. Att. snatch, preceding next Rape rape assault assault assault robbery pocket reported type of crime picking

Rape 7.8 3.9 10.4 1.3 6.5 2.6 2.6 1.3 Attempted rape 0.5 8.2 3.1 4.6 10.7 0.5 3.1 1.O Serious assault 0.2 0.8 8.8 5.6 15.8 2.8 1.4 1.3 Minor assault 0.3 0.5 5.6 10.3 16.6 1.6 1.4 1.4 Attempted assau It 0.2 0.5 3.5 4.0 29.2 1.O 1.4 0.6 Robbery 0.3 0.5 6.3 3.7 9.5 11.1 3.4 2.9 Attempted robbery 0.2 0.8 4.6 3.2 11.1 4.2 8.3 1.9 Pcrse snatchinglpocket picking 0.2 0.3 3.4 3.1 7.7 4.3 1.5 7.5 Attempted purse snatching - 3.2 2.1 10.8 2.1 3.2 1.1 Personal larceny, $50 and over 0.1 0.3 2.2 2.0 7.9 1.2 0.9 0.9 Personal larcency, under $50 0.1 0.2 1.5 1.8 8.2 0.8 0.9 0.9 Attempted personal larceny 0.1 0.2 1.7 2.3 7.9 1.5 1.6, 1.O Burglary, forced entry 0.2 0.6 3.0 2.0 6.6 1.4 0.8 0.9 Burglary, no forcible entry 0.2 0.2 1.9 2.4 7.3 1.O 0.8 0.9 Attempted burglary - 0.4 2.1 2.1 7.6 1.4 0.7 1 .O Household larceny, $50 and over 0.1 0.2 1.9 1.8 7.2 1.3 0.7 0.9 Household larceny, under $50 0.1 0.2 1.1 1.9 627 0.9 0.6 0.8 Attempted household larceny 0.1 0.5 1.3 1 .O 9.0 0.5 1.3 0.4 Motor vehicle theft 0.1 0.1 2.5 2.1 6.8 1.7 1 .O 1.4 Attempted motor vehicle theft - 0.1 1.6 2.1 8.1 1.1 1.6 0.7 All next reported incidents 0.1 0.3 2.3 2.5 10.3 1.3 1.1 1 .O Number next reported incidents 81 197 1,316 1,437 5,892 741 606 573 I No incidents reported Table 3. Percent distribution by next reported type of crime for major preceding types of crime reported by households with two or more victimizations of the household and its members: All household and person victimizations, July 1,1972, to December 31,1975

Next reporredVpe of crimeg Total

Type of crime? D,.rrs I I "IS I preceding next Motor reported crime Rape Assault Robbery ~~~~~;~~~~~~'Burglary larQny vehicle Percent Number nirkinn theft I - -- I Rape 9.5 Assault 0.8 Robbery 0.8 Purse snatching, pocket picking 0.4 Personal larceny 0.3 Burglary 0.5 Household larceny 0.3 Motor vehicle theft 0.2 Total 0.5 15.1 2.3 1.1 39.3 16.7 21.6 3.4 100.0 57,407

'AII types of crime include both actual and attempted crimes.

There is considerable variation in patterns of all reported victimizations. 9 percent of Since rape is a form of assault, some of repeat victimization for the different all rapes occurring in households reporting interest attaches to victim proneness to major types of crime, however, as the fol- two or more victimizations were followed rape and other types of assault (serious, lowing summary based on Tables 2 and 3 by a rape. There appear to be differences in minor, and attempted assault). Somewhat discloses. victim proneness to actual and attempted more rapes than expected in households (I) Despite the fact that rape is an infre- rape. Most rapes preceded or followed by reporting two or more victimizations were quent event accountingfor only 0.4percent an attempted rape are also attempted tapes, and a substantial majority of rapes preceded or followed by an actual rape are actual rapes.

Percent distribution by next reported type of crime for major preceding types of crime reported by households with two or more victimizations of the household and its members: All household and person victimizations, July 1, 1972, to December 31, 1975

Next reported type of crime

Per- House- Att. Att. Bur- House- Att. Per- sonal per- Bur- Att. Att. purse larceny, glary, bur- hold house- motor Total sonal no hold larceny hold vehicle match under larceny under Iaz::' $50 larceny force force glary $50+ larceny theft theft

9.1 20.8 6.5 2.6 5.2 2.6 11.7 1.3 3.9 100.1 1.5 5.6 21.9 2.6 3.6 4.1 6.6 3.6 13.8 1.O 2.6 1.5 100.1 0.2 7.4 17.3 1.9 5.8 6.8 3.9 5.0 10.8 1.2 2.4 0.6 100.0 0.3 6.3 21.4 2.0 4.3 5.6 2.2 5.6 11.1 1.1 1.7 0.8 100.0 0.1 6.4 21.6 2.4 3.4 5.2 3.2 4.0 9.7 1.2 1.5 0.9 100.0 0.1 9.5 16.3 2.6 5.1 6.8 2.9 5.1 98 0.6 1.9 1.6 100.0 8.5 24.0 3.2 4.0 5.7 2.5 4.2 9.7 1.1 2.0 0.9 100.1 0.7 7.9 23.1 3.6 6.2 6.9 4.3 4.9 7.9 1.3 2.8 2.5 100.1 10.8 9.7 19.3 5.4 4.3 4.3 1.1 3.2 108 2.1 6.5 100.0 0.2 17.0 27.4 3.4 4.6 6.7 3.1 6.3 10.8 1.1 2.6 1.4 100.1 0.1 8.9 44.2 3.0 2.7 6.0 2.3 4.0 10.9 1.O 1.5 1.0 100.0 0.3 10.7 30.5 10.2 3.6 4.9 3.2 4.7 9.7 1.3 2.4 2.3 100.1 0.1 7.0 14.9 1.8 22.0 7.8 6.5 6.0 13.0 1.8 2.6 1.0 100.0 0.2 8.1 21.0 1.7 5.9 22.7 3.1 5.8 12.6 1.3 2.0 0.9 100.0 6.9 18.0 2.0 8.7 7.8 16.4 5.3 14.9 1.8 1.5 1.4 100.0 0.1 10.6 19.2 2.0 5.4 7.9 3.7 14.3 16.7 2.0 2.5 1.5 100.0 0.2 6.6 21.6 1.6 4.6 7.2 3.6 6.7 30.7 2.1 1.8 1.0 100.0 0.2 7.9 19.5 2.9 4.0 5.9 5.7 7.5 19.8 8.8 1.9 1.8 100.0 0.2 11.6 22.0 2.2 6.4 6.6 4.2 6.4 11.0 0.7 10.6 2.4 99.9 0.1 10.1 20.5 , 4.3 4.7 5.2 3.5 5.1 12.6 3.0 4.7 10.9 100.0 0.1 8.9 27.8 2.6 5.2 7.7 3.8 5.7 14.4 1.5 2.1 1.3 100.0 87 5,100 15,942 1,517 2,995 4,417 2,153 3,269 :8,271 854 1,223 737 57,407 - followed (18 percent) by an assault. Of member of the household reporting the hold larceny, or assault being equally likely some interest also is the fact that actual same kind of victimization. There is a as next reported events. rapes were far more likely than expected to strong tendency for reports of actual to be (5) There is considerable victim prone- occur in households that next reported a followed by actual purse-snatching or nessfor victims ofpersonal larcezy without serious assault (10 percent). pocket-picking and attempted to be fol- contact. Although personal larceny with- (2) Repeat victims are only slightly lowed by attempted purse-snatching or out contact is the most frequently occurring more prone to assault than are victims re- pocket-picking. major crime against a household and its Among repeat victim households report- porting only a single victimization. For members accounting for 39 percent of all households reporting two or more victimi- ing a purie-siatching or pocket-pickikg by victimizations, 54 percent of all personal zations, 15 percent of all victimizations one of their members. the risk of victimiza- were an assault while about 13 percent of tion is greatest for personal larceny without all single victims reported an assault. contact (35 percent), with burglary, house- There is substantialproneness to assault among victims reporting an assault. Given the occurrence of an assault on a household member, 35 percent of all preceding and following incidents reported for the household are an assault. Serious and minor assaults were about as likely to be followed by a serious or minor as by an attempted Table 4. assault, but attempted assaults followed by an assault are ordinarily followed by an attempted assault. (3) Repeat victims are only slightly more prone to robbery than aresingle-time victims. Of all reported victimizations, 2.1 percent are robberies while 2.4 percent of Type of crime all incidents reported by multiple victim- reported as Rape ized households are robberies. and Serious Minor Att. preceding incident Robbery There is substantial proneness to rob- att. assault assault assault bery among victims of robbery. Given the rape relatively low probability of a robbery, a substantially greater proportion (14 per- Rape and attempted rape +461 +10 +1 -* -* cent) of all robberies reported against Serious assault +6 +252 +51 +40 +22 household members in households with Minor assault +3 +72 +360 + 57 +* two or more victimizations were preceded Attempted assault -5 +34 +49 +2019 -3 or followed by a robbery of a member. Robbery -* +600 Attempted robbery +l +55 +1+5 +* +41 Moreover, actual robberies are generally Purse snatchlpocket picking -*+3 +I5+4 +1 -3 +39 preceded and followed by actual robberies and attempts and attempted by attempted robberies. Personal larceny, $50 and over -+ -* -6 -27 -* Among repeatedly victimized house- Personal larceny, under $50 -11 -45 -29 -65 -32 holds reporting robbery, their risk of Attempted personal larceny -1 -2 -* -8 +* repeat victimization by robbery is less than Burglary, forced entry +6 +6 4 -40 +* -* their risk of victimization by the major Burglary, no force -2 -* -38 -2 Attempted burglary -1 -* -1 -1 6 +* crimes of personal larceny without contact Household larceny, $50 and over -1 -3 -6 -31 +* (32 percent) or assault (19 percent), but Household larceny, under $50 -6 53 -13 -100 -9 about the same as that for the much more Attempted household larceny +* -3 -8 -1 -4 Motor vehicle theft -2 +* -1 -1 4 +3 frequently occurring crimes of burglary -2 -2 -* -3 -* and household larceny. Attempted motor vehicle theft Rape and attempted rape 2.6 (4) Purse-snatching and pocket-picking Serious assault 1.4 are relatively infrequent events accounting Minor assault 2.1 for only 1.4 percent of all crime incidents Attempted assault 11.6 Robbery 3.4 reported in the victim survey and an even Attempted robbery smaller proportion of those for multiple Purse snatchlpocket picking victimized households (1.1 percent). Yet, and attempts much as in the case for the infrequent event Personal larceny, $50 and over Personal larceny, under $50 of rape, there is considerable proneness to Attempted personal larceny repeat victimization among those victim- Burglary, forced entry ized by purse-snatching or pocket-picking; Burglary, no force 9 percent of all purse-snatching or pocket- Attempted burglary picking incidents were followed by some Household larceny, $50 and over Household larceny, under $50 Attempted household larceny Motor vehicle theft Attempted motor vehicle theft

x2 = 17,461;d.f. = 289 * = less than .5 + = Observed > expected frequency; -= < expected frequency. Goodmen-Kruskal Index (0) .20 * .004.

< larcenies without contact were followed by Minor personal larcenies show thegreat- (6) There is likewise considerable victim that same type of crime. Major ($50 or est propensity to repeat victimization by proneness among victims of burglary. more), minor (under $50) and attempted minor personal larceny and are less likely About a third of all burglaries of house- personal larcenies without contact are all than the other types of personal larceny holds reporting two or more victimizations most likely to be followed by a minor per- without contact (major and aiiempted) to were preceded or followed by a burglary. sonal larceny without contact in repeat be followed by an attempted or major per- Attempted burglaries were about as larceny victimization. Nonetheless, a major sonal larceny. This propensity perhaps re- likely to be followed by an actual as an personal larceny is more than twice as flects differences in the victim composition attempted burglary but actual burglaries likely ta be followed by another major per- of larceny victims by type of larceny. A with or without force were quitelikely to be sonal larceny as would be expected from substantial number of minor personal lar- the risk of major personal larceny for all cenies involve school-age victims where victims. repeat victimization involves minor personal larcenies at school.

Actual and percent cell contribution to chi square of pairs of victimizations in a crime-switch matrix for repeat household victims of detailed person and household crimes: All household and person victim@ations for households reporting two or more victimizations, July 1,1972, to December 31,1975 Type of crime reported as following incident I Purse per- Per- Att. Bur- Bur- House- Att. Att. snatch, sonal sonal Att. House- hold larceny, per- glary, glary, bur- larceny, house- motor robbery larceny, under sonal forced no hold vehicle vehicle plcklng $50+ larceny, under and att. $50 larceny entry force 'Iary $50+ $50 larceny theft theft Table 5. Actual and percent cell contribution of chi square of pairs of victimizations in a crime-switch matrix for repeat household victims of major household and person crimes: All household and person victimizations for households reporting two or more victimizations, July 1,1972, to December 31,1975 1 Type of crime reported as following incident I Type of crime Purse Personal reported as Motor preceding incident Rape Assault Robbery sn~~~~g'$g:lt Burglaw vehicle theft picking contact

Rape t460 +3 -3 -6 -1 -2 -* Assault +13 i2.246+2 +7 -2 -200 -84 +I37 -20 Robbery +4 +17 t782 +22 -21 --8 -27 -I Purse snatching, pocket picking -8 -* +33 t346 --4 -* -1 7 +8 Personal larceny, without contact -1 1 -172 -25 -3 + 1,223 -319 -283 --9 Burglary +1 -74 -5 -1 -334 +1,624 -5 -2 Household larceny -5 -201 -25 -251 -5 +1,460 -2 Motor vehicle theft 4 -1 6 +1 3 -7 -1 -5 +635 Percent of total chi square I Rape 4.1 Assault 20.1 1.8 1.2 Robbery 7.0 Purse snatching, pocket picking 3.1 Personal iarcenv.. . without contact 1.5 10.9 2.8 2.5 Burglary ~ouseholdlarceny Motor vehicle theft

x2 = 11,190;d.f. = 49;Goodman-Kruskai Index (G) = .26f .005. *Less than .5 + = Observed > exuected freauencv I followed by the same kind of actual bur- other mqjor types of crimes are about as where the observed frequency is substanti- glary. Thus, 22 percent of all actual bur- likely events as is motor vehicle theft in ally greater than the expected frequency. glaries with force were followed by an their repeat victimization. Indeed, the diagonal cells in Table 4 actual burglary with force compared with 8 account for 78.1 percent of the total value This brief description of victim proneness of chi-squared and in Table 5, for 78.4 per- percent followed by burglary with no force in repeat victimization of a household and and 7 percent followed by attempted bur- cent. We can conclude then that the its members has emphasized the proneness chances a household or one or more of glary. Similarly, 23 percent of all actual to repeat victimization by the same type of burglaries without force were followed by its members will be successively victimized crime despite substantial differences in the an actual burglary without force compared by the same type of crime are greater than probability of victimization among the one w~ouldexpect given the chance aN with 6 percent followed by an actual types of crime. The test of proneness has burglary with force and 3 percent followed households and their members have of been the departure of these patterns from by attempted burglaries. being victimized by that type of crime. By expected frequency of occurrence, given this measure, then, in repeat victimization. (7) Households victimized by house- the distribution of types of crime among all there is household victim proneness to the hold larceny are prone to repeat victimiza- repeat victimized households. The test of same type of crime. The chances of next tion by household larceny. While 22 per- divergence between the actual crime-switch being victimized by a robbery, for example, cent of all households reported a house- matrix and an expected one based on the are greater if the previous victimization hold larceny, 38 percent of all households types of crime reported by repeat victims was a robbery than if it was some other type victimized by household larceny reported a used was the chi-square test for homogene- of crime. preceding or following incident of house- ity of proportions. The chi-square test for hold larceny. As for personal larceny, any an 18 by 18 detailed type of crime matrix is Readers should take note that proneness to household larceny followed by a household presented in Table 4 and for an 8 by 8 major victimization by the same type of crime larceny is most likely to be a minor house- type of crime matrix in Table 5. does not predict the most likely next victimization by a major type of crime. That hold larceny with a loss of $50 or less. But a Given the substantial number of pairs, is, proneness to victimization by the same substantially greater proportion of major 57,407, in the matrices, the chi-square is type of crime does not say that whenever a household larcenies ($50 and over) are fol- expected to be significant. Our attention in lowed by a major household larceny than household or one of its members is victim- these tables, therefore, focuses on the cells ized by any major type of crime, it has a expected. A similar pattern holds for in the crime-switch matrix that contribute attempted household larcenies. greater chance of next being victimized by significantly to the chi-squared. the same rather than by some other type of (8) Motor vehicle theji victims also The diagonal cells in Tables 4 and 5 are crime. The chances that a victim of a rob- show a propensity to repeat victimization those where the same type of crime is re- by the same type of crime. This propensity poited in a pair. Each of these cellscontrib- holds for both attempted and actual motor utes significantly to the value of chi-squared vehicle theft. As for other infrequently and they are the only cells in these tables occurring crimes, motor vehicle theft is most likely to be preceded or followed by a personal larceny without contact but the bery or a motor vehicle theft will next be household members were victimized by The second condition for symmetry is that victimized by a personal larceny are greater, robbery, the propensity tostay home might the probability of any two pairs that differ for example, than victimization by the reduce the risk of it being followed by a only by order of occurrence differ from same type of crime. Rather, for any major robbery. that of all other pairs. This condition of type of crime, the chances of next beingvic- symmetry is more or less satisfied for major timized by any major type of crime are An answer to the question of the effect of types of crime though it is less apparent for greater than chance only for the same type prior or subsequent victimization by type many of the pairs for detailed types of of crime. of crime is provided by examining the ex- crime. Generally, however, there is sym- tent of symmetry in paired victimizations There are eight cells in Table 5 where the metry in the pairs involving major crimes by type of crime. When any two types of against .persons and households.2 observed frequency of pairs is significantly crime are paired by their order of occur- less than expected, given the type of crime rence, the pairs aresymmetrical if the prob- There is considerable variation, however, distribution for all multiple victimized ability of their occurrence is the same and it in the probability that any two types of households and their members. These cells differs from other crime pairs. Even if the crime incidents will be consecutive victimi- account for an additional 16.8 percent of full conditions of symmetry are not met but zations. The probability of consecutive vic- the total value of chi-squared or all but 5 the probability of occurrence remains the timization by the same type of crime varies percent of the remaining variance. They in- same for paired orders, there would be little directly with the probability of occurrence volve selected combinations among the four evidence that prior victimization has had a of that type of crime among all victims. most frequently occurring crimes of per- substantial effect on type of crime victimi- Moreover, the greater the probability of sonal and household larceny, burglary, and zation in repeat victimizafion. victimization by any type of crime, the assault. The eight cells can be regarded as more likely it is to occur in consecutive vic- four symmetrical pairs with (1)assault with Among the 12 person and 8 household timization with any other type of crime. personal larceny, (2) assault with house- detailed types of crime in Table 2 that can hold larceny, (3)personal larceny with bur- be reported as victimizations by households glary, and (4) personal larceny with house- and their members reporting two or more Switches in type of household hold larceny occurring lessfrequently than victimizations, there are 400 possible pairs crime in repeat victimization expected. Thus an assault, for example, is of incidents by type of crime when each in- of households less likely to be followed by a personal lar- cident is paired with the next succeeding in- We shall next consider briefly the house- ceny than expected and a personal larceny cident by type of crime. Twenty of these hold as the unit at risk in repeat victimiza- is less likely to be followed by an assault pairs occur when the same type of crime is tion for household crimes only-those of than expeAed. Just why multiple victim- reported for two consecutive incidents. The burglary, household larceny, and motor ized households and their members should remaining 380 pairs of consecutive inci- vehicle theft. In general, repeat victims of be less prone to these four symmetrical dents could comprise 190 symmetrical household crimes are no more or less prone patterns of victimization is not apparent. pairs. Similarly, among the five person and to victimization by certain household three household major types of crime in crimes than are all victims (Table 6). Motor All other pairs of victimization by type of Table 3, there are 64 possible pairs of inci- vehicle theft may occur somewhat less crime occur about as often as expected. A dents; eight of these occur when the same rape followed by an assault or an assault often amongrepeat than among all victims, type of crime is reported for two consecu- but the difference is very small. followed by a rape, for example, occurs tive incidents. The remaining 56 pairs of about as often as expected. consecutive incidents could comprise 28 Among major crimes against households, When examining the effect that victimiza- symmetrical pairs. When the 400 and the 64 the most likely household victimization is tion by a type of crime has on the chances pairs are ordered by their actual rate of that of household larceny (52 percent) with of victimization by any other type of crime occurrence among 10,000 pairs among burglary somewhat less common (40 per- in repeat victimization, the question arises households reporting two or more victimi- cent) and motor vehicle theft least common whether the order of victimization by a zations, the order of occurrence ofa type of (8 percent). Actual household crimes occur type of crime has an effect. Such effects crime in a pair has little effect on theprob- with greater frequency than do attempted could be presumed to occur were victims to ability of occurrence of a pair. One of the ones. Attempted household crimes are par- alter substantially their behavior to avoid conditions of symmetry with respect to pair ticularly un;ommon for household larEeny repeat victimization by a serious type of order thus is satisfied; any two types of where only about I in 14 household larcen- crime, and take precautions that reduce the crime have essentially the same probability ies is reported as an attempt. The compara- likelihood of victimization by even less of occurrence regardless of the order of vic- ble odds for burglary are that 1 in 4 is an serious types of crime which would not be timization. For example, the probability of attempt while almost 1 in 3 motor vehicle taken were one previously victimized by a household larceny less than $50 being thefts is an attempt. The odds areabout the the less serious crime. Thus, if one or more followed by a personal larceny less than same for repeat as for all victims during the $50 is 310 in 10,000 pairs, while it is 305 for three and one-half years for which victimi- a personal larceny less than $50 being fol- zation was reported. lowed by a household larceny less thanS50. ?A more succinct test for symmetry is presented in the There is no evidence then that victims or companion paper by Fienberg. offenders have any effect on the order of victimization by different types of crime for repeat victimization. Where there is repeat victimization by the same type of crime, however, it is quite possible that victims and offenders have an effect, given their significant departure from chance occurrence. Table 6. Percent of each type of crime for order of reporting household victimizations: All household victimizations, July 1,1972, to December 31,1975 Order ,of reporting victimization

Reported as Reported as Reported as Reported as All Type of preceding following reported first last incident incident household crime incidents* incident incident of a air of a pair

Number Percent Number Percent Number Percent Number Percent Number Percent

Burglary, forced entry 4,140 12.7 4,102 12.6 2,257 13.4 2,215 13.1 6,362 12.8 Burglary, no force 5,978 18.3 6,005 18.4 3,062 18.1 3,087 18.3 9,074 18.3 Attempted burglary 2,914 8.9 2,891 8.9 1,565 9.3 1,541 9.1 4,458 9.0 Household larceny, $50and over 4,359 13.4 4,323 13.2 2,295 13.6 2,262 13.4 6,621 13.4 Household larceny, under $50 11,387 34.9 11,403 34.9 5,881 34.8 5,889 34.9 17,286 34.9 Attempted household larceny 1,107 3.4 1,I 26 3.4 587 3.5 606 3.6 1,713 3.4 Motor vehicle theft 1,740 5.3 ' 1,816 5.6 740 4.4 816 4.8 2,562 5.2 Attempted motor vehicle theft 999 3.1 970 3.0 497 2.9 468 2.8 1,469 3.0 Totals 32,624 100.0 32,636 100.0 16,884 100.0 16,884 100.0 49,545 100.0 *The entries for "Reported as first incident" and "Reported as following incident of a pair" do not always sum to the total, "All Reported Incidents," for each type of crime because there are 37 incidents for which month of occurrence is unreported.

There is some variation in patterns of zation by the same type of crime (stayer or joint probability of victimization. That is, repeat victimization for the different diagonal cells in Table 8) is substantial. excluding victimization by the same type of detailed and major types of household These are the only cells where the observed crime, for every major type of household crime (Table 7). frequency is signficantly greater than the crime, the probability that it will occur with expected and they account for 81 percent of every other major type of household crime There is substantial proneness to repeat the variance in chi-squared for repeat vic- in repeat victimization varies directly with victimization by the same major type of timization by detailed types of crime and 68 their expected probability of occurrence household crime. While the odds of house- percent of the variance in major types of based on the experience of all victims. hold larceny are roughly 5 in 10 for all crime. One other pattern is worth noting. household victims, they rise to between 6 Actual burglaries-occur significantly leis Conclusion and 7 in 10 for households previously vic- often with actual household larcenies than timized by a household larceny. Similarly, one would expect given the chances of vic- Within a population of victims, there is while the burglary odds are 4 in 10 for all timization for all households. This is sur- considerable multiple or repeat victimiza- household victims, they are almost 6 in 10 prising given the close relationship between tion. Evidence on repeat victimization for households previously victimized by the two types of crime and the possibilities makes it clear that victimization is not a burglary. The odds for victimization by for misclassification. random occurrence but that there is prone- motor vehicle theft are less than I in 10 for ness to repeat victimization. Moreover, in all victimized households, but almost 3 in As one might expect from the substantial repeat victimization, there is a proneness to 10 when a motor vehicle theft is previously differences in the probability of victimiza- repeat victimization by the same type of reported. tion among different types of household crime. Apart from a marked proneness to crimes, there is considerable variation in Regardless of the type of burglary, the odds victimization by the same type of crime in the probability that any two types of house- are that the next household victimization repeat victimization, most patterns of vic- hold crime will be consecutive victimiza- timization by type of crime in repeat vic- will be a burglary. There is, moreover, a tions. The probability of consecutive vic- substantial propensity for victimization by timization occur about as often as timization by the same type of household the same type of burglary. The same expected. crime generally varies directly with the pattern holds for household larceny. For probability of occurrence of that house- The order of occurrence of a type of crime motor vehicle theft, however, the odds are hold crime among all victims. Moreover, in a pair has little effect on the probability that the next victimization will be a house- the greater the probability of victimization of occurrence of a pair. There is, moreover, 'hold larceny or burglary, though there is by any type of household crime, the more a general symmetry in the pairs involving nonetheless a substantial propensity for re- likely it is to occur in repeat victimization major types of crimes against persons and peat victimization by motor vehicle theft. with every other type of household crime. households. The probability of consecutive The odds on repeat victimization by motor victimization by the same type of crime vehicle theft are four times greater for those For every major type of household crime varies directly with the probability of previously victimized by motor vehicle also, the probability that it will occur con- occurrence of that type of crime among all theft than they are for all household victims secutively in repeat victimization with any victims. The greater the probability of vic- and more than seven times greater for other type of crimes is a function of their timization by any type of crime, the more attempted motor vehicle theft. likelv it is to occur in consecutive The chances that a household will be vic- victimization with any other type of crime. timized by the same type of household crime, then, are substantially greater than Reference one expects given the chances all households havefor victimization by that type of Dodge, Richard W. (1975) National Crime Survey: Comparison of vic- crime. Further evidence for this is found in timizations as reported on screen questions with Table 8. The propensity to repeat victimi- their ,final class~fication. 1974. Washington, D.C.: U.S. Bureauof thecensus Memorandum, December 1, 1975, p. 5. # Table 7. Percent distribution by next reported for precedingdetailed and major types of householdcrime for households reporting two or more householdvictimizations: All householdvictimizations, July 1, 1972, to December 31, 1975' Percentdistribution by following detailed type of household crime I I I Type of crime reported as following incident Total I Type of crime House- House- Att. Att. Total reported as hold hold Motor nrotor preceding preceding incident An' larceny larceny h:i7- vehicle vehicle incidents force brce burg'aw S5Oand under theft theft over $50 Burglary, forced entry 34 14 11 10 22 3 5 2 Burglary, no force 11 39 6 11 25 2 4 2 Attempted burglary 15 13 26 9 28 3 3 3 Household larceny, $50 and over 10 15 7 26 30 4 5 3 Household larceny, under $50 8 13 6 12 51 4 4 2 Attempted household larceny 7 12 10 15 36 14 3 3 Motor vehicle theft 13 14 9 14 23 2 20 5 Attempted motor vehicle theft 9 11 8 10 25 5 10 22 All next reported incidents 13 18 9 13 35 4 5 3 100 16,884 Percent distribution by following major type of householdcrime Type of crime reported Total Type of crime as following incident reported as Number of precedingincident Household Burglary 2:;:; Percent preceding larcenytheft incidents Burglary 57 Household larceny 29 Motor vehicle theft 32 All next reported inclden~s 40 52 8 100 16,884

Table 8. Actual and percent cell contribution to chi square of pairs of household crimes in a crime-switch matrix for repeat household victims of crime: All detailed household victimizations. Julv 1.1972 to December 31 1975 I - - 1 Type of household crime reported as following incident I Tvm of -1 house6bldceime Household Household Attempted Motor Attempted reported as Burglary, Bu:Fyl precedingincident forcible forcible I~$~~'household vehicle ::;iL entry entry over $50 larceny theft theft Burglary, forcible entry Burglary, no forcible entry Attempted burglary Household larceny, $50 and over Household larceny, under $50 Attempted household larceny Motor vehicle theft Attempted motor vehicle theft - - -- I Percent of total chi square Burglary, forcible entry 15.5 2.2 Burglary, no forcible entry 15.6 2.0 Attempted burglary 10.7 Householdlarceny, $50 and over 5.3 Household larceny, under $50 2.4 1.7 9.2 Attempted household larceny 3.7 Motor vehicle theft 7.7 Attempted motor vehicle theft 13.7,

x2 = 4,826; d.f. = 49; Goodman-Kruskal Index = .22 * .008. Less than .5 Statistical modelling in the analysis of repeat victimization

STEPHEN E. F~ENBERG Department of Statistics and Department of Social Science Carnegie-Mellon University

The National Crime Survey's panel struc- from one victimization to subsequent ones, individual's "victimization propensities" ture allows for the longitudinal analysis of from the timing of the victimizations (i.e., given his current victimization state, i.e., individual victimization records. In this information on the inter-victimization time his value of Y(t). paper, further details are provided on a intervals). If the Markov-chain component (2) Ajamily of waiting time distribu- semi-Markov model for such longitudinal of the semi-Markov process is of order one, tions, 9 = { Gll(t), G12(t), ..., G~r(t) analysis proposed in Fienberg (1978). The then we only need to examine a one-step G21(t), ..., Grr(t)}, that characterize the, 'relationship between this model and some transition matrix for repeat victimization. inter-victimization intervals (i.e., the times analyses of Reiss (1980) on data for repeat Thus a version of the model of Section 2 is between victimizations) and which depend victimization are noted. Finally, Reiss's consistent with the analysis of the crime- on the future victimization state as well as .data are reanalyzed using a variety of log- switch matrix presented by Reiss (1980) in the current state of the Markov chain. linear models. The resulting models are in- the preceding paper. The link between terpreted in the context of victim vulner- Reiss's approach and the use of semi- ability or proneness. Markov models is outlined in Section 3. of waiting times, Then in Section 4 we present a reanalysis of Reiss's crime-switch matrices using multi- the Markov chain. We also note that this 1. Introduction, plicative (or loglinear) models of the sort modelling approach can be extended to The National Crime Survey (NCS) has a discussed in Bishop, Fienberg, and Holland handle more complicated processes involv- longitudinal structure that potentially (1975). This method of analysis leads to a ing m-step (for m > 2) transition prob- allows for the analysis of individual and more systematic exploration of patterns of abilities in place of M, and corresponding household victimization records over time. repeat victimization and risk than has been wsiting time structures in place of 9 or In particular, this longitudinal structure proposed to date. The results of our reanal- 9. can be used for the examination of the yses lead to a somewhat different and more A useful way to think of this semi-Markov extent of repeat victimization, and for an parsimonious interpretation of the crime process is in terms of a sequence of random explorat!on of the concept of victim prone- switch data than that presented by Reiss variables ness. Fienberg (1978) briefly outlined a (1980). ~ro~osalfor the use of a semi-Markov (XI, SI, X2, s2.\.. . ,Xn, Sn) (2) *oiel for multiple victimization over time. 2. Semi-Markov models where n itself may be a random variable. In Section 2 of this paper we give more de- for multiple victimization The Xi's take values 1,2, ...,r, and they tails for this model and point out some of form a discrete-time, first-order Markov its implications for the analysis of longi- The basic idea suggested by Fienberg chain with transition matrix M, where tudinal victimization records. This paper (1978) was the modelling of victimization presumes a knowledge of various concepts for an individual or household as a point ' k-l k and phenomena related to the NCS and process p(t) > 01, where Y(t) = j at Y(t)=XkforCi=O St

'This value of x2differs slightly from that reported by Reiss (1980). whocombines the categoriesfor rapeand attempted rape, and for purse-snatching and attempted purse-snatching, yielding an 18 18 table. Reiss reports X2 = 17,461 with 289 d.f. for this collapsed table.

Table 1.

Purse Type of crime Att. Serious Minor Att. Att. snatch, reported as Rape rape assault assault assault robbery pocket preceding incident picking

Rape 6 3 8 1 5 2 2 1 Attempted rape 1 16 6 9 21 I 6 2 Serious assault 2 11 119 75 212 37 19 18 Minor assault 4 8 83 152 244 22 20 21 Attempted assault 11 29 199 228 1,685 59 81 37 Robbery 2 4 50 30 89 27 23 Attempted Robbery 1 5 30 21 7672 27 54 12 Purse snatchlpocket picking 1 2 21 19 47 26 9 46 Attempted purse snatch 3 2 10 2 3 1 Personal larceny, $50+ 7 15 110 99 401 61 44 44 Personal larceny, under $50 16 33 238 292 1,314 126 136 144 Attempted personal larceny 1 3 25 34 115 22 24 15 Burglary, forced entry 7 17 90 59 199 42 25 27 Burglary, no forcible entry 9 11 85 107 319 45 34 41 Attempted burglary 8 46 46 166 30 15 23 Household larceny, $5Ot 4 8 62 61 238 43 24 30 Household larceny, under $50 7 18 89 154 554 7 5 49 64 Attempted household larceny 1 4 11 8 74 4 11 3 Motor vehicle theft 1 1 29 24 78 20 11 16 Attempted motor vehicle theft 1 12 16 62 8 12 5

Total number 81 197 1,316 1,437 5,892 741 606 573

*Correspond to Table 2a in Reiss (1980). w sponding 8 diagonal blocks of cells.2 The We continue, dropping pairs of cells above associated with crimes of similar type. This resulting quasi-homegeneity model again is and below the diagonal (i.e., (ij] and (j,i)), observation should lead to further investi-, an improvement over the preceding model, and fitting the model of quasi-homogeneity gations regarding the vulnerability or but still does not fit the data well(G2= 1140' to those that remain. At each stage we drop "proneness" of certain groups of house- and X2 = !238 with 309 d.f.1. the pair with the !argest standardized holds to certain types of crime. Rather than continue the analysis on Table residuals and, if there is no clear choice, we .try a few likely candidates and take that We note in conclusion that those pairs of 1, we choose at this point to switch to Table cells, singled out as departing from the 2, which uses only the 8 major crime types. pair which reduces the value of G2 the most. The resulting chi-square values and quasi-homogeneity model in the preceding Again, for this reduced table the model of analysis, differ from those singled out by quasi-symmetry fits well (G2 = 24.4 and corresponding d.f. are reported in Table 4. Model (g) in Table 4, which is singled out the techniques used by Reiss (1980), and X? = 24.0 with 21 d.f.), while the model of by this procedure, fits the data reasonably the resulting model seems much easier to homogeneity of row proportions fits interpret. poorly (G* = 8762 and X2 = 11,190 with 40 well (G2 = 62.3 and X2 = 64.7 with 29 d.f.), especially when we recall that the sym- d.f.). The quasi-homogeneity model based metry is still not being handled directly by 'on the table dropping the diagonals once 5. Suggestions for future the modelling here. A closely related model again gives a remarkable improvement in analyses of longitudinal fit, but still does not fit the data adequately with the same d.f., which actually fits the victimization records (G2 = 383.9 and X2 = 404.3 with 41 d.f.). data better and is more easily interpretable, is given in the last line of Table 4. What it The semi-Markov model proposed in Sec- The 8 groupings involved rows and columns as fol- suggests is elevated occurrences above tion 2 leads to the separate analyses of data lows: [1,21, [3.4,51,[6.71, [8.91, [10,11,121. [13,14,15]. those expected from the quasi-homogeneity on victimization switches or transitions [16.17,18], [19,20]. Since 4 diagonal blocks of 9 cells model for pairs of successive crimes involv- and of data on inter-victimization interval and 4 diagonal blocks of4 cells are dropped, there are ing personal violence (categories 1, 2, and distributions. In Sections 3 and 4 we have 361 - 4 x 9 - 4 x 9 = 309 d.f. for this model. 3) as well as those involving theft without suggested some analyses that can be use- personal contact (categories 5, 6, and 7) fully performed on the victimization switch plus elevated occurrences of the pairs of data. successive crimes involving purse-snatching and personal larceny. The reasonable fit of this model suggests that those patterns detectable in repeat victimization data are

Repeat victimization data for 20 crime categories: Reported crimes by households with two or more victimizations while in survey, July 1, 1972, to December 31, 1975

Type of crime reported as following incident

House- Att. Bur- Bur- H;;;- hold Att. MO:or Att. sonal motor Total purse larceny, larceny, Per- gla~, glary,no bur- larceny, house- snatch sonal larceny, under hold vehicle number $50+ larceny force force glary $50+ $50 larceny theft theft , Table 2. Repeat victimization data for eight major crime categories: Reported crimes by householdswith two or more victimizations while in survey July 1,1972, to December 31,1975 (adapted from Table 1) [Source: Reiss (1980) I 2nd victimization Purse in pair/ ,st victimization Rape Assault Robbery Snatchingl pocket larceny brg!ary Hy::z'd $%: Totals in pair picking theft

Rape 26 50 11 6 82 39 48 11 273 Assault 65 2,997 238 85 2,553 1,083 1,349 216 8.586 Robbery 12 279 197 36 459 197 221 47 1,448 Purse snatching. pocket picking 3 102 40 67 243 115 101 38 703 Personal larceny 75 2,628 413 229 12,137 2,658 3,689 687 22,516 Burglary 52 1,117' 191 102 2,649 3,210 1,973 301 9,595 Household larceny 42 1,251 206 117 3,757 1,962 4,646 391 12,372 Motor vehicle theft 3 221 51 24 678 301 367 269 1,914 Totals 278 8,645 1,347 660 22,558 9,565 12,394 1,960 57,407

These analyses of the first-order observed We also need to begin analyzing inter- transition matrices represent only a first, victimization interval data and to concern The author is indebted to Albert J. Reiss, Jr., and very exploratory step in the analysisof ourselves with the overall usefulness and who providedthe data analyzedinSection4and longitudinal victimization data from the goodness-of-fit of the full semi-Markov whose original analyses suggested those carried NCS. In addition to disaggregating the model. out in this paper. Thanksare also due to Dennis data in the various ways suggested in Sec- Jennings, who assisted with the computations tions 3 and 4 and repeating similar analy- Because of the peculiaritiesassociatedwith and analyses. ses, we also need to address more carefully the data from the NCS (see Fienberg 1978), many of these more elaborateanalyseswill the procedures used to order the unordered References victimizationincidents and to handleseries require new statistical methods or innova- victimizations and how they related to the tive adaptations of existing techniques. Bishop, Y. M. M., S. E. Fienberg, and P. H. Holland (1975) occurrences of other victimizations. Discrete multivariate ana!rpsis: Theory and practice. Cambridge, Mass.: M.I.T. Press. Cinlar, E. (1975) Introduction to stochastic processes. Engle- wood Cliffs, N.J.: Prentice-Hall. - Table 3. The goodnessof-fit for various loglinear models applied to repeat victimization data of Table 1 Fienberg, S. E. (1978) "Victimization and the National Crime Sur- Likelihood ratio Pearson vey: Problems of design and analysis." In K. Model df. chi-square chi-square Namboodiri (ed.), Survey sampling and meas- ~2 ~2 urement, New York: Academic Press, pp. 89-106. (Reprinted in this volume.) Homogeneity of row proportions 361 12,420 18,410 Penick, B. K., and M. E. B. Owens (eds.) Quasi-symmetric 169 174.9 167.1 (1976) Quasi-homogeneity Surveyingcrime. Washington, D.C.: National (a) dropping diagonal cells 341 2,261 2,505 Academy of Sciences. (b) plus blocks of cells for 8 major crime groupings 309 1,140 1,238 Reiss, A. J., Jr. (1980) - "Victim proneness in recent victimization by . type of crime." (In this volume.) Table 4. The goodnessof-fit for various loglinear modelsapplied to repeat victimization Data of Table 2

Likelihood ratio Pearson Model d.f. chi-square chi-square ~2 ~2 Homogeneity of row proportions .49 8,762 11,190 Quasi-symmetry 21 24.4 24.0 Quasi-homogeneity (a) dropping diagonel cells 41 383.9 404.3 (b) plus (6.7) pair 39 234.9 252.2 (c) plus (2,3) pair 37 172.4 189.7 (dl plus (3,4) pair 35 128.7 131.6 (a) plus (1.2) pair 33 103.7 105.9 (f) plus (2.7) peir 31 83.5 85.4 (9) plus (2,8) pair 29 62.3 64.7 Quasi-homogeneity dropping diagonal cells plus (121, (1,3), (2,3), (3,4), (5,6), and (5,7) pairs 29 67.4 72.1 Quasi-homogeneity dropping diagonal cells plus (121, (1,3), (231, (3,4), (5.6) and (6,7) pairs 29 51.6 53.2 Sentencing andparok

Quantitative approaches to the study of parole RICHARDPERLINE Department of Psychology University of Chicago

HOWARDWAINER Bureau of Social Science Research Washington. D. C.

The first part of this paper,uses Federal The second part of this talk deals with (1) "Just dessertsp'-"you did something parole data in an attempt to develop a parole data and their adequacy. In this sec- bad so youstay in-the badder the longer." model for the parole system as it stands and tion we shall discuss data from individual to predict recidivism by treating it as a states gathered under the auspices of the (2) Rehabilitation-"you are more likely latent trait. The second part discusses the Uniform Parole Reports project (hereafter to recidivate than he is, so you stay in adequacy of Uniform Parole Report referred to as "UPR Data''). We have re- longer." (UPR) data for states. cently had the opportunity to do an evaluation of the UPR data for LEAA, and the These two schools of thought are con- appalling results have important implica- cretized in the parole standards. The rec- Omnia quae evenlura sun:, tions for those interested in doing parole ommended bounds are a matrix in which in inrerro jaren:.' research. We shall keep federal data sepa- the rows reflect the seriousness of the offense-the least serious at the top, the THE AREA OF PAROLE RESEARCH is rife rate from state data. This does not mean that federal data are better than state data, most serious at the bottom. Seriousness with dissension and disagreement, which was determined through some sort of appears to us to be entirely justifiable. We but only that we don't know about the reliability of the federal data. scaling, although how and by whom, I would like to add to the disagreements don't know. without further obscuring the vast darkness of the topic. This paper will be broken The columns of this matrix are determined Establishing a quantitative model by "Salient Factor scores,"in which a set of into two parts. The first part deals with for de facto incarceration rules some analyses we have done on Federal I1 variables are scored zero-one. The sum parole data. In this section we will try to Parole standards are set to indicate to the of the convict's scores on these variables develop a model for the parole system as it parole board how long a particular kind of yields his salient factor score, which is sup- stands and to predict recidivism by treating convict should stay in prison. These are in posed to be related to the probability of it as a latent trait. For those who are in a the form of upper and lower bounds for recidivism (r* = 0.07). The federal guide- hurry, our results are at least as good with each cell in a two-way categorization. The lines collapse these salient factor scores this approach as with any other, but still categorization reflects two schools of 'into four categories (0,1,2 = I; 3,4,5 = 11;6, leave a great deal to be desired. thought on incarceration: 7,8 = 111; 9, 10,ll = IV). The midpoints of the recommended sentence length intervals '"Everything which is to come lies in uncertainty" are shown inTable 1 by offender categories (from preface to Raleigh's Hislory of :he World, 1614). and by five seriousness of offense categories (in months for adults).

Table 1. Offender category

1 2 3 4

Offense severity 1 8 10 12 14 category 2 10 14 18 22.5 3 11 15 19 23.5 4 14 18 22 26 5 23.5 29.5 34 39 Improvement? "" '. Having identified the de facto structure of I Row Row effects I parole policy, the road toward possible im- 1 2 3 4 medians (row median.-gr. md.) I I provement is clear, and involves two steps: (1) Improve the accuracy of the estimates of seriousness of crimes, so that a more accurate classification is possible.

Grahd median 1.23 (2) Improve the scaling of prisoner char- I 1 acteristics so that the prisoner effects more closely correspond to the likelihood of Table 3. recidivism. Let us briefly look at step (1). Shown in Figure 1 and Figure 2 are plots of seriousness effects plotted against category. It is clear that categories 1-4 for both juveniles and adults are linearly related to incarceration length, but when crossing into category -.I5 -.04 .04 .ll column medians = column effects 5 there is a major jump. It would seem that I there is room for about4 intermediate categories between the crimes which correspond The same multiplicative model (with dif- to category 4 and those in category It Table 4. 5. ferent values.for the parameters) holds for would seem that finer discriminations are juveniles as well. This model and its fit are Residual from model (in logs) possible. Of course such fine discrimina- shown in Table 6. tions are made as viewed by the increased We are then reasonably well assured that width of allowable sentences for the more the existing parole policy corresponds serious crimes. Why not make this explicit? -.OI .02 closely to a multiplicative model in which We did not do the obvious scaling experiment, but the details of how to do such a .02 .1 study are clear (Torgerson 1958). Use clas- characteristics among adults, and about sical scaling methodology with some twice as much amOngjuveniles. Thurstonian model and have expert judges Our first interest was to identify the mode1 decide which of two paired crimes is the underlying this structure. The sentence more serious. lengths were originally determined empirically as a measure of the de facto sentence Step (2) was one which we found interest- structure for the majority of offenders. We ing. Could we improve upon the results analyzed these data using traditional two- that Hoffman and his colleagues (Hoffman way table decomposition methods. That is, and Beck 1974) had obtained through their inspection showed that an additive model use of multiple regression? They regressed was not appropriate (this is easily seen by a variety of variables against the binary fitting an additive model and seeing the variable (Recidivate-yes or no). We know substantial trends in the the residuals). We very well that alternative models appear, at thus tried a multiplicative model by first least on the surface, to be more suitable for calculating logs and taking out row medians; these correspond to seriousness effects (Bishop, Fienberg, Holland 1975; Tukey 1977; Neithercutt, Moseley, Wenk 1975). We then calculated column medians of the residuals and subtracted them; these correspond to offender effects. The resulting matrix of residuals corresponds to the residuals from the model. As can be easily seen, these are all small. The effects were then transferred back to months and the total model specified.

Table 5.

Adults

Offender effects .71 .89 1.10 1.35 19.95 .2 .2 -. 1 -.8 .55 -1.2 0.0 .7 1.2 .79 Offense -. 2 .2 .I .1 1 .OO seriousness -.3 .1 .7 .3 1.29 effects -1.4 -. 2 -. 3 -1.7 2.29

Residuals (months) Residuals = Data Fit Fit = (19.95)x Offender eff. x Offense eff. test. We used a Rasch logistic model Table 6. (Rasch 1960) to fit these data (n = about 500) and looked at goodness-of-fit of the I Youth model. (We used differential slope models I Offender effects 1 as well, but the fit wasn't increased and so we stuck with the equal slope model.)

.9 .8 .8 .7 .6 Associated with each variable is its "diffi- -. 7 .2 1.2 2.6 .9 Offense culty," here interpreted to mean how easy it -.9 -.3 .3 1.4 1.2 seriousness -.3 -.4 -.4 -.5 1.2 effects is to have that variable scored I. Thus .9 .4 -1.5 -. 3 1.9 "planned living arrangement" is the "easiest" (86 percent had them) whereas Residuals (months) Fit - (17.0) x offender eff. x offense eff. "drug history" is the "hardest" (only about I 22 percent had one). Each person also had an "ability" score (perhaps "returnability" ance among Haward students is accounted is a better term). The difference between a Figure 1. for by SAT scores, but 1 imagine it isn't person's returnability and the difficulty of Adult offenders overwhelming. This same restriction of the item describes the likelihood of that ,range presumably exists in parole decision. person having that particular character- Thus we must not be over-hasty in deni- istic. To predict recidivism we calculated grating the 7 percent figure. the probability of a person having the char- Serlousness 1 75 effect 1 50 Our approach was to think of the individ- acteristic "recidivate." The r.h,, reflects the (~nmonths) 25 relationship between each "item" and the 1 00 ual's background data as a test that he takes. There were eight variables that en- total test. Note that the r.h,, associated with 75 recidivism (squared 50 tered into this test which can be considered = .57 = .32). 1 2 3 4 5 @0@@ "predictor variables" and a single criterion We can see from the results in Table 7 the Serlousness category variable "parole revoked." The eight vari- general extent of fit, and those variables ables are shown in Table 7. There is which seem to fit. Note that such variables A nothing magicai about the choice of the as "planned living arrangement" don't criterion var%ble;except that we chose it to seem to load too heavily on this trait. One a binary criterion than linear regression. be different from the other variables. We could use such schemes to make decisions Also, it didn't seem that it would be that might just as well wish to predict one of the as to the importance of various kinds of in- hard to improve on a method whose cross- other variables, so we included "parole formation. The variables chosen and their validated accuracy only accounted for 7 revoked" as one of the "items" and judged scoring were taken precisely from the percent of the variance. It should be noted how well it is described by the rest of the methodology Hoffman et al. developed. that there is a severe restriction of range "test" by looking at its r.b,, with the total We were not given free access to all data, ~roblem.in that we should give proper.. - and so had to content ourselves to these. credit to'parole boards for knowing something. hat is that they tend to keep in the Thus these preliminary results look prom- really bad characters. The ones released are ising. Upon cross validation on a neutral at the upper end of thedistribution and it is sample there was some shrinkage. Our best therefore harder to discriminate among guess as to the amount of variance ac- them. At a guess, I would think that we counted for on a neutral sample is between psychometricians don't do all that much better; 1 don't know how much of the vari-

Figure 2. Juvenile Offenders

seriousness '" ,'*" Hypothetical effects 1 00 .75 .50 12345678B' Seriousness category

Table 7.

fit Variable Difficulty Ann sq. '.his Prior conviction 1.12 .61 .76 Age at first commitment -1.36 .63 .57 Prior Incarcerations -0.07 .65 .82 Parole revoked -0.83 .74 .57 Verified employment -0.23 1.05 .41 Grade claimed 0.88 1.06 .38 Auto theft -1.18 1.07 .33 Drug history -1.57 1.36 .20 Planned living arrangement 2.20 1.73 .lo 15 and 20 percent. A bit of an improvement, decade and contain a variety of useful in- will be useful and reliable. We know for but nothing to write home about. formation. After a careful examination of sure that the reporting agencies will no these data, I decided that the most valuable longer be anonymous. A careful analysis of fit indicated that the thing 1 could do with this forum would be model could be rejected, but what does it to issue a short warning on the use of these then mean to say that there is a single un- data. Although these data have been de- Refeences derlying dimension of "likelihood of recid- clared "reliable enough" by their original Bishop, Y., P. Holland, and S. Fienberg (1975) ivism?" We tried a variety of other schemes: gatherers (Neithercutt et al. 1975), our best Discrete multivariate analysis. Cambridge, the most interesting one was using Krus- Mass.: M.I.T. Press. kal's monotone analysis, which showed guess is that they are not. A number of Hoffman, P. B., and J. L. Beck (1974) that the best monotonic transformation to "shoe-box" reliability studies were carried out in which a very small number of cases "Parole decision-making: A salient factor additivity did not fit much better than the score." Journal of Criminal Justice 2:195-206. Rasch model. We conclude from this that were recoded, and the differences between although the Rasch model doesn't fit, it their original coding and second coding Neithercutt, M. G., W. H. Moseley and were examined (n's in these were abdut E. A. Wenk (1975) does about as well as any single factor Uniform Parole Reports: A notional correc- model. 160). The following results obtained: the percent agreement between the two codings tional data system. Davis, Calif.: NCCD. Parole data-UPR for a seemingly foolproof variable like Rasch, G. (1960) "ID#" was as low as 93 percent. This was Bobabilistic models for some intelliaence and The preceding analyses were done on Fed- called 'high"-I would call it embarrassing. attainment tests. copenhagen: ~anrnarksPaed- eral parole data. There exists another data The worst variable (in terms of reliability of ogodiske Institut. set, with longitudinal records running 3 coding) was "other prior sentences" which Torgerson, W. (1958) years on very large samples. These are the averaged about 53 percent but for some Theory and methods ofscaling. New York: Uniform Parole Reports data. These data agencies was as low as 27 percent. Thus if Wiley. have been gathered by the National one were using such a variable in any pre- Tukey, J. W. (1977) Council on Crime and Delinquency.2 diction scheme accuracy of prediction Exploratory data analysis. Reading, Mass.: These data have been gathered for almost a would certainly suffer. Overall accuracy Addison-Wesley. was 80 percent which included such (rela- 2~ubstantialimprovements have been made in this program since this paper was prepared. For current tively) failsafe variables like "is he dead?" information, write to Dr. James L Galvin, NCCD, One agency got "sex" wrong 4 percent of 760 Market Wt,Suite 433, San Francisco, California the time. 94102; telephone (415)956-5651. There is great variability of accuracy across reporting agencies. Sadly, the reporting agencies are anonymous so you can't be sure how good your data are. These problems are being corrected, and we have reason to hope that in the future UPR data Linear logistic msdeis ike parole decisionmaking problem KINLEYLARNTZ School of Statistics University of Minnesota

This paper considers the use of quantitative DeGostin (1974), are given in Table 1. The petition," and "completed at least 10th aids in parole decisionmaking. Current guidelines for sentence length, also from grade.") The scale construction was based practice employs a Burgess scale which Hoffman and DeGostin (1974), are given in on the analysis of data collected on 93 1 out weights items equally and ignores theinter- Table 2. For information on the develop- of about 1500 individuals released from val (or ordinal) quality of the data. We pro- ment and recommended use of these guide- Minnesota prisons in 1970 and 1971. The pose logistic regression as an alternative lines, see Gottfredson, et al. (1974). data set was divided into a construction statistical decisionmaking guide, and illus- group of 485 cases and a validation group trate use of these techniques on data from Various states have also developed Salient of 446 cases. A number of regressions as the State of Minnesota. Also discussed are Factor Scores that apply to their respective well as Burgess scales were tried out before prison populations. The Federal set of nine the final scale was selected. Note that the the problems of selecting a few items from a items is not directly applicable because of pool of many items for construction of the final Salient Factor Score was one of the the substantial differences in state and scale. best scales on both the construction and Federal crimes. In Minnesota the Parole validation samples. Thus, in fact, all 931 Decision-Making Project, headed by Dale cases played a role in selection of the final 1. Introduction Parent, developed a Salient Factor Score nine items. for aiding in state parole decisions; see A recent trend in parole decisionmaking Parent and Mulcrone (1978). Table 3 gives In scale construction, each individual was has been the use of objective scores, to be the nine items found to be important in classified as a "success" if, in the 2-year 'calculated for each potential parolee, Minnesota. (In later implementation of the period following release, the individual was which attempt to estimate that individual's scale, three items were deleted: "juvenile not convicted of a new felony. Low scores chance of parole success. Specifically, a commitment," "had a sustained juvenile on the scale correspond to good prognosis; Federal Hearing Examiner is given a po- high scores to poor prognosis. Table 4 gives tential parolee's Salient Factor Score the group failure rates for the pooled con- which, along with the type of crime, struction and validation samples. Failure provides guidelines for sentence length. rates range from a low of 13 percent to a The Salient Factor Score is the sum of re- high of 54 percent. In Minnesota the Sali- sponses to nine items, seven of which are ent Factor Score is used, as in the Federal scored 0 or 1, and the other two are scored system, in conjunction with a measure of 0, 1, or 2. The items for the Salient Factor seriousness to aid in determining a release Score, as reported by Hoffman and date.

Table 1. Items in salient factor score

ltem A No prior convictions (adult or juvenile) = 2 One or two prior convictions = 1 Three or more prior convictions = 0 ltem B No prior incarcerations (adult or juvenile) = 2 One or two prior incarcerations = 1 Three or more prior incarcerations = 0 ltem C Age at first commitment (adult or juvenile) 18 years or older = 1 Otherwise = 0 ltem D Commitment offense did not involve auto theft = 1 Otherwise = 0 ltem E Never had parole revoked or been committed for a new offense while on parole = 1 Otherwise = 0 ltem F No history of heroin, cocaine, or barbiturate dependence = 1 Otherwise = 0 ltern G Has completed 12th grade or received GED = 1 Otherwise = 0 ltem H Verified employment (or full-time school attendance) for a total of at least 6 months during the last 2 years in the community = 1 Otherwise = 0 ltern I Release plan to live with spouse and/or children = 1 Otherwise = 0 Solomon's final model was a logit model Table 2. Guidelines for decision-making: average total time served before relese with four variables: (including jail time) -Adults _ Offender characteristics parole prognosis PIJ~~ Severity of (Salient Factor Score) log -= w + Wl(,) + WZb) offense 1 - pykl behavior Very good (3 9-9) Good (8-6) Fair (5-4) Poor (3-0) (2.1)

6-10 8-12 10-14 12-16 LOw months months months months wherepiJk1represents the true rate of failure 8-12 12-16 16-20 20-25 Low moderate for individuals in the cross-classification months months months months cell (i,j,k,l), and 12-16 16-20 20-24 24-30 Moderate months months months months 16-20 20-26 26-32 32-38 High months months months months 26-36 36-45 45-55 55-65 Very high months months months months C WW) = 0, and 2 wzclj= 0. Greatest (Greater than above-however, specific ranges are not given due k L to the limited number of cases and the extreme variations in severity possible within the category.) Table 5 gives the variables, categories, and weights for his final model. Using these r weights we can calculate the estimated fail- Table 3. Final items for Minnesota Salient Factor Score ure-rate for an individual with no priorcon- ' Label Name Category score victiork, no parole revocations, no auto - - - theft, and planning to live with spouse as Juvenile commitment YES 1 XI NO 0, No prior convictions -0.6450 Number of prior parole/probation failures 2 or more 1 No parole revocations -0.2344 x2 0.1 0 No auto theft -0.2210 Number of prior incarcerations 1 or more 1 Plan to live with spouse -0.3852 0 0 Constant x3 Had a sustained juvenile petition YES 1 NO 0 e-2,7s'' Estimated failure rate = Age at first adult conviction 19 or under 1 -+ e1.75:1 x4 2OUP . 0 Conviction previously-this offense YES ? x, N0 0 Completed at least 10th grade N0 1 X6 For additional reading on logit models, see YES 0 Cox (1970) or Fienberg (1977). This offense was burglary YES 1 "7 N0 0 The important difference between Solo- X, 3 or more felony convictions YES 1 mon's final logit scale and the nine-item NO 0 ' Federal Salient Score is the weight assigned to each item. First, the logit model Section 2 of this paper discusses a pub- contains only four items. This has the effect Table 4. Group failure rates lished reanalysis of the Federal data. Sec- of giving zero weight to the other five items. for Minnesota data base tion 3applies the same reanalysis technique In addition, for the included variables, dif- Salient Factor Failure to the Minnesota data base. In Section 4an ferent weights were attached to each. In Score -rate alternative technique, logistic regression, is contrast, the Salient Factor Score assigns 0-1 13% presented and applied to the Minnesota equal weights to each included item. Essen- 2 - 3 17% data. Section 5 gives a simple validation of tially, only the sign (positive or negative) of 4 29% the various procedures, and the concluding 5-6 42% an item's estimated effect on failure rate is 7-9 54 % section gives the implications of this re- considered important. This method of search for future studies. forming a scale, based on equal weighting This paper presents a reanalysis of the of items, is often referred to as the Burgess Minnesota data base. The objective of the 2. Solomon's ~eanalySi8 method. reanalysis is to explore logistic regression 01 the Federal data The main contribution of Solomon's study as a tool for predicting succ~ss.The Solomon (1976) reanalyzed the basic data was to offer an alternative to the Burgess data base split employed by the Minnesota set for 2497 prisoners used in construction method for this decisionmaking problem. Department of Corrections was also used of the Federal Salient Factor Score. He Previous studies had compared the Burgess here, i.e., the same 485 construction cases showed that the nine items, used withequal method to linear regression analysis, and and 446 validation cases. No new random weights, could be reduced to four items, found the Burgess technique superior- splits were tried. provided unequal weighting was allowed. mainly on the grounds of robustness. How- His final modkl showi decisively that the ever, the assumptions for linear regression Salient Factor Score collapses groups that are not usually met for this type of data. have.substantially different rates of risk. Solomon's proposal offers a statistical technique specifically tailored to the categorical nature of the data. Table 5. Weights for Solomon's final logit model dependent variable, also measured as zero- one, we can view the data in the form of a Independent 2 x 116 = 232 cell contingency table. For variables Categories w - each cell, expected frequencies can be cal- Number of prior convictions I Dl 0 -0.6450 culated based upon a particular logit : 1-2 +0.1054 3 or more +0.5396 model. The following two goodness-of-fit statistics compare the actual cell counts I D, : Prior parole revocation No Yes +0.2344 with the expected frequencies. D~: Auto theft No -0.2210 Y0s +0.2210 (Observed - Expected)2 9 (3.3) D,: Plan to live with spouse and/or children Yes -0.3852 X2 Expected =call +0.3852 No cells Constant - -1.2675 Observed * G2= 2x(~bserved)log(-).(3.4) all Table 6. Weights and goodness-of-fit statistics for Minnesota logit models cells

Model Model Model Model Model If the expected frequencies are large, it is Variable -I -I I -Ill -Iv -v reasonable to assess goodness-of-fit by - comparing the calculated statistic with the XI .68385 .66484 .78213 .82426 - xz .89731 .97447 1.0480- 1.0029- - percentage points of a chi-squared distri- x3 .23198 .26712 - - bution with the appropriate degrees of free- x4 .I3693 .71692 .74209- - - dom. However, here the expected cell fre- x5 .56074 .54484 - xs .65332 .66840 .67259 .65932 - quencies are small., In such a case, the x7 .45491 1.6642 1.7314 .54767 xs .07271 .01055 - - - Pearson statistic X- has a level near the -1 -1 x4 x7 - .SO50 .SO80 - - nominal rate, as long as the expected cell CONST. -2.2979 -2.7047 -2.5823 -2.1067 -.91196 frequencies are not too small (Larntz 1978, xa 132.31 120.09 126.57 141.27 196.31 Koehler and Qrntz 1980). The likelihood G~ 151.14 137.73 141.21 155.38 225.50 df 107 106 109 11 1 115 ratio statistic G- tends to be inflated if there are a large number of moderate (1 to 4) expected frequencies. 3. Logit models for Minnesota Table 6 gives the estimated heights for sev- data set eral logit models. Model I is the logit model Our situation involves large numbers of with all eight 'variables included, i.e.. moderate and small expected frequencies: Following Solomon's example, logit mod- p(x1, x2, . . . ,xg) does not depend upon Thus by looking at the goodness-of-fit sta- . els were fitted to the 485 cases of the Min- (XI,. . . ,XX).Model IV excludes four of the tistics listed in Table 6, we can see that nesota construction group. The variables variables which seem to have little impor- Model V certainly does not provide an ade- used were those reported in Table 3 with the tance in the construction sample. Models 11 quate fit, Models 11 and 111 are clearly exception of "Number of Prior Incarcera- and I11 are different in that an interaction describing the data well, and Models I and tions''-it was omitted because of a coding term was added to the basic Models I and IV are borderline cases. It is intefesting to problem in our data base. Because of the IV, respectively. This is accomplished by note that for the Burgess scale G' = 157.12 zero-one nature of each of the X,'s, the logit merely adding a cross-product term to the (1 14 df). Degrees of freedom for the vari- model may alternatively be written as: model, e.g., for Model 111, ous models were calculated by considering the data as a 2 x 116 = 232 cell contingency p(x1, - . 7 ~8) log table. Thus, Model V, which tests indel 1 - p(x1, .. . ,xa) pendence in this table, has (2 - 1) x (1 16 - 1) = 115 degrees of freedom. Other degrees of wherep(x1, x2, . .. ,xg) represents the true freedom were calculated by subtracting rate of failure (felony conviction within 2 one degree of freedom for each free param- years of release) for individuals with scores To assess how well these models describe eter added to the corresponding model. the 485 cases, goodness-of-fit statistics (XI, . . . , XX)on variables (XI, . . . , X8). The term ~4x7was the only one of the 28 There is a one-to-one correspondence be- were calculated. For the eight independent variables there are 28 = 256 possible com- possible interaction terms close to statisti- tween logit models written as in (3.1) and cal significance at a standard level. To those written as (2.1). The estimated logits binations; however, only 116 patterns actually appeared in the data. Adding the judge the statistical significance of the will be exactly the same irrespective of interaction, we look at differences in the which form of the model is selected. Essen- G'-statistics for models fit with and with- tially, (3.1) is a regression analogue of the out the interaction. In our case, analysis of variance model (2.1). It is interesting to note that the Burgess scale (i.e., Gif,,.,,,, i,i= GI?- G: = 13.41 Salient Factor Score) says that ~(XI,x2, (1 df) .. . ,xg) is merely a function of XI + x2 + . . . or alternatively xs. if,,.,^,^,,^ = GA - CAI = 14.17. (2 df) values of previously dichotomized varia- Table 9 gives the estimated regression Table 7. Weights for the burglary X 4. bles are now used. Also, sex has been added coefficients based on the construction ( a first conviction interaction -1 as a variable and juvenile record and edu- sample for five logistic regression models. Age at 1st cation have been deleted. Many more items Attempts at adding interactions did not adult conviction -Burglary were collected by the Parole Decision- prove fruitful in this case. The -2 logf value No Yes Making Project, but data were missing on gives twice the log of the likelihood ratio 20 up 0.00 1.73 many variables for a number of cases. assuming each of the 482 observations is 19 down 0.74 0.67 (Three individuals were excluded altogether Bernoulli with failure rate p, as in (4.1) (see because of missing data. Although it was Efron 1978). Again differences between not done in this analysis, it should be noted likelihood ratio statistics can be used in In both cases, the interaction is significant that, assuming the omitted data were comparing models; no overall goodness- at 0.05 level, even after adjusting for the "missing at random," the missing values of-fit test is possible here, however. From fact that all 28 possible two-factor inter- can be estimated via the EM algorithm difference comparisons, Model 111 and actipns were examined. Table 7 gives the. (Dempster et al. 1977). Thus, all informa- Model 1V emerge as candidates for the best weights for the interaction cells. Note that tion in the full data set could be utilized in a model. Model I11 needs only two variables "burglary" is not an important factor for complete analysis.) for an assessment of an individual's risk, "age at first adult conviction less than 20," i.e., number of parole/probation failures but has a large effect for those "20 or over The logistic regression model describes the risk for individual i as and age at first conviction. Thus, an indi- at first conviction." The risk of parole is vidual with one failure, first convicted at greater for burglars first convicted at an age 20, would have estimated logit older age. log P = Po + PIZI+ prZ,r 1 -p, A log -%I -P = 0.2803 1 + 0.22982(1) 4. Logistic regression models This model has exactly the same form as The logit model with X's taking on 0 - 1 the logit model (3. I), but here we are allow- values can be extended to permit continuing the independent variables (Z's) to take and estimated risk of a new felony convic- ous X variables or even a mixture of con- on any value, while in(3.1) the independent tion of fi = 0.263. Someone first convicted tinuous and discrete variables (Nerlove and variables (X's) were constrained to be zero at age 18 with 7 prior failures would have Press 1973, Fienberg 1977, Cox 1970). or one. Recent comparisons of logistic reestimated risk of 0.623. Table 8 lists the variables considered in this gression with linear regression have indi- analysis. Note that a number of variables cated that for certain uses, such as classifi- 5. A simple validation listed in Table 8 overlap with those in Table cation, logistic regression may possess cer- of procedures 3. However, where possible, the actual tain advantages (Press and Wilson 1978). A criticism that is often made of statistical model fitting is that although the final Table 8. Variables for logistic regressions model fits the construction sample quite well, it does not do nearly so well when -Label Description applied to new data. To avoid such criti- 21 Number of parole/probation cism of their work, the Parole Decision- failures Making Project divided the data into con- 22 Number of incarcerations struction and validation groups. The final 23 Age at first adult conviction Salient Factor Score (see below, Figure 8 Zq Number of felony convictions and Table 11) did well on both groups. We 1 = Male now examine how well the logit and logistic Z5 Sex 2 = Female regression models did when applied to the Z6 Age at release validation sample. 27 1 if offense was burglary, 0 otherwise

Table 9. Regression coefficients for lpgikic regressions

Model Model Model Model Model Variable -I -II -Ill -Iv -v 21 .21955 .21645 .22982 .22061 - (2.81) (2.76) (3.17) (3.03) zz -.I1502 -.16966 - - - (-.go) (-1.30) 23 -.09425 -.lo352 -.00708 -.07426 - (-2.97) (-3.20) (-3.49) (-3.36) 24 .09990 .09991 - - - (.96) (.95) 2s -1.3631 -1.1829 - - - (-1.79) (-1.55) 26 .00810 .01809 - - - (.41) (.88) 27 - .6 1 760 - .6122 - (2.53) (2.59) CONST. 0.4901 0.3586 0.28031 0.07633 -.91339 -2 log f 525.7 519.4 531.6 525.1 577.3 df 475 474 479 478 481 Note: Approximate t-statistics are in parentheses. Table 10. Results from applying Logit Model I in selecting 230 parolees 1 Table 11. Maximum D and average D Felon -Total LOWrisk 43 230 Model High risk 82 - - 216 Logit I Total 125 446 Logit II Logit I II NOTE: PNF = gi = .583 pF = = -344 Logit IV a Burgess Logistic 1 Logistic I I Logistic I I I Logistic IV

There are several possible techniques for viduals. Table 10 summarizes logit Model Model 1. The same is true for logit Models checking the degree of validation for a pre- 1's performance in "parolingn 230 individ- I1 (Figure 2) and 111 (Figure 3). Thus, as dictive scale. One standard method is to uals. Of the 230 lowest risk scores 187 be- expected, there is no gain in adding non- separate the validation sample into several longed to nonfelons. To measure how well significant variables to the logit model. groups according to predicted risk and see the predictive scale separates the felon and Similarly, although the interaction term is whether the proportions of felons and non- nonfelon groups calculate the difference of statistically significant, when we compare felons differ in the groups. Ideally, the low the proportion of nonfelons assigned to the Figure 1 with Figure 2 and Figure 3 with risk group would contain predominantly low risk group minus the proportion of Figure 4, the validation curves indicate that nonfelons, while the high risk group would felons assigned to the low riskgroup. In the inclusion of the interaction term is helpful contain predominantly felons. The statisti- example, for some values of pr~l(0.2,0.4) while not cal signifancance of the degree of separa- helpful for others (p1o.1= 0.4,0.6). The Bur- tion of felons and nonfelons could be gess scale curve (Figure 5) is comparable to evaluated using a chi-squared test. It the logit models and perhaps even a little should be noted that this technique and higher, but it must be kept in mind that its depends upon the nuhber of groups nine items were selected on the basis of the formed as well as the actual groupings. D = 0.583 - 0.344 = 0.239. same construction and validation samples Different group formation could yield Note the proportion "paroled" in this being used here, i.e., the full data. different degrees of validation when sample was fixed at applied to the samc data. The logistic models (Figures 6-9) are clearly better when fewer variables are For comparisons in this.paper we have included, i.e., logistic Models 111 and IV. used the following method which has the Logistic Model 111 (the two-variable advantages of (1) not depending upon any Now consider calculating D for each possi- equation) is particularly strong for p101= arbitrary grouping of the validation ble "paroling strategy," i.e., for paroling 0.6, yielding the highest D value for any sample, (2) allowing direct comparisons 1,2,3, .. . ,445 individuals, or equivalently validation. However, it does not do as well between different predictive scales, whether forplol = 1/446,2/446,3/446,. .. ,4451446. as other models for p101near 0 or 1. This or not the scales actually calculate an esti- Figure 1 gives a graph of D vs.plo~for logit may be unimportant sincep101near 0 or 1 mated risk (the method requires only an Modell. The higher D is for a given value imply strategies of paroling few or nearly ordering of the risk), and (3) providing a of pltn, the better the predictive scale in all eligible prisoners. natural graphical output illustrating the separating nonfelons from felons. In Figure 1, the peak value of D is 0.2480. An Although not improving greatly over the degree of validation. Burgess scale, the better logit and logistic "ideal scale" would have a peak value of D To illustrate the technique let us consider of 1.000. models do perform well on the validation' logit Model I. For each individual in the sample. The two-variable logistic model validation sample, calculate the estimated Figures 1-9 present graphs of Dvs.pror for did particularly well, especially considering risk using the logit model weights given in 4 logit models, the patterns for all figures that these two variables were selected from Table 6. Order the individuals from low to are the same, although the peak values of D a pool of only seven items. The nine items high by this calculated risk. A good predic- occur at different values of pr~.Table 11 in the Burgess scale were selected from a tive scale would have a large proportion of gives the peak values of D and also the much larger pool, and since the same items the nonfelons in the "parole" group, while average values of D (this corresponds to were used in the logit models, the logit having a large proportion of the felons in the area under the curve) for the nine models' performances on the validation the "nonparole" group. Now suppose, for scales. Logistic Model I11 hss the largest D sample should not be surprising. In both example, that we were to "parole"230 indi- value, while the Corrections Department logit and logistic cases, restricting the scale has the largest mean. model to include only "significant" variables improved the validation performance. We now examine the individual figures more closely. First, logit Model I (Figure 1) and logit Model IV (Figure 4) are virtually identical, except for the noise caused by the four extra variables included in logit 6. Discussion Figure 1. One aspect of the logit and logistic models Figure 5. Validation - Logit I that has been ignored in the compari- Validation - Burgess Scale D 0.3- sons is the actual estimated risk value. Does this estimated risk have a frequency 0 2. interpretation? To answer this question, we conducted a sampling experiment. Using 0.1. the 9,'s of the validation sample, Bernoulli random variables were generated to randomly assign an individual as a felon or 0.0 - nonfelon with probability j, or 1 -j,,respectively.1 Figures 10, 11, and 12 give - 0 1 - I 1 ' I 3 I ' plots of D vs. plol for the Monte Carlo 00 0.2 04 06 08 10 runs on logit Model 1, logit Model IV, and P TOT logistic Model 111. If the j,'s are good I quantitative estimates of risk, the Monte Carlo curves should look the same as the original validation plots. The general Figure 2. shapes in all three cases are fine, but the Validation - Logit II values of Dm,, as given in Table 12 are shifted for both logit models. This is undoubtedly due to the greater degree of selection for the items comprising the logit scales-and thus also for the Burgess scale items. Note that the logistic Model 111 curve and Dm,, are quite similar to those seen in Figure 8. Thus, when a great deal of selection occurs as in the Burgess scale constructio~,the usual construction-validation splitting is not enough. Double -01- . , 1 , , , , , , cross-validation (Mosteller and Tukey 00 02 04 06 08 10 1977) consisting of using separate samples PTOT for (1) choosing items, (2) estimating coefficients, and (3) testing the scale likely would have reduced the overall effects of selection. Figure 3. The practical implications of thedata anal- Validation - Logit Ill Figure 7. ysis results reported here are (I) to question Validation - Logistic II the efficiency of the construction-validation D 03 splitting as currently practiced and (2) to offer a technique, logistic regression, whose assumption requirements are more 02- in keeping with the data as collected. Re- lated to the first point, we recommend use 0 1- of double cross-validation when data are plentiful, and consideration of jackknifing 00 techniques (Mosteller and Tukey 1977) -0.1 , , . , , , . , , when more must be squeezed from limited 00 02 04 06 08 10 -01- . , , , , , , , , data. For the logistic regression versus 00 02 04 06 08 10 PTOT " Burgess scale question, only experience with both will decide which, if either, is TOT

3 better. We recommend their joint consideration in any future projects, and certainly Figure 4. feel that logistic regression will prove to be Validation - Logit lV a better competitor than linear regression has been in the past. 'Computations were performed using FORTRAN programs on a CDC 6400 computer. Bernoulli random variables were generated from uniform random numbers by classifying the uniforms into one of two categories using the boundaries (O,lj,,I). The uniform random numbers were produced by a multiplicative con- gruential generator using modulus 2" and multiplier 5".

-01 , , , , , , , , a 00 02 04 06 08 10 PTOT i References Figure 8. Cox, D. R. (1970) Figure 10. Validation - Logistic Ill The analysis of binary data. London: Monte Carlo - Logit I Methuen. 0 03 Dempster, A. P., N. M. Laird, and D. B. Rubin (1977) 0 2- "Maximum likelihood from incomplete data via the EM algorithm." Journal of the Royal 0 1 - Staristical Society 39: 1-38. Efron, B. (1978) "Regression and ANOVA with zero-one data: 0.0 - Measures of residual variation." Journal of the American Statistical Associarion 73: 113-121.

-01 n , n , 8 , 7 , . Fienberg, S. E. (1977) 00 0.2 04 0.6 0.8 1.0 00 02 04 06 08 10 The analysis of cross-classfled categorical PTOT data. Cambridge, Mass.: M.I.T. Press. PTOT 4 Gottfredson, D. M., C. A. Cosgrove, L. T. Wilkins, J. Wallenstein, and C. Rauh (1978) Figure 9. Figure 11. Validation - Logistic IV Classijicarion for parole decision policy. Washington, D.C.: U.S. Government Printing Monte Carlo - Logit IV 003 Off ice. D 04j Gottfredson, D. M., L. T. Wilkins, P. B. Hoffman, and S. M. Singer (1974) 0.3 1 The utilization of experience in parole decision-making Summary report. Washing- 02- ton, D.C.: U.S. Government Printing Office. 01: Hoffman, P. B., and L. K. De Gostin (1974) "Parole decision-making: Structuring discre- 0.0 - tion." Federal Probation (December). -0 1 , , . , . , . , , Koehler, K. J., and K. Larntz (1980) -0.1 , , . , . , . , , 00 02 04 06 08 10 "An empirical investigation of goodness-of-fit 0 0 0.2 0.4 0.6 0.8 1.0 PTOT statistics for sparse multinomials." Journal of TOT the American Statistical Association 75:336- 344.

& Acknowledgments Larntz, K. (1978) "Small-sample comparisons of exact levels for Figure 12. This research project grew out of material on the chi-squared goodness+f-fit statistics." Journal Monte Carlo - Logistic Ill Federal Parole Project presented at the Work- of the American Statistical Association shop on Criminal Justice Statistics, held in 73:253-263. Washington, D.C., July 1975. The workshop was sponsored by the Social Science Research Mosteller, F., and J. W. Tukey (1977) Council Center for Coordination of Research on Data analysis and regression. Reading, Mass.: Social Indicators and the Law Enforcement Addison-Wesley. Assistance Administration. The sponsors also Nerlove, M., and S. J. Press (1973) provided additional financial assistance for this "Univariate and multivariate log-linear and project. 1 am grateful to Sanford Weisberg, logistic models." Technical Report R-1306-ECA/ Ronald Christensen, and Sharon Yang for col- NIH, Rand Corporation, Santa Monica, Calif. laborative efforts in the early stages of this research. In addition, Stephen E. Fienberg pro- Parent, C. G., and T. G. Mulcrone (1978) -0.1, 9 , , a , . , . vided valuable detailed comments on both the "The development and operation of parole - research and its presentation. The University of decisionmaking guidelines in Minnesota." In 0.0 02 04 06 0.8 10 Minnesota Computer Center provided a grant D. M. Gottfredson, C. A. Cosgrove, L. T. Wil- PTOT for computing costs. Special thanksare owed to kins, J. Wallenstein, and C. Rauh, Class~pcation Dale Parent, Minnesota Department of Correc- for parole decision policy, Washington, D.C.: tions, who provided the raw data and was par- U.S. Government Printing Office. ticularly helpful in clarifying the coding pro- Press, S. J. and S. Wilson (1978) Table 12. Maximum D for Monte Carlo cedures. "Choosing between logistic regression and samples from three predictive scales discriminant analysis." Journal of the American Staristical Association 73:699-705. Monte Carlo Validation Model Solomon, H. (1976) - -Dmax "Parole outcome: A multidimensional con- Logit I .3885 .2480 tingency table analysis." Journal of Research in Logit IV .4072 .2729 Crime and Delinquency (July) 107-126. Logistic 1 11 .3075 .2844 The effects of plea bargaining on the disposition of person and property crimes: A research note DAVIDW. BRITT Criminal Justice Program Nova University

KINLEYIARNTZ Department of Applied Statistics University of Minnesota

Many of the studies which have examined common experience-let alone the alterna- the various points in the process and if the the impact of offender and offense charac- tive paradigms for viewing the operation of outcomes at one stage had no independent teristics on sentence severity have been mis- the criminal justice system. For example, a bearing on the operation of these factors at specified because they have ignored (or recent analysis of the construction of judi- a later stage. Unfortunately, such assump- tried to hold constant) events such as pre- cia1 decisions has observed that for a tions appear to be invalid. Consequently, trial plea bargaining which took placeat an sample of judges having flexible attitudes many of the studies which have examined earlier stage in the process but which have a toward law and order, blacks and those the impact of offender and offense charac- critical bearing on the outcome of sentenc- with larger numbers of current charges teristics on sentence severity have been ing decisions. Our approach to the analysis were more likely to receive short sentences misspecified because they have ignored (or of these phenomena is similar to the than whites and those with smaller num- tried to hold constant) events, such as pre- exploratory study by Burke and Turk bers of current charges (Hagen 1975:379). trial plea bargaining, which took place at (1975)in that we are considering a sample Such results are at odds both with an earlier stage in the process but which of all post-arrest dispositions. Our study conceptions of the criminal justice system have a critical bearing on the outcome of differs from theirs in that we attempt to which stress a bias against the dis- sentencing decisions. include the impact of plea bargaining on advantaged andconceptions whichempha- subsequent sentencing decisions. size offense characteristics. ~t is apparent A thorough review of the entire that models of post-arrest disposition have justice process as it isaffected by character- omitted variables which are crucial to an istics of the offender, the offense, and THE TESTING OF WHAT PASSES for understanding of the dynamics of the dis- in the structureat different points conventional wisdom often leads to position process, and it is these specifics- is beyond the of this paper. Suffice it conclusions which are apparently para- tion errors which have resulted in some of that the works On sentence doxical. Such is the case for recent the paradoxical results observed in recent length tHagen 1975; Burke and Turk 1975; attempts to structure and analyze the bias studies. Tiffany et al. 1975, for example) have been in criminal justice systems. As Burke and unable to come up with plausible interpre- Turk (1975:313) have Faced with the problem of disentangling tations for what appear to be bizarre conventional wisdom of criminology hasthe the serial processes which un&rlie the patterns in the operation of offender held that the socially disadvantaged are processing of ''criminals" within the characteristics (race, sex, age, prior convic- more likely than the advantaged to be criminal justice System, n~uch current tions), characteristics of the offense (sever-' engaged by the criminal justice system, to research has sought to simplify the task by ity of offense, number of current charges) be prosecuted, tried, convicted, and to examining discrete aspects of this Process and system characteristics (type of counsel, suffer more severe upon convic- as a first step in the ultimate integration of bench vs. jury trial). What is missing from tion. Yet the findings of empirical analyses these separate analyses. Such an attack on all of these studies is some notion of the have been both ambiguous and occasion- the problem would be reasonable if the operation of pre-trial plea bargaining on ally at odds with the received wisdom of Same set of factors affected dispositions at the outcome of the sentencing decision. Some of thesestudies (Hagen 1975; Tiffany et al. 1975) have sought to minimize the Table 1. Results of testing the hypothesis that the variable is independent of incarceration influence of pre-trial factors by limiting the given seriousness and type of crime. sample of cases processed by the system to those above a minimum level of seriousness Variable df G~ x2 T~ - - - - P-value(xz) which have reached trial. Since fewer than Sex 6 13.31 9.23 11.66 .25> p>.10 10 percent of the initial cases reach trial in Race 8 8.65 7.40 7.56 p>.25 most jurisdictions (Blumberg 1967; Heis- Plea 15 30.58 24.48 27.01 .lo> p>.05 mann 1975), and since cases which reach Charge 10 25.03 20.38 21.81 .05> p>.025 trial are biased in that they have rejected

No. initial charges , 7 2.61 2.70 2.66 p>.25 the plea-bargaining alternative (Tiffany et No. convicted charges 6 6.96 4.77 5.82 p>.25 al. 1975), this would seem to be an unac- NO. previous arrests 9 32.23 28.31 29.31 p<.005 ceptable way of controlling the influence of Felony convictions 10 41.08 35.43 41.88 p<.005 pre-trial factors. Employment status 8 8.22 7.69 7.28 p> .25 Our approach to the analysis of these phe- Resisting arrest 8 12.44 10.99 10.80 .25> p>.IO nomena is similar to the exploratory study Weapon usage 7 10.84 8.32 9.03 p>.25 by Burke and Turk (1975) in that we are Table 2. 138 Criminal sentences classified by type of crime, seriousness of charge plea, change in charge, previous record and incarceration Good Fair Poor Previous record previous record previous record Type of crime, seriousness and 1 change Plea No jail Jail No jail Jail No jail Jail

Person, Guilty 1 3 2 5 no change Nolo contendere 2 2 0 of charge Not guilty 0 0 0 Person, Guilty charge Nolo contendere changed Not guilty Property, Guilty low seriousness, Nolo contendere No change of charge Not guilty

Property, Guilty low seriousness, Nolo contendere charge changed Not guilty

Property, Guilty moderate seriousness, Nolo contendere no change of charge Not guilty Property, Guilty moderate seriousness, Nolo contendere charge changed Not guilty Propeny, Guilty serious crime, Nolo contendere no change of charge Not guilty

Property, Guilty serious crime, Nolo contendere charge changed Not guilty Property. Guilty very serious crime, Nolo contendere no change of charge Not guilty

Property, Guilty 0 2 very serious crime, Nolo contendere 1 charge changed Not guilty 0 considering a sample of all post-arrest dis- charge the same as the initial charge or was Analysis and results positions. Our study differs from theirs in there some reduction in charge? With the number of variables that we that we are attempting to include the (6) Number of initial charges. impact of plea bargaining on subsequent (7) Number of convicted charges. deemed important to consider and the rela- sentencing decisions. tively small sample size, we opted to make (8) Number of previous arrests: Low (0, an initial pass through the data toselect the 1, 2) or high (3 or more). most important factors. Our review of the Data (9) Number of adult.felony convictions: literature showed that seriousness of Low (0) or high (1 or more). charge and type of crime were both impor- Two hundred sample cases were selected (10) Employment status: Was the indi- from the Denver, Colorado, courts under tant factors in explaining the number of vidual employed or unemployed at the time individuals jailed. To decide which of the the auspices of State Courts Sentencing of the offense? Project. Sixty-two of these cases were other variables to include, each variable (I 1) Type of crime: (a) Against prop- was tested to see if the hypothesis of condi- eliminated from this sample: 5 because of erty, (b) against person but at most slight inadequate data and 57 because of their tional (given seriousness and type of crime) injury, or (c) against person with serious independence between the variables and being so-called "victimless" crimes. The injury. remaining 138 cases were analyzed to incarceration was plausible. The chi-' (12) Resisting arrest: Did the individual square statistics and p-values for these tests determine the major factors used by judges resist arrest? in reaching the decision of whether or not are given in Table 1. The four variables (13) Weapon usage: Did the crime yielding the lowest p-values were selected to incarcerate an individual convicted of a involve use of a weapon? criminal offense. Thirteen variables were for further analysis. initially considered as possible factors: The dependent variable was incarceration, In the initial data analysis it became clear (1) Sex. i.e., whether or not the individual was sent that sentences for crimes against property (2) Race: White, other. to jail by the judge. had a different structure compared to sen- (3) Plea: Guilty, nolo contendere, or not tences for crimes against persons. To deal guilty. with this structural dissimilarity, the anal- (4) Seriousness of charge: Low, moder- ysis was split into two parts: crimes against ate, serious,or very serious. property and crimes against persons. Table (5) Change in charge: 1s the convicted 2 gives the data as used in the final analysis. Of those who either chose or were not I Table 3. Results of logit mowfittings for crimes against property allowed to enter into plea bargaining (at 1 Variables included in modal df G2 X2 TZ I least with respect to an exchange of charge reduction for a plea of guilty), those who Previous record, plea, charge seriousness 30 23.00 21.49 17.79 Previous record, plea, charge 33 29.79 22.97 23.91 pleaded guilty had the highest chance of Previous record, plea, seriousness 31 23.14 21.56 18.09 going to jail (78 percent). Those who were Previous record, charge, seriousness 32 23.02 21.57 17.75 able to plead nolo contendere had only a39 Plea, charge, seriousness 32 57.59 49.33 46.21 Previous record, plea 34 31.11 24.21 25.35 percent chance of going to jail. Pleading Previous record, charge 35 29.94 23.17 24.03 guilty was associated with a 50 percent Previous record, seriousness 33 23.20 21.56 18.11 Plea, charge 35 67.1 1 57.24 54.73 chance of going to jail. These figures are Plea, seriousness 33 57.59 49.28 46.25 dramatically altered by the apparent Charge, seriousness 34 63.00 51.19 52.23 exchange of plea for charge reduction. For Previous record 36 31.12 24.22 25.35 Plea 36 68.07 57.14 55.97 those who plead guilty with a reduced Charge 37 70.74 55.28 59.60 charge, the chances of being incarcerated Seriousness 35 63.61 51.73 53.06 None 38 73.40 56.59 62.89 drop from 78 percent to 48 percent. A similar drop in incarceration chances is noted *x2 = C (Obs - EX^)' /Exp for those pleading nolo contendere: from T' = C (JUE+JVDS+ 1- J4 txp + n2 39 percent to 14 percent.' G2 = 2 C Obs loge (Obs/Exp) When cell expectations are small, as they are in our examples, we examine all three chi- Discussion and conclusions square statistics to evaluate the model fit (Larntz, 1975). Dispositions of crimes against property

-- appear to be related to variation in the seri- Table 4. Results of logit model fitting for crimes against persons ousness of the crime and the offender's pre- I vious record in a relatively straightforward I Variables included In model df G2 X2 T2 1 way. As the crime becomes more serious Previous record, charge, plea 7 13.82 and the offender's previous record becomes Previous record and charge 9 19.90 poorer, the chances of the individual's Previous record, and plea , 8 18.41 Charge and plea 9 13.96 being incarcerated increase. Interestingly, Previous record only 10 24.54 as long as the previous record of the indi- Charge only 11 20.84 vidual has not involved more than two Plea only 10 18.47 None 12 25.13 arrests and no adult felonv convictions. Record x plea + charge 3 12.15 there seems to be a bias against sending thd Record x charge + plea 5 10.17 Charge x plea + record 6 12.77 individual to iail-no matter how serious Charge x plea only 8 12.90 the present droperty crime is. Once the -- - individual has been arrested more than *See footnote for Table 3 I twice previously, or has had a previous felony conviction, his chances of being Note tnat crlmes against ~ersonswere not and previous record-with the latter play- incarcerated for the present offense esca- classified by seriousness: this was because ing a more important role-provides an late rapidly. But this appears to be the only almost all of these crimes were classified as adequate fit to the data. Table 5 gives the bias in the property-crime dispositions, for serious offenses. Also number of previous estimated percentage incarcerated based neither characteristics of the offender (sex, arrests and felony convictions were com- on these two variables. Those with poor race, employment status) nor his pleas or bined into a new variable, previous record. records who have been convicted of a very charge reductions appear to directly affect A "poor" previous record meant the indi- serious crime have roughly a 95 percent the decisionmaking process. vidual had one or more adult felony chance of being incarcerated. The impact These results for property crimes overlap convictions. A "fair" record resulted from of previous record on incarceration' substantially with those of Burkeand Turk at least three previous arrests but no felony chances may be better appreciated by (1975:326), who noted that the effect of convictions. An individual had a "good" examining two other cells in Table 5. Even previous incarceration on disposition record if there were at most two recorded if the seriousness of the present crime was severity remained important even after arrests with no adult felony convictions. quite low, if the prior record of the con- controlling for the nature of the offense.* victed defendant was poor, he/she had They argued that such a pattern increased The procedure for analyzing the data in almost a 60 percent chance of going to jail. Table 2 was to find the logit variant (Dyke the tenability of an explanation based on But if the prior record of thedefendant was ex-convicts' "vulnerability to the biases of and Patterson 1952, Goodman 1970) of the good, he/she had only negligible chance of loglinear model (Bishop, Fienberg, and legal control agents" and initiated an going to jail no matter how serious the argument based on the presumed greater Holland 1975; Haberman 1974) that pro- present crime. vided the closest fit to the data. "propensity of ex-convicts for relatively For crimes against persons, where almost serious crimes." In other words, even Table 3 presents the results for the models all crimes were categorized as being though there may be an association fit the property crime sentences*and serious, the logit model also includes just between prior record and offense seri- Table 4 similarly presents the results for the two variables: change and Table person crime sentences. BY examining the the estimated incarceration rates for 'Weshould note here that the length of sentence has not significance of the overall goodness-of-fit crimes. been taken into consideration. Hence, while these data chi-sauares as well as the differences be- suggest a rational strategy of pledgingnolocontendere tween' the chi-square statistics when one or of guilty if the plea bargainingoptionis unavailable, a different pattern might have emerged had we been model is a submodel of the other, infer- able to take length of sentence into account. ences may be drawn as to the major factors ?Burkeand Turk (1975) found that agealso directly af- influencing the incarceration decision. fected the dispositional process, although the impact of age was complica~edand not amenable to For crimes against property, the logit nonspecu~ative.plausible explanation. model including only seriousness of'charge - ual's contact with the criminal justice Table 5. Estimated percentage incarcerated for crimes against property system has become frequent and/or Seriousness of charge felonious. Low Moderate Serious Very serious To argue that offender characteristics (sex, race, previous record) do not have a direct Good O (12) (13) O (5) O (1) impact on incarceration rates for crimes Prior i record Fair 21 (9) 27 (3) 48 (6) 82 (5) against persons does not mean that they are Poor not involved in the dispositional process. 58 (7) 66 (15) 83 (5) 96 (3) It's quite possible that a defendant's prior Note: Estimated percentages are calculated from logit model: record, in conjunction with other indica- P.. tors of his recidivism chances and the solid- log L=p+ai+p. 1-p.. 1 ness of the state's case against him, set 11 boundaries for the kinds of plea bargaining where P.. is the probability of incarceration. #I which can be struck. In our future investigations we will be examining these possibilities. ousness, each makes a contribution to the charges were reduced in exchange for both reconstruction of the observed distribution nolo contendere and guilty pleas, and as of incarceration rates. expected, engaging in the plea-bargaining Our results speak to the possibility of a process decreased one's chances of being This paper is an outgrowth of a workshop on threshold of vulnerability to bias on the sent to jail for both kinds of pleas. Those criminal justice systems sponsored by the Social who came out of these negotiations having Science Research Council, July-August 1975. part of legal control agents. Some degree of The authors would like to thank Leslie T. "criminality credit" appears to be granted to plead guilty had a greater chance of going to jail than those who were able to Wilkins for providing the data upon which this to individuals who have had "good" prior enter nolo contendere pleas. Where plea paper is based. records, so that individuals appear to be bargaining did not take place, those who buffered from jail sentences until their contact with the machinery of the state has pleaded guilty had the highest chance of References been relatively frequent or serious. If these being imprisoned, those who pleaded nolo Bishop, Y. M. M., S. E. Fienberg, and contendere had the least chance, and those results have any validity, one implication is P. W. Holland (1975) that socially disadvantaged individuals are who entered not guilty pleas were in the Discrete multivariate analysis. Cambridge, not being directly discriminated against at middle. Mass.: M.I.T. Press. this point in the dispositional process. It is It must be remembered that at least for our Black, Donald, and A. J. Reiss, Jr. (1975) quite possible, of course, that variation in sample of 200 cases, almost all of the crimes "Police control ofjuveniles." American Socio- both the seriousness of crimes and against persons were considered to be logical Review 35:63-77. poorness of records could be traced to both relatively serious. Consequently, serious- Blumberg, Abraham S. (1967) race and occupational status (Burke and ness could not play much of a role in the Criminaljustice.Chicago: Quadrangle Books. Turk 1975). It is also possible that more dispositional process. Offender character- Burke, Peter J., and Austin T. Turk (1975) complicated interactions of race and age istics, on the other hand, varied but did not "Factors affecting postarrest dispositions: A might affect the propensity to commit affect the chances of being jailed once the model for analysis." Social Problems22:313-32. serious offenses (Black and Reiss 1970) charge-reduction and plea process was Dyke, G. V., and H. D. Patterson (1952) and/or the poorness of prior record. But in taken into consideration. "Analysis of factorial arrangements when the our admittedly small sample (as well as in In sum, the dispositional dynamics for data are proportions." Biometries 9:l-12. that of Burke and Turk), blacks do not Goodman, L. A. (1970) appear to be diyferentially vulnerable to person and property crimes appear to be different, with plea bargaining having a "The multivariate analysis of qualitativedata: being labelled as a "repeat offender," or Interactions among multiple classifications." "career criminal." Were this the case, we much greater impact on the former than the latter. In neither case does the disposi- Journal of the American Statistical Association should have at least observed an interac- 65:226-56. tional process appear to be biased once tion of race and prior record in the dispo- Haberman, S. J. (1974) sition process. plea bargaining is incorporated into the analysis. What bias there is operates with The analysis of frequency data. Chicago: A somewhat different picture emerges respect to the defendant's previous rec- University of Chicago Press. regarding the structuring of disposition~of ord-and even here there is evidently a Hagan, John (1975) crimes against persons. To recapitulate, buffering process at work until the individ- "Law, order and sentencing: A study of attitude in action." Sociometry 38:374-84. Heumann, Milton (1975) Table 6. Estimates of the incarceration rates for crimes against persons "A note on plea bargaining and case No change Charge ' pressure." Law & Socie!I. Review 9:5 15-28. in charge reduced Larntz, K. (1975) Guilty 78 48 "Small sample comparisons of exact levelsfor chi-square goodness-of-fit statistics." Technical Plea Nolo contendere 39 14 Report No. 242. University of Minnesota School of Statistics. Not guilty 50 Tiffany, Lawrence P., Yakov Avichai, and Note: Estimated percentages are calculated from logit model: Geoffrey W. Peters (1975) "A statistical analysis of sentencing in federal P.. log JL = p + ai+ pi courts: Defendants convicted after trial, 1967- l-pii 1968." Journal of Legal Studies 4:369-90. P.. Where 11 is the probability of incarceration. *No information in data - The deterrent efsects of punishment

Alternative estimates of the impact of certainty and severity of punishment on levels of homicide in American states

COLINLOFTIN Department qj' Sociology and Center ,for Research on Social Organization University qj' Michigan

Jack Gibbs' paper, "Crime, Punishment, studies of the effects of law enforcement and Deterrence," has been widely cited as activity on crime rates have gone consider- where C is the crime rate; E represents eti- an important part of an accumulating body ably beyond these studies in terms of theo- ological factors, that is, "extralegal condi- of evidence which consistently demon- retical specifications and estimation proce- tions which are conducive to crime strates a negative relationship between dures. Nevertheless the estimates of . . ." (Gibbs 1968517); and R represents repres- crime rates and the certainty and severity of deterrence effects from these early studies sive factors, that is "aspects of reaction to punishment. In this paper we providea new continue to be cited in current discussions set of estimates of the effects of the crime which operate as deterrents ..." as part of an accumulating body of evi- (Gibbs 1968:517). However, his actual certainty and severity of punishment on dence supporting the existence of general investigation of homicide rates fails to homicide rates. The estimates are derived deterrence effects. In this paper we provide include any etiological factors. He esti- using a structural model of violent crime a new set of estimates using a model which mates the relationship between the two which was developed independently of was specified independently of Gibbs' repressive factors and homicide rates while Gibbs' research. When the effects of the research, and which includes a much larger ignoring etiological factors. The two other variables in the model are taken into number of etiological (or environmental) repressive factors specified in the study are: account, the estimated effects of the variables than do any of the other deter- (1) Estimated severity of sentence re- punishment variables are very small. The rence studies. When the effects of these ceived and served for criminal homicide, data are consistent with a model in which etiological variables have been removed which he measured with the median certainty and severity of punishment have from Gibbs' measures of the certainty and months served on a homicide sentence by no effects on homicide rates. severity of punishment, the estimated ef- persons in a state prison on December 31, fects of the punishment variables are very 1960 (Gibbs 1968:520-521). Background small and provide reason to question (2) Estimated certainty of imprison- whether the data provide any support for In 1968 Jack Gibbs presented the results of ment for criminal homicide, which he real effects of certainty and severity of pun- an influential study of the effects of cer- measured as the number of persons ishment on homicide rates. tainty and severity of punishment on admitted to state prisons in 1960ona hom- murder rates in American states. While he Before presenting the new estimates it will icide sentence, divided by the average was appropriately cautious in interpreting be useful to briefly review the results of the number of criminal homicides reported by his estimates as doing no more than chal- other studies of Gibbs' data. Gibbs' origi- the police in 1959 and 1960. The dependent lenging the "common assertion that no nal paper specifies the following general variable is the average annual criminal evidence exists of a relationship between model for crime rates: homicide rate per 100,000 population for legal reactions to crime and the crime rate" 1959 to 1961.1 (Gibbs 1968529-530), subsequent discussions have interpreted his study as provid- Gibbs'statistical analysis is done with con- ing support for deterrence effects (see, for tingency tables by dividing each distribu- example, Tullock 1974:107, Tittle and tion at the median. From this analysis, he, Logan 1973, Antunes and Hunt 1973, concludes that both certainty and severity Tittle 1975). Gray and Martin (1969) and of punishment are negatively related to Bean and Cushing (1971) reanalyzed state homicide rates. Gibbs' data, with slight modifications in 'New Jersey's values for certainty and severity were statistical procedures and theoretical mod- estimated from the average of New York and el, and concluded that the data are consist- Connecticut. ent with a model which includes direct negative effects of certainty and severity of punishment on murder rates. More recent New estimates of certainty Table 1. Selected results of previous analyses of Gibbs' Data and severity of punishment on homicide rates Gray and Martin (1969) Sociological theories of homicide, though not incompatible with utilitarian formula- tions which characterize most deterrence studies, suggest that homicide is an extreme manifestation of the "culture of violence" which is generated by high levels of personal frustration and extreme socioeconomic deprivation (Wolfgang 1958, Bean and Cushing (1971) Wolfgang and Ferracuti 1967, -~rearl~

A 1932, Coser 1967). Some crimes of violence (1) H =_Po -.289 P(I) -.374 T + u may be incidental to participation in other p/sp = (-2.1 9) (-2.84) forms of illegal activity, but most homi- R' = .218 cides are known to occur among friends,

A family, and acquaintances and are not by- (2) H =!,_ -.I96 P(I)-2.05 T + .717 R + u products of other crimes (Wolfgang 1958, @/Sflo = (-2.39) (-2.33) (8.31) 1968). They are likely to be acts of passion 13' = 596 that grow out of high levels of frustration

A and subcultural reinforcement of interper- (3) ~=p,_ -.I79 ~(1)-.I67 T+ .77 B + u sonal violence. B/spO = (-22.38) (-2.16) (9.87) A previous study by Loftin and Hill, R2 = .751 drawing on studies done by Gastil (1971) and Hackney (1969), specified a model Notes: The regression coefficients are for varialrles in standard form, that is, they are which is derived from sociocultural expla- beta weights. H = homicide rate, P(I) = probability of imprisonment (Gibbs' measure of certainty of punishment), T = median time served (Gibbs' measure nations of homicide rates. The key element of severity), R = region (South is coded I, nonsouth is coded 0). and B = percent in this model is a six-variable index of population black. Gray and Martin do not provide estimates of standard errors or t values. Their coefficient for P(I)in equation appears to be an error. referred to as an index of "structural Our own analysis is consistent with Bean and Cushing's results. poverty" which redundantly measures the -proportion of a state's population at the extremely low end of the socioeconomic Gray and art in (1969) extended Gibbs' substitute "percent of the population that is class distribution. The components of that study by investigating several different black" for "region" in their model and find index are: forms of the relationships between certain that the proportion of the variance (1) Infant Mortality Rate (Grove and "uniquely accounted for by the etiological ty, severity, and homicide in an ordinary Hetzel 1968: Table 41). factors" increased, and thus that the data least squares regression analysis. Table 1 (2) Percent of persons 25 years old and are consistent with the hypothesis that the summarizes the major elements of their over with less than years of school etiological significance of region is due to analysis which led them to conclude that (Renetzky and Greene 1970:38). the data are consistent with a model in percent black (Bean and Cushing 1971: (3) Percent of families with income which certainty and severity of punishment 288). under $1,000 (U.S. Bureau of the Census Operate in a nonadditive way reduce the Other studies which have estimated deter- 1964a:Table 137). homicide rate (Gray and 19P9: rence effects for homicide, but which use (4) Percent of the population illiterate 394-395). Note that their invest1gat10n9'Ike data different from Gibbs, include Tittle (Greene and Renetzky 1970:38). Gibbs'3 derived estimates of certainty and (1969), Chiricos and Waldo (1970), Antunes (5) Armed Forces Mental Test Failures severity effects under the assump- and Hunt (1973), Logan (1972, 1975), (August 1958-December 1965) (American that can be knored'Bailey, Martin, and Gray (1974). All of Education 1966:9). That etiological factors were these studies, except Logan (1975), esti- (6) Percent of children living with one included in the estimated model. mate significant negative deterrence ef- parent (U.S. Bureau of the Census Bean and Cushing (1971) recognized thk fects, but none of them includes more than 1964b368). importance of specifying a model which one variable to represent etiologicalfactors These variables account for 87 percent of allows for etiological as well as repressive and most of them do not include any etio- the variance in 1959-1961 mean homicide factors, but the models that they investi- logical variables. The major exception to rates in Loftin and Hill's analysis.' this generalization is Ehrlich (1973, 1975), gated included only one etiological vari- Hill,s homicide rate is based on the U.S. able at a time. They found that when a who reports several investigations of the Vital Statistics rather than on the uniform Crime variable representing region (South versus effects of law enforcement variables On Report and thus is slightly different from Gibbs' Nonsouth) was included in a linear specifi- homicide rates, all of which use models homicide rate. See Loftin and Hi11 (1974:718 and 720) cation (see Table 1 above), the estimates of which take into account more than one eti- fP,',"??~~",$Si$~~~ betweenthe two the certainty and severity effects were ological factor, and allow for simultaneous reduced, but that they were still large relationships between crime rates and law enough to be "consistent with the deter- enforcement variables. His results are rence hypothesis" (Bean and Cushing consistent with most other studies in that 1971:289). Also they conclude that the his deterrence variables are negatively and linear specification which included region significantly associated with homicide was as adequate as alternative nonlinear rates.2 'pecifications of the they -cent evaluations of Ehrlich's findings raise serious questions about the sensitivity of his results to minor changes in the model (see, for example, Bowers and Pierce 1975). probability of arrest and prosecution de- Table 2. Correlations between Gibbs' measures of the homicide rate, the certainty of clines as the number of crimes increases punishment, the severity of punishment and the six components of the does not seem appropriate for the situation Loftin-Hill Index I I in the United States in about 1960. Con- Homicide Certainty of Severity of temporary Northern Ireiand and Lebanon rate punishment punishment probably fit the model, but they represent Infant mortality rate (IMR) -.222 -.332 very extreme cases far outside of the range Percent of persons with less than 5 of variation represented in Gibbs' data. years of education (LOWED) It is also unlikely that judges, juries, and Percent of population illiterate (ILLIT) parole boards adjust sentences on the basis Armed forces mental test failures of the homicide rates. It is more plausible (TESTFAIL) that these decisions are made primarily on Percent of families with less than the basis of judgments of the seriousness of $1,000 income (LOWINC) the crime and the probability that offend- Percent of children living with one ers are committed to violent crime as a way parent (ONEPARENT) of life, along with the particular circumstances of the crime (see, for example, Wilkins 1974:244-245). Thus the degree of Table 2 shows the correlations between the. (12) Number of hospital beds per criminal intent and extenuating circum- components of the index and Gibbs'three 100,000 population (U.S. Bureau of the stances as judged by juries and parole variables (homicide rate. certaintv-. of Dun- Census 196280). boards are probably the key factors, not ishment, and severity of punishment). Note To derive our estimate of the effects of the general level of homicide. that the components are all positively cor- Gibbs' repressive factors we simply use related with the homicide rate and neg- Certainly general public sentiments and Gibbs' homicide rate as the dependent vari- atively correlated with the. certainty and public opinion will have an impact on pun- able and add his measures of the certainty severity of punishment. This suggests a ishment levels, but again public opinion is and severity of punishment as independent model, which Gibbs acknowledges (1968: probably responsive primarily to social variables, along with those used in the pre- 528) but does not investigate, in which and cultural variables rather than to the vious study (Loftin and Hill 1974). It sociocultural variables, such as those homicide rate. should be noted that while there is an measured in the Loftin-Hill index (erio- element of arbitrariness in the selection of The hypothesis that homicide rates influ- logical factors in Gibbs' terminology), the sociocultural variables to be included in ence certainty and severity of punishment operate to increase homicide rates in some the homicide model, the model that we use remains an open question which should be states and simultaneously to reduce the cer- in this analysis was developed independently examined carefully in future research. Our tainty and severity of punishment. Little is of research on deterrence, and thus no argument is that, for our present purposes, known about the determinants of variables selection of variables which maximize or it is just as reasonable to derive estimates such as Gibbs'certainty and severity, but it minimize the effects of the repressive assuming no simultaneous relationships is plausible that they are reduced when a factors was possible. 'between homicide rates and repressive fac- significant proportion of the population is -. --- tors as it is to derive simultaneous estimates extremely poor and uneducated, both be- Our use of ordinary least squares regres- under the extremely restrictive assump- cause of the direct effects of the sociocul- sion analysis to estimate the parameters of tions that would be necessary for such an tural factors and because of common the model implies that the homicide rate is analysis. Without pursuing a detailed cri- causes. This suggests that estimates of not simultaneously determined with the tique of simultaneous estimations that deterrence effects, to the extent that they sanction variables. While this may not have been made in deterrence studies, it have not taken social and cultural variables generally be the case it is plausible that, at should be noted that many of-the variables into account, may have overestimated the least in the case of homicide and for the that have been treated as instrumental vari-. size of these effects. range of variation represented by Ameri- ables and thus excluded from crime func- can-states in about (960, repressive vari- tions and included in punishment functions The complete specification of the homicide ables are unresponsive to homicide rates. model that Loftin and Hill use and which seem very arbitrary and inconsistent with Homicide is a rare crime with a very high existing theory. For example, it is not at all we will use in the present analysis includes clearance rate. In 1959 the clearance rate six other variables: clear why such variables as region, percent- for murder and nonnegligent manslaughter age of the population that is nonwhite, age, (7) Dye's Gini Coefficient of income for all geographic divisions of the United inequality for American states (Dye 1967). and government expenditures should be States, according to the Uniform Crime excluded from crime functions, yet this has (8) Region (a binary variable coded 1 Reports, was 92.7 with a standard devia- for former Confederate states, 0 otherwise). been the practice in existing studies that tion of only 3.1 across the nine Uniform have made simultaneous estimates.5 (9) Percent of population nonwhite Crime Reports' geographic divisions.4 (U.S. Bureau of the Census 1964a:Table Large increases in the amount of. violent When one adds to these difficulties the fact 56). crime might reduce the effectiveness of that we are deriving our estimates with a (10) Percent of the population age 20 to police investigations and strain other re- relatively small number of observations (N 34 (US. Bureau of the Census 1964b:23). sources of the criminal justice system, but = 48) and that simultaneous estimation (I I) Percent of the population living in the analogy with a riot situation where the procedures such as two-staged least rural territory (US. Bureau of the Census 1964a:Table 21). "he data are based on 2094 cities with a toal popula- sSee Nagin (1975) for a critical discussion. tion of 77,695,412 (Uniform Crime Reports 1959: Table 13, p. 83). The comparable figures for 1960 and 1961 are 92.3 and 93.1 for the clearance rate; thestand- ard deviations are 5.9 and 4.1. squares do not provide substantial im- I provements over direct ordinary least 1 Table 3. Ordinary least squares estimates of models which include only certainty and square estimates unless sample size is large 1 severity of punishment I (Namboodiri et al. 1975517). there seems A. Linear model H = Po + P1 P(l) + P2 T + u to be no strong reason for expecting that simultaneous estimates will be superior to p^ pis; direct estimates. Certainty -.07036 -2.19053 Severity -.062 -2.83778 Table 3 presents our estimate for two mod- Constant -14.93599 els which contain only Gibbs' repressive 3 = .20144 factors. In both the linear and the multiplicative forms the estimates of the effects of certainty and severity of punishment are B. Multiplicative model H = fl0P(I)" TP2 e" negative and greater than twice their standard errors.-he d-statistic in Table 3 provides a means of comparing the goodness In Certainty of fit of the two models in terms of the 1n Severity residual sums of squares.' The multiplic- Constant- ative form clearly fits better than the linear R2 = .36509 form; the residual sum of squares for the transformed linear model is almost twice as large as the multiplicative model, and the C. Comparison on linear and multiplicative models d-statistic is significant at well beyond the d = 13.35339 0.01 level. All of this is consistent with previous analyses of the data and is presented here as a basis of comparison with the estimate derived from the more complete Table 4. Ordinary least squares estimates of models which include certainty and severity forms of the model. of punishment along with components of the Loftin-Hill Index Estimates from linear and multiplicative A. Linear model H =Po + P1 P(1) + f12T + Pg IMR +. . .p8 ONEPARENT + u forms of a model which includes the six components of the index used by Loftin p^ -cs; and Hill along with Gibbs' repressive fac- Certainty -.01906 -1.112 Severity 7.01340 -1.085 tors are presented in Table 4. In the linear IMR .31587 3.384 form of the model the adjusted coefficient ' LOWED .84948 2.790 ILLIT -2.34584 -2.812 of determination8 increases from 0.20 to LOWINC -.I8781 -1.380 0.83 when the index variables are added to TESTFAIL -.00557 w.095 the model; in the multiplicative form the ONEPARENT .49 164 2.153 increase is from 0.37 to 0.78. More impor- (Constant)- -6.84304 tant, however, for present purposes is the R2 = .83248 reduction in the magnitude of the estimates Z el *2 = 6.01917 of the punishment effects in both forms of 8. Multiplicative model H = P~P(I)~~TP 2 1 P3.~ ~ . . ONEPARENT~~~U the model. In the linear specification the estimated certainty effect falls from -0.070 p^ ;st to -0.019 and severity falls from -0.063 to Ln Certainty -.25591 -1.360 -0.013. In both cases the estimated regres- Ln Severity -.53973 -2.725 sion coefficients are considerably less than Ln IMR 1.39258 2.078 Ln LOWED 1.46564 1.932 6The multiplicative model is estimated by expressing Ln ILLIT -1.34457 -2.31 1 Ln LOWINC -. 16483 -.677 each variable in terms of its natual logarithm. In this Ln TESTFAI L .05066 .I90 form the multiplicative model can be expressed as Ln ONEPARENT 1.37484 2.921 InH = In& + PIInP(1) + /32 InT+ u.Subsequent multi- (Constant) -5.021 70 plicative models are estimated in the same way. - 'To compute d the homicide rate was multiplied by a R2 = .78210 constant, C, which is defined as C e2*2 = 5.64538 C. Comparison of linear and multiplicative models d = 1.53868 Then both models were estimated using the transformed homicide rate. The residual sums of squares 1 are used to derive d as follows: \ twice their standard errors. In the multi- severity effect, we have examined the good- = 21 In- Sei+'I plicative form the estimated effect of cer- ness of fit for the two forms in some detail. \'ef2 tainty falls from -0.852 to -0.256 and the The d-statistic indicates that although the The error sum of squares for the linear model is desig- estimated effect of severity from -1.269 to multiplicative form has a smaller residual nated Sef' and Sefyor the multiplicative model. See sum of squares (5.645 as opposed to 6.019 Rao and Miller (1971:107-1 I I) for a discussion of the -0.540; only the severity estimate is more procedure. than twice its standard error. Since the two for the linear specification), the difference The adjusted coefficient is defined as forms of the model lead to different con- is not significant at the 0.05 level. More- clusions about the importance of the over, a plot of the residuals against the expected normal order statistics shows that there is one extremely deviant value for the where N is the total observations and k is the number multiplicative specification (the case is of parameters estimated, including the constant term. Rhode Island) and there is a noticeable deviation from a linear relationship near the lower end of the plot. Since there is no Table 5. Ordinary least squares estimates of models which include certainty and severity compelling theoretical reason for selecting of punishment and all of the Etiological variables the multiplicative specification and since A. LinearModel H=@o+PIP(I)+P2T+P31MR+ ...flI4GINI+~ there is evidence that the linear model fits the data at least as well as if not better than p^ pjs; the logarithmic model, we are inclined to - Certainty -.02276 -1.556 select the linear form as the better specifica- Severity .00397 .349 tion. Howevcr, as the next segment of our IMR ,18016 1.789 LOWED .34358 1.151 analysis will demonstrate, the choice ILLIT -1.60651 -1.921 between the linear and logarithmic specifi- LOWINC -.05938 -.319 cations becomes less important in assessing TESTFAIL .03874 .631 ONEPARENT .30235 1.495 the importance of the punishment vari- NONWHITE .03865 .694 ables when the other variables in the homi- RURAL -.01734 -.568 AGE .60985 2.561 cide model are introduced. HOSPBEDS -.00203 -1.81 1 REGION -1.85923 -2.182 In the analysis described in Table 5 we add GIN1 ,01676 .960 the remaining six variables in the homicide (Constant) -14.93599 model. With the exception of the estima- - tion of the certainty effect in the linear Fi2 = .89166 specification, which remains essentially the Eel = 3.30905 same, the estimated effects of the punish- B. Multiplicative Model H = POP(I)'IT~~IMR~~...GIN1 '14eu ment variables are reduced still further, and in no case are the estimates of punish- p^ ;IS; ment effects greater than twice their Ln Certainty -.I8257 -1.126 standard errors. Moreover, in the linear Ln Severity -.00721 p.032 Ln IMR .73758 1.206 specification the estimate of the effect of Ln LOWED -.06035 -.077 severity of punishment has changed its sign Ln lLLlT ,48048 -. 798 Ln LOWINC -.05027 -.I34 from negative to positive. Ln TESTFAI L ,17835 .787 Ln ONEPARENT 1.12196 2.757 Since both forms of the model lead to the Ln NONWHITE .31237 3.532 same general conclusions about the signif- Ln RURAL .I7588 .810 Ln AGE 2.31 579 2.179 icance of the punishment variables, the Ln HOSPBEDS p.38872 -1.404 selection between the linear and the multi- REGION -.03707 -.I95 Ln GlNl 1.20806 .492 plicative forms is less important than it (Constant) -15.37168 appeared to be in the earlier specification - (Table 4) where the form of the model R~=.86442 made a difference in the significance of the Xe2 *2 = 2.98574 severity estimate. The multiplicative form C. Comparison of Linear and Multiplicative Models seems to fit a little better than the linear d = 2.46752 form but the d-statistic (2.467) isconsistent with the conclusion that they were drawn Note: REG1ON was coded arbitrarily as a binary variable so it was not expressed as a from the same population. logarithm in the multiplicative form of the model. It remained in its original form. It should also be noted that the reduction of the punishment effects to an insignificant size does not depend onenteringall 12 Table 6. Ordinary least squares estimates of multiplicative model which includes the certainty and severity of punishment, the components of the Loftin-Hill Index, of the etiological factors. We have already and percent of population nonwhite shown that in the linear specification the estimated repressive effects are less than p^ $sp^ ___) twice their standard errors after the six Ln Certainty -.I3560 .857 components of the index are introduced. In Ln Severity -.I8916 1.035 Ln IMR 1.32200 2.381 a step-wise analysis of the multiplicative Ln LOWED .04173 .055 specification, percent nonwhite entered on Ln ILLIT -.54782 1.063 the first step after the punishment variables Ln LOWINC .07524 .361 Ln TESTFAIL .09962 .453 and the six components of the.index had Ln ONEPARENT 1.24587 3.187 been entered. At that point the estimated Ln NONWHITE .33250 4.344 severity effect is less than twice its standard -(Constant) -5.20431 error and remains there until all the vari- R~ = .85067 ables in the model have entered (see Table 6). The 12 eriological variables in the model the multiplicative specification three meet also generally have small estimated effects; this criterion (percent of children living only two estimates are greater than twice with one parent, percent of population liv- their standard error in thehear specifics- ing in rural territory, and percent age 20 to tion (percent age 20 to 34, and region); for 34). However, this is to be expected given the fact that the 12 e~iologicalvariables,to a very large degree, reflect a single socioeconomic dimension and thus represent redundant indexes which divide up the socioeconomic variance among themselves References Table 7. Coefficients of determination (R~)for regression of each independent variable American Education (1966) on the set of other independent variables 2: no. 9. Washington: U.S. Office of Variable taken Coefficient of determination Education. as dependent R2 Antunes, George E., and A. Lee Hunt (1973) IMR .85667 "The impact of certainty and severity of pun- LOWED .98837 ishment on levels of crime in American states: ILLIT .98011 LOWINC .94671 An extended analysis." Journalof Criminal Law TESTFAI L .95816 and Criminology 64:486493. ONEPARENT .89702 NONWHITE .9 1490 Bean, Frank, and R. Cushing (1971) RURAL .79563 "Criminal homicide, punishment, and deter- AGE .60534 rence: Methodological and substantive recon- HOSPBEDS .49285 REGION .79129 siderations." Social Science Quarterly 52: GIN1 .88510 277-289. CERTAINTY .34090 SEVERITY .48702 Bowers, William J., and Glenn L. Pierce (1975) "Deterrence, brutalization, or nonsense: A critique of Isaac Ehrlich's research on capital punishment." Unpublished manuscript. resulting in small estimates of independent rejection or acceptance of the deterrence effects. The etiological factors are included doctrine." (Gibbs 1975:l) We do not Brearly, H. C. (1932) to purge the punishment variables of their attempt to discuss these problems here. Homicide in the United States. Chapel Hill: dependence on etiological factors so that Excellent discussions are available else- University of North Carolina Press. their independent effects could be more where (Gibbs 1975, Nagin 1975, Greenberg Chiricos, Theodore G., and Gordon P. Waldo clearly evaluated; thus the size of individ- 1975). Our objective has simply been to (1970) ual eriological effects is not important for demonstrate that the application of reason- "Punishment and crime: An examination of present purposes. able statistical estimation procedures to a some empirical evidence." Social Problems 18:200-217. model that adequately controls for socio- The pattern of high multicollinearity cultural variables can provide evidence Coser, Lewis A. (1967) among the 12 eliological factors can be that is quite different from that provided by "Violence and social structure." In Continu- seen in Table 7 where the coefficient of previous analyses of Gibbs' data. ities in the study of social conflict (Lewis Coser, determination has been calculated from the ed.), New York: Free Press, pp. 55-71. regression of each independent variable on Dye, Thomas R. (1969) the set of other (k-1) independent variables. A cknow~ledgments "Income inequality and American state poli- Note that while the 12 eriologicalvariables The original work on this paper began in the tics." American Political Science Review are very highly intercorrelated with each Working Group on Deterrence Research at the 63: 157-162. other (the average R2 is 0.84), the repressive Workshop in Criminal Justice Statistics which Ehrlich, Isaac (1973) factors are not highly correlated with each consisted of David Britt, Kinley Larntz, Colin "Participation in illegitimate activities: A other (r2= 0.00052) or with the other inde- Loftin, Dan Nagin, and David Seidman. At var- theoretical and empirical investigation." Journal pendent variables (R2 = 0.341 for certainty ious points other members of the workshop of Political Economy 8 1:52 1-565. made important contributions to my thinking. and 0.487 for severity). This indicates that Ehrlich, Isaac (1975) the relatively large standard errors of the The original calculations for the research were done in Washington during the workshop, but "The deterrent effects of capital punishment: estimates of the repressive variables are not all calculations have been repeated with the orig- A question of life and death." American a result of multicollinearity and provides inal Loftin-Hill data rather fhan the data that Economic Review 65:397417. support for the inference that the punish- were hastily collected during the workshop. I Gastil, Raymond D. (1971) ment variables do not have independent spent two days visiting with Kinley Larntz and "Homicide and a regional culture of violence." effects on the homicide rate. Stephen Fienberg at the Department of Applied American Sociological Review 36:4 12-427. Statistics of the University of Minnesota. That Gibbs, Jack (1968) Conclusions experience had a major influence on the paper as . well as on my general education. Michael "Crime, punishment and deterrence." South- Our purpose in this paper has been to show Timberlake and Robert Parker, students in the western Social Science Quarterly 48515-530. that when the effects of sociocultural fac- Department of Sociology at Brown University, Gibbs, Jack (1975) tors are removed from Gibbs' measures of assisted with some of the data analysis presented Crime, punishment, and deterrence. New certainty and severity of punishment, the in the paper. 1am responsible for thedraft of the York: Elsevier. report and any errors that it contains. estimates of their independent effects on Greenberg, David F. (1975) homicide rates are reduced to the point that "Theft, rationality and the methodology of they might reasonably be considered to be deterrence research." Paper presented to the nonexistent. Such a demonstration is very Annual Meetings of the American Sociological important because previous, widely cited Association, August 1975. analyses of the same data have concluded Greene, Jon S.,and Alvin Renetzky (eds.) (1970) that they provide evidence for independent Standard education almanac. Los Angeles: deterrent effects. One should not conclude, Academic Media. however, that the data provide very strong Grove, Robert D., and Alice M. Hetzel(1968) evidence for either position. The analysis Vital statistics rates in the U.S. 1940-1960. must remain inconclusive because of seri- U.S. Department of Health, Education, and ous theoretical and methodological limita- Welfare. Washington, D.C.: U.S. Government tions on the research design. Gibbs himself, Printing Office. after a recent, thorough review of deter- Hackney, Sheldon (1969) rence studies, concluded that ". .. horren- "Southern violence." American Historical dous problems preclude a categorical Review 74:906-925. Henry, Andrew F., and James F. Short (1954) Tittle, Charles R. (1969) U.S. Bureau of the Census (1964a) Suicide and homicide: Some economic, socio- "Crime rates and legal sanctions." Social U.S. Census ofpopularion: 1960. Vol. I, part logical, and ps~~chologicalaspecrsof aggression. Problems 16:409-423. I. Washington, D.C.: U.S. Government Printing New York: Free Press. Tittle, Charles R. (1964) Office. Loftin, Colin, and Robert 3. Hi11 (1974) "Certainty of arrest and crime rates: A further U.S. Bureau of the Census (1964b) "Regional subculture and homicide: An test of the deterrence hypothesis." Social Forces Statistical abstract of the United States. examination of the Gastil-Hackney thesis." 52:455-462. Washington, D.C.: U.S. Government Printing American Sociological Review 39:714-724. Tittle, Charles R. (1975) Office. Logan, Charles H. (1970) "Deterrence or labeling?" Social Forces Wilkins, Leslie T. (1974) "On punishment and crime (Chiricos and 53:399-410. "Current aspects of penology: Directions for Waldo, 1970): Some methodological commen- Tittle, Charles R., and Charles Logan (1973) corrections." Proceedings of the American tary." Social Problems 19:280-284. "Sanctions and deviance: Evidence and Philosophical Societ.r' 1 18:235-247. Logan, Charles H. (1972) remaining questions." Lonsand Society Review Wolfgang, Marvin (1958) "General deterrence effects of imprisonment." 7:371-393. Patterns in cariminal homicide. Philadelphia: Social Forces 5 154-73. Tullock, Gordon (1969) University of Pennsylvania Press. Logan, Charles H. (1975) "Does punishment deter crime?" The Public Wolfgang, Marvin (1968) "Arrest rates and deterrence." Social Science Interesr 36: 103- 11 1. "Homicide." Inrernational Enc:,.clopedia of Quarterly 56:376-389. U.S. Department of Justice (1959) the Social Sciences. New York: Macmillan. . Nagin, D. (1975) Uniform Crime Reports 1959. Washington, Wolfgang, Marvin, and Franco Ferracuti (1967) "An investigation into the association be- D.C.: U.S. Government Printing Office. The subculture of violence: Towturd an tween crime and sanctions." Unpublished Ph.D. U.S. Bureau of the Census (1962) integrated theory in crin~inclogy. London: Tavistock Publications. dissertation, Carnegie-Mellon University. Sratisrical abstracr of the United States. Namboodiri, N. K., L. F. Carter, and H. M. Washington, D.C.: U.S. Government Printing Blalock, Jr. (1975) Office. Applied multivariate analysis and experimental designs. New York: McGraw-Hill. Orsagh, Thomas (1973) "Crime, sanctions, and scientific explanation." Journal of Criminal Law and Criminol- ogy 64354-361. Phillips, Llad, and Harold L. Votey, Jr. (1972) "An economic analysis of the deterrent effect of law enforcement on criminal activity." Journal of Criminal Law,, Criminologj~,and Police Science 63:330-342. Rao, Potluri, and Robert LeRoy Miller (1971) Applied econometrics. Belmont, Calif.: Wads- worth. Recent econometric modelling of crime and punishment: Support for the deterrence hypothesis?

STEPHENS. BRIER Department of Statistics University of Iowa

STEPHENE. FIENBERG Department of Statistics and Deparment of Social Science Carnegie-Mellon University

In this paper we review some recent The punishment of criminal offenders has The problem of absolute deterrence relates to the attempts to develop econometric models played an important role in both the eco- question, does this particular criminal sanction for assessing the deterrent effect of punish- nomic and sociological approaches to the deter? The problem of marginal deterrence re- ment on crime, as well as analyses carried control of crime. Although retribution was lates to such questions as, would a more severe out to validate these models. The formula- penalty attached to this criminal prohibition long considered to be a primary rationale more effectively deter? In the capital punishment tion of the basic econometric model con- for punishment, this view has given way, at debate the issue is not that of absolute deter- sidered here is due to Becker (1968), and least partially, to the position that punish- rence-whether the death penalty is a deterrent. the detailed specification of the model, ment of offenders will lead to a subsequent It is that of marginal deterrence-whether it is a along with much of the empirical work re- reduction in or prevention of crime. The more effective deterrent than the alternative viewed, has been carried out by Isaac possible mechanisms for the prevention of sanction of long imprisonment.1 Ehrlich. We find serious flaws with the crime through punishment, other than ret- Most people can accept the notion of the Becker-Ehrlich model, with the data used ribution, are several: absolute deterrence effect of many forms of in its empirical implementation, and with (1) Incapacitation. By removing an of- punishment. For example, the removal of Ehrlich's conclusions regarding evidence to fender from society for some period of all sanctions for a crime such as robbery, support the deterrent effect of punishment time, we can prevent that offender from most would agree, would lead to an in- on crime. Indeed, we can find no reliable repeating his offense or committing other crease in the rate at which robberies are empirical support in the existing economics ones while he is not in contact with society. committed; others might argue that the literature either for or against the deter- (2) Education. By administering pun- reason for the increase is not the removal or rence hypothesis. ishment for antisocial acts (such as'crimes), threat of punishment but rather the re- government and its agencies achieve a moval of the educational and moral value Introduction moral and educational effect on individ- the punishment provided for society as a uals in general. Society thus instructs that The threat to person and property from whole. The issue which is explored in this these crimes are counter to its norms, and paper and which has been the subject of crime is a central problem of social concern by doing so educates individuals and in- in the United States today. But crime is not recent concern is that of marginal deter- fluences their behavior. rence, i.e., we are interested in the potential a new problem. "Crime in the streets" and (3) Rehabilitation. Through the use of "the need for law-and-order" have been effects of shifts in the level of sanctions on education, correctional "treatment," or subsequent criminal behavior. slogans used by politicians at least since the vocational training during imprisonment, early 1960's to exploit popular fears of society attempts to "change" offenders so Measuring the effects of these different crime, and the study of crime as a social that they will not commit crimes in the mechanisms through which punishment phenomenon has played a prominent role future. might prevent crime is a far more difficult in American sociology throughout the (4) Deterrence. By enforcing punish- task than it may at first seem. As we just twentieth century. With the surge in re- ment on an offender, society warns the noted, it is often difficult to separate the ported crime in the 1960's, considerable offender, and the community at large, and educational and general deterrent compo- public attention was focused on the control thus inhibits the offender or others in the nents of the effects of punishment. Simi- of crime through President Lyndon B. community from engaging in criminal ac- larly, it is difficult to separate out the effects Johnson's Commission on Law Enforce- tivity in the future. of incapacitation from those of deterrence. ment and Administration of Justice and The difficulty is in fact one of explaining the subsequent implementation of the When it is the sanctioned offender who is Commission's recommendations. At the inhibited from committing crimes by the 'Zimring and Hawkins (1973: 14). same time economists began to study law actual experience of punishment we speak enforcement as an economic problem in- of specific deterrence; when individuals volving the allocation of scarce resources other than the sanctioned offender are so (e.g., see Becker 1968). inhibited we speak of general deterrence. With regard to the deterrent effect of pun- Copyright @ 1980 by Sage Publications, Inc. Reprinted by permission, with minor changes, from Evaluation ishment we need to make a further distinc- Revieu'. VOI. 4, NO.2, April 1980, pp. 147-191. tion, suggested by Zimring and Hawkins (1973). between absolute and marginal deterrence: exactly what the mechanism of incapacita- of punishment, we need to attempt to get at Thus our conclusions are in agreement tion actually entails. those on the margin of criminal activity. with those of the National Academy of A simple-minded argumerit to explain the The size of the group of individuals on the Sciences Panel on Research on Deterrent effect of incapacitation might go as fol- margin limits the potential deterrent effects and Incapacitative Effects: There is no em- lows. Suppose we imprison a 20-year-old of any form of punishment. Since eco- pirical evidence to warrant an affirmative male for a period of 2 years for committing nomic theory so often deals with the mar- conclusion regarding the deterrent effect of the crime of burglary. Then, if that offender ginal effects of various policy changes, the punishment in general, and the available had been committing burglaries at the rate appeal of crime and punishment as an correlational or observational studies on of, say, 12 per year, the simple fact of his application of economic modelling is great. homicide provide no useful evidence on the removal from society for 2 years will pre- What remains to be seen is whether such deterrent effect of capital punishment. The vent the commmission of 24 burglaries. economic models are consistent with em- only available evidence that give support Then, in any modelling we do, we would pirical observations. for the notion of general deterrence comes wish to remove these 24 burglaries from the In this paper we review some recent at- from "natural experiments" such as Ross's overall effect of the 2 years of punishment tempts to develop econometric models for (1973) study of the British Road Safety Act on the future burglary rate. assessing the deterrent effect of punish- (see the discussion in Cook 1977). More- ment on crime, as well as analyses carried over, given the limitations of aggregate Even if we knew the rate of offending for data on crime and incarceration, we believe each imprisoned offender, the calculation out to validate these models. The first section discusses the possible types of empiri- that much more attention in the future in this argument may completely distort should be focused on studies of individual the actual effects on the overall crime rate cal investigations that might be used to study deterrence. Next we briefly describe criminal behavior. We do not expect any of incapacitating various individuals. In empirical research, at least in the near the case of the 20-year-old burglar, we need the Becker-Ehrlich econometric model for crime and punishment. Then we describe future, to provide definitive evidence on to know more about the nature and circum- the deterrent effects of capital punishment. cumstances of his offenses. If he were a some of the general problems in the em- member of a group of burglars, all of whom pirical implementation of this model. The work together, then his imprisonment may next two sections outline the pliblished em- Possible vehicles not have any effect at all on the number of pirical tests of the model along with some tor studying deterrence of our own reanalyses. One deals with burglaries committed by the group. Indeed, As with many other social ohenomena. the if he was arrested and convicted because he cross-sectional data for 1960 and 1970, while the other deals primarily with longi- relationship - between p;nishment 'and was the worst burglar in the group, the crime can, in principle, be explored either other members of the group might well re- tudinal data for homicide and includes a special look at the deterrent effects of capi- in an experimental setting or by an obser- cruit a superior replacement or simply in- vational study. crease their criminal activities, and thus the tal punishment. overall number of burglaries the group Finally our own conclusions regarding the In a randomized controlled field trial, ex- commits could easily increase. Cook(1977) empirical evidence on deterrence are pre- perimental units-individuals, collections discusses this replacement effect in an eco- sented. They can be summarized briefly as of individuals, political or legal jurisdic- nomic context in terms of its relationship follows: tions, etc.-are randomly assigned to treat- to the quality of crime opportunities. Reiss (I) The Becker-Ehrlich model has glar- ment grovps and are then carefully (1980) has argued persuasively that the ing shortcomings and, when examined crit- followed to assess the actual effects of the interpenetrating social networks of offend- ically, does not lead to the claimed testable treatment. The randomization allows the ers and their victims need to be better hypotheses regarding the effect of punish- experimenter to avoid the dangers of self- understood before we can make any seri- ment of crime. selection, and it allows for the control of ous attempt to separate out the effects of (2) The use of the Becker-Ehrlich model variables not included directly into the de- incapacitation from those of deterrence. At for aggregate data requires extensive justi- sign of the field trial. The "controlled" the same time no empirical model for meas- fication that has never been given. nature of such field trials implies that the uring the deterrent effect of punishment (3) The crime and imprisonment data choice of treatment for an experimental can be complete unless it also includes the used to empirically examine the Becker- unit is that of the investigator and that at related incapacitation effect in some form. Ehrlich model are so untrustworthy as to least two treatments (or levels of treatment) (See also the discussion of incapacitation in render any serious analysis meaningless. are being compared (see Gilbert, Light, and the report of the National Academy of (4) The empirical implementations of Mosteller 1975) for further discussion). Sciences Panel on Research on Deterrent the Becker-Ehrlich model are badly flawed The randomized controlled field trial is the and lncapacitative Effects (Blumstein et al. and have extremely grave statistical short- most demanding of all research strategies 1978).) comings and most published conclusions for investigating social innovations, but the increased reliability gained from a random- Let us explore the mechanism of deterrence from them are not to be trusted. (5) Even if one accepts the Becker- ized trial can often far outstrip the costs. somewhat further. The effects of deter- For a field trial involving deterrence the rence can be thought of only in the context Ehrlich model, and Ehrlich's choice ofdata of those who are likely to commit a crime to implement it (which wedo not), Ehrlich's and who are influenced by the threat of affirmative conclusions regarding the de- punishment for that crime if apprehended terrent effect of punishment on crime in and convicted. The nature and extent of $.eneral, and of capital punishment on mur- punishment can have no effect on those der in particular, do not stand up to careful who do not need to be deterred from crimi- statistical scrutiny. nal activities and on those who are not or cannot be deterred by the threat of punishment. Thus, to measure the deterrent effect treatments would involve different levels of (2) The number of offenses and the pun- might be consistent with the economic punishment and/or the threat of punish- ishments meted out. model. Most murders, however, occur in ment. Unfortunately, there have been few (3) The number of offenses, arrests, and the home, involve members of the same examples of randomized controlled field convictions and the public expenditures on family, and seem unpremeditated." trials dealing with deterrence. Zimring and police and courts. The net result of this econometric model- Hawkins (1973) note that "[ilt is difficult to (4) The number of convictions and the conceive of an acceptable experiment in ling is a functional relationship between the cost of imprisonments or alternative pun- number of offenses committed by individ- which, after random assignment, the sever- ishments. ity of sanctions threatened for a violation ualj, O,, and- (5) The number of offenses and the (a) his probability of conviction, p,, of a particular criminal law was varied private expenditures on protection and (b) his punishment given conviction,f;, betweenJhe two groups." While we do not apprehension. (c) his rate of return (benefits) if he suc- completely agree with their statement, we cessfully commits the crime, w,,(istands for do recognize the many legal and possibly We do not discuss (5) any further here since illegal returns), moral roadblocks to careful experimenta- it plays no role in Ehrlich's empirical imple- (d) the rate of returns from alternative tion on deterrence. Because of this diffi- mentation of Becker's model nor in the legal activities, w~,(I stands for legal re- culty in mounting experiments, most inves- bulk of the related literature we consider. turns), tigators resort to alternative research strat- Becker's basic premise is that criminals (e) the probability of legal unemploy- egies, two of which are highly prominent. maximize their expected gains (according ment, UI,,and In the first approach the researcher at- to some utility function) from illicit activ- (f) a vector of other variables, v,: tempts to assess the effect of a change in the ity. A person commits an offense if the level of sanctions by comparing reported expected utility he will receive exceeds the crime rates before and after the change in a utility he would receive by engaging in The function (1) is the one discussed by given jurisdiction. To reduce the potential other activities. Thus the criminal's deci- Ehrlich (1973), and is simply an elabora- biases and errors of such an approach, in- sion is based on benefits and costs of both a tion of Becker's supply-of-offenses func- vestigators often compare the change in monetaryeand psychic nature. According tion. To arrive at (I), one must adopt many rates with those in other jurisdictions to Ehrlich (1973) an individual allocates a untested and possibly untestable assump- where no changes in the level of sanctions fixed amount of time among legal and il- tions regarding criminal behavior and its took place. For a recent discussion of such legal income-generating activities. The determinants. "natural" experiments with regard to the effects of this time allocation are introduced only implicitly by Ehrlich through There is little or no discussion by Becker or deterrent effect of capital punishment, see Ehrlich regarding those "economic" vari- Baldus and Cole (1975); with regard to the effects of time allocation on wealth. From the basic model Ehrlich goes on to ables not included in (I). Nor do they pro- other deterrent effects, see Cook (1977) and vide support for the forms of the variables Zimring (1978). derive some behavioral implications, such as: An increase in the probability of appre- appropriate for inclusion for the empirical The other approach to the measurement of hension and punishment, with no change in validation of the model. This is a serious deterrent effects of punishment is the gath- other variables, reduces the incentive to matter. No amount of utility theory, sys- ering of aggregate data on crime and pun- participate in illegitimate activities. tems of partial differential equations, ishment as well as on various social and Kuhn-Tucker first-order optimality condi- economic variables. The researcher then Block and Heineke (1975) have examined tions, and analogies to the supply and studies the variations in crime that occur Ehrlich's model with great care and have demand for bread and butter (see Ehrlich either among jurisdictions or over time. shown that if the allocation of time is intro- and Gibbons 1977) can make up for the This is the approach adopted by Ehrlich duced explicitly into the utility analysis, the logical leaps that lead to the specification (1973, 1975a, 1977b) in his attempt to de- behavioral implications of the model de- of (1). velop an econometric model for the effect rived by Ehrlich do not necessarily hold. The first step adopted by Ehrlich and of varying sanctions, and the inherent diffi- Moreover, they note that, contrary to the assumptions of Becker and Ehrlich, it is not others in making the model of expression culties in this approach are the primary (I) suitable for empirical examination is subject of this paper. necessarily true that monetary equivalents to labor and penalty attributes of an of- the aggregation of data across individuals. fense exist. As a result, propositions re- Thus Ehrlich uses the aggregate function The Becker-Ehrlich model garding the deterrent effect of punishment for crime and punishment become empirical questions rather than theoretical consequences subject to empiri- where 0* is the aggregate number of of- Becker (1968) introduces his attempt to cal validation. fenses in a particular jurisdiction,p* is the model crime and its optimal control by aggregate probability of conviction, and so noting that "'crime' is an economiCally im- Implicit in the utility analysis of Becker, on. The justification for such aggregation. portant activity, or 'industry', not with- Ehrlich, and others is the assumption that typically rests on the assumption that either standing the almost total neglect by econo- criminals or potential criminals are rational mists." His model involves basically five decisionmakers in that they make their de- behavioral relationships which he claims cisions according to a list of axioms. The underlie the costs of crime-the relations appropriateness of such an economic between: model of crime is clearly open to question. (1) The number of offenses and their For example, Avio and Clark (1976) state cost. that: "It would be difficult to argue that perpetrators of violent crimes behave according to the usual set(s) of axioms. .. . Murders involving some form of premed- itation and motivated by economic gain the parameters used to specify the relation The actual rate of, ding in any commu- usually handled by separate juvenile justice (I) are constant across individuals or the nity for any specific .ne during a specific systems and are rarely sent to prison. Indi- parameters are stochastic, coming from time period is not Known. What we have vidual offenders are not tracked over time some common distribution. Actually, to available are data on offenses reported to through the criminal justice system, and justify the aggregation, one needs further the po!ice. As a substitute for 0* (the the aggregate figures for those imprisoned to specify a specific functional form. For actual offense rate), Ehrlich (1973, 1975a) that are available for jurisdictions such as example, suppose log O; is linearly related uses Q/N, where Q is the number of of- states include individuals whose crimes to the logarithms of the variables on the fenses reported to the police and recorded may have been committed in other states. right-hand side of (1). Then, if the coeffi- by them for a jurisdiction, and N is an esti- These aggregate figures also include cients are the same across individuals, the mate of the population size for that juris- offenders whose crimes took place possibly aggregate number of offenses, O*, is diction. It is well known that not all several years prior to incarceration. Thus related to the geometric means of the indi- offenses committed are reported to the the use of contemporaneous values of C vidual values for the other variables. Thus police. Estimates of the ratio of Q to Q*, and Q by state can lead to sizeable discrep- the justification of functional form must the true number of offenses, vary from as ancies between C/ Q and p*, which can be ultimately be established at the individual low as 10 percent for rape to close to 100 shown to vary from state to state in occa- rather than the aggregate level. Since percent for murder. In the case of automo- sionally very strange ways. We discuss this aggregation also takes place over time, we bile theft there have been occasional re- problem further in the next section. need to assume some form of constancy or, ports that Q exceeds Q* because of non- at a minimum, stochastic stationarity of thefts reported to the police for insurance Third, Q now appears on both the left- and the parameters in the functional specifica- purposes. right-hand sides of the operational version tion (see e.g., Kuh and Welsch 1976). of equation (2). As is noted in the report of Unfortunately, the ratio of Q/Q* can vary the National Academy of Sciences (Blum- One of the few empirical examinations of a dramatically from jurisdiction to jurisdic- stein et al. 1978), variation in the error in related functional specification at the indi- tion. For example, Skogan (1976) notes measuring Q*, the true number of crimes vidual level was carried out by Witte (1977). that in the 26 city victimization surveys committed, can induce a spurious negative Her analyses show the importance of the conducted under the auspices of the Na- relation between the offense rate and the specification of individual sociodemo- tional Crime Survey Q**/ Q*(where Q** is punishment rate, when no such relationship graphic variables, such as race and age, and the number of crimes reported to the actually exists. Klein, Forst, and Filatov are supportive of arguments indicating the police) for robbery varied from 52 percent (1978) demonstate how such errors can inappropriateness of the aggregate data to 76 percent.2 The estimates of the ratio of induce a similar bias in the estimated rela- used by most investigators in this area. the number of crimes appearing on police tion between murder and execution rates. records (i.e., Q) to the number actually Alternatives to the Becker-Ehrlich model reported (i.e., @*) for these 26 cities, The source of the data used by Ehrlich and exist. These are based on concepts such as however, varied from 19 percent to 100 others to analyze the deterrent effects of the saturation of the resources of the crimi- percent! punishment in the United States is the Uni- nal justice system (Cook 1977), and form Crime Reports (UCR) produced by "homeostasis,"the apparent stability of im- The quantity Q is also used by Ehrlich to the Federal Bureau of Investigation (FBI). prisonment, and effective prison capacity get a measure of p*, the aggregate subjec- UCR data are collected as part of a volun- (Blumstein and Cohen 1973; Nagin 1977). tive probability of punishment (i.e., appre- tary reporting system involving state and While we do not directly discuss the empiri- hension and imprisonment). He uses C/ Q local law enforcement agencies and are cal examination of these alternatives, we as an estimate ofp* where Q is the number based on crimes recorded by these agencies. note that they cast doubt on Ehrlich's of recorded crimes in a given period of time In addition to the problems of reporting claims regarding marginal deterrent effects and C is the number of offenders impris- and recording offenses noted earlier,UCR of punishment. oned during the same time period for the rates may seriously distort the level of same jurisdiction. There are three problems offenses because multiple crimes with pos- here. Moving toward empirical examination sibly multiple victims often are recorded as of the Becker-Ehrlich model First, C and Q involve different units. C single offenses, and conversely single crimi- deals with offenders, and Q deals with nal events often involve multiple offenders, To move from the aggregate supply-of- offenses. There is not a one-to-one corre- etc. offenses model of expression (2) to an em- spondence between the two. pirical study of deterrence, one needs to Since the beginning of the UCR program in (a) Specify in detail the "other" varia- Second, for a fixed period of time and a 1933, both the number and the percentages bles to be included as part of the vector v*. given jurisdiction, it is impossible to deter- of law enforcement agencies reporting to (b) Describe how the variables are to be mine which of the offenses that are included the FBI have increased dramatically. measured. in Q ultimately lead to apprehension and Moreover, reporting practices have also (c) Specify the actual functional form of imprisonment. For example, juveniles are evolved, and officials generally agree that a the relationship. larger proportion of offenses made known 'These rates are subject to substantial sampling error, to the police now get reported to the FBI Ehrlich (1973, 1975a) provides a priori and some of the variability can be attributed to this than was the case in the past. Finally, specifications for (a) and (c) which we call source. although the proportion of units reporting into question in our reanalysis of his data. has increased over time, specific police de- Thus we defer our discussion of these mat- partments that are once included in the ters to later sections of this paper. In this UCR data base may not be included at later section we discuss (b). points in time. e 1 1 Ehrlich S 1960 data Table 1. Variables used in Ehrlich's analysisa Ehrlich (1973) analyzed data from 47 states. The states omitted from theanalyses : Crime rate (the number of offenses known per capita) 63 were Alaska, Hawaii, and New Jersey (see : Crime rate lagged one year Vandaele 1978). New Jersey was omitted : Estimated probability of apprehension and imprisonment (the number because certain key variables could not be of offenders imprisoned per offenses known) obtained. The listing and definitions of all : Average time served by offenders in state prisons variables used in Ehrlich's study are given : Median income of families in Table 1. : Percentage of families below one-half of median income To implement the aggregate model of : Percentage of non-whites in the population expression (2), Ehrlich chose to use a : Percentage of all males in the age group 14-24 Cobb-Douglas production function of the : Unemployment rate of civilian urban males aged 14-24 and 35-39, form respectively '-1 4 : Labor-force participation rate for civilian urban males ages 14-24 Ed : Mean number of years of schooling of population 25 years old and over SMSA : Percentage of population in standard metropolitan statistical areas : Per capita expenditure on police in fiscal 1960, 1959, respectively I where Q/N is the operational attempt to estimate the offense rate. O*. M : Number of males per 100 females C/N is the operational attempt to D : Dummy variable distinguishing northern from southern states estimate the probability of (south = 1) punishment, p*.

a~ subscript j denotes that the variable is indexed by specific crime categories. T*, the average time served by prisoners in state prisons, is the empirical measure off*, The UCR data used by Ehrlich for his robbery, respectively. Cook (1977) insome the punishment given convic- cross-sectional analyses (discussed in the simple preliminary analyses shows that the tion. next section) are based on the UCR for the "usual" negative correlation between the W, the median family income, years of interest. The data used in his na- UCR reported burglary rates and the cor- and X, the percentage of fami- tional longitudinal analysis of murder (dis- responding UCR clearance rates is greatly lies below the median income, cussed later) are not the reported rates for diminished when city data from the NCS are used as replacements for each point in time. Rather, they consist of are used in their place. The Wilson and the differential monetary re- FBI estimates of what the reported crime Boland (1976) study, which does find a sig- turns of crime relative to legal rates would have been had the units in- nificant negative effect using NCS data for alternatives, i.e., w,* and WI*. cluded in the UCR system been the same as robberies, unfortunately suffers from many VII, the male urban unemployment in 1972. Unfortunately there is no published of the methodological flaws discussed in rate for ages 14-24, and LI4, description of the procedure used by the the remaining sections of this paper. Given the labor force participation FBI to reestimate the rates. We have no the serious technical problems with the rate for this same group, are way to assess the appropriateness of the NCS city data (see Penick and Owens used in lieu of ul*, the proba- FBI's reestimation procedure, but it is 1976), we do not see the use of victimiza- bility of legal unemployment. reasonable to conclude that it is likely to tion data as a way of correcting the prob- NW, the percentage of nonwhites, add further biases and increased variability lems associated with UCR data. and A14, the percentage of to an already poor measure of crime. males in the 14-24 age group, are the "other variables," v*. We do not believe that UCR data collected The analyses of U.S. cross- a, and b, for i = 1, 2, . . . ,8, are prior to 1960 merit serious attention since sectional crime data parameters to be estimated. are completely I,., this section we discuss some recent anal- e is a random error term. are subject to enormous errors and biases. ySeS that have attempted ex- The relationship among the variables in (3) Any substantive conclusions one might amine the Becker-Ehrlich econometric draw from the analysis of these data are not is multiplicative, and we must take logs- model of crime and punishment using rithms of both sides of the equation to probe trusted' Even Ihe longer cross-sectional data for the United States. duce linearity (we use natural logarithms, 1960because Wishes data prior We have attempted to replicate some of of doubts regarding their We denoted by these results, and we report on our findings have serious reservations regarding the in this regard along with some additional quality and validity of the 1960 UCR data = bo + blln + b21nT* analyses. (g) (g) used by Ehrlich and others. Nonetheless, we discuss the 1960 data and national lon- + b~lnW + bJnX (4) gitudinal UCR data for murder from 1933 + btln V14 + bhlnL14 through 1969 in the following two sections. + bllnN W + bslnA14 + e. One alternative to the use of UCR data is (Here we take b~ = lna.) As a result of a the use of data from the special city surveys variety of statistical analyses, Ehrlich con- associated with the National Crime Survey cluded that v1.1, L14,and AIJhad virtually (see Penick and Owens 1976). Cook (1977) no effect on the rest of the estimated equa- and Wilson and Boland (1976) have used tion and so he dropped them to yield the NCS city data to examine the effects of model: sanctions on the crimes of burglary and C (d) When fallible measures are used for Table 2. Estimated coefficients of selected variables in equation [51. Estimates obtained key variables in a regression or simultane- by two-stage least squares ous equation model, it does not suffice to substitute them directly into the model, as Offense Intercept (C/O)i -Ti' -W --X NW Ehrlich did with equation (3). The prob- Robbery -1 1.030 -1.303 -0.372 1.689 1.279 0.334 lems of dealing with models where there are (-1.804)a (-7.01 1) (-1.395) (1.969) (1.660) (4.024) errors in the variables are well-known (e.g., Burglary -2.121 4.724 -1.127 1.384 2.000 0.250 see Sprent 1969 or Zellner 1971). (-0.582) (-6.003) (4.799) (2.839) (4.689) (4.579) (e) There is a special statistical technol- Larceny -1 0.660 -0.371 -0.602 2.229 1.792 9.142 (-2.195) (-2.482) (-1.937) (3.465) (2.992) (2.019) ogy especially suitable to problems where Auto theft -14.960 -0.407 -0.246 2.608 2.057 0.102 there are multiple indicators available for (4.162) (4.173) (-1.682) (5.194) (4.268) (1.842) given unobservable variables (see Joreskog Property crimes -6.279 -0.796 -0.915 1.883 2.132 . 0.243 1970 for a general formulation, and Bielby, (-1.937) (-6.140) (4.297) (4.246) (5.356) (4.805) Hauser, and Featherman 1977 for an illus- Murder 0.316 -0.852 -0.087 0.175 1.109 0.534 trative application). Ehrlich simply ignores (0.085) (-2.492) (-0.645) (0.334) (1.984) (8.356) this matter. Rape -0.599 -0.896 -0.399 0.409 0.459 0.072 (-0.120) (-6.080) (-2.005) (0.605) (0.743) (0.922) (f) The equations for all of the crimes in- Assault -7.567 -0.724 -0.979 1.650 1.707 0.465 clude the monetary variables W and X, (-1.280) (-3.701 ) (-2.301 ) (2.018) (2.1 11 ) (3.655) even those equations for violent crimes Crimes against 1.635 -0.803 -0.495 0.328 0.587 0.376 such as murder, assault, and rape. We see the person (0.380) (-6.603) (-3.407) (0.570) (1.098) (4.833) no justification for this. (Parenthetically, All offenses -1.388 -0.991 -1.123 1.292 1.775 0.265 (-0.368) (-5.898) (4.483) (2.609) (4.183) (5.069) we note that Ehrlich classifies robbery as a property crime, whereas the FBI classifies umbers in parsntheses are t-ratios (i.e. the estimated coefficients divided by their it as a violent crime.) estimated standard errors). (g) The equations for each crime type are analyzed separately and not linked. In are obtained by two-stage least squares our view a more realistic model would re- (using a weighting scheme) and also by the late crime rates to one another because of method of "seemingly unrelated regressions" the known tendencies of career criminals to due to Zellner (1962). In all cases the co- substitute one crime type for another (e.g., efficient of most'interest, b~,has a negative see Petersilia, Greenwood, and Lavin Ehrlich uses a simultaneous equations ap- estimate and is judged to be significantly 1978). proach to estimate the coefficients in equa- different from 0 (based upon its t-ratio Vandaele (1978) reanalyzed Ehrlich's 1960 tion (5) in which the crime rate (Ql N), the being larger than 2). We give Ehrlich's two- data, incorporating a number of different probability of imprisonment (CIQ), and stage least squares estimates of the coef- model specifications as well as an attempt the amount of police expenditures per ficients in Table 2. to identify possible outliers, i.e., states capita (El N) are simultaneously deter- Ehrlich's final conclusion, based on the whose data do not fit the pattern of the re- mined or endogenous variables. Ehrlich analyses just outlined, is that these 1960 mainder. His analyses lead him to essenti- does not present a system of structural data provide strong support for the theory ally the same conclusions as Ehrlich. We equations for the entire system but only that sanctions deter crime. We take issue merely outline here some of the highlights gives the one determining the crime rate, with this conclusion. We present detailed of Vandaele's work. He supports Ehrlich's i.e., equation (5). In this system, however, it comments on these analyses, but first we use of weighted least squares but notes that is the variables W, X, and NW (the only mention a few key points relating to model weighting the variables does not have any socioeconomic variables included) that formulation and the statistical methods real effect on the conclusions. His analyses "identify" equation (5) and allow for the used: are also done in the logarithmic scale, estimation of the key coefficients of the (a) Ehrlich assumed a priori the specifi- although he does obtain one set of esti- punishment variables, 61 and bz. Fisher cation of equation (3) thus leading him to mates for a model in which Q/ N is in the and Nagin (1978) have noted that usiqg estimate a relationship that was linear in log scale and all other variables are un- socioeconomic variables to identify simul- the logarithmic scale, i.e., equations (4) or transformed. The results of this analysis taneous relationships can be hazardous. (5). He made no attempt to check the ap- are not very different from the others. Two We address this point below, but empha- propriateness of this assumption, or to different models for the supply-of-offenses size again that Ehrlich does not present his assess the overall goodness of fit of his equation that Vandaele fits include (a) the entire system so it is impossible for anyone model. Many alternatives are available model of equation (9,where the reduced to completely judge his specification (see which are consistent with the original form contains only the 6 variables in this the related criticisms by Hoenack et al. econometric formulation. model together with (El N)59, and (b): 1978). (b) As noted above the use of the vari- Ehrlich estimates the parameters in (5) for ables, W, X, and N W to identify the crime each of the seven basic crime types and for rate equation, (9, is highly suspect. various combinations of crime. Estimates (c) NOjustification is given for the use of Wand X in place of the variables measuring the differential monetary returns of crime. not agree with Vandaele's claim. We see Table 3. Estimated coefficients of In (C/Q)j and lnTj (from Vandaele (1978) evidence of sensitivity of the conclusion to changes in the specification of the model, Equation [51a Equation [51 Equation [5]C Offense In(CQ)j lnTj ln(CQ)j- lnTj In(CQ)j lnTi and given the comments of Fisher and Nagin (1978) concerning identification, Murder p.492 -.124 -2.944 .I29 2.178 -.482 (-.35)d (-.69) (-1.68) (.35) (.11) k.1 I) this finding casts doubts on any inferences drawn. Rape -.771 -.316 -1.347 -.699 -2.979 -1.240 (v.38) (-1.39) (-.78) (4.92) (-2.30) k.43) Continuing our analysis in a purely ana- Assault -3.882 -7.216 -.968 -1.412 3.851 5.754 (7.35) (-.37) (-3.37) (-2.36) (22) L23) lytic framework, we note that multicol- Robbery --4.223 -1.336 -1.584 ' -.465 -1.109 -.357 linearity is a serious problem in this data k.57) (-.SO) (-6.49) (-1.46) (-2.19) (-1.24) set. The correlation matrix indicates very Burglary -.445 -.793 -.884 -1.31 7 -.416 -.547 high correlations am0r.g the socioeconomic (-2.73) (-2.99) (-6.05) (4.91) (-2.81) (-2.43) variables. Our computations were done Larceny -1.441 -2.127 -1.554 -2.287 -1.231 -1.637 (-1.63) (-1.93) (-1.65) (-1.52) 1 I ) (-1.58) using a CDC 6600 computer and, although Auto theft -.616 -.341 -.880 -.460 -.650 -.246 we did not run into any problems in calcu- (-2.58) (-1.66) (-3.65) (-1.76) (-3.22) (-1.25) lating the inverses of matrices, it is well All offenses -1.021 -1 .I56 -1.249 -1.407 -1.043 -.824 known that even a nearly singular design (-3.84) (-3.4) (-5.43) (4.30) (-3.70) (-2.57) matrix can lead to unstable estimates of parameters. Another problem is that of a~odelidentified by the exclusion of In (k) 59' "outliers" or what would be more appropriately called influential observations (see b~odelidentified by the exclusion of In (k) and In (g) 59 59' R. D. Cook 1977). These are points that are a large distance away from the "x-space" 'Model identified by the exclusion of In (i) spanned by the other points. Vandaele just 59' looked at univariate plots to determine if d~umbersin parenthesis are t-ratios (i.e., the estimated coefficients divided by their estimated standard errors). any outliers were present, but the use of univariate plots may be very misleading. Figure 1 shows a point which is clearly far where the reduced form includes only the Using the data reported in Vandaele's from the others but the two univariate plots variables (6) together with (E/N)ss. The paper we have reestimated the parameters along the axes do not show this at all. An estimates of the coefficients of In Pand ln T for the equations determining murder and adaptation of Cook's techniques suitable for these two models are given in Table 3, burglary. In both cases we were able to for use in simultaneous equations prob- along with estimatesfor the model in which duplicate Vandaele's estimates up to round- lems would have been of great help in Van- the crime rate equation is identical to (5), off error. For these two crimes our findings daele's and our reanalyses. but where (Q/ N)59 is used as an additional agree with those of Vandaele in that the The most serious problem with Ehrlich's reduced form variable. Vandaele's overall burglary estimates are insensitive to data and Vandaele's reanalyses of them, conclusion is that the inferences about de- changes in specification while those for however, lies with the data themselves. We terrence are not sensitive to changes in the murder are not. We have done the analysis, are trying to estimate effects of certain vari- specification of the model. A careful exam- in both cases, using a model that is linear in ables on others but we cannot observe what ination of Table 3 raises doubts about this the original scale and found that the results we desire. For instance, N Wis actually the conclusion which we will return to later. are consistent with those for the logarith- percentage of blacks in the population, not Finally, Vandaele notes that some states mic scale. The residual analysis (see, e.g., the percentage of nonwhites. If this vari- (Utah, Vermont, and Wisconsin) have re- Daniel and Wood 1972) indicates that able is attempting to measure minorities corded values for some variables that are either of the models fits the data adequately. then it may be very misleading. We will see inconsistent, e.g., the estimate of C/Q, the We also agree with Vandaele's findings that below in a reanalysis of 1970 data that probability of conviction for assault in deletion of the states with values of C/Q changes in the way some of the variables Vermont, is given as 1.56. These are not greater than 1 does not change the results, are measured can yield very different re- mistakes in recording but result from the but we do not agree that this is not a problem. sults. Our biggest stumbling block is with way in which the variables such as ClQare Vandaele has stated that his conclusions Ehrlich's measure of the probability of con- defined (see Table 1). As we noted earlier are not sensitive to changes in the specifica- viction, one of the keys to the analysis. the problems here include the lag between Since this measure is determined by the ratio offenses and imprisonments as well as tion of the model. This point is a crucial one since there is not nearly enough theo- of the number of convictions to the number cross-overs between states. After redoing of offenses, the "probability" may be larger the analysis with certain of these states retical knowledge of the system to determine which a priori assumptions are cor- than 1. While Vandaele minimizes this by omitted, Vandaele claimed that the results showing that states with probabilities are not substantially changed. He con- rect. Indeed many are likely to be incorrect. Thus different estimates for the key coef- larger than 1 do not make a difference, he cludes that, although the question of what misses the point raised by the obviously is the proper model specification needs to ficents corresponding to different specifi- be studied further, the fact that the esti- cations would force us to do more thinking mates do not depend on the specification about the correct form. A careful examina- lends support to the theory that sanctions tion of Table 3 shows that, especially for are an effective deterrent. the violent crimes of murder, rape, and assault, the estimates do change for the four specifications described above. Note also that there was some instability in the estimates for murder and assault. Thus we do w persons between 18 and 20 years of age the multiplicative one assumed by Ehrlich. Figure 1. while Ehrlich uses the proportion between He states that this is the more appropriate Why one-dimensional graphs do 14 and 24; he measures population density model because of the higher RZ(a com- not always indicate influential from Census data while Ehrlich uses ment which is incorrect statistically). observations SMSA, the proportion living in standard Another point of difference is that Ehrlich metropolitan statistical areas. In addition, assumed that the variance of the errors Y Forst uses four variables for which there decreased with N, state population, and are no corresponding measures in Ehrlich's hence he performed weighted least squares analysis; namely MIGR, BRHO, QJ, and with flas weights. Forst did not, em- A VTMP. We will see below that the first pirically, find a need for such a weighting two of these prove to be quite important. and hence did not use one. At any rate we will see later that the weighting does not .. Forst models the criminal justice system have much of an effect on the conclusions. .. using a five-equation structure: . . Forst's estimated coefficients are given in -. CR =fi(PJ, A VSENT, QJ, MIGR, Table 5. These estimates imply conclusions URB, BRHO, MFY, YDSPR, very different from those of Ehrlich. Neither f UMPL, TEEN, MALE, G? 0 of the deterrence variables has significant N WITE, AUTEMP) coefficients and, in fact, the coefficient of PJ =h(POL$, CR, SOUTH, URB) (7) A VSENT is positive. Note further that vm. - X QJ =I;( Y/ POP, SOUTH) MIGR, URB, and BRHO appear to have 4 POL$ =fj(Y/ POP, CRl-I) strong effects on the crime rate. These three variables were not included in Ehrlich's wrong estimated probabilities. This vari- COR$ =A(Y/ POP, CRt-I) analysis. Forst also replicated Ehrlich's able is clearly not measuring (or at least not where5 represents an affine function of the analysis, as closely as possible, using the very well) what it is supposed to, and there included variables. This formulation allows 1970 data. He does not present specific re- is no way of determining whether a value for transformations of variables such as sults in his paper but notes that the esti- of C/ Q equal to 0. l or to 0.2 is an accurate PJ, which is a bounded dependent variable mated elasticities of the two deterrence reflection of the probability of conviction in the second equation. Two important dis- variables are substantially smaller than in that state! We can all agree that an esti- tinctions between this model and Ehrlich's Ehrlich's. It is difficult to judge how differ- mated probability of 1.6 is wrong because are that Forst considers police expenditure ent things are since he provides no standard we know that probabilities cannot exceed to be an exogenous variable (determined in errors. It must be pointed out again that one in value. When we observe estimated this case by Y/ POP and CR I)and, more Forst provides no assessment of the fit of probabilities of conviction of 0.9 or 0.5 or importantly, Forst uses considerably more his model, aside from reporting RZvalues. 0.3, however, what are we to do? Why variables to determine the crime rate. We More will be said about this analysis as we should we trust the estimates of magnitude also note that Forst analyzes only the present our analysis of this data set. 0.9 or 0.1 any more than we trust those of aggregate crime rate, not the rates for 1.1 or 1.6? The problem may be that there individual crimes. are transitions between states which pre- The data set that we used in the analysis of clude using this measurement of the prob- Once again we will focus only upon the esti- the 1970 data was identical to that of Forst ability. At any rate, it seems impossible to mation of the crime rate, the first equation with the exception of three variables, justify seriously any inferences made using in (7). Forst presents his analysis with the Y/POP, YDSPR, and UMPL. We took this measure of sanction, especially since variables measure in their original scale, Y/ POP to be "personal income"and these Ehrlich uses ln(C/Q) in his equation rather i.e., the additive relationship as opposed to data were obtained from the Statistical Ab- than C/ Q. When C/Q is close to zero a small error in estimate is greatly magnified 1 by taking logarithms. Table 4. Variables used in Forst's analysis

: Number of FBI index crimes per 100,000 residents Forst S 1970 data C R PJ : Estimated probability of apprehension and imprisonment Forst (1976) presents an analysis of 1970 AVSENT : Average time served by offenders cross-sectional data that parallels that of QJ : Expenditures on correction system per prisoner Ehrlich. This analysis is based on data from POL$ : Expenditure on police per state resident all 50 states plus Washington, D.C. A COR$ : Expenditure on correction system per state resident description of 'the variables used is given in MlGR : Population migration rate (population growth divided by number of Table 4. Many of these variables are similar residents) to Ehrlich's but there are some important URB : Proportion of residents living in places defined as "urban" by the Census differences. Bureau BRHO : Proportion of households that are not husband-wife households There are four variables that are measured MFY : Median family income differently in the two data sets: Forst meas- Y(P0P : Income per capita ures the average length of prison sentence YDSPR : Income dispersion (difference between median family income and na- from the Statistical Abstract (1972) while tional poverty level, weighted by proportion of families below poverty Ehrlich uses National Prisoner Statistics; level) UMPL : Proportion of the adult population that is unemployed or not in the labor he uses YDSPR to measure income disper- force sion while Ehrlich uses the proportion of TEEN : Proportion of residents between ages 18 and 20 families earning below the median family MALE : Number of males divided by the number of females income; he measures the proportion of NWITE : Proportion of residents who are non-white AVTMP : Average temperature (Fahrenheit) South : Dummy variable distinguishing northern and southern states (south = 1) I obtained are given in Table 6. The only sig- Table 5. Estimates of the crime-rate equation in [5] nificant variables in our analysis are MFY Forst analysis Our reanalysis and YDSPR. Evidently the slight differences between Forst's variables and ours -Variable -Elasticity t-Ratio Elasticity t-Ratio Coefficienta are giving very different results. The residual plots for this model, however, showed a PJ -.02 -.I4 .OO .O1 31x10~ . AVSENT .01 .10 -.oo -.oo 46x 1o-~ definite need for fitting the additional QJ -.07 -.64 -.06. -.60 -16 x 10-3 variables, URB and MIGR, so we would MIGR a 3.42 -.OO 3.70 33 x 102 URB .71 2.17 .74 2.40 26 x 102 not want to use the model, as it stood, for BRHO .96 2.13 .97 2.30 78 x lo2 making inferences. MFY .60 1.51 .57 1.50 15 x 10-2 YDSPR .40 1.93 .33 1.80 13 x 10-1 UMPL .ll .21 .20 1.90 98 x 102 Despite these discrepancies, our conclu- TEEN .63 1.45 .69 1.70 30 x 103 sion is the same as that of Forst: Usingvari- MALE .65 .65 .43 .20 21 x102 ables measured similar to those in his NWlTE -.07 -1.51 -.07 -1.70 -15 x 102 AVTEMP .ll .37 .21 .70 study, we find no evidence that, in 1970, 9.3 x 101 sanctions were an effective deterrent to 'Not computed by Forst. crime. The explanation for the discrepancy be- stract (1975). In computing YDSPR we variables. However, eliminating either or tween Ehrlich's results for 1960and Forst's took the national poverty level to be$3,601 both of these points does not change the ones for 1970 may be simply that behavior as given in the Statistical Abstract (1975). results either. One final point of note is that patterns of criminals changed in these 10 The other discrepancy was for UMPL, there was a tendency for the variance of the years. While certainly a possibility, this which was supplied by Forst, but over aver- residuals to increase with URB. However, cannot reasonably be inferred from the age value differs from that given by Forst. no heteroscedasticity was observed when data at hand. In comparing the two analy- the residuals were plotted against N. ses, it must be remembered that the 1970 Using the same model as Forst, we derived data include only an overall crime rate and the estimated coefficients for thecrime rate In Table 6 we give estimates for the coeffi- there has been no individual analysis for equation given in Table 5. Our estimates cients when the model has all variables in different crimes. Of course, we can com- are similar to Forst's with only that for the logarithms and when only CR is in loga- pare the two results in terms of the overall coefficient of UMPL being substantially rithms. Again the seemingly important crime rate but this may not be very fruitful different. Note that our estimate of the PJ variables remain the same. In both of these as there are surely different structural rela- coefficient is in fact positive although there models there are no outlier problems nor is tionships for different crime types which is no strong evidence, in either case, of the nonconstant variance apparent. Hence are masked by such an aggregation. actual coefficient being different from 0. there is evidence that the logarithmic scale Our analysis of the residuals from the fitted is the better one to work in, although the Other analyses of cross-sectional data equation indicated that Michigan might be choice of scale doesn't affect the findings in for murder a possible outlier (it had a standardized a meaningful way. residual of 2.6). Although testing this point Given the widespread interest in the poten- As mentioned above, Forst replicated Ehr- as an outlier using a Bonferroni t-test (see tial deterrent effect of capital punishment lich's model as closely as possible and ob- Miller 1966) did not lead to rejection, we on the commission of homicide, several in- tained results for 1970 data that were not reestimated the parameters with this state vestigators have done special analyses of consistent with Ehrlich's. We have also omitted and found that they did not change cross-section data by state specifically for done this but our results do not agree with substantially. Scatter plots of the variables this crime. These include Passel1 (1975) indicated that the District of Coumbia (due either Forst or Ehrlich. The estimates we who examines data for 1950 and 1960, to very high values of N WITE, BRHO, and Forst (1977) who analyzes data for 1960 POL$) and Alaska (with a very high per- and 1970 (actually he used differences), centage of males) were well away from the Ehrlich (1977b) who uses data for 1940and center of the array of independent 1950 (his analysis of murder for 1960 was described earlier in this section), and Loftin (1980) who examined a quite different data Table 6. Estimated coefficients for various models fit to Forst data set for 1960 which had been explored earlier by several sociologists. Because the Variable Model (1 la Model (2) Model (3) longitudinal analyses described in the next h section deal only with homicide, we defer a PJ 11 XIO-~ ( .42)b 2.2 ( .22) -.21 AVSENT 3.7 x 10'~ ( .13) -1.9 x ( -30) -.I6 discussion of these cross-sectional studies QJ -3.9 x 10.~ ( -.20) -1.0 x lo-z ( -.77) - until the end of that section. MlGR 80 x ( 3.33) 1.3 ( 3.17) - URB 81 x10-~ ( 2.46) 1.4 ( 2.75) - BRHO 57 X lo-2 ( 1.12) 2.1 ( 1.31) - MFY 1.2 ( 2.67) 97 x lo-6 ( 2.11) 1.7 YDSPR 62 x ( 2.95) 73 x ( 2.09) 1.O UMPL 31 XIO-~ ( 2.82) 4.9 ( 2.04) - TEEN 91 X ( 2.17) 20 ( 2.41) - MALE -2.0 ( -.91) -2.5 ( p.61) - NWlTE -6.9 x (-1.97) -.79 (-1.98) .04 AVTEMP 33 X ( .92) 45 lo-5 ( .76) -

he three models used are: (1) All variables, except SOUTH, transformed to natural logarithms. (2) Only CR is transformed to natural logarithms. (3) This corresponds to Ehrlich's model using the 5 corresponding variables available in this data set. b~umbersin parentheses are t-ratios. Deterrence, capital punishment, and murder Table 7. Variables used in the time-series analyses

-Q : Murder rate (per 1000 civilian population) Ehrlich S longitudinal data for murder N : Probability of arrest (percent of murders cleared) One of the most controversial studies of : Proportion of those charged that were convicted of murder deterrence is that of Ehrlich(1975a). Based : Number of executions for murder in the year t + 1 divided by the number of upon a time series of aggregated national convictions in year t data for the years 1933-1969, Ehrlich : Number of executions for murder in the year t divided by the number of claims to have found strong evidence that convictions in year t the death penalty has a deterrent effect L : Proportion of the civilian population in the labor force upon potential murderers. In this section U : Proportion of the civilian labor force that is unemployed we review Ehrlich's analysis as well as A : Proportion of population in the age group 14-24 prominent criticisms of it. We then present : Friedman's estimate of (real) permanent-income per capita in dollars the results of our reanalysis of essentially Y~ the same data set. T : Time (years) NW : Proportion of non-whites Ehrlich's model is one in which the murder N : Civilian population (in 1000's) rate, probability of apprehension, and XGOV : Per capita (real) expenditures (excluding national defense) of all governments probability of conviction given apprehen- in millions of dollars ;ion are -having XPOCl : Per capita (real) expenditures on police in dollars lagged one year simultaneous effects on each other over : Violent crime rate (offenses of rape, robbery and aggravated assault) time, while a number of socioeconomic variables are considered to be exogenous variables along with the probability of exe- ders that would be prevented by one addi- cution given conviction. The murder ~l"($) )' Po + BIAlnPd + P?A1np~]a tional execution per year. He estimates this supply function, by an elaboration of the to be between 7 and 8. earlier arguments, now replaces p* andf* + PXAlnP,J, + p,AlnU of equation (2) by P, (the probability of + Br AlnL + PsAln Y, Ehrlich concludes that his analyses show arrest), P,I, (the probability of conviction +&AT+ e, the deterrent effect of capital punishment. given arrest), and PelL(the probability of He claims that he has analyzed the data in where, for a generic variable Z, the value of scales other than the logarithmic one with- execution given conviction). The empirical AZ at time is implementation of this function, using the * out the conclusions changing substantially, variables described in Table 7, takes the, AZ = Z - ~ZI-I, and he also states that his results are unaffected by the time period of analysis. We form: and Po = 1nC. show below that there is considerable P P- P P Pr In a simultaneous equation framework, doubt about these two claims. (i)= CP, IP.~:P~:U .L (8) one must be concerned with whether or not Criticism of Ehrlich's conclusions can be Ph P7 the structural equations are identified. This divided into two broad categories: the rele- x Y, A exp (BxT) exp (4. particular equation is identified by omit: vance and accuracy of the data sources, and Note that T (time) is entered into this ting a number of socioeconomic variables the methodology used. We address these in equation in a manner different from all from this equation. The variables that were turn. The reliability of the data sources that other variables. Time is used here as a sur- omitted must have a direct effect on some Ehrlich used has been questioned before. rogate for the improvement of medical of the other endogenous variables so that We noted earlier the severe shortcomings technology over time and, as a variable, it equation (10) can be identified, i.e., for the of the UCR crime rates. They are not plays a crucial role in the analysis, as we parameters to be distinguishable. Fisher accurate measures of the variables that shall see below. and Nagin (1978) point out the difficulty they claim to represent. Furthermore, Since the observations all involve aggre- inherent in using socioeconomic variables Bowers and Pierce (1975) point out that the gate national data measured annually for to identify the parameters in a structural UCR arrest and clearance rates are especi- equation. 1933-1969, Ehrlich assumes that the errors It is impossible to determine ally suspect, primarily in the earlier years. are subject to first-order serial correlation, whether Ehrlich has validly identified his What is particularly troublesome is that l.e., structural equations because he only pre- recording practices have changed so much sents the one equation given in (10). over time. Moreover, while the UCR u1 = PUI- I + el, (9) Ehrlich presents estimates of the param- murder rates have been reestimated for the where p is the serial correlation and the el eters in equation (10) using six different earlier years, the arrest and clearance rates are independent random errors. The equa- measures of P,I,, the probability of execu- have not been so adjusted. When one is tion whose coefficients he thus sets out to tion given conviction. Two of these are de- making inferences based upon a time series, estimate is fined in Table 7. In all but one of the six such dramatic changes in the coverage of cases Pel, is viewed as an exogenous vari- data collection inevitably are confounded able. He finds that for all six measures the with any real effects that are present. estimated coefficient of the P,I, variable is A second data-related problem is concep- negative. Also, for four of the six, the esti- tual as well. The variable Pelc relates to mated coefficient is significantly different crimes of murder subject to punishment by from zero (having a ratio smaller than -2). execution, actually a small proportion of He also repeats the analysis after excluding some years from the beginning and some from the end of the series. These modifications do not change his resultsappreciably. Using two of the estimates, Ehrlich derives an estimate of the average number of mur- Table 8. Comparison of estimated coefficients in equation [lo]

A P Constant 'a P PXQl U L A T - - -cia - - - -Y~ - - Ehrlich's estimates a) .257 -3.1 76 -1.553 -.455 -.039 .067 -1.336 1.481 .630 p.047 I ( -.78) (-1.99) (-3.58) (-1.59) (2.00) (-1.36) (4.23) (2.10) (-4.60) I Our estimatesa b) .257 -2.02 -.56 u.25 -.038 .01 -.91 .65 .71 -.02 (-2.61) ( -.55) (-1.57) (-1.24) ( .26) ( I (2.64) (2.28) (-2.6) "our estimate of p was actually $=.55 but we present estimates using the same value as Ehrlich obtained for comparison purposes. Our estimates were not sensitive + changes in p except for p near 1.

all murders and one which varies from state Assuming that the variables used in the precious degrees of freedom. While there is to state. Yet the UCR data used by Ehrlich study are faithful measures of what we some validity to Ehrlich's response, the for the number of murders, the number of really want to observe (which we believe to deletion of these points is not arbitrary if a arrests, and the number of convictions be untrue), there are still a number of meth- fundamental change in American society refer to all murders and nonnegligent odological questions to be answered. took place around 1963, as has been argued homicides rather than to only capital Ehrlich's model is linear in the logarithmic by many criminologists and sociologists. crimes. If both capital and noncapital mur- scale (although he leaves Tuntransformed) Moreover, as we found in our reanalyses der rates have production functions of the and a number of authors have shown that described below, these years stand out as form (8), then the overall murder rate can- the conclusions reached are dependent discrepant in various forms of residual not have a production function of this form upon the scale of measurement. Passel1 and analysis. (see the related discussion in Hoenack and Taylor (1977) and Bowers and Pierce Weiler 1977). Ehrlich's discussion of this (1975), using data sets that are effectively K1ein, Forst, and Filatov a problem is noninformative and sidesteps identical to Ehrlich's, find that the coeffi- number of the issues. cient of PC(,is not significantly different that Ehrlich might have used. One is the from zero when estimated in a model that is average length time served by The data used for PC],present further prob- murderers-it very well may be that this is lems. particular, the data for P,,d and linear in the original scale of measurement. Finally, we note that all of the variables the for explaining the XPOL were not available for odd years increase in murders. lhese from 1913-1951. Ehrlich estimated these actually used by Ehrlich are fallible measures of the variables of interest, and that data are not available. Another values by a regression technique that he the models of real interest should thus in- variable that they do use is an overall index does not describe. Among the many prob- valve errors-in-the-variables, and multiple- of violent crime. The justification for its in- lems inherent in this type of procedure is indicator structures. ~h~ difficulties here elusion is that murder may be increasing as the loss in real degrees of freedom due to a by-product of an overall increase in the the missing data. The effective degrees of are the same as those described in the last section. level of lawlessness. Reanalyzing Ehrlich's freedom for estimation is an important data, they find that with this extra variable issue here and more will be said about it Another methodological question is whether in the structural equation the coefficient of later. the relationship between theactual variables Pel,is no longer significantly different from A fourth problem that ~-,~li~hfaced was used is changing over time. Passel1 and zero. that there were no executions after 1967. Taylor and Bowers and Pierce indicate that the data for Years after 1963 exert heavy in- Hoenack and Weiler (1977) reanalyzed the He arbitrarily defined the number of execu- Bowers-Pierce data, using a fully specified tions in those years to be one in order to be fluence on the estimated coefficients. In their analyses, both sets of authors show simultaneous system of equations, a theo- able to take logarithms. This is indicative retical justification for which is given in of a basic flaw in the production function that the effect of Pel,is not significant when these later Years are deleted from the data Hoenack, Kudrle, and Sjoquist (1978). model of equation (8). ~t is simply inappro- Their model interprets Ehrlich's murder set (see the related discussion in Klein, for application to a social structure supply function as the society's response to allowing zero executions, since it predicts Forst, and Filatov (1978)). Passell and perform an F-test determine if murder behavior, not vice versa. For their an essentially infinite murder rate for such specification, the coefficient of the execu- situations if the coefficient pl is negative the regression function is the same for the tion variable is positive although never (i.e., the sign associated with a deterrent years before 1963as for the years after 1963 more than one standard deviation from effect of capital punishment). and conclude that it is not. (Unfortunately, as Ehrlich (1977a) notes, the properties of zero. A key feature of their specification is An overriding issue related to the data is their test statistic are not known.) Further, the of the the pro- the choice of aggregate data for making In- Bowers and Pierce argue that doing the portion of the population between the ages ferences. Baldus and Cole (1975) include an analysis in the logarithmic scale gives more of 14 and 24, into two parts: one for the excellent discussion of the dangers of weight to these later years. In his rebuttal to proportion of juveniles (ages 14-18) and making causal inferences using nationwide Bowers and Pierce, Ehrlich (1975b) claims One for young (ages 19-24). We crime data. They note that crime patterns that there is no justification for arbitrarily "Ote that their re- have differed over time from state to state deleting data points and that doing so loses quire the inclusion of T(its estimated coef- as has the use of the death penalty. If mur- ficient is essentially zero when included); this der rates increased in states that used the point is especially interesting given the cru- death penalty often, but rates decreased in cia1 role played by Tin Ehrlich's analysis states not using the death penalty, the use and specification, which we discuss in of nationwide data might completely ob- detail shortly. scure this fact. These criticisms raise a number of ques- We take issue with Ehrlich's arguments for results, greatly simplifies the estimation, tions. The estimated coefficients differ de- the endogenous variables Q/ N, P.,, and P,I, and allows for detailed residual analyses pending on the scale in which theanalysis is having simultaneous effects on one another. based on standard methods for multiple done, but which is the proper scale? The It makes far more sense to us to think of a linear regression. Those residual plots that estimates are affected by the later years criminal's subjective assessment of punish- we have examined indicate that this (1963-1969) but what distinguishes these ment rates as affecting his current behavior, assumption may not quite be met, but later years from the earlier ones? A further but that the murder rate affects the punish- when we have reestimated the parameters criticism deals with the basic formulation ment variables after some delay of time. assuming different values for the first- of the model as a simultaneous set of equa- The delay might be 6 months, 1 year or order serial correlation coefficient we have tions and the identification of the key struc- even 2; however, since the data only allow found that the estimates do not change tural equation for the supply of murders. for delays which are multiples of a year, we substantially. The residual plots indicated We use a somewhat different approach in have arbitrarily fixed on a delayed effect of that the correlation might be of greater our analysis and try to answer some of murder rates on punishment of 1 year. This than first order but this possibility was not these and other questions. assumption means that our system of equa- explored. If such higher order serial tions, unlike Ehrlich's, is recursive not si- correlation exists, it affects Ehrlich's In our analyses we have used data furnished multaneous, and thus we do not have analyses as well as our own. by Bowers and Pierce and used in their Ehrlich's identification problem nor the analyses. Ehrlich consistently refused to Table 9 gives estimates of the coefficients in problem of making inferences about struc- the murder rate equation for different make his data available to us and to others tural parameters. Our model differs in this for reanalysis. The only versions of the transformations. Note that the first two way from those used byLEhrlich, Bowers sets of estimates are for an equation that variable Pel, that we had values for were and Pierce, and Passel1 and Taylor, and we PXQl and PXQ2. The bulk of our analysis does not include C, the violent crime level use it primarily to make a series of meth- index. We considered three different meas- focused on using either PXQl or its lagged odological points. values, PXQlI-I], as a measure of probabil- ures of PC(,:PXQI, PXQI1-11, and PXQ2. ity of execution given conviction. Our model for reanalysis is thus of the The only significant coefficients (whose form: t-values, which are given in parentheses, are Our first goal was to see if we could repro- in excess of 2) are for PXQi when variables duce Ehrlich's results using this data set. In are measured in the original scale or when Table 8 we give our estimates, along with only Q/ N is measured in the logarithmic Ehrlich's, of the coefficients in the murder scale. These equations are the only ones to rate equation. Note that the signs of all co- contain significant coefficients for the efficients agree but that there are some dif- other punishment variables, namely P,I,. ferences. The likely cause of the different estimates is in Ehrlich's estimation proce- Bowers and Pierce (1975) conclude that dure based on the method of Fair (1970). Ehrlich's results are heavily dependent on We have programmed a method suggested the analysis being done in the logarithmic by Fair ourselves to get estimates, while scale. They state that due to the very low Ehrlich used a packaged routine. We sus- number of executions after 1962, taking pect the problem is in how the modified logarithms of PXQl emphasizes the effect first differences are created. Fair actually of these later years thus yielding a negative suggests a number of different methods, coefficient which is significantly different some of which are asymptotically more from zero. Our conclusion, after studying efficient than thers. The method that we the residual plot shown in Figure 2 as well where the errors, e,,are assumed to be,inde- adopted uses (8,- pPI=l)as the values for as other graphs, is in conflict with theirs. the endogenous variables in the second pendent with mean 0 and variance a; (i.e., Taking the logarithms of PXQl moves the stage regression. Thus in our analysis the independent for different points within values of PXQIin later years far from the effective years are from 1934-1969. Ehrlich equations). A subscript of (-1) indicates center and tends to flatten out the slope. appears to have used a somewhat different that the variable was lagged by 1 year. By These residual plots do, however, support differencing operation which allowed an assuming that the errors are independent the conclusions of Bowers and Pierce and analysis only for the period 1935-1969. At for different points within equations, we of Passell and Taylor that the years after any rate, the conclusions based upon our have set p = 0. This zero value for the serial 1962 do not fit the pattern of the previous estimates are not substantially different correlation is completely consistent with ones. our findings in the replication of Ehrlich's from Ehrlich's. A ' major discrepancy Other residual plots that we examined in- occurs in the estimates of b. We found a = dicated a second problem which has not 0.55 while Ehrlich reports a=0.257. Since Figure 2. been noted in previous analyses. Large our estimates were not very sensitive to residual values corresponding to 1934 Residual plot for the crime rate changes in 0 (except near 1) we used point to it as a possible outlier. Looking at equation in [I 21 Ehrlich's value to get the remaining the original data, we find that for 1934 estimates. .10-,69 there is a very large value of PXQl and a a 68 small value of Q/ N. We suspected that this - .05... @67 ...... point might have a strong effect on the esti- J ...... 0 0 :----.--mates so we reestimated the coefficients in 2 .. . . both the original and the logarithmic scale. -:05

64 63 062 -15: ; k a a : ! : : + -4 -2 0 2 3 LnPXQ, i . 1 Table 9. Estimated coefficients for equation [I21 under various transformations 1 PXQ,

-Pa 2P PXQ~ ----L u A Y~ -T c 1b - -.99 .I4 .063 -64 -. 084 .81 w.029 -.13 .39 (-1.16 (1.00) (1.91) (7.49) (-1.83) (3.00) k.09) (-.93) (1.95) gb -1 .0x104 -1 .8x104 -7.6x10-~ -.20 4.0x10-~ .035 1.1 xlw5 -.002 9x10.~ k.38) (-1.5) (-1.04) (-3.33) (-2.35) (.78) (1.31) (-7.62) (9.00)

aTransforrnations are designated as follows: 1. All variables in logarithms, 2. All variables except T in logarithms, 3. All variables untransformed. 1 4. in logarithms, all others u.transformed. b~hedata for 1934 were deleted in estimating the coefficients.

These estimates, given in Table 9, show degrees of freedom actually are in a two- Earlier we noted the arbitrary choice by that things do change considerably once stage estimation problem. In Ehrlich's first Ehrlich of the use of logarithms for all vari- 1934 is deleted. The estimated coefficient in stage regression, there are 18 independent ables but T, time. In Table 9 we show some the original scale is still negative but not variables in addition to the 9 independent equations where in T was used in place of T significant while the estimate in the loga- variables in the second stage regression. As in a fully logarithmic specification. The rithmic scale is now positive. The residual far as we know, there has been no work changes in sign for the coefficient of PXQ plots after deletion of this point do not done on determining the appropriate that go with this change in specification are indicate any other outlier problems. We degrees of freedom for this type of problem suggestive that the choice of scale for the note that in Ehrlich's analyses, a significant but we would think there are considerably variable T may have a strong influence on result is obtained when using PXQI but fewer than 25. The difficulty in computing the coefficient. Now the arbitariness of not with PXQI.With the lagged variable, degrees of freedom is compounded by Ehrlich's choice hits home. Why choose T PXQl (- I,,the value for 1934 is used while Ehrlich's estimation of the missing values or log Tinstead of TI, or In(T- 1900), or for PXQl that year's data are excluded of P,[,and XPOLusing the remainingdata. even In(T - 1776)? In other reanalyses we from the analysis. This seems to support have discovered that suitable transforma- our finding regarding the suspect nature of Table 9 contains only the results for equation (12) of our three-equation model. We tions of Tcan dramatically change the size the 1934 data. and sign of the coefficient of PXQl. have analyzed the other equations as well It is not surprising that one point can exert but do not report on them-here since they In summary, we find that these data do not such a strong effect on the estimated coef- do not affect the deterrence hypothesis. support Ehrlich's conclusion that there is a ficients. Even in our recursive model there deterrent effect created by an increase in are only 25 degrees of freedom available for the probability of execution. First, we find estimating the coefficients in the model. In the model formulation suspect, and inap- Ehrlich's model the problem is much propriate for application in-situations with worse. Although Ehrlich, as well as other essentiallv zero execution rates. Second. authors, have routinely computed the we the choice of data used td degrees of freedom associated with their measure key variables in the model. Third, estimates, it is not clear what the effective we have noted that the analysis is sensitive to the specification of the model. Using a recursive model we have obtained results that are different from Ehrlich's. The question of which model is more appropriate is Conclusions not an easy question to answer, but we think that there is as much apriorisupport Becker's (1968) paper has stimulated many for our model as for Ehrlich's. Our residual economists and others to use modern sta- analysis does not indicate any lack of fit where Iis the percentage of the family pop- tistical methods for the analysis of regression and simultaneous equations models to other than the two problems discussed ulation below an arbitrary cash income search for evidence in support of the deter- above; in contrast Ehrlich does not poverty line, and M is the ratio of net non- rence hypothesis. Following Ehrlich's examine the goodness of fit of his model. white migrants in the previous 10 years to (1973a, 1975a) pioneering attempts to im- Others, such as Bowers and Pierce (1975) the total population. Using both ordinary plement Becker's theoretical model, the and Hoenack and Weiler (1977), have also and two-stage least squares he found posi- flood of papers and manuscripts on the formulated alternative model specifications tive (but not significant) estimated coeffi- analysis of crime and punishment data has which when used in analyses make the cients for PQX, and negative (and signifi- been almost overwhelming. deterrent effect of capital punishment dis- cant) estimated coefficients for C/ Q and appear. In all, there are far too many flaws T*. Passell's specifiction, unfortunately, What has this work contributed to our in Ehrlich's model, his data, and his analy- has little more to recommend it than does knowledge of the deterrent effects of pun- ses for him to claim that a real deterrent Ehrlich's, but his results do illustrate the ishment on crime? We have concluded that effect of any sort has been found using this importance of the specification on the re- little or no progress has been made during form of longitudinal data. sults and the inferences one is likely to draw the past 10 years in our understanding of from the analysis. the potential deterrent effects of punish- Cross-section analyses of murder rates ment on crime. Indeed much of the contro- Forst (1977) examined data on the change To buttress the arguments in his paper on versy that erupted over Ehrlich's work has in the crime and punishment measures that the analysis of the longitudinal data on served to divert the efforts of serious occurred between 1960 and 1970 for all 50 murder, Ehrlich (1977a) has also analyzed scholars of crime from more productive states. In regressions based on a subset of the cross-sectional variations of murder 32 states for which complete data were pursuits to a battle with Ehrlich and his and execution in 1940 and 1950. The basic available, he found the execution variable supporters. The battle has raged before the regression model used in his analyse~ to have a positive coefficient. Although his United States Supreme Court, which heard resembles equations (4), (9, and (10). results appear to be in agreement with arguments based on Ehrlich (1975a) and Passell, they are almost certainly domi- Passel1 and Taylor (1977) in the case of nated by the fact that PXQ for 1970 for all Fowler v. North Carolina. It has filled the states was zero! Forst models the change in pages of many different journals. Some the homicide rate, A(Q/ N), as a function of journals devote entire issues to the topic the change in execution rates, A(PXQ), (e.g., see Journal of Behavioral Economics, and changes in other variables. Since Vol. 6, Numbers 1 and 2, Summer/ Winter, PXQ = 0 for all states in 1970, Forst thus 1977). It has been investigated by a panel Ehrlich uses ordinary least squares to esti- models A(Q/ N) as a function of PXQ for established by the National Academy of mate the coefficients in equation (15) and 1960 and the changes in other variables. Sciences. And in the end we seem to be no uses data first for states with positive exe- We do not understand the logic behind this further ahead of where we were 10 years or cutions, and then for all states. He also specification. more ago. attempts to compare the results of a fully In this paper, we have reviewed a large pro- linear specification with (15), using an Finally we note the analyses carried out by approach suggested by the method of Box portion of the empirical attempts to model Loftin (1980) for 1960 cross-sectional data the economics of crime and punishment, and Cox (1964). His comparison strongly using a markedly different set of variables favors the log-log specification of (15). including the work of Ehrlich (1973a, aside from C/Q and T*, motivated pri- 1975a) based on the model suggested by Ehrlich finds the estimated coefficients of marily by sociological rather than economic T*, Q/ C, and PXQ (measured in several Becker (1968). We have concluded that: considerations. Loftin finds little to sup- (a) The Becker-Ehrlich model has glar- different ways) to be negative and signifi- port the inclusion of the punishment vari- cant at at least the 0.05 level both for the ing shortcomings and, when examined crit- ables in a regression equation with either a ically, does not lead to the claimed testable linear and log-log specifications. His con- linear or a log-log specification. clusion is that these data and the analyses hypotheses regarding the effect of punish- of them corroborate his earlier analysis of We have concluded that these cross- ment of crime. the longitudinal data. sectional analyses offer no support to the (b) The use of the Becker-Ehrlich model conclusion that there is a deterrent effect of for aggregate data requires extensive justi- As in Ehrlich (1975a) these conclusions capital punishment, and the conflicting fication that has never been given. seem at first sight convincing, until we note results for the other punishment variables (c) The crime and imprisonment data that the data used have even greater short- cast serious doubt on any attempt to infer used to empirically examine the Becker- comings than those noted earlier and that deterrent effects. Ehrlich model are so untrustworthy as to almost all of the other analytical problems render any serious analysis meaningless. mentioned earlier remain. Moreover, Ehr- (d) The empirical implementations of lich's results run contrary to those of other the Becker-Ehrlich model are badly flawed investigators who have examined cross- and have extremely grave statistical short- sectional data. For example, Passe11 (1975) comings, and most published conclusions used 1950 and 1960 data to estimate theco- from them are not to be trusted. efficients in the model, (e) Even if one accepts the Becker- Ehrlich model, and Ehrlich's choice of data to implement it (which we do not), Ehrlichf affirmative conclusions regarding the deterrent effect of punishment on crime in general, and of capital punishment on murder in particular, do not stand up to careful statistical scrutiny. Ehrlich's critique of the National Academy References Ehrlich, I. (1973) of Sciences Panel's report (Ehrlich and Avio, K., and C. S. Clark (1976) "Participation in illegitimate activities: A Marks 1978) is essentially an attempt at Propern. crime in Canada: An econonietric theoretical and empirical investigation." Journal self-justification. He argues that only his stud?.. Toronto: Ontario Economic Council. of Political Ec~norn.&~8 1:52 1-565. version of the econometric model of deter- Baldus, D. C., and J. W. L. Cole (1975) Ehrlich, 1. (1975a) rence is relevant, that any work inconsistent "A comparison of the work ofThorsten Sellin "The deterrent effect of capital punishment: A with it can be dismissed out of hand, that and lsaac Ehrlich on the deterrent effect of capi- question of life and death." American Economic only analyses done by Ehrlich (or those tal punishment." Yale Law Journal85:170-186. Review 65:397-417. confirming his findings) are correct or ap- Becker, G. S. (1968) Ehrlich, 1. (1975b) propriate, and that all of the work of others "Crime and punishment: An economic ap- "Deterrence: Evidence and inference." Yale whose conclusions run counter to Ehrlich's proach." Journal of Political Econo~li.~~78: Lau8Journal 85:209-227. is incorrect, distorted, technically flawed, 169-217. Ehrlich, I. (1977a) theoretically eclectical, or irrelevant. This Bielby, W. T., R. N. Hauser, and "The deterrent effect of capital punishment: is hardly a dispassionate perspective, and D. L. Featherman (1977) Reply." American Economic Review 67:452-458. we find little in the critique which counters "Response errors in nonblack males in models Ehrlich, 1. (1977b) the crucial points made in the preceding of the stratification process." Journal of' the "Capital punishment and deterrence: Some sections and in the Panel's report itself. American Statistical Associarion 72:723-735. further thoughts and additional evidence." Journal of ~o?iticalEconomy 85:74 1-788. We find no reliable empirical support in the Block, M. K., and J. M. Heineke (1975) existing econometrics literature either for "A labor theoretic analysis of the criminal Ehrlich, 1.. and J. C. Gibbons (1977) choice." American'Econotnic Rerliew 65:3 14-325. or against the deterrence hypothesis. "On the measurement of thedeterrent effect of Blumstein, A., and J. Cohen ( 1973) capital punishment and the theory of deter- Moreover, we believe that little will come rence." Journal of Legal Studies 6:35-50. from further attempts to model the effects "A theory of,the stability of punishment." of punishment on crime using the type of Journal of' Criminal Law and Criminology Ehrlich, I., and R. Marks (1978) 64:198-207. data we have described in this paper. "Fear of deterrence." Journal ofLegalSrudies Blumstein, A., J. Cohen, and D. Nagin (eds.) 7:293-316. (1978) Fair, R. C. (1970) Deterrence and incapacitation: Estimating the "The estimation of simultaneous equation Acknowledgments e~fectsof criminal sanctions on c-rime rates. models with lagged endogenous variables and The authors are indebted to several of the partic- Washington, D.C.: National Academy of the first order serially correlated errors." ipants of the SSRC-LEAA Workshop whose Sciences. Econometrics 38:507-5 16. ideas and ?suggestions inevitably have found Bowers, W. J., and G. L. Pierce (1975) Fisher, F. M., and D. Nagin (1978) their way into this article, although perhaps in a "The illusion of deterrence: A critique of lsaac "On the feasibility of identifying the crime distorted way. In particular, thanks are due to Ehrlich's research on capital punishment." Yale function in a simultaneous model of crime rates Albert D. Biderman, Alfred Blumstein, William La\+* Journal 85: 187-208. and sanction levels." In A. Blumstein et al. (eds.), Fairley, Kinley Larntz, Colin Loftin, Daniel Deterrence and incapacitation: Estimating the Nagin, Albert J. Reiss Jr., David Seidman, and Box, G. P., and D. Cox (1964)- "An analysis of transformations." Journal of effects of criminal sanctions on crime rates, Leslie Wilkins. We also wish to thank the many Washington, D.C.: National Academy of others who have shared their thoughtsand work the Royal Statistical Society, (B)26:211-243. Sciences. . with us, including William Bowers, Phillip Cook, P. (1977) Cook, Franklin Fisher, Brian Forst, Stephen "Punishment and crime: A crit~queof current Forst, B. E. (1976) Hoenack, Paul Meier, Frederick Mosteller, findings concerning the preventive effects of "Participation in illegitimate activities: Fur- Glenn Pierce, Christopher Sims, Walter Vandaele, punishment." Lak*and Contemporarr Prohknis ther empirical findings." Policy Analysis 2: Ann Witte, and William Weiler. William 41: 164-204. 477-492. Bowers, Brian Forst, and Walter Vandaele all Cook, R. D. (1977) Forst, B. E. (1977) provided their data for our reanalyses; lsaac "The deterrent effect of capital punishment: A Ehrlich consistently refused to make his data "Detection of influential observations in linear regression." Technometrics 19: 15-18. cross-state analysis of the 1960's." Minnesota available. LonvReview 61:743-767. Daniel, C., and F. S. Wood (1971j Fitting equations to data. New York: John Wiley and Sons. Draper, N., and H. Smith (1966) Applied regression ana!rsis. New York: John Wiley and Sons. Gilbert, J. P., R. J. Light, and F. Mostellex Passell, P. (1975) U.S. Bureau of the Census (1975) (1975) "The deterrent effect of the death penalty: A Statistical abstract qf the United States (96th "Assessing social innovation: An empirical statistical test." Stanford Law Review 28:61-80. edition). Washington, D.C.: U.S. Government Printing Office. base for In A. R. Lunsdaine andc. A. Passell, P., and J. B. Taylor (1977) Bennett (eds.), Evaluation and experiment: "The deterrent effect of capital punishment: Vandaele, W. (1978) Some critical issues in assessingsocialprograms, Another view." American Economic re vie^' "Participation in illegitimate activities: I. New York: Academic Press. 67:445-45 1. Ehrlich revisited." In A. Blumstein et al. (eds.), Deterrence and incapacitation: Estimating the Hoenack, S. A., T. T. Kudrle,and D. L. Sjoquist Penick, B. K. E., and M. E. B. Owens (eds.) e[fects of criminal sanctions on crime rates,. (1978) (1 976) "The deterrent effect of capital punishment: A Washington, D.C.: National Academy of Surveying crime. Washington, D.C.: National Sciences. question of identification." Po1ic.v Anahsis Academy of Sciences. 4:49 1-527. Wilson, J. Q., and 6. Boland (1976) Petersilia. J.. P. W. Greenwood, and M. Lavin "Crime." In W. Gorham and N. Glazer (eds.), Hoenack, S. A,, and W. C. Weiler (1977) (1978) "A structural model of murder behavior and The urban predicament, Washington, D.C.: The Criminal careers of habitua,felons. Washington, Urban Institute. the criminal justice system." Unpublished D.C.: National lnstitute of Law Enforcement manuscript. and Criminal Justice, Law Enforcement Assist- Witte, A. D. (1977) Joreskog, K. G. (1970) ance Administration. "Estimating the economic model of crime with "A general method for analysis of covariance individual data." Working Paper 77-6. Chapel Reiss, A., Jr. (1980) Hill, N.C.: Department of Economics, Univer- structures." Biometrika 57:239-25 1. "Understanding changes in crime rates." This sity of North Carolina. Klein, L. R., B. E. Forst, and V. Filatov (1978) volume. "The deterrent effect of capital punishment: Zellner A. (1962) Ross, H. L. (1973) "An efficient method of estimating seemingly An assessment of the estimates."In A. Blumstein "Law, science, and accidents: The British unrelated regressions and tests for a regression et al. (eds.), Deterrence and incapacitation: Esti- Safety Act of 1967." Journal of Legal Studies bias." Journal of the American Statistical Asso- mating the~effectof criminal sanctions on crime 2: 1-78. rates, Washington, D.C.: National Academy of ciation 57:348-368. Sciences. Skogan, W. G. (1976) Zellner, A. (1971) "Crime and crime rates." In W. G. Skogan An introduction to Bayesian inference in Kuh, E., and R. E. Welsch (1976) (ed.), Sample surveys of the victims of crime, econometrics. New York: John Wiley and Sons. "The variances of regression coefficient esti- Cambridge, Mass.: Ballinger. mates using aggregate data." Econometrics Zimring, F. E. (1978) 44:353-363. Sprent, P. (1969) "Policy experiments in general deterrence: Models in regression and related topics. 1970-1975." In A. Blumstein et al. (eds.), Deter- Loftin, C. (1980) London: Methuen. 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A prolegomenon for a macro model for criminal justice planning: JUSSIM Ill

ALFREDBLUMSTEIN Urban Systems Institute Carnegie-Mellon University

GARYC. KOCH Department of Biostatistics University of North Carolina

JUSSIM I is a deterministic, steady-state, I. Background and need, is important to begin consideration of the nonqueueing flow simulation of a multi- for the model future generation of such planning models. stage system like the criminal justice In this paper, we expand the view of the system. The flow is processed through The principal computerized model in cur- existing JUSSIM models to introduce the stages, and the process is characterized by rent use in the criminal justice planning following additional considerations: process is the JUSSIM I model (see Belkin an input into the first stage and by stage-to- (1) Explicit concern for the demograph- stage branching ratios. At each stage, et al. 1971) which examines the "down- stream" flow through the criminal justice ic and socioeconomic characteristics of the resources are applied to the units of flow, population generating criminality. resulting in linear costs and resource con- system beginning with crimes and following the handling of such crimes as they (2) Explicit concern for the demograph- sumption. JUSSIM I1 expands on JUSSIM ic and socioeconomic characteristics of the I by incorporating the feedback flow of become associated with suspects, defendants, convicted offenders, and prisoners. population generating victims. recidivists through subsequent arrests. In (3) Explicit concern for the effect of the this paper, an expanded "JUSSIM 111" is JUSSIM I1 (see Belkin et al. 1974) incorpo- criminal justice system on crime reduction outlined. JUSSIM 111 incorporates a rates recidivism into that model through through incapacitation and deterrence. crime-generation process and a victim- the addition of the feedback features (4) The effects on crime of environmen- generation process from the characteristics associated with re-arrests. These features tal factors such as the state of the economy of offenders and victims. Offenses are gen- include probability of re-arrest at various or social conditions. erated by first-time offenders coming from points of departure from the criminal jus- the general population and recidivists re- tice system, the time lags until recidivism, a Even though the information on most of leased by the criminal justice system. Simi- crime-type-switch process reflecting the these relationships is still extremely limited, larly, the population produces first-time transformation from a previous crime type there are nevertheless im~ortantreasons victims from a potential victim population, to a subsequent crime type, and a distinc- for pursuing the development of a model and "victim recidivism" provides an oppor- tion between virgin arrestees (those ar- that incorporates them. Such a model tunity for further victimization, which rested for the first time) and recidivist forces an identification of the relevant vari- could be influenced by the victim's self- arrestees. ables in those relationships, and so iterates protective actions. The offense and victim- with the data collection process to assure ization processes interact in a "victimiza- The JUSSIM I model has seen fairly that the information to be collected is con- tion events" stage. The paper considers the widespread implementation (as discussed sistent with the formulation of that model. various sources of data which could be in Cohen et al. 1973 and Blumstein 1975), Alternatively, as the data arrive from the used to generate the parameters of such a but very little actual use has yet been made model and the statistical approaches to of the JUSSIM I1 model. This is true identifying the important parameters and largely because of the limited availability of for developing estimates for them. data on recidivism, and to a lesser degree, because the intelligent use of this more complex and advanced model demands greater technical sophistication. JUSSIM I1 is, however, now ready for implementation in a number of jurisdications, and so it Figure 1. (3) The increasingly computerized criminal- history records (or "rap sheets") such as the FBI's Computerized Criminal History I (CCH) file which records for each individual the sequence of his arrests and any relevant dispositional information that subsequently becomes available for each arrest. In addition, a variety of computerized systems are being developed for handling the specific functions of various subsystems of w w I' Virgin the CJS. For example, the PROMIS Potential Offenders Victimization system, designed to aid prosecutors, offender Switch events copulation matrix maintains detailed information on defend- Slk 5 Milk ants as they are handled through the prosecutory processes. Total v~ctimizations 1 All of these data systems were devised and are used for reasons other than the Compensatlonf )r restltutlon formulation and use of a planning model, Non-reports and most of them are relatively unrespon- Precaution sive to the information demands of such a J 1 model. Nevertheless, the data they do provide can often be transformed into appro- Non-arrests b priate inputs for a planning model. In addition, the planning model can indicate * variables central to planning but for which Arrests Vlct~m no appropriate data collection system has - reactlon yet been organized. Those variables, once I Dlsmlssed identified, might then be appended to existing collection efforts or, in some cases, might warrant an entirely new data collection effort. Trial a Even though the principal value of such a. model at this time is in shaping data collection and manipulation and in the formula- Recidivists tion of functional relationships, it could Offender Conviction ultimately. become an important policy reaction instrument when it is developed and Release provided with appropriate and valid data. That role, however, will continue to be limited by the validity of the assumed relationships incorporated into the model. As 1 Institution 1-4 community 1 1 the forms of those relationshipsare revised, further modifications of the models will become necessary. 1 II. Basic structure of the model / A. Flow diagram. The basic structure of the model is shown in Figure I, which various data collection programs, they pro- The need for developing models is particu- depicts the flow of virgin offenders from a vide a stimulus for reshaping the formula- larly important today in view of the major "criminal population" and of virgin victims tion of the model. This interaction between data collection efforts being undertaken. from a "victim population" (both of which, the data and the model represents an These include: of course, are drawn from the same total important contribution of any such model (1) The Offender-Based Transaction population) into a "victimization events" formulation. Statistics (OBTS) system, which tracks stage where the offender and the victim individual crimes and arrestees in their interact with each other or with other recid- processing through the criminal justice ivist victims and/or offenders in the system. (2) The National Crime Panel's victimization survey, which collects a wide variety of personal and crimeexperience data from a sample of householdsand businesses. generation of victimization events. Subse- ables such as age, race, sex, and marital preventive patrol, or CJS sanction vari- quent to that victimization, the event is status, as well as socioeconomic variables ables. These functions could be as large and either reported or unreported and, if re- such as education, income, and employ- as elaborate as could validly be built from ported, an offender may or may not be ment status. The partitioning is intended to the available data and statistical evidence. arrested. If arrest occurs, then the suspect is divide the total population intosubpopula- (4) CJS resource consumption. As is handled through the criminal justice tions which have reasonably homogeneous seen in Figure I, the flow of reported system; he may be dropped out at any one crime-propensity rates (t,~)which can then crimes and arrestees through the criminal of a number of stages of successive penetra- be measured for each crime type, k. justice system is structured similarly to tion through the system; and then he may (2) Victim population (V,r). Similarly, JUSSIM I, and the JUSSIM I structure either recidivate or desist from future could be used for examining the resource criminal activity. the total population is partitioned into victim subpopulations which are indexed by use associated with this model. The princi- The victimization process has a similar subscriptsj = 1, 2, . . . ,Nv.This partition is pal extension would involve the incorpora- "recidivism" loop in which a victim may likely to be different from the partition into tion of the victim and offender attributes. subsequently engage in various forms of which the offender population was struc- (5) Rehabilitation (@,r,A,L).The offender preventive action reducing his vulnerability tured, for it represents groups with inter- feedback loop used here is very similar to to victimization, and he may or may not nally homogeneous victimization risks. that associated with JUSSIM 11; the subsequently become a victim again. In This might reflect their "value" as victims feedback here, however, is to the vic- both the offender and the victimization of crime as well as their vulnerability to timization event rather than to re-arrest as recidivism processes, there is a "crime- potential offenders. The strycture might in JUSSIM 11. The feedback is character- switch" process reflecting the possibility include business or commercial enterprises ized by parameters of recidivism probabil- that a subsequent appearance involves a as well as individuals. Here also, a victim- ity or (the complement) desistance probability different crime type than the previous ization rate (g,~)would reflect the rate at (@,I).These could be introduced as average appearance. which a member of the j'h victim subpopu- values, or, more richly, as functional forms lation becomes a victim of crime type k. This structure deals with all the functional of the exogenous environment in a way aspects explicitly incorporated into the (3) Victimization events (M,,L).The cen- similar to that discussed previously for vic- JUSSIM I and JUSSIM I1 models, tral feature of the model is the stage labeled timization events. Effort would be directed particularly the considerations of flow, "victimization events." This stage involves towards identifying the functional rela- resource consumption, and CJS workloads the convergence,of the offenders who come tionships of recidivism probability (I-@,k) associated with JUSSIM Iand the rehabili- initially from the "potential offenders" and the mean time until recidivism (or its tationlrecidivism aspects of JUSSIM 11. In population and the victims who come initial- reciprocal, the mean recidivist crime rate addition, however, it introduces a number ly from the "potential victims" popula- (h,~)for the offender subpopulation of new considerations. First, it goes back tion. Both of these "potential" populations groups. More elaborate functional structures from the crime or arrest stage to identify first generate first-time or "virgin" of- could be introduced to account for the the relevant criminal population and the fenders and virgin victims, many of whom contemporary socioeconomic environment, relevant victim population in terms of their reappear subsequently as recidivist of- the criminal justice system's deterrent activ- demographic and socioeconomic charac- fenders and recidivist victims. A victimiza- ity, the nature of the rehabilitation teristics. In addition, it incorporates the tion event involves the joint interaction of treatment offered, and other factors that effects of the various "environmental an offender of type i with a victim of type j might reflect the individual's prior criminal factors" (e.g., economic conditions, social in a crime of type k, and so the victimiza- history and his last treatment by the CJS. conditions) as considerations in their crimi- tion events are characterized by rate (6) Victim vulnerability (v,~).Just as the nality or victimizationvulnerability. Other- parameters M,,r, which would involve vir- model displays a feedback process for wise, the model attempts to reflect the gin or recidivist offenders and virgin or criminal offenders, it also includes a deterrent effects of actions within the recidivist victims (i.e., the four combina- feedback loop for victims, with their associ- criminal justice system on the criminality tions of potential victimization activity). ated "recidivism" rates., v,i.... This rate can be of the relevant potential criminal popula- The M,,Lentries could be absolute quan- affected by factors related to the compensation tion as well on the recidivism character- titative rates reflecting the respective rates of victims or to restitution by the offender istics. The following discussion of each of of victimization, or they could be more or by various types of protective action these aspects of the model indicates how general functions reflecting the way those taken after a victimization event in order to these representations would be accomplished. rates vary with other exogenous variables. reduce further victimization. These could include contemporary eco- B. Identification of parameter groups. In nomic conditions, factors in the social (7) Offender-victim-crime-switch proc- this section, the major groups of variables environment, police deterrent activity like ess (T).In each cycle through the recidi- are identified, and their individual struc- vism process, it is possible for each dimen- tures, their relationships to each other, and sion of the previous path to be transformed. the effects of exogenous variables are explored. First, there is the potential of straightforward transformation of crime type (a (I) Potential offender population (si~). burglar switches to larceny or a victim of The potential offender population is robbery has his automobile stolen the next created by exhaustively partitioning the time). There can also be transformation of total population (a)into subpopulations indexed by a subscript i=1,2, . . . ,NO.The partitioning is based on demographic vari- both the offender's and the victim's sub- Ill. Structure of the model This potential criminal population would group, either through internal processes, parameters give rise to an input of virgin criminals Kk, such as aging, or by exogenous effects, reflecting the number of offenders of the ih The basic variables in the model include the such as change in socioeconomic status potential offender group committing crimes following: through change in economic and employ- of type k. ment conditions. A large switch matrix, T, (1) Criminal population, their charac- is included to reflect these transformations. teristics, and their criminality. B. Oflender recidivist population. The (2) Recidivist population and their recidivist population is similarly charac- (8) Incapacitation effects. Changes in recidivism probabilities and crime rate. terized by a pair of variables, 4,~and h,k, incapacitation strategy in the criminal jus- (3) Victimization population and their where @,k is the probability of desistance of tice system would be reflected through characteristics. a person of type i who last committed a branching ratios associated with incarcera- (4) Victimization event rates reflected in crime of type k (where desistance in this tion (e.g., reflecting the increased use of the M matrix. case implies complete cessation of crime prison) or through the effect of longer sen- (5) Offender-victimcrime switch process. committing behavior). In addition, those tences on the longer observed time between (6) Branching ratios of the criminal jus- who do continue to commit crimes do so at criminal events, with the associated reduc- tice system. a rate A,k, reflecting the reciprocal of the tion in the individual crime rate (ilk) for (7) Resource costs and workloads as time until the next crime by a person of persons routed through prison. used in the JUSSIM I model. type i who has just previously committed a crime of type k. (9) General-deterrenceeflects. The gen- In this sectio?, we examine these various The attributes associated with the eraldeterrent effect of sanctions used in groups of variables and the structure asso- recidivist population could include the the criminal justice system (e.g., appreciated with estimating these variables from same ones characterizing the criminal hension probability, conviction probabil- available data. In many cases, we try to ity, probability of imprisonment and sen- population, augmented by the individual's indicate our current best judgment of the prior criminal record (the number of prior tence) would be reflected through the func- appropriate data elements in estimating arrests, convictions, sentences) and by the tional relationships among the sanction these variables, but these will of course levels and the virgin criminality the treatment last given him by the criminal (t), depend on the degree to which data on the justice system (failure to arrest, arrest but desistance probability (@),and the recidi- indicated variables are available and the no charge, acquittal at trial, conviction but vist crime rate (A,k). As these relationships degree to which they do indeed serve to released into community supervision, or develop from the deterrence literature, they estimate the relevant variables, since they institutionalization). In any of these, any could be incorporated directly into estimating could well be augmented by other elements level of detail appropriate to alternative these parameters. or replaced by other more efficient estimat- specific treatment programs could be ing variables. Thus, the specifics of the (10) Environmental factors. It is well incorporated into such a model. known that a wide variety of factors in the variables identified serve more as illustra- C. Victim population. The structure of the socioeconomic environment are highly tions than as the ultimate definitive set that victimization population would be devel- correlated with crime rates, both cross- will eventually be used. oped in a manner similar to that of the sectionally and longitudinally. It would be A. OSfender population. The offender extremely desirable to incorporate the population is characterized by a set of at- offender population. The dominant demo- effect of these factors into the victimiza- tributes reflecting the demographic and graphic, social, and economic variables tion-event functional relationships to re- socioeconomic characteristics along which would include age, race, sex, marital status, flect the issues surrounding the question of they are best partitioned to generate sub- education level, and income. It may well the "causes of crime." These factors would groups with homogeneous offending rates. turn out, however, that an examination of the detailed data will suggest a different be reflected in a manner similar to the The presumed relevant attributes include structuring of the individual variables for deterrence variables, i.e., through the the following: the victimization population than for the desistance and crime rates associated with (1) Demographic variables-age, race, offender population, even though the basic the recidivist population. If they could be sex, marital status. variables would be the same. adequately identified, these would provide (2) Socioeconomic status variables- In addition, the victimization popula- important policy bases for crime-control education level and income level. tion would also be characterized by some actions that go beyond the confines of the The demographic variables might include measure of exposure. This measure would criminal justice system. As with the other binary partitions of race and sex, a three- include a combination of considerations of relationships in the model, the problems way split for marital status (never married, relate to the difficulty of estimating these assets or vulnerability to victimization as currently married, and previously married well as considerations of self-protective relationships, particularly in an identified but not currently), and some type of group- causal form. actions taken to reduce the risk of ing for the age variable. For the socioeco- victimization. nomic status variables, an initial estimate might include for education (less than 8 years, 8 to 12 years, 12 years, and more than 12 years) and for income (less than $5,000 per year, $5,000-$10,000 per year, $10,000-$20,000 per year, and more than $20,000 per year). In addition, there would be a variable reflecting the individual's em- ployability or skill level. D. Rate of victimization events. The rate To the extent that data do not permit JUSSIM 111 will require a more elaborate of victimization events is indicated by the determination of the M,]k functions in switch process. First, it must incorporate entries in the victimization matrix, M,,r,the terms of environmental factors and deter- the offender's crime-type switch as in rate at which a victim of c1ass.j is victimized rence factors, then these factors should be JUSSIM 11. It will also require transforma- by an offender of class i for a crime of class brought into the relationship for determi- tions of both the offender class and the k. The structure of the matrix isdictated by nation of the virgin crime-propensity from victim class on subsequent recidivism. the structure of the offender and victim the potential criminal population (0,and Thus, an offender would transform from populations. The entries would be the rate for the determination of the recidivism type i to i', a victim from type j toy, and the of aggregate victimizations by aggregate parameters, A and 4, associated with the crime type from type k to k'. For example, offenders (combining the virgins and recid- recidivist offenders. It is probable, however, an offender might age, change his education ivists of both offender and victim groups). that the relationship will be more easily level (perhaps because of an educational The entries in the matrix would be either a determined for the victimization rates than component of his treatment program) simple scalar value for the rate of victimiza- for the offenders, because most criminal increase his earnings, or change his marital tion events or, more generally, a function records do not make an adequate distinc- status between successive incidents. The of current environmental factors, the deter- tion between virgin and recidivist offenders. switch matrix would therefore reflect those rent effects of current criminal justice Therefore, the relationship may well be rates of state transition. For victims, the sanctions, and the effect of such police more easily applied directly through the transition might reflect similar changes in practices as preventive patrol. M,,k matrix than partitioned into separate demographic structure or changes in Examples of the relevant environmental relationships for virgins and recidivists, exposure reflecting various actions taken factors include: with the recidivists' relationship partitioned for self protection. The matrix would be a (1) Population density as measured by between the desist probability (4) and the square matrix with rank equal to the people per acre in the district being studied, associated crime rate, A. product of the number of offender types by the number of victim types by the number such as a census tract. E. Victim recidivism. Recidivism is built in of crime types on each of its dimensions. (2) A measure of the housing condition for victims just as it is for offenders. The in the district, as measured, for example, by parameters for the victimization recidivism G. Branching ratios in the criminal justice the persons per room or the measured state process, identified as victimization at a rate system. For the flow through the criminal of dilapidation of the housing in the area. vJr would be a parameter very similar to A,r justice system, JUSSIM 111 requires (3) A measure of the migratory mobility for the offender recidivists. The victimiza- branching ratios similar to those associated of the population in the area as measured tion-recidivism function would be associ- with JUSSIM I and JUSSIM 11. These by the percent of population resident in the ated with each victimization population branching ratios, however, must now area for less than 2 years. group j, and would be designed to incorpo- reflect the much richer "characteristic" or (4) A measure of the state of unemploy- "crime-type" structure of the JUSSIM 111 ment in the area as measured by the percent rate consideration of the victims' prior history, just as offenders' prior history is model. Thus, the branching ratios would employed, the percent seeking employment depend in general on the characteristics of but unemployed, and the percent eligible taken into account in estimating the recidi- v,k the offender, the characteristics of the for employment but no longer seeking vism parameters. In addition, would take into account the victims' reactions to victim, and the crime type. This provides employment. the opportunity for reflecting the differ- (5) A measure of the state of family their prior victimization experiences and to ential treatment given to offenders or disintegration in the region as reflected, the compensation or restitution envi- defendants based on their different demo- say, in the percent of one-parent families. ronment. For example, if compensationar- graphic or socioeconomic attributes. It (6) A measure of the differences across rangements tend to reduce the incentives also provides the opportunity for reflecting regions, as measured by a variety of for self-protective action, then an environ- the influence of a victim's characteristics on regional indicator variables. ment that provides victim compensation would be expected to stimulate a higher the treatment accorded his attackers (e.g., The deterrence variables would be reflecting a difference in the courts' reflected through additional functional victimization-recidivism risk. If prior victimization history stimulates self-protective responses to intergroup events rather than relationships on the M matrix. These to intragroup ones). relationships would include variables such action such as target-hardening or escape, as the probability of arrest given a crime, then the victimization-recidivism rate H. Resources, costs, and workloads. The the probability of conviction given an would be reduced correspondingly. JUSSIM 111 model would include data on arrest, the probability of imprisonment F. Offender-victim-crimeswitch. JUSSI M the resource costs and workloads just as given conviction, and the mean time served I1 calls for a crime-switch matrix reflecting they are incorporated in the basic JUSSIM for those imprisoned. the transformation from a prior crime type I format. If the parameters are independent The police crime prevention activities to a subsequent one by recidivists; of the offender or victim class, their values might include the intensity of preventive would simply be replicated for that patrol (as measured, for example, by the segment of the workload vector. If the mean patrol passage time for a random workloads are sensitive to either class, then point in the district), by the percentage of that relationship would be reflected in unmarked patrol activity, as well as by the richer detail within the workload vector. rate of various forms of police crime- The resource costs would depend only on prevention activity, such as the use of the resource and would be independent of family crisis intervention units. any of the crime type, victim, or offender characteristics, as in the previous versions of JUSSIM. IV. Statistical considerations (vii) Whether a victimized person expe- Similarly, if simultaneous information for riences a subsequent victimization or not both the offender and victim can be The statistical issues underlying the devel- during a particular time period after the opment of the JUSSIM I11 model pertain obtained for individual victimization events previous victimization. to the formulation of valid methodological and consecutive pairs of victimization strategies for estimating the functional The independent variables would reflect events, appropriate contingency tables can relationships which characterize the re- the specific nature of such exposure units also be formulated to determine the spective model components. For this as: victimization rate structure ~{,]k)and the purpose, attention must be directed to the (a) The demographic, socioeconomic, crime switch structure {T,k,,tllk;,~~ll~k~~) following four basic problems: and vulnerability characteristics of poten- respectively. More realistically, hqwever, (1) The specification of the structure of tial victims. such data would be very difficult, if not the data array required for the estimation (b) The demographic, socioeconomic, impossible, to obtain. For this reason, a of a particular functional relationship and and opportunity characteristics of potential more practical estimation strategy may be its corresponding parameters. offenders. to apply synthetic estimation ("raking") (2) The specification of methods of sta- (c) The crime type and the environmen- procedures (as described in Appendix A) to tistical analysis for parameter estimation tal characteristics for reported victimiza- adjust analogous arrest data like (d) to the corresponding separate marginal struc- from appropriate data arrays. tions together with any available informa- tures for victims and offenders like the (3) The specification of available data tion for the involved victim and offender as sources and their possible limitations as a in (a) and (b). {vk)and {S,k). However, as indicated in basis for parameter estimation. (d) The demographic, socioeconomic, the next section, such methods should be used cautiously because they presume that (4) The specification of the potential and ~reviouscriminal record character- the joint victim-offender crime association need for new data sources in terms of istics-of an arrested person together with alternative sampling and measurement corresponding information for the in- structure for victimizations is the same as procedures. volved victim as in (a) and the crime type for arrests. The remainder of this discussion is and environment as in (c). In summary, various types of multidimen- concerned with the implications of these (e) The demographic, socioeconomic, sional contingency tables can be con- considerations for the JUSSIM 111 model. and criminal record characteristics of a structed as a basis for estimating the person released from the criminal justice A. Spec8cation of data array structure parameters in the JUSSIM 111 model. system (either prior to trial, at the end of for parameter estimation. Since the JUSSIM Some of these tables may involve rather trial, etc.) and their opportunity character- 111 model is concerned with the rates of crude data while others may require highly istics for committing subsequent vidmhtions. occurrence of discrete events (victimiza- sophisticated data. In either situation, the (f) The demographic, socioeconomic, tions, arrests, trials, etc.), the data arrays critical issue is the formulation of such previous victimization history, and vulner- required to estimate the various functional estimation problems in terms of contin- ability characteristics of a victimized relationships in its structure are multidi- gency tables which can then be manip- person. mensional contingency tables which link ulated via the methods of analysis in the frequencies of such events to the Thus, the parameters in the JUSSIM 111 Appendix A to determine the functional characteristics of the corresponding vic- model can be estimated through the relationships which characterize the model tims, offenders, and environmental sub- analysis of such contingency tables as: components. In any event, a considerable populations. In this framework, the (1 (i) vs.(a) to determine the structure effort in data collection, analysis and assumption testing can be anticipated dependent variables would pertain to the (3)of the victim population and the outcome (or response) status for exposure virgin victimization rates {q,k). before valid and credible relationships are developed. units at risk for such phenomena as: (2) (ii) vs. (b) to determine the structure (i) Whether a person of a particular type {s,L)of the offender population and virgin B. Specification of available data sources. experiences any victimizations during a offender rates {hk). The JUSSIM 111 model described in this particular time period (the most recent day, (3) (iii) vs. (a) and (iii) vs. (b) to paper is extremely elaborate in order to week, month, year). determine the reporting rate structure for account for the diversity of victim types, (ii) Whether a person of a particular victimizations from the victim and of- offender types, and crime types. For this type commits any victimizations during a fender perspectives. reason, obtaining data for the formal con- particular time period. (4) (iv) vs. (c) to determine the arrest struction of the model will require (iii) Whether a victimization event is rate structure for reported victimizations. extensive use of available data sources as reported to police by either the involved (5) (v) vs. (d) to determine the prison well as the development of new data persons or witnesses. rate structure for arrests. sources in the future. In this section, (iv) Whether a reported victimization (6) (vi) vs. (e) to determine the recidi- various existing data sources are discussed event ultimately leads to an arrest. vism rate structure {h,k)and the desist rate in terms of their applicability to the (v) Whether an arrested person is structure {4,k). JUSSIM 111 model. ultimately sent to prison or experiences (7) (vii) vs. to determine the victim- (0 The FBI's Unljbrm Crime Reports (UCR) other sanctions. ization recurrence rate structure { vjk). (vi) Whether an arrested person com- present basic data for police reported mits a subsequent victimization (and/ or is crime rates in different parts of the United re-arrested) or not during a particular time States. The corresponding arrest data period after release from the criminal jus- provide some inforniation concerning of- tice system (either prior to trial, at the end fender demographic status as well as the of trial, or at the end of prison sentence or environmental situations in which the re- other sanction). spective crimes have occurred. On the Another relevant information source is the C. Specification of new data sources. A other hand, the principal limitation of criminal history record or "rap sheet." primary motivation underlying the formu- these data is that the arrest process can These records typically include data on the lation of the JUSSIM 111 model is its involve a biased selection of the offender age, race, sex, and possibly other demo- potential usefulness as a planning instru- population, some offenders being more graphic characteristics of the offenders, as ment for criminal justice system policy arresi prone than others. Thus, estimates well as the sequence of offenses for which decisions. However, this type of applica- obtained from the UCR data for offender they were arrested, the dates of arrest, and, tion is appropriate only if the estimated characteristics need to be contrasted with when reported, the disposition of each functional relationships in the model are corresponding results from other sources arrest. Thus they provide a basis for the based on valid data. Thus, the inherent of information like victimization surveys estimation of the recidivism behavior of weaknesses of the existing sources of infor- and offender self-report studies in order to offenders. The rap sheet data and the mation, like those described previously in evaluate the general magnitude of this bias. OBTS data are largely complementary. Section IV. B, imply the need for new data Such comparisons also provide a basis for They also provide some opportunities for collection systems havingless selection bias the adjustment of competing estimators consistency checks, but they are not likely in their sampling procedures and more from alternative data sources to a common to be available for all offenders in all juris- accurate measurements. From a statistical framework by synthetic estimation (rak- dictions for a long time to come. Special point of view, each of the respective types ing) procedures as described in Appendix adjustment procedures will be required to of contingency tables (1)-(7) described in A. Other comparisons of UCR crime data use such data in jurisdictions other than the Section IV.B, together with the corre- with victimization data and offender self- few for which good data are available. sponding dependent variables (i)-(vii) and report data can be used to estimate the ex- independent variables (a)-(f), should be Other aspects of criminal history, like non- tent to which various crime types are considered in this light, edch requiring reported or not reported to the police. reported offenses or offenses for which no detailed specifications to obtain data with arrests were made, can be analyzed with the required validity. Thus, a realistic dis- The victimization surveys provide the pri- offender self-reports. Such self-reports are cussion of the development of the new mary sources of information for estimating unquestionably suspect a priori, but fur- information sources required warrants a functional relationships in the victim- ther study is required to determine the separate research effort beyond the scope ization process. In addition, victim recidi- degree to which there is distortion in the of this paper. Nevertheless, some brief re- vism information is potentially obtainable self-reporting process (both suppression marks about the general requirements for from the longitudinal aspects of the na- and elaboration) and to identify methods such data collection efforts can be given to tional survey, which obtains information for adjusting for such distortions. In this motivate those future investigations. repeatedly from panel members. The panel context, the most important use of self- data could be used to construct estimates report information would be the estima- First of all, attention should be directed for the intervals between victimizations or tion of association parameters for offender toward improving the quality of the data the rate of victimization and the nature of characteristics which could then be synthe- pertaining to the processing of arrests the crime switch process for victims. All of sized with analogous data from rap sheets through the criminal justice system. A this analysis, however, should be under- and from victimization surveys. national sample of jurisdictions will be taken with caution because of the errors needed in order to obtain complete follow- In summary, these available data sources with which individuals recall victimization up information on the ultimate disposition provide a basis for estimating in at least a events, especially sequences of such events. (e.g., dismissal before trial, acquittal after preliminary way many of the parameters of trial, probation after conviction, prison Where available, the Offender Based the JUSSIM 111 model, even in the face of sentence of specific duration) for anappro- Transaction Statistics (OBTS) are particu- their respective limitations and even larly well suited as data sources for the priately defined parallel set of stratified though none of them is available at the vic- subsamples of different types of arrests branching ratios throughout the criminal tim-offender-crime level of detail for justice system. Typically, these can be esti- (e.g., all homicides, 30% of all other felo- victimization events. Moreover, a wide va- nies, 10% of all misdemeanors, etc.). mated for each of the offender demo- riety of special-purpose studies (e.g., the Moreover, such data should be collected in graphic groups since the OBTS incorpo- Kansas City Police Patrol Experiment a manner which is not biased by the rate offender characteristics as part of the 1974, the Wolfgang, Figlio, and Sellin 1972 selected police departments and courts, regular record. If the OBTS contain some birth cohort study, etc.) represent addi- does not interfere with their everyday limited victimization information, such tional sources of information for estima- operation, and encourages their coopera- data might provide preliminary estimates .ting various parameters after appropriate tion and participation. for the interactions in the joint offender- adjustments have been made for their victim victimization rate structure. special character or the particular jurisdiction where they took place. Thus, although suitable caution must be exercised, existing data sources can be used to form preliminary estimates for various functional relationships in the JUSSIM 111 model, and those estimates will stimulate the collection of better data and the improved specification of relationships, eventually resulting in a reasonable and useful formulation. 1 Table 1. Predicted values for prison rates from linear model contingency table analysis I Prior Arrest Total Defendants Predicted offense1 arrests promptness2 lncome3 Defendants Steon',":?,"," prison I- rate NRB One or more S L NRB One or more S HU NRB One or more A L NRB One or more A H U NRB None S L NRB None S H U NRB None A L NRB None A H U RB One or more S L RB One or more S H U RB One or more A L RE One or more A H U RB None RB None R B None R B None OFML One or more OFML One or more OFML One or more OFML One or more OFML None OFML None OFML None OFML None

NRB = nonres, burg.; RE = res. burg.; Residual goodness of fit O (D.F.=21) = 6.01 OFML = larceny (felony and misdemeanor) Total variation 12(D.F.=23) = 87.71 2~ = arrest same day as offense; A = later day Percent unexplained variation = 7% 3~ = low; HU = high or unclassified

Secondly, a national sample similar to that that victimizations are publicly perceived corresponding victimization events and described for arrests will be needed for at an aggregate level (for instance, a 1- possibly previous events. Obviously, the information on the subsequent experience month time period for all persons who live principal disadvantage of this data source of convicted offenders who are released in a specific census tract) as relatively would be the bias associated with its reli- from the criminal justice system via proba- prevalent events, but are experienced as ance on volunteer reporting. Nevertheless, tion, parole, or other means. This infor- very rare events by specific individuals for if the reporting rates for victimizations mation source would also involve a multi- such isolated time periods as 1 week or 1 were high, then the effects of this bias might stage selection beginning with institutions, month. Thus, data collection systems like be reduced by using matching procedures such as courts, full probation, halfway the victimization surveys which focus on to link such information to that obtained houses, and prisons, and ultimately the recent experience of selected individ- from police records and victimization focusing on released offenders. Various uals can provide only a limited amount of surveys and applying multiple-record- types of data would then be collected for information about the reported victimiza- system statistical estimation procedures the individuals in the sample by both active tions themselves (ignoring temporarily the like those described in Bishop, Fienberg, (interview) and passive (reports of subse- corresponding measurement error prob- and Holland (1975, Chapter 6), Koch, El- quent arrests by the police or FBI) methods lems) because of the relatively small Khorazaty, and Lewis (1976a), and Marks, for a particular fixed future time period of number who are involved even in verv. large- Seltzer. and Krotki (1974). perhaps as long as 10 years. samples. They do, however, provide useful Finally, other types of new information The formulation of new information information about different types of systems may be of interest with respect to sources about the arrest process, although victimization rates in the exposed popu- certain specific aspects of victimization perhaps prohibitively expensive in prac- lation at risk. Thus, another data source is tice, is straightforward in principle. The events. In this regard, a national sample of needed for obtaining more extensive long-term cohort studies on virgin victim- questions pertaining to improving the coverage of victimization events. One sys- quality of victimization data are consider- izations would provide useful data similar tem which could be developed for this pur- to that provided by Wolfgang, Figlio, and ably more difficult. Thecritical issue here is pose would be a national system of victimization reporting centers whose locations were based on an appropriate sampling plan. The explicit mission of these centers would be to provide free counseling and legal advice in a confidential manner (i.e., without specific notification to the police or other official agencies) to both offenders and victims; and their implicit mission would be to obtain information about the Sellin (1972) on virgin offenses. Moreover, eligible combinations of variables in a multi- For the burglary and larceny arrest data consid- a national follow-up sample for suitably variate relationship. The first variable selected ered by Clarke and Koch (1975), Phase I led to identified victims who are linked to arrests was the one having the largest (x2/d.f.) with the selection of type of offense, income, prior or other methods of reporting might respect to its first-order (two-way) relationship arrest record, and arrest promptness, respec- to prison outcome. Additional variables were tively. These four variables were then cross- obtain information about their subsequent selected by applying a similar selection rule using tabulated with prison status to produce a five- victimization experience. (x2/d.f.) computed for three-way, four-way, etc. dimensional contingency table. Phase I1 then In summary, the formulation of aJUSSIM contingency tables involving all of the involved the fitting of a model to the prison rates 111 model helps to identify several new previously selected independent variables suc- for all combinations of the selected independent cessively with each of the eligible remainingvari- sources of data for the measurement of variables. For this purpose, the weighted least ables vs. prison outcome. Phase 1alsoincluded a squares methods described in Grizzle, Starmer, crime and the activities of the criminal jus- procedure for terminating the selection process and Koch (1969) were used to formulate an ef- tice system. A broad range of possibilities when the remaining variables were not statis- fective additive linear model for characterizing exists for the design of such future tically important. Two different types of statis- the variation among prison rates by systemati- information systems, but their specific tics were used for this purpose: cally removing unimportant sources of variation development requires a substantially more (A) The Pearson X2-statisticsfor the partial such as higher order interaction effects. Such comprehensive investigation. The JUSSIM association (from two-way contingency tables) effects are not retained unless they are significant I11 model sketched here represents an im- of a specific eligible variable vs. prison outcome at an appropriate level like a = 0.05. In addition, portant instrument for generating an summed over all possible combinations of vari- the model is not considered to be satisfactory ables that have already been selected. agenda of future research in the develop until a residual goodness of fit statistic Q (B) A Xz-statistic developed by Cochran becpmes small (i.e., not significant at a = 0.25), ment of criminal justice statistics for use in (1954) and Mantel and Haenszel (1959), which for otherwise not all of the important sources of the planning process. combines information with respect to the effect variation have been identified. A final criterion of a specific eligible variable on prison outcome for model effectiveness is a measure of unex- Appendix A: over all combinations of previously selected plained variation, analogous to (I - R~)in mul- Specification of methods wriables. tiple regression, which is defined as the ratio of the goodness of fit statistic for the model to an of statistical analysis The statistic (A) reflects both the main effects of analogous statistic for total variation among all The principal objective underlying statistical a specific variable and its interactions with previ- the prison rates (i.e., the goodness of fit statistic analyses for contingency tables such as (1)-(7) in ously selected variables. After the first few steps for a model which implied that all the rates were of the selection process, this statistic tends tolose Section 1V.A pertains to the characterization of equal). U the relationship between dependent outcome its usefulness for two reasons. First, its degrees variables such as (i)-(vii) and correspondingsets of freedom increase rapidly causing selection to Analyzing prison rate data in this way leads toan of independent variables such as (a)-(f). Atten- become overly stringent. Second, the data be- efficient description or smoothing of the data as tion is directed at identifying which of the come thinned to the extent that many of the cell shown in Table 1. These results indicate that the independent variables account for the variation frequencies in the multidimensional contingency functional relationship between prison status in the respective dependent variables together table become smaller than 5 so that this criterion and the independent variables which were with the extent of the interaction among them. begins to lose its validity as a chi-squarestatistic. included in the analysis can be summarized in One approach for dealing with these questions is At this point, statistic (B) becomes useful terms of four distinct predicted values or clusters given in Clarke and Koch (1975), who consid- because it combines information across all as follows: ered the relationship between the probability of combinations of previously selected variables Cluster I. High prison rate = 53.7 percent if prison sentence and independent variables cor- and is thus more resistant to the thinning nonresidential burglary and low income and responding to the defendent's age, race, sex, problem. This statistic is highly sensitive with arrested same day as offense. income, employment, type of offense charged, respect to detecting weak but consistent CIusrer 2. Moderate prison rate = 30.4 prior arrest record, and arrest promptness (a relationships for variables which have not yet percent if nonresidential burglary and (a) low been selected; however, it has the disadvantage income but not arrested same day, or (b) arrested proxy for strength of evidence against the defendant) for a sample of certain types of that it reflects the "average"effects of a variable same day but not low income, or (c) one or more burglary and larceny arrests occurring in as opposed to its "total contribution," which arrests but not low income and not arrested same Mecklenburg County (Charlotte), North Carolina, includes interactions with other variables. For day, etc. during 1971. Their analysis consisted of two the most part, this difficulty should not often Cluster 3. Low prison rate = 19.3 percent ry phases: pose a major problem because statistic (A), larceny and one or more arrests and low income. Phase I: A screening of the variables to select which is used in the earlier stages, does pertain to Cluster 4. Very low prison rate= 7.2 percent if those responsible for the greatest amount of the "total contribution" of a variable. In the later not in Clusters 1, 2, or 3. variation in prison rates among the subpopu- stages of the selection process where statistic (B) These "predicted values" are different only if lations defined by different combinations of the is used, the "average effects" of variables are the the corresponding observed values are signifi- independent variables. ones of primary interest becausethe interactions cantly different; moreover, they represent better Phase II: The fitting of a parsimonious model with other variables are likely to be of minor estimates (i.e., with smaller standard errors) of involving the independent variables selected as importance because the relationships to which the prison outcome probabilities than the actual important during Phase 1. they apply are generally weaker. In summary, observed rates for the respective subpopulations statistic (A) is used to decide whether to termi- corresponding to the cross-classified independ- Phase I was conducted in the same spirit as step- nate selection after the first two or three vari- ent variables, because they are based on the wise multiple regression, but in a context appro- ables have been selected, and statistic (B) is used entire set of data rather than on its component priate for the categorical nature of the discrete thereafter. In each case, the basis for terminating subsets. Thus, a clearer and more simplified variables under investigation. In this regard, cer- selection is failure to meet a significance level of framework is obtained for interpreting the rela- tain Pearson Xz-statistics divided by their a = 0.10 or a = 0.05, as in forward stepwise re- respective degrees of freedom were used like the gression. Finally, in some situations, certain "F to enter" statistic in multiple regression as variables are known apriori to be of importance. measures of relative importance for suitably These can be included either at the beginning of Phase 1 or at the end, depending on their potential causal role with regard to the dependent variable. tive effects of the important independent In summary, a broad range of statistical meth- Freeman, D. H., Jr., and G. G. Koch (1976) variables than would be possible from casual ods are available to estimate functional relation- "The asymptotic covariance structure of esti- inspection of the full multidimensional contin- ships for the components of the JUSSIM I11 mated parameters from marginal adjustment gency table. model. Some of these are based on weighted (raking) of contingency tables." 1976 Proceed- least squares computations while others are ings of the Social Statistics Section of the An alternative framework for Phase 11 analysis American Statistical Association 330-335. is based on the use of log-linear models. These based on the Deming-Stephan Iterative Propor- types of funct~onalrelationships are discussed tional Fitting procedure. Thus, for any specific Goodman, L. A. (1970) extensively in Bishop, Fienberg, and Holland application, the critical issue is to use that meth- "The multivariate analysis of qualitative data: (1975), Goodman (1970, 1971), and Ku and od which is most appropriate to the estimation Interactions among multiple classifications." Kullback (1974). They can often be applied to problem under consideration. Journal of the American Statistical Association contingency tables such as the previously con- 65:226-256. sidered prisondata by the Deming-StephanIter- References Goodman, L. A. (1971) ative Proportional Fitting procedure in con- "The analysis of multidimensional contin- junction with an appropriate set of marginal Belkin, Jacob, A. Blumstein, and W. Glass (1971) gency tables; stepwise procedures and direct subtables. For this reason, the resulting esti- estimation methods for building models for mated parameters have reasonably robust and "JUSSIM, an interactive computer program - for analysis of criminal justice systems." Urban multiple classifications." Technometrics 13: stable statistical properties even for sparse con- 33-6 1. tingency tables (w~thmany small frequencies Systems Institute Report, School of Urban and which are less than 5). Their major disadvantage Public Affairs, Carnegie-Mellon University, Grizzle, J. E., C. F. Starmer, and G. G. Koch is the possibly unclear interpretation of the log- July 1971. ( 1969) linear model parameters, particularly when Belkin, Jacob, A. Blumstein, and W. Glass "Analysis of categorical data by linear interaction is present in the relationships among (1974) models." Biornetrics 25:489-504. the dependent and independent variables. "JUSSIM 11, an interactive feedback model Ireland, C. T., and S. Kullback (1968) Further discussion of the relative merits of linear for criminal justice planning. Urban Systems "Minimum discrimination information esti- vs. log-linear models is given in Bhapkar and Institute Report, School of Urban and Public mation." Biornetrics 24:707-7 13. Koch (1968a, 1968b). This subject is alsoconsid- Affairs, Cainegie- ello on University, January ered in Koch et al. (1976b) In the context of a 1974. Kelling, G. L., T. Pate, D. Dieckman, and C. E. general methodolog~calstrategy for estimating Brown (1974) log-linear model parameters, which is based on Bhapkar, V. P. and G. G. Koch (1968a) The Kansas City Preventive Patrol Experi- the simultaneous use of weighted least squares "Hypotheses of 'no interaction' in multidi- ment: A technical report. Washington, D.C.: and lterative Proport~onal Fitting or other mensional contingency tables." Technometrics Police Foundation. 10: 107-123. related computational algorithms. Koch, G. G., D. H. Freeman, Jr., and J. L. Bhapkar, V. P., and G. G. Koch (1968b) Another statistical method of potential use with Freeman (1975) "On the hypotheses of 'no interaction'in con- "Strategies in the multivariate analysis of data respect to the JUSSIM 111 model is synthetic tingency tables." Biometrics 24:567-594. estimation ( or "raking") for contingency tables. from complex surveys." InternationalStatistical This analytical procedure permits an observed Bishop, Y. M. M., S. E. Fienberg, and P. W. Review 43:59-78. table corresponding to a sample from a specific Holland (1975) Koch, G. G., M. N. El-Khorazaty, and A. L. population to be adjusted to yield estimators for Discrete multivariate ana!vsis: Theory and Lewis (1976a) other target populations, e.g., (I) local or region- practice. Cambridge, Mass.: M.I.T. Press. "The asymptotic covariance structure of log- al subdivisions of a sampled national population; Blumstein, Alfred (1975) linear model estimated parameters for the (2) other local or national populations which "A model to aid in planningfor the total crim- multiple recapture census." Communications in partially overlap a sampled local population. inal justice system." In Quantitative tools for Statistics A-5: 1425-1445. The assumptions required for the validity of this crimrnal justice planning, Washington, D.C.: Koch, G. G., D. H. Freeman, Jr., P. B. Imrey, approach are: U.S. Department of Justice, Law Enforcement and H. D. Tolley (1976b) (I) Certain. marginal distributions for the tar- Assistance Administration. "The asymptotic covariance structure of esti- get population, referred to as the "allocation mated parameters from contingency table log- structure," are known on the basis of census or Brock, D. B., D. H. Freeman, Jr., J. L. Freeman, linear models." Proceeding of 9th International other data. and G. G. Koch (1975) (2) The higher order interactions across the "An application of categorical data analysis to Biometric Conference, Cambridge, Mass., August subsets in (I), referred to as the "association the National Health Interview Survey." Pro- 1976. structure,"are the same for the target population ceedings of the Social Statistics Section of the Ku, H. H., and S. Kullback (1974) as for the sampled population. American Statistical Association. "Log-linear models in contingency table anal- Given these considerations, the estimated Causey, B. C. (1972) ysis." The American Statistician 28: 1 15-1 22. table for the-target population can be obtained "Sensitivity of raked contingency table totals to Mantel, N., and W. Haenszel (1959) by using the Deming-Stephan Iterative Propor- changes in problem conditions." The Annals of "Statistical aspects of the analysis of data tional Fitting algorithm which preserves 'asso- Mathematical Statistics 43:656-658. from retrospective studies of disease." Journalof ciation structure" as it successively adjusts the the National Cancer Institute 22:719-748. observed table to the components of the "allo- Clarke, S. H., and G. G. Koch (1975) cation structure." Additional details pertaining "Who goes to prison? The likelihood of receiving Mark, E. S.. W. Seltzer,and K. J. Krotki (1974) to the statistical properties of this procedure are an active sentence." Popular Government Population growth estimation. New York: given in Bishop, Fienberg, and Holland (1975). 41:25-37. The Population Council. Causey (1972), Ireland and Kullback (1968),and Cohen, Jacqueline, et al. (1973) Seidman, D. (1975) Freeman and Koch (1976). As indicated by "Implementation of the JUSSIM model in a "Simulation of public opinion: A caveat." Seidman (1975) in a more general context, such criminal justice planning agency." Journal of Public Opinion Quarterlv 39:33 1-342. synthetic estimation methods should be used Research in Crime and Delinquency, June 1973. cautiously because of the potentially severe bias Uniform Crime Reports (1 973) they may suffer when assumptions (I) or(2) are Cochran, W. G. (1954) Washington, D.C.: Federal Bureau of Investi- not justified or are incorrectly applied. "Some methods of strengthening the common gation, U.S. Department of Justice. X' test." Biornetrics 10:417-451. Wolfgang, E., R. M. Figlio, and T. Sellin Finally, Kochetal. (1975)and Brock etal. (1975) M. (1972) discuss weighted least squares methods of analysis for contingency tables based on com- Delinquenc:~in a birth cohort. Chicago and London: University of Chicago Press. plex sample surveys such as those used to measure victimization. These procedures are directly analogous to those described in reference to the prison rate from Clarke and Koch (1975). Redesigning the Kansas City Preventive Patrol Experiment

STEPHENE. FIENBERG Department of Statistics and Department of Social Science Carnegie-Mellon University

KINLEYLARNTZ Department of Applied Statistics University of Minnesota

ALBERTJ. REISS,JR. Department of Sociology Yale University

The most striking result of the Kansas City groups of 3 matched beats each, on the (a) what explanatory model lay behind Preventive Patrol Experiment (KCPPE) basis of reported crime counts, calls for the KCPPE. was that no significant differences were police service, and demographic data. (b) what was measured and what was not found among the three types of beats ("re- Within each triplet one beat, the "control," measured. active," "control," and "proactive") in was to be patrolled by a single police car in (c) what the results really were. reported crime, rates of victimization, level the usual fashion whenever it was not (d) what aspects of the experimental of citizen fear, or level of citizen answering calls. In a second beat in each design and its execution may have led satisfaction with the police. In this paper, triplet, routine preventive patrol was directly to these results. we focus on several related shortcomings of eliminated and officers were to respond (e) whether the foregoing facts may in the design and implementation of the only to calls for service. These were any way compromise the conclusions KCPPE. These include (1) the orientation referred to as the "reactive" beats. Finally, reached by Kelling and his coworkers and toward proving rather than disproving the in the third beat in each triplet, routinepre- others commenting on the experiment. null hypothesis of no differences among ventive patrol was increased to 2 or 3 times (f) if the conclusions are compromised, treatment effects, (2) the confusion of man- the usual level. These were referred to as whether there is a different experiment that power differences and treatment (patrol the "proactive" beats. Complete details of an appropriate police department might strategy) differences, and (3) the lack of the experimental design and its imple- conduct which would get around many of control of other variables affecting the mentation can be found in Kelling et al. the problems associated with the KCPPE. (1974). outcome of the experiment and the lack of A major difficulty with the KCPPE and proper randomization in assigning treat- The strik.ing result of this Kansas City Pre- any consideration of it are the terms "pre- ments to beats. Following this discussion ventive Patrol Experiment (KCPPE) was vention" and "preventive patrol." Basi- of the KCPPE, we outline the design of a that there were no "significant" differences cally, the problem is that "prevention" is a class of randomized controlled field studies among the three types of beats in reported black box, and exactly what police officers for patrol-related experiments that are crime, rates of victimization, level of citizen do with time spent on what is called "pre- adaptable to most large citiesand thatcould fear, and level of citizen satisfaction with ventive patrol" is difficult to determine. have yielded considerably more informa- the police. There was simply no apparent The KCPPE did not actually manipulate tion than the actual design used in Kansas effect that could be related todifferences in this elusive concept of preventive patrol. City. patrol manpower allocation, deployment, Rather, the experiment attempted to ma- and operation. Now this result appears to nipulate the amount of manpower and its I. The Kansas City experiment fly in the face of conventional wisdom that deployment. We return to this issue in the increases in police patrol should reduce the foilowing sections. From October 1, 1972, through September levels of street crimes such as robbery and 30, 1973, the Kansas City, Missouri, Police automobile theft. Since one of the purposes II. Experimenting Department conducted an experiment of the experiment was "to determine designed to assess the impact of routine with police manpower whether the Kansas City Police Department preventive patrol on the incidence of crime could safely divert resources ordinarily Most social experiments, especially those and the public's fear of crime. The experi- allocated to routine preventive patrol to involving the police, are not really experiment involved 3 variations in the level of other, possibly more productive patrol ments in the statistical sense, but are in fact preventive patrol used in 15 of the 25 beats strategies," the results would appear to innovations for which there are no direct comprising the Kansas City South Patrol have important policy implications regarding means available for separating out or con- Division. The 15 beats were blocked into 5 the use of various manpower allocation schemes. It is therefore incumbent upon us to reexamine the experimental setup and the results of the KCPPE with great care in order to determine: trolling the effects of a change in public Ill. Shortcomings of the KCPPE Because the no-difference outcome of the KCPPE has such important social and pol- policy from concomitant changes in related Our discussion of the design and analysis of icy implications, it is important to ask variables. For example, "Operation 25," a the KCPPE here focuses on several whether the design chosen sufficiently con- 4-month "experiment" conducted by the interrelated issues: trols for crucial sources of variability to New York City Police Department in 1954, (1) proving rather than disproving the allow for the detection of the effects of true involved the more than doubling of police null hypothesis. treatment differences when they exist. strength in Manhattan's 25th Precinct. (2) the difficulty in actually assessing the Although reported street crime went down treatment differentiation. The following example, adapted* from markedly over this 4-month period, no (3) the absence of adequate measure- Kempthorne (1952), may help clarify the direct information was available for the ment of treatment implementation. issues just raised. A soft drink manufac- true crime rates. Alternate explanations of (4) the confusing of manpower differ- turer has developed a new procedure for the observed decrease were available, and ences and treatment (patrol strategy) producing its best-selling cola. The ques- no effort was made to assess the possible differences. tion to be resolved is whether or not people deleterious effects of the increased man- (5) the possible contamination of data can detect a difference in taste between the power on adjacent areas or to determine in experimental beats by the patrolling colas produced by the new and old proce- what the reported crime would have been strategies in adjacent beats (whether they dures. The manufacturer's statistician sets had the changes in manpower not been in- be experimental or not). up the following experiment. A panel of n = stituted. Far better than "Operation 25" (6) the lack of proper randomization in 6 tasters is presented with 3 glasses of cola, was the 1966 experiment in New York's assigning treatments to beats. 2 produced by the old process and 1 by the 20th Precinct (see Press 1971, 1972), al- new. Each taster is asked to pick the one though it too had its problems. Other cola whose taste differs from the other two. A. Proving the null hypothesis examples of innovations in police practice The tasters work independently of one an- are readily available. In 1953, the Kansas A primary purpose of carefully designed other, and the colas are presented in a ran- City Police Department carried out a com- statistical experiments is to control for as dom order to each taster. The null hypoth- plete 24-hour changeover from two-man to many sources of variation as possible in esis, Ho,specified by the statistician is that one-man patrol cars, and the 24 patrol order to maximize the probability of "no differences are detectable," and when areas were reorganized into 41 substantial- detecting differences in the effects of MI is true the probability of detecting the ly smaller beats (see Brannon 1956). No different treatments when these differences cola produced by the new process isp = 113. adequate evaluation of such a change was do in fact exist. Because the KCPPE was possible. unable to detect*anydifferences in outcome There are 7 possible results of this experiment, indexed by the number of tasters In light (or perhaps we should say shadow) attributable to the differences in the level of preventive patrol, we must therefore ask who correctly picked the cola from the new of these earlier attempts to evaluate the process. llnder fi, the probabilities of effects of changes in police patrol practices, whether this result is due to the true lack of observing these results are: the KCPPE would appear to provide a treatment effect differences or simply the model worthy of careful study. Patrick weakness of the experimental setup when Murphy, President of the Police Founda- in fact differences do exist. The framework No. correct Probability tion which supported the KCPPE, has of hypothesis testing adopted by the au- 6 11729 = 0.001 thors in their report is geared toward been quoted as saying that the preventive 5 121729 = 0.016 patrol project "ranks among the very few rejecting the null hypothesis (in this case major social experiments ever to be com- that of no difference) in favor of some 4 601729 = 0.082 pleted and was unique in that never before alternative, by giving heavy weight to the 3 1601729 = 0.219 had there been an attempt to determine null hypothesis unless it is demonstrably 2 2401729 = 0.329 through such extensive scientific evalua- false. In technical terms we fix the level of tion the value of visible police patrol." significance (the probability of falsely re- While the KCPPE does not quite measure jecting the null hypothesis) at some low up to the well-evaluated randomized con- value (e.g., a = 0.05) and the probability of If all 6 tasters correctly pick the cola from trolled field trials of large-scale social failing to detect the alternative hypothesis the new process then we would appear to action programs described by Gilbert, when it is true is determined. Unless the have strong evidence that HOis false. Even Light, and Mosteller (1975), it represents a latter is also small, we end up weighting the if only 5 tasters are correct the evidence is major step forward in the design and strat- experiment in favor of the null hypothesis. strong, but if only 4 tasters are correct, we egy of police research. It is only because of The danger of "proving" the null hypothe- might have observed a result so extreme the use of sophisticated statistical tech- sis by means of a weak experiment haunts with probability 0.001 + 0.016 + 0.082 = niques and their extensive documentation much of the literature on social experimen- 0.099 0.1. This is not a very rare event in the Technical Report (Kelling et al. tation. and, even if a small difference between the 1974) that we are able to assess very care- colas exists, we would likely not take the fully the various aspects of design and result of 4 out of 6 as being indicative of analysis. The KCPPE has not only shown such a difference. Thus we take 5 or 6 cor- that a police department can successfully rect as evidence against Ho and in favor of experiment with patrol strategies without some alternative hypothesis. disastrous consequences, but it has also In order to evaluate how good an experi- provided a starting point for future experiment this really is, we need to ask what mentation in this area. would happen if some alternative to HCis really true. Suppose, for example that p = 112, and the cola from the new process is In its ultimate design the project would be a rig- observed time in the experimental area more likely to be picked than is indicated orous and systematic attempt to test the out- turned out to actually be noncommitted, by fi.Then the probability of getting5 or 6 comes of different patrol strategies and and only a fraction of the noncommitted correct is now (1 / 64) +(6164) ~0.109.Thus ultimately could lead to cost-benefit analyses of time is used for activities that might be even though there is a difference we would varied strategies to determine the most efficient labelled preventive patrol. The uses of methods of undertaking patrol. It was likewise noncommitted time by officers do not seem fail to detect it about 8 out of 9 times using felt that the preventive patrol experiment would our criterion of 5 or 6 correct. The help to maintain a climate of innovation and to vary very much for officers assigned to probability 0.109 is referred toas thepower self-evaluation, not only on the part of the the beats with the three different levels of of our test for the alternativep = 112, and in department as a whole but alsoamong individual preventive patrol. Since calls for service the present case it would appear that the officers. The task force and the Police Founda- and other routine uses of committed time experiment as planned will simply not be tion realized that since the effectiveness of rou- were treated in a similar fashion in all powerful enough to detect an alternative as tine preventive patrol was not self-evident and experimental beats, the differences among big asp = 213 (for which the power is only because the capacity to deal with crime is a cen- the levels of treatment are not nearly as 0.35). The experiment appears to be tral police function, the preventive patrol exper- great as they appear to be from the initial iment would fill a real professional need hereto- experimental description. Moreover, offi- stacked in favor of the null hypothesis, and fore not addressed by other police agencies. unless we are careful we might erroneously cers on reactive beats used their preventive conclude that p = 113 even when it really is The notion of preventive patrol in this patrol time either on the perimeter of their as large as p = 213. Note the importance description is really a "black box,"and the own beats or in patrolling proactive beats here of explicitly stating what effects we problem for the experimenter is that it is to compensate for manpower shortages. would like to be able to detect if they are hard to manipulate such a "black box." As The amount of time spent on the beat present. Riecken and Boruch (1974) note: perimeters in reactive areas is not given, A specified treatment allows a much more pow- but it should have been carefully assessed Basically, there are three ways to make an erful experimental test than does a "black box." due to the shape and relatively small size of Furthermore, specifying treatments helps to experiment more sensitive to detecting several of the beats. Finally, officers often achieve comparability between different experi- cross beat boundaries in response to calls reasonable alternatives to H,: mental sites. ..when an experimental treatment (1) increase the sample size. is repeated (replicated) it should be kept the for service. Since there are more officers on (2) reorganize the structure of the same or deliberately and systematically altered, patrol in the proactive beats, they are more experiment. rather than being allowed to vary haphazardly. likely to be free to cross into reactive or control beats in response to service calls (3) refine the experimental technique. What was actually manipulated in the In the cola experiment we could employ than the other way around. Finally, as KCPPE was some combination of changes Davis and Knowles (1975) note, specialized all three of these methods, but in the in manpower, the deployment of manpow- KCPPE where there are severe limitations units (helicopters, K-9 units, etc.) were er, and visibility. Each of these variables deployed independently of the preventive on how big we can make the sample size, we contributes in a partially undefined way to clearly must know how to reorganize and patrol experiment at a level consistent with the level of activity in each experimental activity in the preceding year. refine the experiment to avoid the trap of unit, and then the level of activity somehow proving the null hypothesis. We address affects the "black box" of prevention. There is a set of incident types defined by these issues in Section IV of this paper. Some of the experimental areas were to Kelling et al. as part of routine preventive continue with the same manpower levels, patrol: traffic violations, building checks, B. Differences in treatments the same deployment, and the same visi- car checks, and pedestrian checks. These bility as before. This was intended to keep routine patrol incidents are presented by Directly related to the issue of "provingthe constant the level of activity in these "con- treatment group in Table 111-5A of Kelling, null hypothesis" is the choice of treatment trol" areas. In a second group of areas the et al. (1974, p. 47). We have recategorized for the experiment. If there is little or no manpower was doubled (very roughly), but these data to assess more easily treatment difference among treatments, then we can the deployment of manpower was to be no differences. If there were no differences in hardly expect to have much luck in different from before. The resulting in- the levels of preventive patrol across beat discovering differences among the resulting crease in activity leads to the label of "pro- type we would expect each of the three sets effects. The treatment standard chosen as active" for these areas. In the third group of of treatment areas to have roughly 33.33 the "control" in the KCPPE was the experimental areas, the level of manpower percent of the routine preventive patrol current patrol strategy and level of patrol was left the same, but deployment was incidents. The 1972 data (collected from used in the individual beats involved in the manipulated. Some of the activities January through September) are reason- experiment. Yet we don't know whether associated with the "controls" were elimi- ably compatible with thisexpectation, with this "control" level of patrol differs nated from these areas, and thus we label percentages varying from a low of 28.97 markedly across beats, nor whether it is the activity as "reactive." These manipula- high, moderate, or even low relative to the tions of treatment variables leave us with levels of patrol that are feasible for a given the three patrol strategies of the KCPPE. beat area or for police patrol beats more generally. The "reactive"and "proactive" patrol strategies appear on the surface to differ Kelling et al. (1974) state the aim of the markedly from the control strategy, but is KCPPE as follows: this in fact the case? Routine preventive patrol is carried out during an officer's noncommitted time, but only 60 percent of percent to a high of 38.69 percent but with activity occurs in the midnight to 8 a.m. the-envelope" model, Larson (1976) esti- most near 33 percent. The 1973 data (also watch, and the least in the peak workload mates that the average frequency of pre- January through September), in which we watch from 4 p.m. to midnight. When these ventive patrol passings in the control areas would expect the proactive beats to have a activities are examined on a day by beat by in 0.164 passes per hour or roughly one considerably larger share of the incidents watch basis we find that we are faced with a every 6 hours. Thus he notes that and the reactive beats a considerably low productivity situation, where big preventive patrol as usual in the experi- smaller share, present a somewhat different treatment changes may be required to mentaI zone is not very much preventive picture. The proactive beats in 1973 had 43 increase or decrease productivity. Since the patrol. Even if doubling the number of cars percent of the car checks, 53 percent of the average number of patrol-initiated activities in the proactive areas doubles the number pedestrian checks, and close tq 33 percent is about one per day per beat per watch, of times a randomly chosen spot is passed of both traffic violations and building how much of an effect can we expect from in a fixed period of time, this is still only checks as opposed to 38, 39, 35, and 34 the supposed elimination of preventive once every 3 hours. Larson notes that the percent, respectively, in these categories in patrol from the reactive areas and the range of preventive patrol coverages in the 1972. On the other hand, the reactive beats doubling of manpower, which likely KCPPE is considerably less than that for in 1973 had 26 percent of the car checks, 24 produces far less than two per day per beat many other U.S. cities on a typical day, percent of the pedestrian checks, 28 percent per watch? In fact, the biggest source of thus calling into question how useful the of the traffic violations, and 28 percent of variation in patrol-initiated activities may Kansas City results would be for other the building checks. These should be well be among watches within beat, rather cities. compared with figures from 1972 of 33,32, than among treatment areas. 32, and 37 percent, respectively. The In summary, there are few (if any) direct control beats were much more stable for measures of treatment conditions in the 1972 and 1973 except that pedestrian C. Treatment inlplementation: KCPPE, and those measurements that are checks dropped from 29 to 24 percent and What was measured.? available tend to point toward minimal differences in treatment effects across the car checks increased from 29 to 37 percent. Kelling et al. (1974) seem to have three types of treatment. There do appear to be differences in the abstracted from the literature on patrol relative proportions of routine preventive strategies the assumption that visibility is patrol incidents across treatment areas, but the main factor underlying patrol variations D. Manipulating manpower the differences are not all that big. What is and that visibility impact on the crime rate versus patrol strategy even more troubleso,me is that the number might be mediated by changes in "fear of of patrol-initiated events that took place in apprehension on the part of crimina1s"and The Kelling et al. report on the KCPPE the "reactive" areas actually increased from "police response time" (see page xvii). The continually speaks of experimenting with 1972 to 1973. Although the proportion of extent to which differences in treatment led police patrol strategies, but as we noted car checks out of the total number that to differences in actual visibility is thus earlier the experiment itself deals only with took place in the reactive areas decreased crucial. The KCPPE used no direct the manpower levels for the proactive from 33 to 26 percent, car checks still measurement of visibility anywhere in the treatment and with one particular strategy, comprised 45 percent of all patrol-initiated study and, while some attempt was made to i:e., reducing preventive patrol for the activities in 1973 data, whereas they measure response time, the data were reactive treatment. But manipulating what comprised less than 36 percent of the scanty and not very reliable. Kelling et al. officers actually do while on patrol may activities for the comparable period of time (1974) note that there was no consequential well have as great an effect on the in 1972. Thus there is some question as to difference in response time to calls for the commission of crimes in an area as the manpower level of the patrol. For example, what the experimental conditions were and three areas based on the KCPPE measure- "stop and frisk" patrol strategies clearly how they were maintained. Larson (1976) ments, but Larson (1976), using a simple involve more intrusive activities than do discusses this point in greater detail. "back-of-theenvelope" operations research model, has shown that, for the experimental routine patrol strategies. By manipulating The figures in the preceding paragraph design used, the expected travel time for both manpower and patrol strategy we may tend to overstate the treatment differ- cars in reactive beats would not increase might produce alternatives to routine ences. To see this it is important to note very much. Since the experimental units preventive patrol at current manpower that, unlike many other cities where man- were beat areas but what was manipulated levels, the effects of which are detectable. It power is scheduled over the day according were beat cars, it is unfortunate that any is, of course, much easier for us to reach to anticipated police activities, Kansas City potentially useful information on reaction this conclusion after examining the KCPPE attempts to equalize its manpower over 24- time is recorded by car rather than by beat and its results than it would have been hour periods by allocating the same area. before it was carried out. number of officers to each of the three 8- hour watches. Thus most preventive patrol Let us return to the issue of visibility. Crimes where offenders are in private places are not accessible to the police for prevention efforts, and the offenders who commit these crimes are not affected by the visibility of police cars. Only street crime may be affected and, even in the case of purse snatchings and auto theft, visibility can aid the offender committing a crime if the visibility is fairly predictable. Because there was no direct measurement of visibility we must try to infer the amount of visibility associated with each of the three "levels of patrol." Using another "back-of- Whenever manpower is highly inefficient, E. Strategies in adjacent beats or has low productivity relative to what it Figure 1. might have, increasing the number of As we noted above, officers are dispatched across beat boundaries in answer to calls Schematic representation of the workers will have relatively little impact on 15-beat experimental area reducing the levels of crime. If a police for service. With more manpower on officer makes only one car check a day routine preventive patrol in proactive areas, officers from proactive beats are when he could easily make 10, then dou- R . C bling the manpower (assuming a constant much more likely to be able to answer calls CR ratio of manpower to activity) would pro- in another beat than are officers from duce only 2 per day but changing the patrol reactive or even control beats. Officers in - one beat may in fact feel compelled to" help strategy could produce 5 times that P C R C number. In short, when we are faced, as we out" their colleagues in adjacent reactive -P are in Kansas City, with very little preven- beats and thus negate the intended effects - tive patrol strategy other than riding and of the experiment. Since controlling the P dispatch of police cars is a near-impossible P sitting around, we can't expect changes in R R manpower to produce very much. Thus task, care must be taken in allocating C leaving the ordinary conditions of produc- treatments to beats to allow a measure of tivity constant, we must ask whether control relating to effective treatment P = Proact~ve changes in manpower will make much differences in adjacent beats. C = Control R = Reactwe difference. To the extent that one can increase levels of output per man by In this regard, we should reexamine the - changes in patrol strategy, one can measure schematic representation of the 15-beat experimental area. The South Patrol the effect of the strategy. An interesting experimental area, reproduced here as Fig- question is whether changes in strategy can ure 1. The striking feature of the layout is Division is bordered at the west by Kansas City, Kansas (which is under different produce more effect than changes in the placement of the 5 reactive beats in the police jurisdiction), and on east and south manpower. Up to some point, there can be 4 corners and in the middle. Proactive and by yet additional suburban Missouri police enormous gain by changes in strategy, and control beats intervene between every pair jurisdictions. Because police rarely if ever similarly only to some given point- of reactive beats, and the only 4 beats with cross jurisdictional lines, let alone state usually spoken of as a saturation point- 2 sides adjacent to areas not in the experi- lines, the geographical arrangement of can changes in manpower have an effect. ment are all reactive. The probability that beats in the KCPPE leads one to wonder Under many conditions, tripling, etc., such an allocation of treatments to beats would happen by chance is quite small how the results might have turned out had manpower does not have the expected mul- a different arrangement been used, espe- tiplicative effect. indeed.' In fact, as the authors of the KCPPE note in the Summary Report: cially one that controlled for what we In an experiment like the KCPPE, whether "The geographical distribution of beats might label "border" effects. we try to manipulate manpower, patrol avoided clustering reactive beats together strategy, or both should depend upon the or at an unacceptable distance from proac- F. Random assignment of treatments level of effect expected per man for a given tive beats. Such clustering could have strategy relative to what might be achieved resulted in lowered [sic] response times in The layout of the experimental area and by increasing output per man. There is little the reactive beats." The consequences of the discussions of it in Kelling et al. (1974) reason, we believe, to increase police the geographical distribution are far more raise considerable doubt whether random- manpower when the current manpower is distressing, both because they indicate a ization was used at all in the assignment of used so inefficiently relative to any strat- lack of random assignment and because of treatments to beats. Is this a serious egy. The problem is complicated by the fact the interactive effects described above. The matter? We believe strongly that it is. The that events are not uniformly distributed in arrangement of beats is of even greater difficulties resulting from a nonrandom- time so that manpower will have less effect concern once we realize the potential sig- ized field trial are many, but as Gilbert, at some times than others and ceiling nificance of a beat's being on the edge of the Light, and Mosteller (1975) note, "The key effects are quickly reached. Between 2 and problem is that the effect of the treatment is 4 a.m., there may be very few people to not distinctive in all cases, so that the 'In experimental situations such as the KCPPE there interrogate and very few cars to check in are several recognizable subsets of possible designs treatment cannot be proved to have caused most beats of even a very large city. Thus which for one reason or another may seem striking. the effect of interest. Selection effects and strategy changes have different limits for While each of these designs might occur with small variability of previous experience have different times. We frankly don't know probability asa result of randomization. the probabil- often led to biases and misinterpretations." ity of chosing a design coresponding to one of the how the experiment we propose in Section recogni7able subsets is substantially larger. IV (or any other experiment) can take these Now it is true that by making certain difficulties into account, particularly because assumptions regarding models and the most strategies attempt to affect the nature of the experimental variability we can hope to surmount the obstacles posed offending populations, and we know so by the lack of proper randomization in an little about police interactions with such experiment or controlled field trial. Yet populations. this hope all too often remains just that, and the only sure way to be able to make River and Missouri-Kansas state boundary beat officer with a view to increasing ap- causal statements after we complete an line, we can cut these requirements to 70 prehension of offenders or to increasing experiment is to randomize at some stage beats for the full experiment and 28 for the their risk of being caught and thus reducing of the allocation of treatments to units. The reduced one (assuming completely regular their level of offending. nonrandomized controlled field trial can beat sizes and shapes). Tactic 11: Neighborhood team policing. be an effective evaluation device, but This tactic emphasizes the creation of a For those not familiar with the sophisti- primarily in the presence of what Gilbert, team of officers who regularly patrol a cated details of the design of statistical Light, and Mosteller call "slam-bang given territory in which they develop a experiments, the experiment described effects," hardly a phrase that can be used in close relationship with potential victims here may seem so complex that we have no describing the results of the KCPPE. and a knowledge of potential offenders. hope of using it to detect interesting results (Bloch & Bell 1976; Schwartz and Clarren It may well be argued that a simple random that we might have discovered had we only 1977; Sherman et al. 1973) assignment of treatments to beats in the tried to manipulate one factor and answer KCPPE would have been inappropriate. one question. The distinguished statis- (2) Environmental intervention strat- But experimental designs that balance the tician, Sir R. A. Fisher (1926), once egies. These strategies involve active patrol allocation of treatments, and yet also pointed out that he believed exactly the intervention in the physical and social involve some form of random assignment, opposite to be true: environment of patrol areas or in the activ- are available. In most experiments.. .the comparisons involv- ities of citizens as they move about the area. ing single factors. ..are of far higher interest and Tactic I: Stop & Frisk. This tactic was examiiied in patrol areas of Chicago, IV. Designing a new patrol practical importance than the much more numerous possible comparisons involving sev- Boston, and Washington, D.C., in studies strategy experiment eral factors. This circumstance, through a by the National Crime Commission in It is possible to design a new experiment to process of reasoning.. .leads to the remarkable 1966. The assumption is that the identifica- examine alternative police patrol strategies consequence that large and complex experi- tion of potential offenders, particularly ments have a much higher efficiency than simple in the spirit of the KCPPE that would over- ones. No aphorism is more frequently repeated those who possess weapons, reduces the come the pitfalls elaborated upon in the in connection with field trials, than that we must risk of their use in crimes. (Reiss 1967) preceding section, although the task is not ask Nature few questions, or ideally, one ques- Tactic 11: Stop and interrogate (ques- at all an easy one. The difficulty comes tion, at a time. The writer is convinced that this tion). This tactic'assumes that questioning when we attempt to control for a variety of view is wholly mistaken. Nature, he suggests, susvicious individuals deters votential different sources of variability. Although will best respond to a logical and carefully offinders. (Boydstun 1975) such control in principle increases the effi- thought out questionnaire; indeed, if we ask her Tactic 111: Directed deterrent patrol. ciency of an experiment, we must retain a single question, she will often refuse to answer This includes a variety of tactics designed sufficient degrees of freedom for the error until some other topic has been discussed. to specify the kind of activity patrol will term in order to keep the power against undertake when assigned to preventive interesting alternative hypotheses high. A. Treatments patrol, e.g., identify vehicles parked in an Because the number of police beats in a area, or check the security status of resi- given city is never very large (e.g., 69 beats In place of simply varying the manpower dences or buildings. (Larson 1972; Tien et in Kansas City, Missouri, and only 24 beats level of routine preventive police patrol, we al. 1976) in Minneapolis, Minnesota), we need to propose to vary the actual patrol activities. Tactic IV: Tactical squads. There is a strike a balance between the control of We do so in part because of what we have large number of possible types of tactical variability and the estimation of residual learned about varying manpower from the squads whose tactics include proactive error. KCPPE. policing. The location-oriented patrol (LOP) and perpetrator-oriented patrol In this section we describe an experimental Before suggesting specific treatments for our proposed experiment, we offer a list of (POP) tactics attempted in Kansas City design for a new patrol strategy field trial following the completion of the KCPPE and several variants of added or diminished treatments built upon the idea of testing are examples (Pate et al. 1976). complexity. The basic design described alternative police patrol strategies and involves 108 beats and thus cannot be tactics: (3) Visibility strategies. These strategies implemented in any but the largest cities in (1) Information processing patrol strat- are based on the presumption that degree the United States. By assuming theabsence egies. These strategies rest on the assump- of visibility- of police patrol affects the rate of all interaction effects we can reduce the tion that sharing information gathered in of offending in an area. The tactics appear required number of beats to 54. By utilizing police patrol among the patrol officers superficially to be contradictory, with natural boundaries such as the Missouri policing a common area will reduce crime unmarked cars as well as marked cars by increasing the risk of apprehension of presumed to have effects increasing the offenders. apprehension of offenders. Tactic I: Information oflicer coordination of beat patrol. This system, pioneered in England, rests on the principal that each beat officer shares information on crime and offenders in his beat with an information officer who also gathers information from the wider criminal justice system. This information is processed and serves to direct the patrol activities of each Tactic I: Unmarked palrol cars. This The ex~erimenterwill find that these strat- B. Do we monitor treatments? tactic is based on the assumption that large egies and the tactics related to themare not We propose to monitor various aspects of manpower allocated to unmarked patrol readily separable from one another. For police activities at the beat level and to cars increases the risk of apprehension of example, it is no simple matter to separate collect basic response information similar offenders committing crimes. foot patrol from the special activities un- to that in the KCPPE. The purpose of Tactic 11: Reactive patrol. Here visibil- dertaken by police officers on foot patrol monitoring police activities is to ensure ity results solely from reactive dispatches that occur in other strategies and tactics. that there is a true difference in treatments, into an area in response to complaints. This Were sample size not a severe and and thus we are interested in havingadirect is a low visibility condition. overriding problem in the present situ- measure of police car visibility. One way to Tactic 'I1: Foot This tactic is ation, we would most likely propose a measure visibility is to use, at a variety of based on the assumption that foot patrol factorial or fractional factorial structure locations, counter devices that candistinguish officers have knowledge of their beat and how to secure it so as to reduce the risk of for treatments aimed at measuring the among patrol cars. Such devices would victimization by crime and the apprehen- effects of three or more strategies and their also provide measures of the presence of sion of offenders. interactions. Since the available number of cars from other beats, e.g., in answer to police beat areas is so small, and for pur- calls for service. Tactic High visibility. This tactic poses of comparability with the KCPPE, assumes that offenders are deterred by the An (expensive) alternative to counter open presence of police officers, either on we have decided to consider only the following threeUtreatments."we recognize systems is an automatic vehicle monitoring patrol or functioning in some other that the proposed interventions require system such as the FLAIR (Fleet Location fashion. changes in police behavior that may be very and Information Reporting) system cur- (4) Crime-specifc strategies. These strat- difficult to achieve. rently being implemented in St. Louis on a egies are based on the assumption that no (A) A search patrol strategy, involving trial basis. The St. Louis FLAIR system patrol strategy is effectiveagainst all crimes high visibility (see Strategy 3, Tactic IV) of a form and that the greatest deterrent and the participating police officers and intru- guidance" technique with apprehension effects arise from tactics that sive forms of patrol involving field inter- Puter tracking to the location of are undertaken for a specific type of crime. rogation of suspicious individuals and each of 25 patrol cars within what is Among those that have been tried are: other forms of environmental intervention be an average accuracy Tactic I: Decoy squads for street (see Strategy 2, Tactics I and 11). feet. Such a system would not only allow robbery. A police team with one or more (B) A basic visibility patrol strategy, for the direct measurement of but members serves as decoys by representing involving a standard level of routine pre- it would also allow for better control of potential victims of street robbery. This is ventive patrol. police operations such as dispatching. intended to increase the apprehension of (C) A reactive no-patrol strategy (see we are also interested in monitoring the career street robbers. Strategy 3, Tactic II), utilizing police offi- amount of interrogation, especially in Tactic 11: Operation barrier for appre- cers wherever possible to handle com- beats using the search patrol strategy. We hending robbers. This tactic dispatches plaints related to particular types of crime suggest the filling out of punched cards by patrol to intercept robbers in flight and is via scheduled appointments and in un- officers for each field interrogation or car designed especially for commercial and marked patrol cars (see Strategy 3, Tactic street robbers. 1). Tactic 111: Identification tactics: Vari- In addition to the basic response data used ous tactics of surveillance including If the effects of these treatments do differ, in the ~cpp~,such as UCR and technological surveillance (e.g., burglar and if we assume that there are no inter- victimization data and citizen response alarm systems linked to patrol operations) active effects of visibility and interrogation data, we suggest the collection of addi- are used to increase the apprehension of (i.e., they are additive), then the differences tional information such as weapons criminals by police on patrol. between beats with treatments B and C will production. What we are seeking here is the be a measure of the effects of the visibility offender protection potential of each (5) Patrol investigation strategy. This component of patrol, and the differences strategy. For example, in car checks, we Strategy assumes that police patrol can between beats with treatments A and B will would like to know how often we produce a increase the apprehension rate as well as be primarily a measure of the effects of hot car, a wanted person on warrants, etc. the effectiveness of detective investigation interrogation. If the experiment we propose ~f we increase that strategy, do we increase if the police on patrol immediately under- here is successful and detects sizeable the numbers of such events? For searches take some investigation of the crime rather differences in the effects of treatments, then of the person, we would like to know how than leaving investigation primarily to the subsequent experiments might explore the often we produce a weapon, burglary tools, detective division. interrogation versus visibility structure in narcotics, etc. In short, what we want is Tactic I: Team patrol to manage investi- further detail. direct evidence from the activity itself. Do gations. This tactic includes the assignment searches produce evidence of a direct of detectives to patrol teams (Bloch and criminal sort, e.g., burglary tools, or of a Bell 1976). more indirect sort, such as weapons since Tactic 11: Combining detective investi- they could be for self-protection, stolen gation with patrol function. Each patrol goods, persons wanted on warrants, etc.? officer does substantial detective investi- We would also want to know whether gation as part of routine patrol. weapons production has any effect on particular kinds of crime rates. Indeed, we

I should expect that increased productivity of weapons 'taken might be related to D. The basic crossover designformat reductions in carrying weapons over time. The basic experimental design that we Figure 2. We also would record separate measure- propose has two key features: ments by "beat-watch." Since there are (I) Different treatments are applied to three standard watches for each beat this the same experimental unit during differ- would give us a trivariate response vari- ent periods, and this results in a crossover able. We could then examine differences or changeover design (see Cochran and among watches within beats, as well as dif- Cox 1957). ferences among beats within watch. (2) The use of primary and secondary experimental units, with the secondary C. How long an experiment? units providing a double insulation between "adjacent" primary units. The KCPPE ran for a I-year time period. The initial experiment analysis is aimed Because of the important seasonal variation at the consideration of the primary units, in the levels of various types of crimes and although the effects of the treatments in exposure, the KCPPE could only use applied to the secondary units are taken one level of preventive patrol in each beat. into account. Depending on the results of Primary un~t= rn We propose an experiment that will run for this initial analysis, subsequent analyses Secondaty unit = 3 years. This expanded time frame will (1) may make use of the secondary units in - allow for the use of all three patrol addition to the primary ones. The units of strategies in each beat for a full year, (2) analysis always remain the individual The reason that this possibility exists is that permit the assessment of effects beyond police beats. each beat contains a somewhat different those considered in the KCPPE, and (3) mix of commercial and residential properties, provide an acceptable number of degrees of We assume that all beats are square and of and we expect to find different crimes at freedom for an estimate of exverimental the same size. While this is far from true in different times of the day associated with error. This approach in effect ailows each practice, we expect that modest variations the two types of properties. For example, in size and shape will not seriously affect beat to serve as its own control, and thus the southwest part of the Southern Patrol the implementation of the design. enables us to control more accurately for Division in Kansas City consists primarily beat-to-beat variations. We begin by dividing the beats into 3 x 3 of upper middle class residential properties, The time period of I year per treatment is blocks of 9. The basic configuration of but one beat in this area contains a modern dictated by the need to accumulate suffi- beats within blocks has the primary unit shopping area, and we would expect the cient data by beat-watch of rare or low pro- surrounded by 8 secondary units as shown mix of crimes associated with this beat to ductivity events. Such a period also in Figure 2. differ from the other beats nearby. At some removes the need to adjust directly for sea- point in the analysis the combination of For any given experimental period we commercial and residential properties sonal effects, and allows police officers intend to use the same treatment (i.e., sufficient time to adapt to different patrol within beats should be examined as a patrol strategy) in all 8 secondary beats possible concomitant variable. strategies. If such surveys were not needed within a block. Because our initial analyses to provide various response measures, will use data from only the primary beats, it The 3-year experimental time frame is more interesting and efficient experimental may seem extremely wasteful to use up a divided into three consecutive I-year peri- designs could be proposed. For example, if total of 9 beats with potential information ods, and for each primary beat we use a one were to use a time period of 4 months to yield only the primary beat. We do so in different patrol strategy during each peri- per treatment, one could apply each order to be able to measure the direct od. This is the crossover feature referred to treatment twice to each beat (so the length effects of strategies in the secondary beats above, and each primary beat serves as its of the experiment becomes 2 years), thus on the primary beat which they surround. own control. We also vary the use of the increasing substantially the degrees of The inability to make such measurement three patrol strategies in the secondary freedom associated with the estimate of appears to have been a serious problem in beats within each block in a similar experimental error. Such a plan would the KCPPE. If these effects involving fashion, so that within each block all 8 assume that the effects of treatment adjacent beats are negligible, then we can secondary beats first use one strategy, then changes could be assessed after only 4 still carry out subsequent analyses using a second, and finally a third. Thus there are months. Moreover, in this 2-year experi- measurements on all beats. 36 possible patrol strategy combinations ment each treatment would not be applied for a given block of 9 beats, since there are 6 to each beat for each of the 4 seasons. In the unlikely event that an effect is more possible orderings of the strategies for the Hawthorne effects, resulting from the likely to be observed in secondary rather primary beats, and for each of these 6 or- seemingly continuous changes in treat- than in primary beat units, the analysis dering~there are 6 possible orderings of the ment, might also result. could be redone taking into account the strategies for the secondary beats. This sug- units surrounding each secondary unit. Although 3 years is a very long period of ests an experiment involving 36 blocks or a time for the implementation of a social total of 36 x 9 = 324 beats, clearly an experiment, we feel the advantages here impossibility! outweigh the potential hazards. By carefully balancing treatment combina- superior experimental balance with addi- Most crossover experimental designs that tions in sets of blocks we can design experi- tional degrees of freedom for estimating assume the presence of residual effects do ments involving 6, 9, or 12 blocks of the error term, we would opt for the latter. so only for the actual time frame of the interest. This leads us to variants on sets of This is because the magnitude of detectable experiment, i.e., they assume that there are Graeco-Latin squares treated in the form effects suggested by all previous controlled no residual effects for period TI.Although of crossover designs. Alternatively we can studies is not that great, and the physical the discussion below is based on such an choose a set of treatment combinations at (as opposed to parametric) interactive assumption, it would seem to be inappro- random from the 36 possible ones. We effect of secondary units on adjacent pri- priate in the proposed experiment. In par- explore both of these possibilities below. macy units is already taken into account by ticular, we might expect to find a residual the model. The next least important among effect during TI in the beat with primary To keep our descriptions of designs the effects would seem to be residual effects strategy C and secondary strategy y, since compact, henceforth we use the following due to secondary-beat strategies. prior to the experiment all beats suppos- shorthand notation for patrol strategies. edly are using the current preventive patrol Capital Latin letters refer to strategies used The model that goes with this experimental strategy (i.e., B and 0). The analyses de- in the primary beats within a block, and structure assumes that each response vari- scribed below can take such effects into Greek letters refer to strategies used in the able (or some function of it, like the loga- account but the modifications result in secondary beats: rithm or log-odds in the case of propor- some additional nonorthogonalities in the A(a) = Search strategy. tions) is the sum of effects attributable to associated analysis of variance breakdowns. B(P) = Visibility strategy. each source. Thus if we are looking at a C(y) = Reactive no-patrol strategy. beat with primary strategy A and second- E. Random crossover designs We denote the three successive I-year time ary strategy P during period Tz,when strategies C and a were used in TI,the model periods as Tl, T?, and T3, respectively. In order to be able to test for all of the with residual effects postulates that the effects listed above we require a minimum For all the designs we discuss below, we are response variate of 9 or 10 blocks (depending on whether we interested in effects due to: = (beat effect) use residual or carryover effects). To (1) blocks of beats. + (main effect due to period T?) ensure a sufficient number of degrees of (2) time period. + (main effect due to A) freedom for error we probably need a (3) patrol strategies in primary units. + (main effect due to /3) minimum of 12 blocks unless we are (4) patrol strategies in adjacent secondary + (residual effect due to C) prepared to assume the absence of units. + (residual effect due to a) interaction effects. We would also like to be able to test for the + (interaction effect due to A x p) + (random error). In this subsection we describe two presence of various interaction effects, examples of "random crossover" designs, such as: If we use carryover effects, then in this one with 12 blocks that can be used to get (5) primary by secondary patrol strategies. model we replace the residual effect due to tests for all of the different effects and a (6) time by patrol strategy (either in the C and the residual effect due to a by a car- second one with 6 blocks that can be used form of residual or carryover effects), for ryover effect of C preceding A and a to get tests for the main effects. both primary and secondary beats. carryover effect of a preceding P. One possible random 12-block design can A residual effect during a particular time Note that the model includes a term be described as follows: period depends only on the treatment labelled "beat effect." All beats do not start (strategy) used in the preceding period. A from the same level of the response vari- carryover effect, as used here, depends on able, e.g., beats differ in their rate of auto- Block both the treatment in the preceding period mobile theft. The crossover design de- 1 and the treatment in the present one. Thus scribed here uses each beat as its own 2 the "carryover" model allows for different control, and attempts to remove the initial effects resulting from the preceding treat- differences among beats by incorporating 3 ment, when the transition is from search to an additive effect due to beats in the model. 4 control or from search to reactive, whereas The fact that beats with low crime produc- 5 the model based on residual effects forces tivity would not be expected to respond to 6 the effect of the preceding treatment to be particular treatments in the same "additive 7 the same in both cases. way" as beats with high crime productivity suggests that when crime rates are used as 8 Of all the effects listed here the one we 9 consider to be least substantial is that of the response variables, the additive model is interaction between the patrol strategy in more appropriate for the logarithm of the 10 the primary beat and the patrol strategy in crime rate. The use of such transformations 11 the secondary beat. If we were forced to is standard practice in modern statistical 12 choose between including this interaction data analysis. in our model and design or achieving - ordering of the effects to be tested may These conditions for balance are for cross- Table 1. ANOVA layout for 12-block make a difference. Of course other random over designs involving only one type of cross-over design with carry-over crossover designs may be better than this treatment, i.e., only one for the Greek or effects one, while many others will definitely be Latin labelled effects used above. Condi- Source -df worse. tions (I), (2), and (3) ensure that main effects are estimable, while if both Blocks (beats) 11 All 6 effects in the original list in Section Time 2 conditions (1)-(3) and (4)-(7) are satisfied, Primary strategy 2 IV-D are estimable with this particular then both main effects and residual effects Secondary strategy 2 random design, and there is not too great a are guaranteed to be estimable and obtain- Primary x secondary 4 disparity in the precision of the estimates if Primary carry-over 3 able in a simple form. Toapply these condi- Secondary carry-over 3 we use a standard Analysis of Variance Error 8 tions to the design problem considered - (ANOVA) model meeting the usual restric- here, we consider them once for treatments Total 35 tions on parameters. Table I lists the effects assigned to primary beats and a second and the associated degrees of freedom for J time for treatments assigned to secondary the model with carryover effects and Table beats. As far as we know, this will still not 2 lists these for the model with residual necessarily ensure that the primary by Table 2. ANOVA layout for 12-block effects. cross-over design with residual effects secondary interaction parameters are esti- As we remarked in the preceding subsec- mable, so for any particular balanced design Source - df tion, modifications in the standard ANOVA satisfying (1)-(7) we must make a special Blocks (beats) 11 analyses are required to take into account check regarding the estimability of these Time 2 Primary strategy 2 carryover effects from the standard treat- parameters. Secondary strategy 2 ment (B and /3) used prior to the experi- The random design described in the previ- Primary x secondary 4 mental period. Primary residual 2 ous subsection satisfies conditions (I), (3), Secondary residual 2 and (6), but not the, others. Clearly any set Error 10 The first 6 blocks'in the preceding design - can be used to illustrate a 6-block random of sequences built using Graeco-Latin Total 35 design that can be used to test the four sets squares of the form of main effects. The resulting ANOVA is given in Table 3.

Table 3. ANOVA layout for 6-block random cross-over design F. Balunced crossover designs Source -df Rather than trust the estimability of the various Blocks (beats) 5 effects of interest to a random selection of (in which each Greek and Latin letter Time 2 12 out of the 36 treatment sequences, we appears only once in each row and column, Primary strategy 2 Secondary strategy 2 can try to prepare a design that balances the and each Greek letter appears only once Error 6 assignment of treatments to experimental with each Latin one), must satisfy condi- - (1 ), Total 17 units in a crossover experiment. Patterson tions (2), and (3). The design in Table4 (1952) has given the following list of 7 con- was built with 4 such Graeco-Latin ditions for balance in a general crossover squares, and the reader may verify that the design: design satisfies Patterson's 7 conditions for Table 4. (1) No treatment occurs in a given both Greek and Latin letters. In this partic- Block sequence more than once. ular design the primary by secondary treat- - T1 -T2 -T3 (2) Each treatment occurs in a given ment interaction parameters are also 1 Aa BP time period an equal number of times. estimable. 2 BY Ca :J (3) Every two treatments occur together 3 CP AT Bci The ANOVA layouts for the balanced de- 4 Ba AT ‘3 in the same number of sequences. 5 Aa (4) Each ordered succession of two signs are the same as in Tables 1 and 2 for 6 A Ca treatments should occur equally often in the random design, but the Graeco-Latin 7 AY BP ca square structure will make several of the 8 Ba CY AP sequences. 9 CP Aff BY (5) Every two treatments occur together sums of squares orthogonal to one another, a situation that did not exist for the 10 Aa CP BY in the same number of curtailed sequences 11 BP AT ca formed by omitting the final period. random design. 12 CY Ba 43 (6) In those sequences in which a given The first six sequences in the above design treatment occurs in the final period, the (or the last six) may be used by themselves As indicated above, each patrol strategy is other treatments occur equally often. to give a balanced design for estimating used exactly once for the primary unit in (7) In those sequences in which a given only the main effects as in Table 3. These6- each block and exactly once for,the second- treatment occurs in any but the final block designs have the added feature that ary units. Because we randomly selected 12 period, each other treatment occurs equal- they allow for the estimation of both pri- of 36 strategy combinations Aappears only ly often in the final period. mary and secondary residual effects. If we twice in TI,while B and C appear 5 times choose to break both of these residual sums each. This lack of balance leads to a nonor- of squares out of the error sum of squares, thogonal analysis of variance where the the resulting error sum of squares has only 2 degrees of freedom, and thus any ANOVA tests will have very low power. In order to ensure that the analyses we are about to describe are proper, theallocation Table 5. Variances of parameter estimates in the model with residual effects of symbols (both Greekand Latin) to treatments, and sequences to blocks of beat --Balanced Random Balanced Random must be madeat random (Patterson 1952). -- Treatments A .07402 .19002 Block B1 .492 .700 A systematic assignment of treatments B .074 .I90 effects B2 .656 .722 simply will not do. C .076 .I14 B3 .492 .697 Insulation a .076 .I31 B4 .492 .493 0 .074 .098 B5 .492 .763 Y .074 .I71 B6 .656 .698 G. Comparing the balance Residual A .I72 .333 B7 ,647 1.16 and random designs treatment B .172 .205 .517 .842 C .149 .247 B9 .517 .462 Although there is an aesthetic appeal to the Residual a .I49 .231 B10 .517 .581 insulation p .I72 ,212 B1l .647 .436 balanced design described above, we have Y .I72 .242 B12 .517 .763 no guarantee that it is in fact superior to the Interaction Aa .241 .483 Time TI .074 .089 random, unbalanced design. In Tables 5 effects Ap .602 .562 T2 .I86 .070 AY ,602 .437 T3 .I85 .088 and 6 we give the variances associated with Ba .241 .734 each of the estimated effects in the two .602 .442 BP .602 .806 complete (12-block) models, the one with CaBy .296 .507 residual effects and the one with crossover .241 .559 effects. Each variance is some multiple of CYCP .234 .SO6 the variance, a2, of the random error term. In Table 7 we give similar expected variances for the two 6-block designs Table 6. Variances of parameter estimates in the model with cross-over effects (random and balances) assuming the presence of neither residual, carryover, nor --Balanced Random --Balanced Random interaction effects. Treatments A .063a2 .14002 Block B1 1.18 .789 B .063 .I85 effects B2 1.08 1.03 For the 12-block experiment and the model C .056 .I32 B3 1.18 .843 with residual effects the balanced design Insulation or .056 .I45 Bq ' 1.18 1.22 seems superior to the random one, except P .063 .lo9 B5 1.18 .921 Y .063 .I66 1.08 .777 _ . for a few primary by secondary interaction Avs B before C! .618 .579 B7 1.08 1.32 parameters. For the model with carryover A vs C before B .619 653 1.18 .960 B vs C before A .619 .353 B9 1.18 .881 effects, however, the results are less clear. a vs f3 before y 519 .482 B10 1.18 .672 The balanced design is superior for the or vs y before P .619 .408 Bll 1.08 .784 main effects due to treatments in the p vs y'before a .618 .467 812 1.18 .903 Interaction Aa .741 .594 Time T1 .074 .I17 primary and secondary beats, but other- effects Ap .852 .701 T2 .I85 .080 wise the random design is by and large .852 .489 T3 .I85 .090 2: .741 .915 superior. All things considered, we prefer .852 .596 the balanced design. For the 6-block BYBP .852 .930 . Ca .296 .606 experiment the balanced design is appar- CP .741 .751 ently superior again. CY .741 .946 Further comparison between the designs has been carried out in terms of the statisti- (1) Survey and questionnaire data, It would be extremely useful to have data cal power of the various tests for effects including results from both community on response time to calls for service. The resulting from the ANOVA. The calcula- and commercial surveys regarding victim- KCPPE collected such data through a pair tions are summarized in a series of tables ization and attitudes. of surveys (one of observers and the other presented in. the Appendix. The power (2) Interviews with officers and partici- of citizens). If an automatic vehicle moni- calculations seem to substantiate the pant observations. toring system such as FLAIR is used to superiority of the balanced design and (3) Departmental data such as those on track police vehicles during the experiment suggest that we have a very high chance of reported crime, traffic, and arrests. as we propose, then departmental data on detecting most effects that are about the Given the nature of the crossover design response times would be available for anal- size of the standard deviation of the ysis. Analysis need not be based on com- random error term in the model. being proposed, carrying out multiple victimization surveys seems highly imprac- plete data for each time period, but meas- tical because of the large sample sizes urements at three points for each condition H. Response variables to be measured required to get useful information (the (beginning, middle, end) seem desirable. The fact that the beginning of one condi- The KCPPE used three types of response sample sizes in the KCPPE were clearly much too small to produce useful information is the end of another simplifies matters variables to assess the effects of different here somewhat. patrol strategies: tion). Therefore we do not propose to carry out any surveys as part of an effort to Not only do we propose to analyze direct directly monitor the ongoing effects of the measures of reported crime and police pro- experiment. duction (e.g., arrests) which are part of Some care must be taken in using the Table 7. Variances of parameter approach outlined here in order to ensure In Section 111-E we discussed problems in estimates in 6-beat design that all of the primary beats do not fall the KCPPE which resulted from some I I adjacent to city and natural boundaries. I --Balanced Random I beats in the experimental area being on the boundaries of the city of Kansas City, For example, if we have 4 blocks resulting Treatments A .ll 1u2 .233u2 in 6 x 9 layout of beats, eliminating all of B .I11 .I92 Missouri. By making a few plausible a C .I11 .I25 assumptions, we can turn what was the exterior secondary beats leads to a layout with all 6 primary beats on the bound- Insulation a .lll .215 formerly a disadvantage into a benefit and, .I11 .I31 ary. Some type of compromise would y .I11 .I92 in the process, cut down on the actual probably be wise in such circumstances. Block B1 .278 .278 number of police beats required to carry effects B2 .278 .278 out the experiment. I 61 .278 .278 Let us suppose that those secondary beats V. Further considerations in a block sharing a side with the primary and summary Time T1 .lll .I59 beat each contribute equally to the appro- For policy decisions regarding police T2 .I11 .I11 priate effect terms, while the four second- deployment and manpower allocation we T3 .111 .159 ary beats that share only a corner with the require as precise estimates as possible of primary beat contribute equal but lesser the effects of one policy versus another. 1/2 departmental records, but we would also amounts (say of the former). Then we Thus once we carry out all of the tests cor- like to have several offender-related can alter the number of beats in those responding to the various sources in the response measures since we anticipate that blocks on a boundary, by eliminating as ANOVA tables of the previous section, we the treatment tactics will have "deterrent" many secondary beats as necessary. For should bolster our estimates of various effects on potential offenders. Some example, suppose we have a design with effects by directly utilizing data from the possibilities are: nine blocks laid out so that the experimen- secondary beats. Since reported crimes are tal area takes the form of 9 x 9 layout of (a) Data on modus operandi for of- a already recorded by beat there would be no fenses. These are hard to get and will be the square beats. If we have an actual area of added cost for collecting additional data on least sensitive to changes. roughly the same size but possessing 49 the secondary beats. beats in a 7 x 7 area, then we eliminate the (b) Data on rearrest rates and place of The experimental designs described in Sec- secondary beats all around the original occurrence of offense for rearrested tion IV may easily be adapted for other design resulting in the layout shown in offenders. experiments involving police deployment Figure 3. (c) Data on characteristics of offenders and manpower allocation, such as ones for crimes against the person, e.g., changes Note that the 4 blocks in the corner have dealing with comparisons between the use in race, age, and sex of offenders in beats. only 3 secondary beats, while 4 others have of one-man and two-man patrol cars. Thus, for example, blacks might commit exactly 5, and only one block has 8. fewer offenses in white areas with an inter- We have noted earlier that the proposed rogation procedure or juveniles might be a Analyzing designs laid out in a fashion experiment involves neither changes in smaller proportion of all offenders. similar to the one above requires modifica- police manpower nor the spatial redistri- (d) The ratio of crimes against persons tions to the more or less standard analyses bution of patrol resources within a city, as to property. This is again a highly indirect for the "complete" designs described ear- was the case in the KCPPE. Thus no policy measure but offenders might shift more to lier, but the modifications are straight- implications regarding levels of manpower crimes of stealth under increased proactiv- forward, corresponding directly to the can possibly result. Moreover, since the ity. On the whole this would be a difficult assumptions regarding the effects from the different patrol strategies will be applied to measure to interpret. secondary beats described above. small areas, even if the results are striking (e) Changes in the population of the policy implications for overall police In Kansas City, not only can we reduce the patrol strategy in a city may be difficult to offenders with afirst arrest and in propor- number of beats required for our designs tion of offenders with a first arrest. Both formulate due to the use of the different by taking advantage of the city boundaries, strategies in adjacent beats in the experi- have defects as measures, yet they could be we can make similar reductions with blocks affected by proactive tactics. ment. For example, if there is no detectable of beats bordering the Missouri River. The difference among treatment effects, we (0 Changesin distance between place of river slices across the city and, according to occurrence of offense and residence of must ask if the results suggest a policy of reports we have had, police patrolling beats "business as usual" or a new overall offender. If an entire city is used, this on one side of the river rarely answer calls should not change if resources were strategy of low visibility patrol. The answer for service on the other side. Thus we may seems unclear. constant, but they are not. Offenders might well be able to reduce the 108 beats be more inclined to go greater distances required for implementing our 12-block where the police have a larger territory to balanced design to the 69 beats that cover with increased proactivity. actually exist in Kansas City. The foregoing is a tentative list of possible response variables to be measured and analyzed. Considerably more work is required to refine this part of the proposal. Many social experiments, as a result of Appendix: Power calculationsfor comparing Figure 3. their failure to control for various sources of variability, end up by proving the null balanced and random designs hypothesis. The analysis of experimental for ANOVA models in Section IV results is structured toward rejecting the The tables in this appendlx glve illustrations of null hypothesis (typically that of no differ- the magnitude of effects capable of detection ence) in favor of some alternative, by giving through the use of standard F-tests with an 0.05 heavy weight to the null hypothesis unless level of significance, with power = Pr(reject IH, it is demonstrably false. The level of true) = 0.50,0.70,0.90, and 0.95. Table A-l is for the 12-block experiment and the model with car- significance (the probability of falsely ryover effects. Table A-2 is for the 12-block rejecting the null hypothesis) is set at some experiment and residual effects. Table A-3 is for low value and then the probability of fail- the 6-block experiment. At least two illustra- ing to detect the alternative hypothesis tions are given for each effect. when it is true is made problematic. Unless For treatment and main effects, the tests were that probability also is small, the experi- based on adjustments first for other maineffects ment will be weighted in favor or the null (this is the standard form of analysis), and then hypothesis. Such, we have argued, was for all other effects including interactions, car- Primary likely the case in the KCPPE because of its ryover effects, and residual effects. weak experimental design, i.e., its failure to How to read the tables. Suppose we are inter- Secondary control for important sources of varia- ested in compared experiments using an 0.05 bility. At least as crucial, in our view, was level of significance. Then the first set of rows in the failure of the KCPPE investigators to the table tell us that, if A = 4.550, B =O,and C= use proper randomization of treatments to +0.550 (where 02 is the varlance of the random Finally we must ask how stable the experimental units. error term), the usual F-tests for treatments estimates of parameters in the experi- would have detected these effects for the bal- mental model will be over time, and across The problem of what design to adopt for anced design with power = 0.50. cities. Variables that influence the behavior social experiments is not easily resolved. Here we call attention to a particular class of offenders may interact with the experi- Acknowledgments mental variables and with the peculiarities of designs that are useful not only for experiments relating to patrol strategies, This paper grew out of mater~aldiscussed in the of cities and times in such a way as to make Workshop on Criminal Justice Statistics,held in estimates highly unstable. If this is the case, but also to other types of social experiments. Our basic design has two key Washington, D.C., July 1975,and sponsored by then changes and refinements in the experi- the Social Science Research Council Center for mental design are required. Further con- features: Coordination of Research on Social indicators sideration must be given to the potential (1) Different treatments are applied to and the Law Enforcement Assistance Adminis- policy implications of the experiment as the same experimental units during differ- tration. We are indebted to Davld W. Britt, part of the design. ent time periods, resulting in a crossover or William Falrly, Rlchard Larson, Katherine C. changeover structure where each unit is Its Lyall, and Richard Sparks for several important Many so-called social experiments are not own control. suggestions and comments. An abbreviated ver- really experiments in the formal statistical (2) Additional control is exercised through sion of an earller draft of thls paper appeared sense. All too often, when trying to evalu- a specialdevice whereby primary experimental under the same tltle in Evaluat~on3 (1976), aTe whether some innovation or social pro- units are insulated from one another by the 124-131. gram has the intended effect, investigators addition of secondary experimental units, During the preparation of this paper, Stephen E. fail to provide a direct means for separating with effects being examined in both the Fienberg's research was partially supported by out or controlling for the effects of changes primary and secondary units. This paper grants from The Robert Wood Johnson Foun- in concomitant variables. To overcome the explores different orders of complexity in dation and the Commonwealth Fund to the difficulties inherent in such studies, social this design and discusses means for Center for Analysis of Health Practices, scientists have turned to the use of evaluating tradeoffs among them. Harvard School of Public Health, and from the randomized controlled field trials. Both the National Science Foundation Grant SOC72- It is apparent that more complex experi- 05257 to the Department of Statistics, Harvard randomization and the control are crucial mental designs controlling for various University. Albert J. Reiss' research was par- to such studies. sources of variation will in general be more tially supported by a grant from the Russell Sage costly, take longer periods of time, and Foundation. involve greater use of repeated measures than the simple experimental design adopted for the KCPPE. If public policy is to rest On social experiments where causal inference is essential, the gain in efficiency associated with complex designs should ordinarily outweigh any increased cost. Table A-1. Carry-over analysis 50% Power 70% Power 90% Power 95% Power (a) Balanced Random Balanced Random Balanced Random Balanced Random Treatment effects A -.55 -.57 -.69 -.72 -.89 -.93 -.99 -1.03 (adjustingonly for B 0 0 0 0 0 0 0 0 main effects) C +.55 +.57 +.69 +.72 +.89 +.93 +.99 +1.03 Treatment effects A -.56 -.80 -.70 -1.02 -.91 -1.31 -1.01 -1.45 (adjusting for an 8 0 0 0 0 0 0 0 0 effects) C +.56 +.80 +.70 +1.02 +.91 +1.31 +1.01 +1.45 Treatment effects A +.63 +.66 +.80 +.83 +1.03 +1.07 +1.14 +1.19 (adjusting only for B -.32 -.33 -.40 -.41 -.51 -.54 -.57 -.60 main effecw C -.32 -.33 -.40 -.4 1 -.51 -.54 -.57 -.60 Treatment effects A +.67 +.98 +.85 +1.24 +1.09 +1.60 cl.21 +1.78 (adjusting for &I B -.34 -.49 -.42 -.62 -.55 -.80 -.61 -.89 effects) C -.34 -.49 -.42 -.62 -.55 -.80 -.61 -.89 Insulation effects 01 -.55 -.57 -.69 -.72 -.89 -.93 -.99 -1.03 (adjusting only for 0 0 0 0 0 0 0 0 main effects) Y +.55 c.57 +.69 +.72 +.89 +.93 +.99 +1.03 Insulation effects ff -.56 -.96 -. 70 -1.20 -.91 -1.55 -1 .O1 -1.73 (adjusting for all P 0 0 0 0 0 0 0 0 effects) Y c.56 +.96 +.70 -1.20 +.91 +1.55 +1.01 +1.73 Insulation effects a +.63 +.64 +.80 +.81 +1.03 +1.04 +1.14 +1.16 (adjusting only for P -.32 -.32 7.40 -.40 -.51 -. 52 -.57 -. 58 main effects) Y -.32 -.32 -.40 -.40 -.51 -.52 -.57 -. 58 Insulation effects a c.63 +.99 +.80 +1.25 +1.03 +1.61 +1.14 +1.79 (adjusting for &I 0 -.32 -. 50 -.40 -.62 -.51 -.81 -.57 -.90 effects) Y -.32 -. 50 -.40 -.62 -.51 -.81 -.57 -.90 (b) Treatment A before C +l. 18 +1.84 +1.47 +2.30 +1.89 +2.95 +2.08 +3.24 carry-over B before C --1.18 -1.84 -1.47 -2.30 -1.89 -2.95 -2.08 -3.24 effects A before B +.59 +.92 +.74 +1.15 +.95 +1.48 +1.04 +1.62 C before B -. 59 -.92 -. 74 -1.15 -.95 -1.48 -1.04 -1.62 B before A 0 0 0 0 0 0 0 0 C before A 0 0 0 0 0 0 0 0 Treatment A before C 0 0 0 0 0 0 0 0 carry-over B before C 0 0 0 0 0 0 0 0 effects A before B 0 0 0 0 0 0 0 0 C before B 0 0 0 0 0 0 0 0 B before A +1.53 +1.53 +1.91 +1.91 +2.45 +2.46 +2.69 +2.70 C before A -1.53 -1.53 -1.91 -1.91 -2.45 -2.46 - - Insulation ff before y +1.18 +1.38 +1.48 +1.73 +1.90 +2.20 +2.07 +2.44 carry-over p before y -1.18 -1.38 -1.48 -1.73 -1.90 -2.20 -2.07 -2.44 effects a before +.59 +.69 +.74 +.86 +.95 +1.10 +1.04 +1.22 y before P -. 59 -.69 -. 74 -.86 -.95 -1.10 -1.04 -1.22 before a 0 0 0 0 0 0 0 0 y before a 0 0 0 0 0 0 0 0 Insulation a before 7 0 0 0 0 0 0 0 0 carry-over 0 before y 0 0 0 0 0 0 0 0 effects a before /3 0 0 0 0 0 0 0 0 y before 0 0 0 0 0 0 0 0 0 0 before a +1.52 +1.84 +1.90 +2.30 +2.44 +2.96 +2.68 +3.25 y before a -1.52 -1.84 -1.90 -2.30 -2.44 -2.96 -2.68 -3.25 (c) Interaction Aff +5.16 +3.72 +6.37 +4.59 +8.19 +5.91 +8.95 +6.45 effects AP -.65 -.47 -.80 -.57 -1.02 -. 74 -1.12 -.81 -.65 -.47 -.80 -.57 -1.02 -. 74 -1.12 -.81 -.65 -.47 -.80 -.57 -1.02 -. 74 -1.1 2 -.81 BP -.65 -.47 -30 -.57 -1.02 -.74 -1.12 -.81 By -.65 -.47 -.80 -.57 -1.02 -.74 -1.12 -.81 Car -.65 -.47 -.80 -.57 -1.02 -.74 -1.12 -.81 CP -.65 -.47 -.80 -. 57 -1.02 -.74 -1.12 -.81 C7 -.65 -.47 -.80 -.57 -1.02 -.74 -1.1 2 -.81 Interaction Aa +3.39 +1.90 +4.18 +2.34 +5.38 +3.01 +5.87 +3.29 effects Ap -.97 -. 54 -1.19 -.67 -1.54 -.86 -1.68 -.94 A7 -.97 -.54 -1.19 -.67 -1.54 -.86 -1.68 -.94 801 -.97 -.54 -1.19 -.67 -1.54 -.86 -1.68 -.94 BP +1.94 +1.08 +2.39 +1.34 +3.07 +1.72 +3.36 +1.88 87 -.97 -. 54 -1.19 -.67 -1.54 -.86 -1.68 -.94 Car -.97 -. 54 -1.19 -.67 -1.54 -.86 -1.68 -.94 CP -.97 -. 54 -1.19 -.67 -1.54 -.86 -1.68 -.94 Cy +.48 +.27 +.60 +.33 +.77 +.43 +.84 +.47 Interaction Act +2.00 +1.12 +2.47 +1.38 +3.17 +1.78 +3.47 +1.94 effects Ap -1.00 -.56 -1.23 -.69 -1.59 -.89 -1.73 -.97 -1 .OO -. 56 -1.23 -.69 -1.59 -.89 -1.73 -.97 -1.00 -.56 -1.23 -.69 -1.59 -.89 -1.73 -.97 B@ +2.00 +1.12 +2.47 +1.38 +3.17 +1.78 +3.47 +1.94 By -1.00 -. 56 -1.23 -.69 -1.59 -.89 -1.73 -.97 Ccl -1.00 -.56 -1.23 -.69 -1.59 -.89 -1.73 -.97 --1 .OO -. 56 -1.23 -.69 -1.59 -39 -1.73 -.97 :; +2.00 +1.12 +2.47 +1.38 +3.17 +1.78 +3.47 +1.94 Table A-2. Residual analysis

50% Power 70% Power 90% Power 95% Power Balanced Random Balanced Random Balanced Random (a) Balanced Random Treatments (adjusting -.53 -.55 -.66 -.68 -.85 -.89 -.94 -.98 only for main effects) 0 0 0 0 0 0 0 0 +.53 +.55 +.66 +.68 +.85 +.89 +.94 +.98 Treatments (adjusting -.62 -.81 -.77 -1 .OO -.99 -.85 -1.10 -1.44 for alleffects1 0 0 0 0 0 0 0 0 +.62 +.81 +.77 +1 .OO +.99 +.85 +1.10 +1.44 Treatments (adjusting +.61 +.64 +.76 +.79 +.98 +1.03 +I .09 +1.14 only for main effects) -.3 1 -.32 -.38 -.40 -.49 7.51 -.55 -.57 -.3 1 -.32 -.38 -.40 -.49 -.51 -.55 -.57 Treatments (adjusting +.71 +I .09 +.88 +1.35 +1.14 +1.75 +I .26 +I .94 for eeffects) -.35 -. 54 -.44 -.68 -.57 -.8 7 -.63 -.97 -.35 -.54 -.44 -.68 -.57 -.87 -.63 -.97 Insulation (adjusting -.53 -.55 -.66 -.69 -.85 -.89 -.94 -.99 only for main effects) 0 0 0 0 0 0 0 0 +.53 +.55 +.66 +.69 +.85 +.89 +.94 +.99 Insulation (adjusting -.62 -.9 1 -.77 -1.13 -.99 -1.46 -1.10 -1.62 for glJ effects) 0 0 0 0 0 0 0 0 +.62 +.91 +.77 +1.13 +.99 +I .46 +1.10 +1.62 Insulation (adjusting . +.61 +.62 +.76 +.77 +.98 +.99 +1.09 +1.10 only for main effects) -.31 -.31 -.38 -.38 -.49 -.50 -.55 -.55 -.31 -.31 -.38 -.38 -.49 -.50 -.55 -.55 Insulation (adjusting +.72 +.89 +.89 +1.11 +1.15 +1.44 +1.28 +I .59 for glJ effects) -.36 -.45 -.44 -.55 -.58 -.72 -.64 -.go b.36 -.45 -.44 -.55 -.58 -.72 -.64 -.SO (b) Treatment After A -.89 -1.24 -1.10 -1.54 -1.42 -2.00 -1.58 -2.21 residual After B 0 0 0 0 0 0 0 0 After C +.89 +1.24 +1.10 +1.54 +1.42 +2.00 +1.58 +2.21 Treatment After A +1.07 +1.49 +1.33 +1.85 +I .72 +2.40 +1.91 +2.66 residual After B -. 54 -.75 -.67 -.93 -.86 -1.20 -.96 -1.33 After C -.54 -.75 -.67 -.93 -.86 -1.20 -.96 -1.33 Insulation After ff -.89 -1.11 -1.10 -1.38 -1.42 -1.79 -1.58 -1.98 residual After P 0 0 0 0 0 0 0 0 After y +.89 +1.11 +1.10 +1.38 +1.42 +1.79 +I .58 +I .98 Insulation After ff +I .OO +1.25 +1.24 +1.54 +I .61 +2.00 +1.78 +2.22 residual After P -.50 -.62 -.62 -.77 -.SO -1 .OO -.89 -1.11 After y -.50 -.62 -.62 -.77 -.80 -1 .OO -.89 -1.11 Interaction Aff +3.11 +3.45 +3.83 +4.24 +4.88 +5.40 +5.33 +5.91 A@ -.39 -.43 -.48 -.53 -.61 -.68 -.67 -.74 A7 -.39 -.43 -.48 -.53 -.6 1 -.68 -.67 -.74 Bff -.39 -.43 -.48 -.53 -.61 -.68 -.67 -.74 SP -.39 -.43 -.48 -.53 -.61 -.68 -.67 -. 74 BY -.39 -.43 -.48 -. 53 -.61 -.68 -.67 -. 74 Cff -.39 -.43 -.48 -. 53 -.61 -.68 -.67 -.74 CP -.39 -.43 p.48 -.53 -.61 -.68 -.67 -.74 CY -.39 -.43 -.48 -.53 -.61 -.68 -.67 -. 74 (c) Interaction Ao! +I .90 +1.74 +2.35 +2.15 +2.98 +2.73 +3.26 +2.99 effects AP -.54 -. 50 -.67 -.61 -.85 -. 78 -.93 -.85 -. 54 -.50 -.67 -.61 -.85 -.78 -.93 -.85 2 -.54 -.50 -.67 -.61 -.85 -. 78 -.93 7.85 BP +1.09 +1 .OO +1.34 +I .23 +1.71 +1.56 +1.87 +1.71 BY -.54 -. 50 -.67 -.61 -.85 -.78 -.93 -.85 Cff -.54 -. 50 -.67 -.61 -.85 -.78 -.93 -.85 CP -. 54 -.50 -.67 -.61 -.85 -.78 -.93 -.85 CY +.27 +.25 +.34 +.31 +.43 +.39 +.47 +.43 Interaction Aff +1.14 +I .03 +I .40 +1.27 +1.78 +I .62 +1.95 +I .77 effects AP -.57 -.52 -.70 -.64 -. 89 -.8 1 -.98 -.89 AY -.57 -.52 -.70 -.64 -.89 -.81 -.98 -.89 BCY 47 -. 52 -.70 -.64 -.89 -.81 -.98 -.89 BP +1.14 +1.03 +I .40 +1.27 +1.78 +1.62 +1.95 +1.77 67 -.57 -.52 -.70 -.64 -.89 -.81 -.98 -.89 Cff -.57 -.52 -.70 -.64 -.89 -.81 -.98 -.89 c@ -.57 -.52 -.70 -.64 -.89 -.81 -.98 -. 89 CY +1.14 +1.03 +1.40 +I .27 +1.78 +I .62 +1.95 +1.77 I ( Table A-3. 6-beat analysis I 50% Power .70% Power 90% Power 95% Power Balanced Random Balanced Random Balanced Random Balanced RandomI Treatment effects

Treatment effects

Insulation effects

References Kelling, G. L., T. Pate, D. Dieckman, and C. E. Press, S. J. (1972) Brown (1974) "Police manpower versus crime." In J. M. Bloch, P. B., and J. Be11 (1976) The Kansas City Preventive Patrol Experi- Tanur et al. (eds.), Statistics: A guide to the Managing investigations: The Rochester unknown, San Francisco: Holden-Day. system, Washington, D.C.: The Police Foundation. ment: A technical report. Washington, D.C.: The Police Foundation. Reiss, A. J., Jr. (1967) Boydstun, J. E. (1975) Kempthorne, 0.(1952) "Studies in crime and law enforcement in Sun Diego field interrogation: Final report. major metropolitan areas." Report of a research Washington, D.C.: The Police Foundation. The design and analysis of experiments, pp. 10-17. New York: Wiley. study for the President's Commission on Law Brannon, B. C. (1956) Enforcement and the Administration of Justice. "A report on one-man police cars in Kansas Larson ,R. C. (1972) University of Michigan. Urban police patrol analysis. Cambridge, City, Missouri." Journalof Criminal Law, Crim- Mass.: M.I.T. Press. Reicken, H. R., and R. F. Boruch (eds.) (1974) inology, and Police Science 47:238-252. Social experimentation. New York: Academic Cochran, W. G., and G. M. Cox (1957) Larson, R. C. (1976) Press. "What happened to patrol operations in Experimental designs (second edition), pp. Schwartz, A. I., and S. N. Clarren (1977) 127-243. New York: Wiley. Kansas City: A review of the Kansas City Pre- ventive Patrol Experiment." Journal of Crimi- The Cincinnati Team Policing Experiment: A Davis, E. M., and L. Knowles (1957) nal Justice 267-297. summary report. Washington, D.C.: The Police "An evaluation of the Kansas City Preventive Pate, T., R. A. Bowers, and R. Parks (1976) Patrol Experiment." The Police Chief, June Sherman, L. W., C. H. Milton, and T. V. Kelly 1957, pp. 22-27. Three approaches to criminal apprehension in Kansas City: An evaluation report. Washington, (1973) Fisher, R. A. (1926) D.C.: The Police Foundation. Team policing; Seven case studies. Washing- "The arrangement of field experiments." Jour- ton, D.C.: The Police Foundation. Paterson, H. D. (1951) nal of the Ministry of Agriculture 33: 503-513. "Change-over trials." Journal of the Royal Tien, J. M., R. C. Larson, and J. W. Simon Gilbert, J. P., R. J. Light, and F. Mosteller Statistical Society (B)12:256-271. (1976) (1975) An evaluation reporc Wilmington Split Force "Assessing social innovations: An empirical Patterson, H. D. (1952) Patrol Program. Cambridge, Mass.: Public base for policy." In A. R. Lumsdaine and C. A. "The construction of balanced designs for Systems Evaluation, Inc. Bennet (eds.), Evaluation and experiment: Some experiments involving sequences of treatments." critical issues in assessing social programs, New Biometrika 39:32-48. York: Academic Press. Press, S. J. (1971) "Some effects of an increase in police manpower in the 20th Precinct of New York City." R-704 NY C. New York: New York City RAND Institute. NCJRS REGISTRATION

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