Journal of Criminal Law and Criminology Volume 64 | Issue 3 Article 10 1974 Crime, Sanctions and Scientific Explanation Thomas Orsagh Follow this and additional works at: https://scholarlycommons.law.northwestern.edu/jclc Part of the Criminal Law Commons, Criminology Commons, and the Criminology and Criminal Justice Commons Recommended Citation Thomas Orsagh, Crime, Sanctions and Scientific Explanation, 64 J. Crim. L. & Criminology 354 (1973) This Criminology is brought to you for free and open access by Northwestern University School of Law Scholarly Commons. It has been accepted for inclusion in Journal of Criminal Law and Criminology by an authorized editor of Northwestern University School of Law Scholarly Commons. THE JOURNAL OP CRIMINAL LAW & CRIMINOLOGY Vol. 64, No. 3 Copyright @ 1973 by Northwestern University School of Law Printed in U.S.A. CRIME, SANCTIONS AND SCIENTIFIC EXPLANATION THOMAS ORSAGH* There is no dearth of theoretical and empirical of the Crime-Sanctions (C-S) relation has been literature dealing with the relation between crime incorrect. and sanctions. In the last decade, interest in It is generally accepted that the relation of the subject seems to have quickened, no doubt crime to sanctions is likely to be quite complex. prompted to some extent by a well advertised and Current theory and empirical research suggest substantial rise in rates of reported crime. Recent that the two variables probably interact with each legalistic developments,1 because of their presumed other and with any number of other variables. But influence on crime rates, have also heightened our knowing this is one thing, coping with it something interest in the subject. Public pressure to "do else. How does one evaluate a highly complex something" about crime and the political responses relation? Instinct says to simplify and to adopt a to that pressure have provided additional stimuli. procedure which is at once persuasively obvious Yet despite a good deal of scholarly attention and and disarmingly direct and easy to apply: analyze society's compelling need to know what relation, one relation at a time. In this case one might try if any, exists between crime and sanctions, we to determine the effect of sanctions on crime as one cannot honestly say that we know much about the independent research effort, and then the effect subject. of crime rates on sanctions as another. To quantify the relation between the two varia- The decision to consider one relation at a time bles we need data, and it is undoubtedly true that may not be improper per se, but the consequences the quality of the data available for empirical of seeking a quantitative measure of the relation investigation is unusually poor.2 Criminal statistics through conventional statistical procedures can be impose constraints on the questions that can be improper. Consider the first relation. In order to asked, handicap the research effort and interject determine the effect of sanctions on crime, a proba- an annoying degree of imprecision in the statistical ble formulation for the relation would be: results. Yet, these deficiencies are troublesome nuisances, not roadblocks, in the path of scientific CRIME = f(SANCTIONS, X), inquiry. The data are not so bad that the truth wherein X represents a collection of control varia- cannot be wrung out of them.' Our poor scholarly bles. Specifically, we might evaluate the effect of performance has another explanation. There is sanctions on crime by hypothesizing the existence good reason to suspect that our problem in under- of a linear relation of the form standing the crime-sanctions relation lies in the nature of the relation itself. The purpose of this (2) CRIME = f ( 0 + 01 SANCTIONS study is to demonstrate that past empirical analysis + 62 AGE + 03 POVERTY +.u), * Associate Professor of Economics, University of North Carolina at Chapel Hill. wherein A represents the conventional error term. 'The right to counsel, the de facto elimination of We would recognize, of course, that (2) is a sim- capital punishment and the lengthening time interval between the criminal act and the initiation of punish- plification of (1) and hence a gross simplification ment come immediately to mind. of our basic conception of the crime-sanctions 2For the crime variable the point is well documented. relation, and that Age and Poverty are but two See, e.g., Biderman, Social Indicators and Goals, in SOCIAL INDICATORS 68 (A. Bauer ed. 1966); 2 PREsi- of many variables subsumed in X which, a priori, DENT'S COMUMSSION ON FEDERAL STATISTICS, FEDERAL deserve consideration. If there is reason to believe STATISTICS (1971). that the other X variable produces only small and 3 Criminal statistics are probably no worse than the data being used, often with little critical comment, in largely self-canceling effects within the universe certain other specialized areas of social science re- from which our observations were drawn, we might search. Consider, for example, the quality of the socio- logical, demographic and economic data utilized in be inclined to believe that the derived coefficients studies of underdeveloped regions. are essentially correct. Hence, if bi, our regression 19731 SCIENTIFIC EXPLANATION estimate of i, is sufficiently large relative to its CRIME standard error, we would be willing to conclude that variations in Crime are associated with varia- tions in Sanctions; or, in other words, a change in Sanctions, holding Age, Poverty and other varia- bles constant, induces a change in Crime. The foregoing is a fair description of the best practice in the field at the present time. It is not always the correct practice. There are a class of relations for which the above procedure is improper even though the usual regression equation condi- tions are met.4 If the true state of the world is not characterized by a single relation between two variables but by a system of relations, the coeffi- cients we estimate within a single regression equa- tion such as (2) can be consistently incorrect not only in magnitude but even as to the sign of the SANCTIONS coefficient. A mathematical proof of the proposition FiGU 1. that single equation estimates are biased in such instances is easily developed,5 but for our purposes Assuming that b1 is large relative to its standard is unnecessary. The flaw in the single equation error, what may we infer from Figure 1? If bi is approach to the C-S relation can be demonstrated statistically significant by our criterion, we must rather easily. conclude fl > 0. However such a conclusion is Suppose the true C-S relation has the form troubling, since present belief, provisional and given by Model 3: imperfect though it is, strongly suggests <_' 0.6 (3a) CRIME = Po + i SANCTIONS No doubt our impulse would be to try a more refined model, such as introducing more of the X + BX +it variables or trying non-linear functions. Yet, no (3b) SANCTIONS = a0 + a, CRIME matter what we do, if Model 3 is a correct descrip- tion of the world, we are destined to obtain biased + AZ + v, estimates of #1 except by the purest of accidents. wherein X and Z represent appropriate collections To illustrate: Suppose, in fact, the conventional of independent variables with their respective sets hypothesis is true, viz. 61 < 0; that is, holding all of coefficients, B and A, and where /z and P are X variables constant, more severe sanctions de- the conventional error terms. Suppose, in the presses the crime rate. Suppose it is also true that, interests of simplification, we proceed with a holding all Z variables constant, an increase in regression analysis as we did with (2). What we crime rates leads to a rise in sanctions. (For ex- might find is a configuration of observations in the ample, society may react to a rising crime rate by C-S plane such as is illustrated by the five observa- imposing increasingly severe penalties.) From an tion points in Figure 1. The Poverty and Age empirical point of view, what would we observe? dimensions are not shown in the diagram. One can If the world is nonstochastic and all X and Z regard the observations in Figure I as having been variables are constant, we would have the result "corrected" for Age and Poverty or as having depicted in Figure 2a. The downward sloping line come from a universe in which Age and Poverty shows Crime as a function of Sanctions, holding are invariant. The estimated (partial) linear X and all random variation constant. The Sanc- regression between Crime and Sanctions is also tions function is similarly interpreted. The interac- shown. tion of the two functions provides a unique equilib- 4The disturbance term must be a random variable 61 refer to "average" situations, and readily concede with zero expectation, constant variance and no inner that aberrant cases may exist for which 6 < 0; as, for correlation, no exact linear relation must exist between example, the case of civil rights workers who com- any two or more independent variables, etc. mitted a crime because legal sanctions would be im- 6See the Technical Appendix infra. posed. THOMAS ORSAGH [Vol. 64 CRIME CRIME SANCTIONS SANCTIONS (a) (A& FiGuRE 2. rium solution: a crime rate of ci and a sanctions tions in both the Crime and Sanctions functions level si. Under the conditions we have stipulated, as shown in Figure 3a; and (2) there may have we would observe only one data point, (cl, Si). been three upward shifts in the Sanctions func- Now suppose one and only one variable is per- tion-with Sanctions being unresponsive to Crime, mitted to assume different values, X, in X. Figure incidentally-and a continuous outward shift in 2b illustrates the configuration of functions and the Crime function, as shown in Figure 3b.