Turnover in the Labor Force

ROBERT E. HALL* MassachusettsInstitute of Technology

EVERY MONTH, AN IMPORTANT FRACTION of the populationmoves from one economicactivity to another:Some are laid off and mustseek work, or they quit to take newjobs; young people leave school and look for work; workersleave the labor force becauseof disabilityor duties at home. The continualprocess of turnoverseems to be the characteristicof the modern Americaneconomy that distinguishesit from those of other developed countries,where the experienceof individualworkers appears to be much more stableover time. Is high turnoverinevitable in a postindustrialecon- omy?How do the variousdemographic groups in the laborforce differ with respectto turnover?What is the relationbetween turnover and unemployment?What are the social benefitsand costs of turnoverand unemployment?These are some of the criticalquestions that I addressin this paper. Any moderntreatment of turnoverand unemploymentmust distinguish betweenthe role of eventsoutside the controlof the individualand the role of his responseto his economicenvironment. Fluctuations in the demand for labor are the most importantexternal source of disturbancesin an individual'scareer, so it is conventionalto distinguishbetween the demand side of the problemand the supplyside. Turnover among jobs wasthe traditional explanationof the frictionalunemployment that exists to some extent in everyeconomy, but until recently,it receivedlittle discussion.Even ten yearsago, economistsconsidered unemployment a simpleshortage of * I am gratefulto Zvi Body, RichardKasten, Meir Kohn, and Steven Shavellfor able assistance.This researchwas supportedby the National Science Foundation. 709 710 Brookings Papers on Economic Activity, 3:1972 jobs, withoutasking how the distributionof the laborforce among the jobs changesfrom month to month. The federalgovernment's accidental experimentation with a high-pres- sure economy startingin 1965 broughtabout two importantshifts in the thinkingof economistsabout unemployment. First, it forceda muchcloser considerationof the role of turnoverin the processthat generatesunem- ployment.Economists can no longer speak of the employedand the un- employedas if they were distinctgroups over time, althoughthis mistake still appearsin popular accounts of unemployment.Second, tight labor marketsprompted an examinationof the role of supply-of the voluntary activitiesof workers-in creatingturnover and its consequentunemploy- ment.Workers can decideto quit, and do so in largernumbers when labor marketsare tight. Further,once looking for work, whetherbecause they chose to or were laid off, workersmake consciousdecisions about what kindsof job to accept.The notion that some componentof unemployment is voluntary,in the sensethat throughdifferent choices workers could lower the unemploymentrate, has been advancedoccasionally. Obviously, there is heavy political content in the debate about the voluntarycharacter of unemployment.Liberals fighting for low unemploymentat the cost of high inflationare reluctantto acceptthe suggestionthat part of the unemployment they hope to reduceresults from the choice of the unemployed. The distinctionbetween the two recent developmentsin the theory of turnoverand unemploymentis critical.A studentof turnoverneed not take a positionon the importanceof voluntaryactivity in bringingit about,and measurementsof turnoverdo not themselvesshed muchlight on the question of the voluntarycharacter of unemployment.The findingthat blacks, women,or teenagersbecome unemployed more frequently than adultwhite malestells nothingabout the responsibilityof unemployedworkers in these groupsfor theirown plights.The firstpart of this paperis devotedto more refinedmeasurement of turnoverusing data that do not permitseparation of the influencesof externalevents (mainly layoffs) from those of the con- scious decisionsof individuals. I shall say somethingabout the relativeimportance of conditionson the supplyside and the demandside, however.Most of my evidenceis indirect, but it leavesthe impressionthat fluctuationsin the demandfor labor are a criticalaspect of the processof turnover. The focus of the paperis almostexclusively on turnoveramong members of the labor force, that is, on the processby which workersleave or lose Robert E. Hall 711 jobs and find newjobs. Inadequatedata make it difficultto deal with the equallyimportant problem of movementsin and out of the labor force.

The Theoryof Turnover

A generaltheory of turnoverunderlies the whole paper.On the demand side I considerthe economyas composedof a largenumber of employers, most of whom accountfor only a tiny part of the whole.' Employerssell relativelyspecialized products and so face randomfluctuations in demand. Most of the fluctuationsare unrelatedto changesin the overallrate of economic activityand thus tend to canceleach other statisticallywhen aggregate outputor employmentis calculated.Employers meet theirfluctuating needsfor laborthrough a personnelpolicy that balancesthe costs of hiring and firingagainst the costs of holding excess workersduring a period of slack or of paying overtimeand using temporarysources of labor during periodsof peak demand.An importantquestion is how muchtraining and knowledgewill be lost if a workerleaves one firmand takes a job with another.2Workers with a good deal of suchtraining-for example,those with positionsin a bureaucracywho communicatewith many other workerswill be held as overheadlabor duringa slumpwhen those whose skillscan be replacedwith little cost will be laid off. Further,the layoff policy of a firm dependson conditionsin the labor marketin which it hires.The ap- parentsensitivity of this dependenceis one of the surprisingfindings of this paper.In slackmarkets, firms have a good chanceof recallingworkers who are laid off, and, in any case, find it easy to recruitqualified replacements.3 Thus, everythingelse held constant,firms should lay off workersmore fre- quentlyin slack markets. Workersalso face eventsthat are random,at least fromthe point of view of the observer.They may learnabout better jobs or decideto changetheir

1. By "employer"I mean the productiveunit, not necessarilythe firm. Large firms producinga variety of productsin a numberof plants should be consideredas a group of separateunits for the purposesof the theory. 2. This is what Gary Becker calls "firm-specific"human capital. See his Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education (Columbia University Press for the National Bureau of Economic Research, 1964), pp. 18-29. 3. This seems to hold even apart from the fact that slack marketsmay have unemployed workersavailable at wages below the marketwage. 712 Brookings Papers on Economic Activity, 3:1972 types of work.Again, theirdecisions to quit will dependon the amountof the loss involvedand the cost of findingnew work. Everythingelse held constant,slack marketsshould discouragequits. Unemploymentis one of the key variablesin a theory of turnoverbe- cause it servesas the main indicatorof distressin labor markets.Basic to understandingthe relationbetween turnover and unemploymentis the fact that only a fractionof those looking for work ever become unemployed. To be recordedas unemployed,a personmust be out of work and looking for work.A workerwho quitshis presentjob to take a new one neverenters unemployment.The samerate of turnoveramong jobs, as measuredby the sum of quits and layoffs,will correspondto a higherunemployment rate if there is a higherproportion of layoffs.As George Perryhas pointed out, the probabilitythat an individuallooking for work will become unemployed is a more sensitiveindicator of conditionsin the labormarket than is the probabilitythat a person,once unemployed,will findwork in a given time period.4

Preview

This paperdiscusses the resultsof two empiricalstudies of turnover.The firstcovers the entirepopulation of workingage and uses data on the number of spells and the numberof weeks of unemploymentreported by in- dividualsto estimatethe probabilitythat an individualwith particular characteristicswill becomeunemployed in a given weekif not unemployed, or that he will leave unemploymentif alreadyunemployed. From these probabilitiesit is possibleto derivethe fractionof the year that each in- dividualshould expect to be unemployed.The resultsof this studycan be used to break down unemploymentrates of demographicand economic groupsinto componentsof frequency,measured directly as the probability of becomingunemployed, and duration,measured as the inverse of the probabilityof leavingunemployment. The secondstudy covers only men aged 45 and above and is concerned withjob changes.It distinguishesvoluntary changes, generally quits, from involuntarychanges, mainly layoffs. The data are drawnfrom employment histories,so it is possibleto examinethe importantrelation between length of tenureand the probabilityof leavingthe job. 4. "UnemploymentFlows in the U.S. Labor Market," BrookingsPapers on Eco- nomicActivity (2:1972), pp. 245-78. Robert E. Hall 713 The thirdpart of the paperbrings the resultsof the firststudy to bearon the issue of the geographicaldistribution of turnover.Data on turnover fromthe officialdata for manufacturingindustries are also discussed. Four mainthemes appear in the discussionof these studies.First, layoffs are a majorsource of turnover,especially of job changesthat requirea spell of unemployment.Further, layoffs are extremelysensitive to conditionsin the labormarket. This showsup most clearlyin the comparisonof cities- Chicago,a city with a tight market,consistently has layoffrates that are a small fractionof the national average.In the concludingsection, I argue that the sensitivityof layoff rates to the degreeof tightnessis one of the obstaclesto a directattack on unemploymentby expansionof aggregate demand:In an economywith low unemploymentand low layoffrates, em- ployerscannot affordto pay real wagesthat are as high as they could pay duringa period of sustainedhigher unemployment.5 Second,turnover is much higheramong workerswho have taken their currentjobs recently.This is shown indirectlyin the patternof declining frequencyof unemploymentwith age revealedin the study coveringthe entirepopulation. It appearsdirectly in the resultsof the study of mature men: The probabilityof both layoffsand quits dropsrapidly over the first few years on the job. The process of gatheringinformation is symmetric betweenemployers, who are likely to dischargea workerin the first few months of employmentif he provesunsatisfactory, and workers,who are likely to leave a job in the firstfew monthsif it provesunsatisfactory. The importanceof the employerin this processshould not be overlooked. Third,most of the verylarge difference between the unemploymentrates of blacksand whitesis associatedwith differencesin the frequencyof un- employmentrather than in its duration.This is apparentfrom the published dataon the durationof unemploymentfor blacksand whites. The contribu- tion of my studyis to show that the conclusionis just as strongafter exten- sive adjustmentfor the personalcharacteristics of the two groups.Further, my studyof maturemen makesit possibleto comparelayoff and quit rates for blacksand whites,a comparisonthat is not possiblewith the published data. The resultsare striking:Blacks have the same likelihoodof quitting but are more likely to be laid off. Finally, the first study sheds some light on the comparisonbetween

5. Here I am comparingone steady state to another.The dynamic operation of the labor marketin responseto fluctuationsin aggregatedemand is beyond the scope of the paper. 714 Brookings Papers on Economic Activity, 3:1972 women and men. The duration of unemploymentis somewhatshorter amongwomen than amongmen, so the differencein their unemployment ratesis less than the differencein theirturnover rates. I have no resultsfor women comparablewith those for maturemen, in which layoffs can be distinguishedfrom quits, but I again caution againstthe conclusionthat high turnoveris a symptomof greaterwillingness to becomeunemployed, or that womenhave only a marginalattachment to the labor force.

APPROACHES TO THE STUDY OF TURNOVER Turnoveris a probabilisticphenomenon. Random events outside the control of an individualaffect his behavior,and his behavioritself may have a randomelement. Any study of turnover,therefore, requires a theo- reticaland empiricalframework in whichthe role of probabilityis explicit. Past work on unemploymentand turnoverhas generallyproceeded by isolatingone dimensionof turnover,defining a variablethat measuredit, and estimatinga regressionmodel relatingit to a variety of right-hand variables.For example,my first paperfor the Brookingspanel presented the resultsof a regressionin which weeks of unemploymentwas the left- hand variable.6George Perry has recentlyused the weeklyprobability of remainingunemployed as the left-handvariable.7 Although I have no fun- damentalobjection to this approach,I believethere may be advantagesto dealingmore directlywith the underlyingprobabilities in a unifiedmodel of turnover,from which results like the averagenumber of weeksof unemploymentcan be derived. The basis of my approachis to considera smallset of alternativeactivi- ties in which an individualmight engage.I then estimatethe probabilities of movingfrom one activityto anotheras functionsof the characteristics of the individualand of his environment,and of his history.From these probabilitiesof movement(and from those of remainingin the same activity) it is possibleto calculatethe probabilitiesof beingin each activityat a given time, no longer conditionalon past activities.Thus the final result of my study of unemployment,for example,is the probabilitythat an in- dividualwill be unemployedat a given time.

6. "Why Is the Unemployment Rate So High at Full Employment?"Brookings Papers on EconzomicActivity (3:1970), pp. 369-402. 7. "UnemploymentFlows." Robert E. Hall 715

Probabilitiesof Enteringand Leaving Unemployment

This sectionpresents the resultsof an empiricalapplication of the very simplestmodel of the sort proposedabove. Only two activitiesare con- sidered:not unemployedand unemployed.8Because of my particularin- terestin the geographicalpattern of unemployment,the form of the model is stronglycircumscribed by the natureof the data available.Much more elaborateand realisticmodels can be estimatedwhen the data consist of actualemployment histories, but at presentno longitudinaldata with satis- factory geographicalcoverage are available.A number of large cross- sections,including the 1967 Surveyof EconomicOpportunity used in this study, report two statisticsthat by a happy coincidenceare suitablefor estimatinga simplebut usefulmodel of turnover-the numberof weeksof unemploymentand the numberof spellsof unemploymentover the course of a year. The model posits a probability,a, that a workerwho is not unemployedin one weekwill be unemployedthe followingweek, and a second probability,3, that a workerwho is unemployedone week will not be unemployedthe next week.Then a measuresthe frequencyof unemployment and A is inverselyrelated to the durationof unemployment.Appendix A discussesthe methodI have used to estimatea and A from the data in the Surveyof EconomicOpportunity (conducted by the Bureauof the Census in the springof 1967) on the numberof weeks and the numberof spells of unemploymentin 1966. The method is based on the fact that, except for spellsat the beginningand end of the year,the numberof spellsis both the numberof times an individualbecame unemployed and the numberof times he left unemployment.The numberof times he could have become unemployedis the numberof weekshe was not unemployed,and the number of times he could have left unemploymentis the numberof weeks of unemployment.Thus, data are availableto constructfrequencies for each individualthat correspondto the underlyingprobabilities, a and 3. To these frequenciesI fitted a statisticalmodel of the logit form in which ax and A are consideredfunctions of the characteristicsof the individual.The 8. Not unemployedincludes both employedand out of the labor force. The data do not permit the distinction between becoming unemployedafter working and becoming unemployedafter an absence from the labor force, though such a distinctionwould be valuable. Since the second source of unemploymentis more important than the first among some groups, excludingthose not in the labor force from my estimatesis not a satisfactorysolution. 716 Brookings Papers on Economic Activity, 3:1972 logit model is not a linearregression, although it can be thought of as a nonlinearregression. Its preciseform is given in AppendixA. Table 1 presentsthe probabilitiescalculated from the statisticalresults of AppendixA. These probabilitiesshould be interpretedin the follow-

Table 1. Weekly Probabilities of Entering and Leaving Unemployment, and Fraction of the Year Unemployed, for Men with Selected Characteristics, 1966 Percent Weeklyprobability Fractionof Of becoming Of leaving the year Characteristic unemployed unemployment unemployed Color Black 0.38 10.2 3.6 Whites 0.22 13.6 1.6 Wage rate per hour (dollars) 1.50 0.28 11.0 2.5 2.00 0.24 12.5 1.9 3.00 0.22 13.6 1.6 4.00 0.16 12.3 1.3 Annual family income per adult (dollars) 2,000 0.21 13.8 1.5 4,000a 0.22 13.6 1.6 7,000 0.15 9.8 1.5 10,000 0.27 10.1 2.6 Age (years) 18 0.22 22.2 1.0 22 0.32 16.5 1.9 30 0.22 13.6 1.6 45 0.16 15.3 1.0 65 0.16 12.6 1.3 Type of worker Not reported 0.12 5.5 2.1 Privatewage or salarya 0.22 13.6 1.6 Government 0.10 12.2 0.8 Self-employed Salaried 0.25 29.9 0.8 Not salaried 0.09 16.0 0.6 Marital status Marrieds 0.22 13.6 1.6 Not married 0.40 12.0 3.2 Source: Calculated from statistical results of Appendix A below. a. Values of the characteristicused in calculations for other categories. Robert E. Hall 717 ing way: Thereis a referencegroup to whichthe constantin the equation refers(white, preschool children only, livingin New York, expectedto earn $3.00 per hour if a man or $2.00 per hour if a woman, familyincome of $4,000per yearper adult,age 30, privatewage or salaryworker, and married).For eachcharacteristic, the probabilitiesare calculatedfor each of its values,holding the othercharacteristics at theirreference values (indicated by note a in Tables 1 and 2). Thus the variationsin the probabilitiesfor alternativevalues of one characteristicmeasure the pureeffects of varying that characteristic.The mathematicalform of the specificationis essentially multiplicative.Thus, for example,the probabilitythat an unmarried22- year-oldman will become unemployedis (0.32/0.22) X (0.40/0.22) times higherthan the probabilityfor the referencegroup of married30-year-olds. Also shownin the tablesis the derivedfraction of the yearunemployed. This is also the fractionof the populationthat is unemployedin a given week.If it remainsthe samefrom one weekto the next, it has the following relation to axand 3:

u = a(1 - u) + (1 - f)u;

of the fraction1 - u of the populationnot unemployedlast week, a have just become unemployed,and of the fraction u unemployedlast week, 1- remainunemployed. This equationcan be solved to get a u = ae + A whichis presentedin the thirdcolumn of Tables 1 and 2. For men, the resultsshow that most of the very substantialdifference betweenthe unemploymentrates of blacks and whites is associatedwith higher frequencyrather than longer durationof unemployment.9Blacks are 73 percentmore likely to become unemployedthan whites, and, if unemployed,are 25 percentless likely to leave unemploymenteach week. Since these resultstake account of the tendencyfor blacks to have other characteristicsthat are associatedwith high turnover-they have fewer

9. Much the same result is reportedby Ralph E. Smith and CharlesC. Holt, in "A Job Search-TurnoverAnalysis of the Black-WhiteUnemployment Ratio," in Gerald G. Somers (ed.), Proceedingsof the Twenty-thirdAnnual WinterMeeting, 1970, Industrial Relations Research Association Series (IRRA, 1971), pp. 76-86. Their analysis of the publisheddata on the durationof unemploymentdoes not consider dependenceof the frequencyand durationof unemploymenton detailed individualcharacteristics, as my method does. 718 Brookings Papers on Economic Activity, 3:1972 skills,are somewhatyounger, and are less likelyto be married-they show ratherstrikingly the magnitudeof the problemthey encounterin the labor market.Blacks have somewhat more trouble than whites in findingjobs,and a greatdeal of difficultyin keepingthem. Discrimination seems to takethe form of restrictingblacks to unstablejobs while whites are able to find permanentand high-payingjobs. I have discussedthis phenomenonat length in my two previouscontributions to BrookingsPapers, and regard theseresults as confirmingmy earlierview with more direct evidence. More- over, evidencefrom my studyof maturemen, discussedin the next section, sheds light on the ambiguityabout wherethe responsibilityfor turnover lies-with the worker or the employer-that my earlierwork left unre- solved.10The resultsfrom the currentstudy tend to supportthe view that it is the instabilityof the jobs opento blacksmuch more than the instability of the blacksthat is the heart of the problem. Workerswith few skills(those expected to earn$1.50 per hour) and those with averageskills ($3.00 per hour) have smallerfrequency and duration differentialsthan is the case with race: Unskilledmen are 27 percentmore likelyto becomeunemployed and 19 percentless likely each weekto leave unemployment. The resultsfor teenagersare inconsistentwith the officialunemployment rates. They suggest that teenagersare about as likely to become unemployed each week of the year as 30-year-olds,and 63 percentmore likely to leave unemploymentin each week of unemployment.Together these imply that 18-year-oldswho have all the referencecharacteristics except tor age spend only 1 percentof the year, about three days, unemployed. Even aftertaking account of the fact that teenagersdo not generallyhave the referencevalues of othercharacteristics-they earn less than $3.00 per hour and areless likelyto be married-the fractionof the yearunemployed is less than that suggestedby the officialdata.11 The resultsfor other age 10. Two years ago I wrote, "Some groups exhibit what seems to be pathological instability in holding jobs. Changingfrom one low-paying, unpleasantjob to another, often severaltimes a year, is the typical patternof some workers."("Why Is the Unem- ployment Rate So High?" p. 389.) Many other writershave made similarstatements. 11. The fraction of the year unemployedis the product of the unemploymentrate and the fractionof the year in the labor force. The officialunemployment rate for white males aged 18 and 19 in 1966 was 8.9 percentand the averageparticipation rate over the year was 65.4 percent,suggesting that they spend 5.82 percent of the year unemployed. Both the SEO and the CurrentPopulation Survey of the U.S. Bureau of the Census obtain data from a single respondentin the household, rarely a teenagerand probably frequentlya person who is not very familiarwith the teenager'sactivities. Robert E. Hall 719 groupsdo not seemto disagreewith the officialdata as seriously.Twenty- two-year-oldmen are 45 percentmore likely than 30-year-oldsto become unemployedand 21 percentmore likely to leaveunemployment each week. Forty-five-year-oldsare 27 percentless likelythan 30-year-oldsto become unemployedand 12 percentmore likely to leave unemployment.It seems clearthat adultsover the age of 30 are ableto find significantlymore stable employmentthan areyoung adults.The magnitudeof the differencesseems consistent,however, with the view that they arisefrom experimentationby employerswith young workers,in which they find likely candidatesfor permanentemployment, and similarexperimentation among young work- erstrying out alternativejobs. The latterprocess, often called job shopping, receives more attention in most discussionsof turnoveramong young adults,but I suspectthe role of employersis just as important. Takentogether, the resultsfor men seemto confirmthe view that differences in turnover,as measuredby the frequencyof unemployment,are if anythingmore important than differencesin durationas a symptomof the adverseexperience of some groupsin the laborforce. At this point I should emphasizethat high turnoveris not necessarilyevidence that unemploymentis somehowvoluntary and thereforenot burdensometo those experi- encingit. In fact, my resultssuggest that the frequencyof unemployment maybe somewhatlower for individualswith higher incomes, while a theory of voluntaryturnover presumably would suggestthat frequencywould rise with income.On the otherhand, the resultsdo offera little supportfor the view that individualswho are betteroff take longerto find work once they are unemployed. Interpretationof the resultsfor women is somewhatmore difficultbe- causethey have lower and more variablerates of participationin the labor force. To overcomethis problem,I have chosen privatewage and salary workersas the referencetype of workerbecause they have high participation rates.The type refersto the job held longest during1966 and among womenmost of the responsesof "not reported"come from those who did not workat all duringthe year.Even so, the variationin participationrates for alternativevalues of a given characteristicshould be kept in mind in interpretingthe probabilitiesof becomingunemployed and the fractionof the year unemployedshown in Table 2 (the latter is the product of the participationrate and the unemploymentrate). Comparisonof Tables1 and2 suggeststhat women who arenot definitely out of the labor force have substantiallyhigher frequencies of unemploy- 720 Brookings Papers on Economic Activity, 3:1972 Table 2. Weekly Probabilities of Entering and Leaving Unemployment, and Fraction of the Year Unemployed, for Women with Selected Characteristics, 1966 Percent Weeklyprobability Fractionof Of becoming Of leaving the year Characteristic unemployed unemployment unemployed Color Black 0.68 10.6 6.0 Whites 0.32 15.1 2.1

Wage rate per hour (dollars) 1.50 0.27 17.5 1.5 2.00a 0.32 15.1 2.1 3.00 0.20 34.5 0.6 4.00 0.12 9.5 1.2

Annual family income per adult (dollars) 2,000 0.40 15.1 2.6 4,000 0.32 15.1 2.1 7,000 0.29 10.3 2.7 10,000 0.04 6.8 0.6

Age (years) 18 0.41 21.5 1.9 22 0.53 15.6 3.3 30a 0.32 15.1 2.1 45 0.24 14.3 1.7 65 0.21 12.8 1.6

Type of worker Not reported 0.09 20.6 0.4 Privatewage or salarya 0.32 15.1 2.1 Government 0.15 14.1 1.1 Self-employed Salaried 1.15 13.8 7.7 Not salaried 0.20 18.1 1.1

Marital status Marrieds 0.32 15.1 2.1 Not married 0.40 14.3 2.7

Source: Calculated from statistical results of Appendix A below. a. Values of the characteristicused in calculations for other categories. Robert E. Hall 721 mentthan do men in practicallyevery category.'2 Black women have more than twice the frequencyof white women in the referencegroup, close to twice that of comparableblack men, and more than three times that of whitemen. Whitewomen are more than 30 percentmore likely than com- parablewhite men earningthe same wage to become unemployed(0.32 percentagainst 0.24 percent).The data do not permitthe divisionof unem- ploymentamong women between that associatedwith movementsinto the labor force afterprolonged absence and that arisingfrom interruptionsof more or less continuousperiods in the labor force.'3 The durationof unemploymentseems to be slightlyless amongwomen than amongcomparable men: Unemployedblack women have a probability of 10.6 percentof leavingunemployment against 9.4 percentfor black men, while white women have a probabilityof 15.1 percentagainst 12.5 percentfor whitemen, again adjusting the figuresfor mento the $2.00refer- ence wage.It is dangerousto inferfrom these figures that womenfind jobs as quicklyas men, since womenare probablymore likely than men to ter- minateunemployment by leavingthe labor force.'4 Sincethe durationof unemploymentis less for womenthan for men, the differencein their unemploymentrates understatesthe differencein their frequenciesof unemployment.The instabilityof employmentof women, especiallyblack women, is a problemof the firstmagnitude. I suspectthat a largepart of the problemarises, as it does with black men, from the instabilityof the jobs availableto womenand not from the instabilityof the womenthemselves.'5 The influenceof other characteristicson frequencyand durationseems

12. The comparison requires some care. The referencewage for men is $3.00 per hour while that for women is $2.00 per hour. Table 1 would be only slightly different if a referencewage of $2.00 were used, but Table 2 would be quite differentif the reference wage were $3.00. 13. Only the longitudinaldata just becomingavailable can answerthis question (see note 16). The CurrentPopulation Survey tabulates unemployment by cause (quit, layoff, new entrant, and reentrant)but provides no information on the previous activity of reentrants. 14. George Perrypresents evidence on this point in "UnemploymentFlows." 15. Part of this is associatedwith the crowdingof women into occupationswith high turnover.Occupation is not includedin the equationbecause it is not a personalcharac- teristic nor a good indicator of the markets that an individualcan participatein. Its inclusionwould give rise to a set of occupationaleffects that would partiallyobscure the differencesbetween men and women without being explicablethemselves. 722 BrookingsPapers on EconomicActivity, 3:1972 to be about the same for women as for men. Frequencydeclines with in- creasingwage rates while duration increases(except for the figure for $3.00per hour,which seems to be a statisticalfluke). Higher income exerts more downwardpressure on the probabilityof becomingunemployed for women than for men, probablymainly because of the negativerelation betweenincome and labor force participationfor women. The patternof decreasingfrequency and increasingduration of unemploymentwith age is similarto that found for men. Unmarriedwomen are somewhatmore likelyto becomeunemployed than married women, but the effectof marital statusis so much less than in the case of men that unmarriedwomen and unmarriedmen have almost the sameprobability of becomingunemployed.

JOB CHANGES AMONG MATURE MEN As a group,mature men exhibitsubstantial employment stability. This is apparentin the results on the frequencyof unemploymentpresented earlier:White males aged 45 have a weeklyprobability of enteringunem- ploymentof only 0.16 percent,or about 8 percentper year. Here I will report brieflyon a studyof annualjob changesamong mature men. The data for this studywere taken from the 1966-67National Longitudinal Surveys, directedby HerbertParnes.16 The data give the statusof about 5,000 men in 1966 and againin 1967,together with partialemployment histories for each. My study is based on changesin jobs betweenadjacent years from 1962to 1967.Using methodssimilar to those discussedin AppendixA, I have estimatedthe probabilitiesthat an employedworker will leave a job involuntarily,because of a layoff, or voluntarily,by quitting.These probabilitiesare functionsof personalcharacteristics-race, years of education, and age-and dummy variablesfor the years. In addition, time on the presentiob is a determinant.17 16. National LongitudinalSurveys-The Survey of Work Experienceof Men 45-59 Years of Age, sponsoredby the ManpowerAdministration of the U.S. Departmentof Labor, and conducted by the U.S. Bureau of the Census. Tabulations from the data appear in U.S. Departmentof Labor, ManpowerAdministration, The Pre-Retirement Years, ManpowerResearch Monograph 15, Vol. 1 (1970) and Vol. 2 (1970). The raw data were obtained from the Bureau of the Census. 17. In this respectthe model is a substantialimprovement over the one appliedto the data on unemploymentin the SEO. The improvementis made possible by the fact that the Parnes data give actualjob historiesand not just summarydata. The readershould also note that my study of maturemen focuses on the probabilityof changingjobs rather than on the probabilityof becoming unemployed. RobertE. Hall 723 Table 3. Annual Probabilities of Males 45-59 Years of Age Taking New Jobs, by Reason, 1962-67 Experience Percent Annualprobability for employedworker

Of takitngnew job next year, by reason Of remaining Characteristic Layoff Quit at samejob Color Whitea 1.2 2.6 96.2 Black 1.4 2.6 96.0 Years on job 0 5.0 15.2 79.9 1 1.9 6.1 92.0 3 1.0 3.6 95.4 6a 1.2 2.6 96.2 15 0.6 1.1 98.3 40 0.2 0.7 99.1 Source: Author's estimates derived from the National Longitudinal Surveys-The Survey of Work Experience of Men 45-59 Years of Age, sponsored by the Manpower Administration of the U.S. Depart- ment of Labor, and conducted by the U.S. Bureau of the Census. Data used here are based on changes in jobs in adjacent years between 1962 and 1967. a. Values of the characteristic used in calculations for other categories.

The resultsare summarizedin Table3. Certainbiases inherent in the data deservemention. First, turnover is understatedbecause the methodof col- lectingthe partialemployment histories causes workers with high turnover to contributefewer years of data to the study.I attemptedto minimizethis effect by using only a few recentyears, discardinga great many observations for earlieryears from morestable workers. Turnover is furtherunder- statedby the use of an annualinterval between observations. A workerwho changesjobs more than once in a year is countedonly once in this study. Third, the probabilityof layoff is understatedbecause only those layoffs that resultedin a job change are counted;those terminatedby recall are ignored, even though they result in unemployment.18Subject to these qualifications,the resultsshow that a white male, 50 yearsold, with a col- lege educationand six years on the job had a probabilityof 1.2 percentof beingforced to changejobs becauseof a layoffin 1965.The probabilityof his quitting,at 2.6 percent,was more than twice as high. A comparable blackwas slightlymore likely to be laid off (1.4 percent)and no morelikely

18. Laid-off workersare counted as unemployedin the official data even if they are confident of early recall. 724 Brookings Papers on Economic Activity, 3:1972 than a white to quit. Among mature men, turnover is only slightly higlher for blacks than for whites, and the difference is in layoffs, not quits. There is no evidence here of greater voluntary instability among blacks. The probabilities of both layoffs and quits are much higher early in a worker'stenure on the job. In the first few months a worker in the reference group faces a probability of 5 percent per year (or about 0.4 percent per month) of losing his job. Layoff here includes any involuntary separation including discharge. It is clear that employers gather information rapidly in the early months of employing a worker, and are much more likely to send him away at that time than after he has accumulated knowledge and training. Institutions operating both through collective bargainingand outside it protect the individual's and the firm's investment in firm-specific human capital by requiring that the least experienced workers be laid off first.19The probability of quitting declines even more rapidly with tenure. Individuals are most likely to leave a job when they have found out exactly what it involves but have not made a substantial personal investmentwhose future returns would be sacrificed by quitting.

Turnoverin Twelve Large Cities

Up to now I have focused on the determinants of individual turnover, taking the economic environment as given. In this section I will reexamine my earlier results in terms of the theory of economic equilibrium. The aim is to say something about the way the economic environment is shaped by the collective actions of large numbers of workers and employers. I have chosen to look at the geographical dimension of turnover, simply because that dimension is identified explicitly in the data. The reader will recognize similaritiesbetween my discussion of differencesamong cities and George Perry's discussion of differencesover time.20 A fair amount of agreement seems to exist about the ingredients of a

19. Inverseseniority provisions that allow the most seniorworkers to be laid off first are a specialform of vacation(with a highlyfavorable tax treatment)and do not involve permanentseparation of the worker from the employer.Martin Feldstein has recently caled attentionto the importanceof unemploymentcompensation and provisionsof collective bargainingagreements in this connection.See his "Loweringthe PermanentRate of Unemployment,"A PreliminaryReport Prepared for the Joint EconomicCommriittee of the U.S. Congress(no date; processed). 20. "UnemploymentFlows." Robert E. Hall 725 theory of geographicaldifferences among labor markets.Following is a list of generalconsiderations that most economistswould find important: 1. Workerscan migratefrom one city to another.Their propensity to do so dependson relativewages, relative stability of jobs, and the relative costs of findingjobs. 2. Employerscan migrateas well. Their location decisionsdepend on relativewages, relative stability of workers,and relativecosts of recruiting workers. 3. Wagesrise fasterin citieswith tight labormarkets than in those with loose ones. Unemployedworkers demand high wages when they become unemployedand lower their aspirationsas theirperiods of unemployment continue. 4. Randomshifts in the demandfor goods producedin each city occur continually.Thus at any point in time, the patternof differencesamong cities will not necessarilyrepresent an equilibriumof the slow-working processof migrationand wage adjustment. 5. Cities differ in their attractivenessto workers and employers.In equilibrium,wages 'iouldembody "equalizing differences" to accountfor these differences. The theoriespropo, Id by variouseconomists differ mainly in the im- portance assigned to these considerations,which in turn varies partly accordingto the contextsin which geographicaldifferences in labor markets have been examined.John Harrisand Michael Todaro, in studying urban and rurallabor marketsin Africa, took wage differentialsand the location of employersas given and examinedthe equilibriumrates of unemploymentthat arise when migrationof workersequates the rural and urbanwages, where the latterare adjustedfor the expectedcost of finding work.2' They concludedthat if urban wages are held higher than rural wages by governmentalor other forces,workers will migrateto the cities until the urbanunemployment rate times the urbanwage is equal to the wage differential.In a recent unpublishedpaper, Joseph Stiglitz has ex- tended their model to considerthe relationbetween the wages and productivityof workersand their rate of turnover.22He argues that wage 21. John R. Harrisand Michael P. Todaro, "Migration,Unemployment and Devel- opment: A Two-Sector Analysis," AmericanEconomic Review, Vol. 60 (March 1970), pp. 126-42. 22. "AlternativeTheories of Wage Determinationand Unemploymentin L.D.C.'s: I. The Labor TurnoverModel," Discussion PaperNo. 335 (Cowles Foundationfor Re- search in Economics at Yale University, 1972; processed). 726 Brookings Papers on Economic Activity, 3:1972 differentialscan be explainedby the low turnoverof urbanworkers, which in turn is explainedby high urbanwages and unemploymentrates. Within the context of the theory of inflation,Lipsey, Archibald,and Tobin have emphasizedrandom shifts in demand across geographical areas.23Although workers and employersrespond to these shifts through migrationand relocation,they do so with a lag so that the marketsare in "perpetualdisequilibrium," in Tobin'swords.24 In my earlierpaper, "Why Is the UnemploymentRate So High at Full Employment?"I studiedthe unemploymentrates in twelvelarge cities of the United Statesin 1966.I concludedthat relativelylittle of the substantial differencesin their unemploymentrates could be explainedby recentran- dom changesin demand,because the patternacross cities is so stable over time. The accumulationof data for two more years has not changedthis conclusion. I also noted a positive correlationbetween wage rates and unemploymentrates in the cities, and offeredthe conjecturethat a process somewhatlike that later proposedby Stiglitz was at work: High wages could be paid in citieswith high unemploymentrates precisely because the high ratesdiscourage quits, and a work force with a low quit rate is more productive.According to this conjecture,an equilibriumcould exist with very differentunemployment rates amongcities in which no incentiveex- isted for eitherworkers or employersto migrate.I think it is worthelabo- ratingon this conjectureby developingan explicittheory along the lines it suggests.I have done so in AppendixB and have summarizedthe results for a singlecity in Figure 1. Workersare in equilibriumwhen the wage in this city, w, adjustedby the unemploymentrate, u, is equalto the adjusted wage elsewhere:

(1- u)w = w, or w = 1-

Employersare in equilibriumwhen the wage they pay is matchedby the productivityof workersin this market,xh(u). The dependenceof productivity on the unemploymentrate is deducedfrom a more elaboratecon- 23. Richard G. Lipsey, "The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1862-1957: A Further Analy- sis," Economica,New Series, Vol. 27 (February1960), pp. 1-31; G. C. Archibald,"The Structureof Excess Demand for Labor," in Edmund S. Phelps and others, Microeco- nomic Foundationsof Employmentand InflationTheory (Norton, 1970), pp. 212-23; JamesTobin, "Inflationand Unemployment,"Presidential Address before the American Economic Association, AmericanEconomic Review, Vol. 62 (March 1972), pp. 1-18. 24. Ibid., p. 10. Robert E. Hall 727 Figure1. EquilibriumWage andUnemployment Rate for a SingleCity

Wage

Employerequilibriuma )v = 3M(u)

Wor-kerequilibriumaio

0 Unernploy;nentrate

Source: Summarized from results of Appendix B below. a. w = wage in this city; w3 = adjusted wage elsewhere; u = unemployment rate; xh(u) = productivity of workers in this city. siderationof the behaviorof workersand employersas they respondto unemploymentand vacancyrates.25 The equilibriumin Figure 1 occursat the intersectionof the two schedulesat a wage and unemploymentrate that puts workersand employerssimultaneously in equilibrium.

25. My use of the term "productivity"is unconventional.The high productivityof workersin cities with high unemploymentarises not becausethey work more effectively when at work but ratherbecause a largerfraction of those employed are at work pro- ducing output at any given time. Fewer are working in the personneland training de- partmentsand fewer are idle overheadworkers if the marketis slack. The readershould note the contrast with cyclical changes in demand, where tight marketsare associated with high productivity. 728 Brookings Papers on Economic Activity, 3:1972 So far I have summarizeda theory of the equilibriumin a single city, holdingconditions elsewhere fixed. The theoryapplies just as well to com- parisonsamong cities: In equilibrium,all cities must have the same effec- tive wage rate and the same effectivecost of labor. The discussionup to now has shownthat in eachmarket there is probablyonly a singlecombina- tion of unemploymentrate and wage that is compatiblewith equilibrium (assumingonly a single intersectionin Figure 1). Thus the theoryimplies that whenall citiesare in equilibrium,they will all havethe samewages and unemploymentrates. The startingpoint for this analysiswas the discoverythat thereare substantial differencesin unemploymentrates among cities, and that these differenceswere stable over time and thereforeprobably characteristic of equilibrium.A theorythat impliesequality among cities seemswide of the mark.However, a simpleand realisticextension of the theoryseems capa- ble of explainingwhat is observed.Cities are not, in fact, identical,and the theoryturns out to predictthat small differencesin the underlyingdeter- minants of unemploymentcan be magnifiedinto large differencesin un- employmentitself. The reasonis apparentin Figure1. Sinceboth schedules slope in the same direction,a small upwardor downwardshift in one of them will causea largehorizontal shift in the locationof theirintersection. In the theorypresented in AppendixB I treat differencesin the attractive- ness of citiesto workersand employersas randomvariables and applythe econometrictheory of simultaneousequations to study the expectedrela- tion betweenwages and unemploymentthat the theoryimplies. The theory suggeststhat unless there is a sharplynegative correlationbetween the attractivenessof citiesand the advantagesof producingin themapart from conditionsin theirlabor markets, the observedset of wage-unemployment combinationsshould be scatteredaround a line that lies betweenthe two schedulesin Figure 1. It is not unreasonableto interpretthe theoryas supportingthe view that in equilibriumsome cities will have high unemploymentand high wages and otherslow unemploymentand low wages.This interpretationimplies the followingabout other conditionsin the markets:First, vacancieswill probablybe lower in high-wagecities, althoughthe theorywill toleratea weak positiverelation between unemployment and vacancies.Second, the rate of job findingwill be lowerin high-wagecities, as unemployedworkers must competewith more of theircolleagues for fewervacancies. Third, the Robert E. Hall 729 rate of job filling will be higher, for the'same reasor-nfewercompeting. employersand more candidatesfor jobs. Fourth, the quit rate will be lower becauseof the greatercost of findingnew jobs. Finally, the layoff' ratewill be higher,since employerscan replaceworkers easily aftera tem- porarydecline in demandand thereforewill hold relativelylittle overhead labor. Only the last of these representsany departurefrom traditional views of the differencesbetween slack and tight labor markets.My main point herehas beento proposean explanationfor the persistenceover time in the geographicaldistribution of slackness. The data availableon turnoverby cities differfrom the conceptsthat would be ideal accordingto the theory.I have estimatedtwo basic probabilities:ax, the probabilitythat a workerwill becomeunemployed, and j, the probabilitythat an unemployedworker will find work. These are re- lated to, but are by no means the same as, the sum of the quit rate and the layoffrate, on the one hand,and the rate of job finding,b, on the other. In the theory,b is the fractionof those peoplelooking for workin a period who find it. It is substantiallylarger than the fractionof the unemployed who findwork because many of those lookingnever become unemployed.26 In the SEO, a worker who quits or is laid off and immediatelytakes anotherjob does not reporta spell of unemployment.As Perrysuggests, a reasonablemodel relatingb and ,Bis the following:

b = s + ( -s), where s is the probabilityof not becomingunemployed when changing jobs. The fractionss, ,B,and b all vary together:In tighterlabor markets thereis a higherprobability of findingwork immediately, and, failingthat, a higherprobability of findingwork in each week of looking.The response of the unmeasureds, however,means that ,Bis a fairlyinsensitive index of the rate of job finding.The patternthat j3traces across cities partially con- ceals a more diverseb pattern. If the flow of job seekersarises from quits, q, and layoffs,y, only, the samemodel suggests the followingrelation between separations, q + y, and the probabilityof becomingunemployed, oa:

= (1- s)(q+y).

26. George Perrydiscusses the same issue in "UnemploymentFlows," and comes to much the same conclusion. 730 Brookings Papers on Economic Activity, 3:1972

High-wage,high-unemployment cities have low quitrates, high layoff rates, and low probabilitiesof findingjobs if separated.As a result, they have high probabilitiesof unemployment,even though their separationrates may be no differentfrom those of citieswith tight markets.This is one key point in reconcilingthe findingthat high-wagecities have high turnoverin the sense of frequentunemployment with the theory that high wages are justifiedin the eyes of employersby the low turnoverof the labor force. In an economywhere the traditionalpattern of specializationwithin the familystill predominates,the theoryoutlined above applies mainly to men. For this reasonI will discussthe empiricalresults for men only, although as symmetrybetween men and women becomesthe rule, the theory will becomeapplicable to womenas well. Substantialchanges in this direction have taken place even since the collectionof the data used in this study.

A Tale of TwelveCities

Figure2 shows the relationbetween the unemploymentrates estimated from the probabilitiesof enteringand leavingunemployment and the real wage rate in the twelvecities identifiedin the SEO. The real wage ratesin the cities wereestimated in the followingway: A regressionwas estimated in which the left-handvariable was the log of the hourly wage and the right-handvariables measured the age, education,race, health, and union membershipof the individual.In addition,dummy variables for the twelve citieswere included.Nominal wages by city wereestimated as the antilogs of the coefficientsof the city dummies,multiplied by the base wage for New York. The resultingwage ratesare fully adjustedfor observeddiffer- ences in the compositionsof the labor forcesof the cities. They werethen adjustedfor differencesin their price levels, but the data used for this adjustmentare inadequate.The officialindex of prices by city, which is used to deflatethe wages shown in Figure2, attemptsto measurethe cost of attaininga specifiedstandard of livingin eachcity, and so is conceptually superiorto a simple fixed-weightindex; but it therebyembodies many arbitraryjudgments about how the weights should vary among cities.27

27. Taken from U.S. Bureau of Labor Statistics, ThreeStandards of Livingfor an UrbanFamily of FourPersons, Spring 1967, Bulletin 1570-5 (1969). RobertE. Hall 731 Figure 2. Real Wage Rates and UnemploymentRates in Twelve Large Cities, 1966 Real vage per hour(dollars) 3.80 1 Baltimore 7 New York 2 Chicago 8 Philadelphia 40 3 Cleveland 9 Pittsburgh 4 Detroit 10 St. Louis 3.60 5 Houstoni 1 1 Satn Francisco 6 Los Antgeles 12 Wa"shingtot, D.C.

110 3.40 106 Regressiontlinte

-.0O_ - __8 I8 D - Workerequilibrium

50 7. 3.00 3 Xa

2.80

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Fractionzof tile year unemployed (percent)

Source: Derived by author from regressions described in accompanying text. The basic city data are from the Survey of Economic Opportunity conducted by the Bureau of the Census, Spring 1967.

A good deal of dispersionappears in Figure2. In additionto that arising from the unmeasureddifferences among cities discussedearlier, dispersion is introducedby the techniquesof measurementused in this study. There are statisticalerrors in the estimatesof the unemploymentrate whose mag- nitudesare indicated by the standarderrors of the city effectsin TableA-1, and similarerrors in the estimatesof the nominalwages. The processof deflationintroduces further errors of unknownmagnitude. Nonetheless, the data do suggest a positive relation betweenthe unemploymentand wage rates.A regressionis a naturalway to show this, and also makes it possibleto incorporateinformation about the reliabilityof the wage data throughthe use of weightedleast squares.The regressionof the real wage 732 BrookingsPapers on EconomicActivity, 3:1972 rate on the derivedunemployment rate, weightedby the inversesof the standarderrors of the wage estimates,28is: w = $3.20 + 0.068u. (0.14) (0.071) (The numbersin parentheseshere and in the followingequations are standarderrors.) That is, the real wagerate in citieswith, say, 2 percentunem- ploymentis about7 centshigher per hour than that in citieswith 1 percent unemployment.The regressionis shown as the top line in Figure2. Also shown thereis the conditionfor workerequilibrium,

1-u with wiset equalto the constantin the regression,$3.20. It is importantto note that the regressionline is steeperthan is the scheduleof workerequilibrium.I have arguedearlier that the regressionline lies betweenthe two schedulesin Figure 1, so this findingsuggests that the relationbetween wagesand unemploymentinduced by the reactionof productivityto conditions in the market is the more steeply sloped of the two equilibrium conditions. The statisticalreliability of this conclusionarouses understandable concern. The size of the standarderror of the slope coefficientsuggests that an estimateof 0.068 or greaterwould be obtainedwith a probabilityof about 15 percent even if the true slope were zero. Some other results may reducethis concern.First, the officialunemployment rate may be a more satisfactoryright-hand variable in this regressionthan is the derived rate, simplybecause the officialrate is estimatedfrom a muchlarger body of data. The weightedregression of my estimatedreal wage rate on the officialunemployment rate (reportedbelow in Table 4) is w = $2.97 + 0.107u; (0.24) (0.072) the slope is significantlygreater than zero at better than the 10 percent confidencelevel. 28. The logic of the weightingis the following:Sampling errors in the wage estimates are largerfor smallercities, so these cities should receivesmaller weights. The statistical theory of weighted least squares suggests that the weights should be inverselyproportional to the standarderrors of the disturbances.The inversesof the standarderrors of the coefficientsof the city dummiesin the wage equationprovide the appropriateweights if sampling errors account for most of the disturbancesin the wage-unemployment regression. RobertE. Hall 733 Second, the errorsin the price index may introducemore dispersion than is justified by the theoreticalimprovement of deflation.A simple model of pricedifferences among cities would have untradedgoods whose priceswere essentially proportional to local wages,and traded goods whose priceswere the same nationwide.In this case the pricesand wageswould be roughly proportional,but wages would vary more than prices. The nominal wage would substitutewell for the real wage except for over- stating its sensitivityto the unemploymentrate. Following this logic, I presentthe weightedregression of the nominalwage on the derivedunem- ploymentrate: w = $3.13 + 0.lllu. (0.18) (0.092) As predicted,the slope is greaterthan in the firstregression. The data and the regressionline appearin Figure3. Finally,the most robustrelation of all is betweenthe nominalwage and the officialunemployment rate:

w = $2.73 + 0.181u. (0.29) (0.088) Taken together,these resultsgive reasonablesupport to the basic pre- diction of the theory that wages and unemploymentrates are positively relatedin a cross-sectionof cities.29Further, at a somewhatlower level of statisticalconfidence, they supportthe view that the productivityof workers is more sensitiveto the unemploymentrate than is the scheduleof workerequilibrium. Table4 summarizesother information available about conditionsin the twelvecities. In additionto the probabilitiesof enteringand leavingunem- ploymentestimated from the SEO and the derivedestimate of the fraction of the year the averageworker spends unemployed, the table reportsthe layoff and quit rates for manufacturingindustries, gathered from employersby the Bureauof Labor Statistics,and the unemploymentrate as estimatedby the state employmentdepartments. Unlike my results,the layoff, quit, and officialunemployment rates are not adjustedfor differences in the compositionof the labor forces of the variouscities. Still, all

29. I have experimentedwith a specificationthat permitteda and ,3 to vary for recent migrants.Although the estimatesshowed the expectedrelationship, the city effects were changed hardly at all. 734 BrookingsPapers on EconomicActivity, 3:1972 Figure 3. Nominal Wages and UnemploymentRates in Twelve Large Cities, 1966

Nomintalwage per hour(dollars) 3.80 1 Baltimore 7 New York l 2 Chicago 8 Philadelphia 3 Cleveland 9 Pittsbuirgh 4, 4 Detroit 10 St. Louis 3.60 5 Houiston 1 1 SaonFrantcisco 6 Los Anigeles 12 WVashington,D.C.

6,- 3.40 120 R s l -

2e 70

- - -- - ~~~Workerequilibriwn 3,0 9,a

3.00 1

5,0 2.80

0< ' I I. 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Fractiont of the year unze,izployed (percent)

Source: Same as Figure 2. of the data seem to conform fairly well to the theory of geographical differencesin labormarkets outlined above. Some cities have tight markets, notablyChicago, Houston, and Washington,D.C. They have low probabilities of unemployment,low layoff rates, high probabilitiesof leaving unemployment,and low derivedand officialunemployment rates. Further, Chicagohas much the highest quit rate of any city. On the other hand, some cities have slack markets-Detroit, Los Angeles, Pittsburgh,St. Louis,and San Francisco.They have high probabilities of becomingunemployed, high layoff rates (except for Pittsburghand St. Louis), low quit rates (except for Los Angeles and possibly San Francisco),low rates of leavingunemployment, and high derivedand officialunemployment rates. Robert E. Hall 735 Table4. SelectedData on Conditionsin the LaborMarkets of TwelveLarge Cities, 1966 Percent

Probability Probability Derived of Manufacturing of fraction Official becoming leaving of year unem- unem- Layoff Quit unemploy- unem- ployment Real Nominal Citya ployed rate rate ment ployed rate wage wage (1) (2) (3) (4) (5) (6) (7) (8)

Washington, D.C. 0.15 0.05 0.48 18.7 0.8 2.4 $3.39 $3.39 Houston 0.20 0.09 0.53 18.1 1.1 2.4 3.13 2.87 Chicago 0.15 0.12 0.74 20.9 0.7 2.6 3.22 3.32 Cleveland 0.22 0.18 0.46 13.8 1.6 2.6 3.03 3.12 Baltimore 0.23 0.30 0.42 15.6 1.5 2.9 3.25 3.02 Pittsburgh 0.41 0.18 0.21 12.4 3.3 3.0 3.19 3.08 Philadelphia 0.21 0.21 0.39 14.9 1.4 3.3 3.25 3.23 Detroit 0.32 0.42 0.42 14.9 2.1 3.3 3.71 3.65 St. Louis 0.30 0.18 0.46 12.2 2.5 3.3 2.98 3.00 New York 0.22 0.53 0.42 13.6 1.6 4.2 3.06 3.33 San Francisco 0.38 0.51 0.51 12.4 3.1 4.4 3.48 3.73 Los Angeles 0.32 0.30 0.65 12.6 2.5 4.5 3.42 3.45

Sources: Columns (1), (4), (5)-Calculated from Table A-1; columns (2), (3)-Employment and Earnings, Vol. 15 (May 1969), Table 3, pp. 136-38, divided by 4.33 to adjust to weekly rates, except San Francisco, which is based on monthly data from various 1966 issues of Employment and Earnings; column (6)- ManpowerReport of the President, 1970, Table D-8, pp. 284-86; columns (7) and (8)-same as Figure 2. a. Data in general are for standard metropolitan statistical areas, identified by the largest cities therein, but there is some variation in the areas covered by the various sources cited.

Only in Pittsburghis there a substantialdiscrepancy between my results and the publisheddata; it has the highestfrequency of unemploymentin my study and yet a low layoff rate and fairly low officialunemployment rate. It is the only city wherethe derivedunemployment rate, standardized for adult white males, exceeds the official rate, which is an unadjusted averagefor all demographicgroups. All of the measuresof conditionsin labormarkets in Table4 show substantialvariation. The least variable,the probabilityof leavingunemployment, is lowestin St. Louis at 12.2percent and highest in Chicago at 20.9 percent,a differenceof 71 percent.The officialunemployment rate almost doubles over the range, from 2.4 percent in Houstonand Washington,D.C., to 4.5 percentin Los Angeles.My derivedunemployment rate shows much wider variation-by a factor of more than 4-from 0.7 percentin Chicagoto 3.1 percentin San Fran- cisco and 3.3 percentin Pittsburgh.The estimatedprobability of becoming unemployedvaries from 0.15 percentin Chicagoand Washington,D.C., to 0.38 percentin San Franciscoand 0.41 percentin Pittsburgh,a ratio over the range of close to 3. The layoff rate in manufacturingseems to 736 Brookings Papers on Economic Activity, 3:1972 be in rough agreementwith the probabilityof becomingunemployed (except for Pittsburgh),but the layoff rate has much more variation,from 0.05 percentin Washington,D.C., and 0.09 percentin Houston to 0.51 percentin San Franciscoand 0.53 percentin New York, a ratio of high to low of more than 10. The averagelevel of the layoffrate is about the same as the probabilityof unemployment,while the quit rate is considerably higher. Since two other major sources of unemployment-entranceand reentranceto the labor force-are omittedfrom the table, it is apparent that in a boom year like 1966 only a small fractionof those looking for work ever becomeunemployed. The relationshipbetween the probabilityof becomingunemployed and the probabilityof leavingunemployment is surprisinglyclose, as shownin Figure 4. Cities with tight marketsappear in the upper left. Workersin those cities have low probabilitiesof becomingunemployed, because layoffs are infrequentand changingjobs without becomingunemployed is

Figure 4. Weekly Probabilities of Entering and Leaving Unemployment, Twelve Large Cities, 1966

Probabilityof leavinigunemploymentt (percent), am 25

1 Baltimore 7 New York 2 Chicago 8 Philadelphia 3 Cleveland 9 Pittsburght .20 4 Detroit 10 St. Louis 20 5 Houstoni 11 San Francisco 6 Los Angeles 12 Washinigtoni,D.C. 5,9 0l2 ~ ~ ~ ~ 1

15 80 44s 7,03

100 60 Ij*0 90

10 , 10 0 0.15 0.20 0.25 0.30 0.35 0.40 Probabilityof becominzguniemployed (percenit), ,s

Source: Table 4. RobertE. Hall 737 Table 5. Weekly Layoff Rate in Manufacturingin Twelve Large Cities, 1962, 1966, and 1970 Percent Year City 1962 1966 1970 Baltimore 0.48 0.30 0.37 Chicago n.a. 0.12 0.25 Cleveland n.a. 0.18 0.39 Detroit n.a. 0.42 0.67 Houston n.a. 0.09 0.09 Los Angeles 0.39 0.30 n.a. New York 0.67 0.53 0.69 Philadelphia n.a. 0.21 0.39 Pittsburgh n.a. 0.18 0.39 St. Louis 0.39 0.18 0.32 San Francisco 0.76 0.51 n.a. Washington,D.C. 0.07 0.05 0.05 Sources: Employmentand Earnings, various May issues. Data are adjusted to weekly rates by dividing by 4.33. Data for New York for all years and for Washington in 1966 and 1970 are for the standard metropolitan statistical area. n.a. Not available.

easy. Onceunemployed, they are able to findwork quickly. Conditions are just the oppositein the cities at the lower right of Figure4. The equilibriumtheory suggeststhat employersreact to differencesin conditionsin labormarkets through the adjustmentof theirpolicies of hiring and laying off. In slack markets,an employercan affordan unstable policy in which most of a fluctuationin demandcan be met by a corre- spondingchange in his labor force, since a large fractionof those laid off will still be availablefor recalleven aftera month or two, and, in any case, newhiring is easybecause of the largepool of unemployedworkers. In tight markets,laid-off workers are less likely to be availablefor recalland new hiresmore difficult, so an employeris inducedto stabilizehis laborforce by holdingidle workersduring fluctuations in his output.The largedifferences amongthe layoffrates of the twelvecities of the studyare quitesurprising. Apparentlythe relationsuggested by the theory is quite strong. Further, just as the patternof unemploymentrates is stableover time, so is the pattern of layoffrates. Table 5 presentsthe publishedrates for manufacturing industries,again at weekly rates, for 1962, 1966, and the recessionyear, 1970. The cities with low layoff rates in 1966-Chicago, Houston, and 738 Brookings Papers on Economic Activity, 3:1972 Washington,D.C.-were low in 1970, as well; Washington(the only one of the three for which data are available)was also low in 1962.

IMPLICATIONS OF THE STUDY OF TWELVE CITIES FOR REGIONAL MANPOWER POLICIES The theory I have proposed suggeststhat relativelysubtle differences among cities can induce fairly large differencesin the conditionsin their labor markets,especially in layoff and unemploymentrates. The data appear to be consistentwith the theoryand to discreditits main competitor, the theory of perpetualdisequilibrium caused by transitoryshifts in de- mandamong cities.30 The theoryhas plainimplications about the potential impact of regional manpowerpolicies. I distinguishtwo main types of policiesintended to deal with the problemof slacklabor markets in certain geographicalareas: those that attemptto increasethe demandfor labor by subsidizingemployers in depressedareas and those that attempt to decreasethe supplyof laborby subsidizingthe relocationof workersfrom slackto tightmarkets. The firstkind is typifiedby the AreaRedevelopment Act of 1961and the secondby more recentexperimental programs of the Departmentof Labor.An expansionof the latterprograms has been advo- cated by CharlesHolt and his colleaguesat the Urban Instituteas part of their proposal for a comprehensiverevision and enlargementof federal manpowerprograms.3' Subsidiesto employersin depressedareas can take a varietyof forms- tax creditsor rebates,provision of free servicessuch as highways,and so forth-but these can be incorporatedat least roughlyin the theory as an upwardshift in the scheduleof employerequilibrium in Figure 1. If that scheduleis steeperthan the one for workerequilibrium, then the intersec- tion shiftsin the directionof lowerwages and less unemployment.Produc- tivity falls by more than the amountof the subsidy,but on the otherhand each workeris employeda largerfraction of the year. If the schedulefor employersis less steepthan the one for workers,just the oppositehappens: Wages and unemploymentrates rise and productivityrises by more than

30. That is, discreditit as a unitaryexplanation of the geographicalpattern of unemployment. Obviously,transitory shifts in demandcause perturbationsaround the equilibrium describedby my theory. In this sense, the two theories are complementary. 31. CharlesC. Holt and others, "ManpowerProposals for Phase III," in Brookings Papers on EconomicActivity (3:1971), pp. 712-22. Robert E. Hall 739 the amountof the subsidy.In both cases the equilibratingmechanisms of the marketdefeat the hope that such policieswill decreaseunemployment and increasewages simultaneously.32 Policiesfor inducingworkers to move from slackmarkets to tight mar- ketswith relocation allowances are not as easyto incorporatein the theory. One way they might operatein practiceis simplyto make low-unemploy- mentregions more attractiveto workers.This can be portrayedas a downward shift in the schedule of worker equilibriumin Figure 1 and has exactlythe same effect as the upwardshift in the other schedulejust discussed. Either unemploymentand wages fall to even lower levels in the low-unemploymentregion, or they both rise. Only in the secondcase does the economymove towardthe equalizationof unemploymentdifferentials that presumablyis the goal of programsthat subsidizerelocation from high- to low-unemploymentareas. My main point is that if the pattern of regionaldifferences is in fact characteristicof equilibrium,the changein the equilibriumbrought about by the policiesmay well be perverse.An understandingof the natureof the mechanismdetermining regional differences in economicactivity is essential to the formulationof appropriateregional policies. I do not believe that the simpletheory of disequilibrium,which seems to underliethe two kinds of policies consideredhere, is a satisfactorybasis by itself for de- signingprograms.

The Social Costs andBenefits of Unemployment

Everycontemporary account of unemploymentgrants the usefulnessof a certainlevel of unemployment.Without a carefulprocess of looking for work on the part of prospectiveemployees, the matching of jobs and workersthat is an essentialfeature of the efficientoperation of the labor marketwould not take place. Most discussionsseem to assume,however, that the privateinterests of individualunemployed workers coincide with the interestsof the societyas a whole,that thereare no externalbenefits or costs associatedwith their individualdecisions. In its extremeform, this view leads to the belief that the level of unemploymentin a competitive economyin equilibriumis optimal.The theoryof turnoversuggests, on the 32. Joseph Stiglitz, in "AlternativeTheories," has made much the same point with regardto policies for subsidizingurban employmentin developingcountries, 740 Brookings PaDers on Economic Activity. 3:1972 contiary, that an importantexternality operates through unemployment. Conditionsin the labor market affect the productivityof workers,and these conditions are affectedby the decisions of individuals.An unemployed workerwho takes a job imposesa cost on the societyby reducing the unemploymentrate and thereby decreasingthe productivityof the economy.He receivesa benefitin the form of the wage he earns.The net social benefitor cost is the differencebetween the two. Social efficiencyis achievedwhen the marginalvalue of putting anotherperson to work is exactly equal to the social cost of the reductionin productivitybrought about as a consequenceof the tighteningof the labor market.I will argue that part of the cost is a true externality,not reflectedby any privatecost, so there is no reason to expect an efficientlevel of unemploymentin a purelycompetitive economy.33 The notion of an optimal amount of excess capacity-of both labor and capital-within a firmis a familiarone. Occasionalidleness is a sign of efficiency,since it means that someone is availablefor high-priority tasks that may arise unexpectedly.I will arguehere that the unemployed performa similarfunction in the aggregateeconomy. The crucialdiffer- ence is that in the firm, privateand social costs and benefitscoincide for decisionsabout the allocationof individualworkers, so the management should choose an efficientlevel of excess labor, while in the aggregate economy, the decision-makingagents face privatecosts that differ from the social costs. The essenceof my argumentis that the unemployedper- form a sociallyuseful function for whichthey are not necessarilycompen- sated,and that employersare not necessarilyrewarded enough (or charged enough)for puttingthe unemployedto work. Why is it necessaryto maintaina labor reserveoutside the firm and to requireindividual workers to financeperiods of unemploymentat least in part from their own funds?The first reactionof most economiststo the suggestionof an externalityis to look for economicinstitutions that could make externalitiesof single individualsinternal to a group. Many such institutionsdo in fact exist; firmsthat supplytemporary clerical help are

33. In "Inflationand Unemployment,"James Tobin has made the generalpoint that externalitiesin the process of job searchinvalidate the presumptionthat the competitive equilibriumis efficient.He mentions externalitiesof a sort not dealt with here but does not consider the relation between the level of unemploymentand productivitythat is central to my argument. Robert E. Hall 741 a clearexample. But thereis a fundamentallimitation to the scope of these institutions.At whateverlevel they operate,they cannot take charge of all of the reserveof workersavailable for employment,because part of the reserveconsists of workersfrom the outside. For a firm, the availability of workerslaid off from other firms in the same industrymakes it un- desirableto meet all fluctuationsin laborrequirements through an internal reserve.Similarly, the availabilityof workersfrom other industrieslimits the scope of an institutionthat maintainsan internalreserve within a single industry,although industrial unions do have this role to a certainextent. Since no rigid boundariesrestrict the occupational,industrial, and geo- graphicmobility of labor, privateinstitutions are incapableof makingthe costs of maintaininga reserveof workersfully internaland private. Not all of the returnsto unemploymentare socialrather than individual. To the extentthat the unemployedsearch actively for jobs, they may cap- ture some of the benefitsof unemploymentfor themselvesin the form of betterjobs. In the extreme,all of the benefitsof unemploymentdescribed above could accrue to the individual.I find this implausiblebecause it suggeststhat the unemployedconsistently improve their prospects by waiting for the rightjob, whereasin fact many of the unemployedfind waiting to be a pureburden because they expectto returnto their old jobs or ones just like them. The point remains,however, that some workerscan make good use of their time while unemployed.Some fraction of the social returnto unemploymentcalculated in the next section is probablycap- turedby the individualunemployed worker. Social efficiencyrequires that a system of taxes be imposedto account for the externalityassociated with unemploymentby makingprivate costs and benefits,after taxes, equal the social costs and benefits.This requires a subsidy for unemployedworkers, to compensatethem for the social contributionthey make by being availableimmediately for work, and a tax on employersfor the social cost of withdrawingworkers from the pool of idle workers. The magnitudeof the compensationand correspondingtax dependson the fractionof the benefitsof unemploymentthat do not accrueto the individual.It is conceivablethat the fractionis largeand that socialefficiency requiresfairly generousunemployment compensation, but no empirical evidenceis availableto supportthis view. MartinFeldstein has recently calculatedthe effectiverates of compensationunder the existingsystem and 742 Brookings Papers on Economic Activity, 3:1972 foundthat they are as high as 90 percentof previouswages for some workers in some states.34Current knowledge cannot answerthe questionabout the efficiencyof these high rates. My main point is that thereis no reason to believethat unemploymentcompensation is invariablya sourceof ineffi- ciency. I contrastmy view with what I believe is the conventionalview among economiststhat unemploymentcompensation is insuranceagainst the risk of unemployment,and that the problemwith it as insuranceis the substantialmoral hazardposed by the individual'scontrol over his own unemployment.35

Are High Turnoverand High UnemploymentInevitable?

Many economistsare reluctantto acceptthe conclusionthat high turnover and high unemploymentare inevitablein view of the verylow ratesof turnoverand unemploymentfound in other highly developedcountries, especiallyWest Germanyand Japan. One of the contributionsof this paperis to identifycomparable examples from the U.S. economy:Chicago has far less new unemploymenteach week than the nationalaverage, and a substantiallylower overallunemployment rate. Advocatesof the view that high unemploymentis inevitableoften dismissthe evidencefrom West Germanyand Japanon the groundsthat theseconservative societies induce much greaterpersonal stability among their members than does the more open, liberalsociety of the United States.One could not equallyplausibly argue the irrelevanceof the evidence from the most American of all Americancities, Chicago. The theory of turnoverpresented at the beginningof the paper and refinedthrough the comparisonof the twelvelarge cities has implications for the aggregateeconomy. In the absenceof internationalmigration, labor mobility does not establishan aggregateconnection between unemployment and wages of the sort proposedearlier. Within a country,the geographicalpattern of wage diflerentialsmust match the patternof differ- entialsin unemploymentrates, but nothingdiscussed so far determinesthe overalllevel of wages (w in my algebraicexposition). On the other hand, the connectionbetween unemployment and wage rates arising from the lower productivityof workersin tight marketsdoes operateat the aggre- 34. "Loweringthe PermanentRate of Unemployment." 35. See, for example, Edmund S. Phelps, Inflationand Unemployment:The Cost- BenefitApproach to MonetaryPlanning (Norton, 1972), pp. 97-99. RobertE. Hall 743 gate level (the value of x is set by the relationbetween prices and costs). Consequently,the aggregateeconomy faces a choice betweentight labor marketsand lower wages on the one hand, and slack marketsand higher wages, on the other. The model can be closed in a varietyof ways. The crudeKeynesian would take the wage rate as fixedand given.The classical economistwould take a particularunemployment rate as an indicatorof marketclearing. The moderneconomist would introducea complex adjustmentprocess linking the wage level to the past history of unemployment. If the adjustmentprocess can be summarizedby a stable long-run Phillipscurve, the choices availableare indexedby the rate of inflation: Tight marketsand low real wage levels will be accompaniedby high rates of inflation, and vice versa. In the limiting case of a verticallong-run Phillipscurve, only a single unemploymentrate, the naturalrate, can be sustainedindefinitely and it impliesa certainset of conditionsin the labor market.Nothing in the theoryof turnoverprovides grounds for optimism about improvingthe performanceof the labor marketthrough aggregate expansionarypolicy by itself. What would be a socially efficientpolicy for labor markets?I have neitherthe theory nor the empiricalresults to deal with this questionfor the contemporaryAmerican economy beyond my generalremarks on the social costs and benefitsof unemployment.I can, however,say something about a mythicaleconomy. Suppose that no artificialfactors barred mobility in the labor marketand that all workerswere effectivelyidentical, so that none of the seriousproblems of the unequaldistribution of unemployment among demographicgroups existed. Suppose further that the aggregate relationbetween productivity and unemploymentin the economywas the following: w = $3.15 + 0.04u. To determinethe hourlysocial returnto unemploymentin this economy, supposethat thereare N manhoursavailable in the labor force of which U are unemployed.Then u = 100 U/N. Total output is the productof the numberof manhoursemployed, N - U, and the productivityof each, w:

X = (N - U)w. Now the net marginalcontribution of one more unemployedworker is the derivativeof X with respectto U: dX - dw ~=(NdU U)--W.~du 744 Brookings Papers on Economic Activity, 3:1972 The first term is the social benefitassociated with the increasedproduc- tivity of the remainingemployed workers and the secondis the social and privatecost of the reductionin employment.Since w = $3.15 + 0.04u

= $3.15+0.04 ??0U N' then dw_ $4.00 dU N' and the marginalsocial benefitof unemploymentis

$400N U

At, say, 2 percentunemployment, the marginalsocial benefitof unemploymentis $3.92per hour,while the marginalsocial and individualcost is only $3.23per hour.In the mythicaleconomy, there is too littleunemployment! In such an economy the reserveof workersis a scarce resourcethat is inappropriatelyrationed because employersare not charged for with- drawinga workerfrom the pool. Similarly,workers do not face the appro- priate incentiveto remainunemployed. The mythicaleconomy needs a policy that increasesthe unemploymentrate to the point of equality of marginalsocial costs and benefits. The mythicaleconomy may bear some slight resemblanceto the market for adultwhite males in the UnitedStates but surelynot to the labormarket as a whole. The marketsin the United States for blacks, women, and youths seem to be separatedfrom the marketfor adult white males by artificialbarriers. The less permeablethese barriers,the more the markets need to be analyzedseparately. Markets for adultwhite males may well be chronicallytight, with unemploymentrates below the efficientlevel, while those for blacks,women, and youthsare chronicallyslack with inefficiently high unemployment.This conclusionis certainlyconsistent with the em- piricalevidence on the turnoverof individualworkers presented earlier in the paper.It has the importantimplication that the socialcost of removing one workerfrom the slack marketis lower than the wage in that market while the social benefitof addinga workerto the tight marketis greater than the wage there, so the wage differentialmay substantiallyunderstate the social benefits of moving workersacross the barrier.Programs for puttingdisadvantaged workers into good jobs, such as those discussedin RobertE. Hall 745 the later sections of my previouspaper, may have social benefitsbeyond the privatebenefits to the individualsin the programs. What,then, of West Germany,Japan, and Chicago?There are both costs and benefitsto tight labor markets.Turnover is a sign of efficiencyas well as a sourceof individualdistress. The existenceof economieswith low turnover and unemploymentrates suggeststhe feasibilitybut not necessarily the desirabilityof achievingsimilar rates in the United States.The present state of knowledgedoes not justify a single-mindedpolicy of tightening labormarkets without attending to the fundamentalstructural problems ot lack of opportunityfor many groupsin the labor force.

APPENDIX A

Estimationof the Frequencyand Durationof Unemployment

THE FREQUENCY OF UNEMPLOYMENTis measured by the probability, a, that a workerwho is not unemployedin one weekwill becomeunemployed in the next; the durationof unemploymentis inverselyproportional to the probability,,B, that an unemployedworker will no longerbe unemployed in the next week.Neither of theseprobabilities depends on the past history of the individual.Thus, at the level of the individual,the modelis a simple Markovmodel. This study differsfrom previousapplications of Markov models to flows in the labor market' in the importantrespect that the transitionprobabilities are functionsof individualcharacteristics.2 Naturalestimates of a and ,Bare the following: numberof times unemploymentbegan numberof times unemploymentcould have begun

1. For example, Martin David and Toshiyuki Otsuki, "Forecasting Short-run Variation in Labor Market Activity," Review of Economics and Statistics, Vol. 50 (February1968), pp. 68-77. 2. Since data are not available on the lengths of individual spells, nothing can be done here about the dependenceof , on the length of the spell. George Perryhas treated this problem in "UnemploymentFlows." 746 Brookings Papers on Economic Activity, 3:1972 and

A _ numberof times unemploymentended A numberof times unemploymentcould have ended' Exceptfor spellsthat beganbefore the yearbegan, or endedafter the year ended,the numeratorsof these two estimatorsare both equal to the number of spells. Further(again except for the case of overlap),the denomi- nator of A is observeddirectly as the numberof weeks of unemployment and the denominatorof d can be obtainedby subtractingthe numberof weeks of unemploymentfrom 52; thus, except for beginningand ending effects,these estimatorscan be calculateddirectly from the data. Now S -1 < E ? S, S -1 < B

~~52- W_ 51 - W and~~

S-1 A S w w- where S = the number of spells W = the numberof weeks of unemployment E = the numberof times unemploymentended B = the numberof times it began M = the numberof times unemploymentcould have ended N = the numberof times it could have begun. Since the probabilityof unemploymentis well below one-half,the best singlepair of estimatorsis probablythat based on the assumptionthat no spell of unemploymentoverlaps the beginningor end of the year: E= B= S,M= W,andN= 51- W.

~~The resulting estimators, a* = S/(51 - W) and A* -S/W, lie within the Robert E. Hall 747 boundsjust givenand arethe ones usedin this study.The followingspecifi- cationswere used for the probabilities:~~

~~ex-. 1 + ex a and ex.7 A 1 +e7~~

where x is the vector of the individual'scharacteristics and a and 7 are vectorsof parametersto be estimated.Estimates were made by the method of maximumlikelihood. The characteristics,x, used in this studymeasure the race, numberand ages of children,wage (imputedaccording to a formulasimilar to that in my study of labor supply3), income (including the value of the time of the worker,but not his actualearnings), age, maritalstatus, city of residence, and type of employment(private wage or salary, government,self-employed, and unpaid family employment).The variableshave the form of dummyvariables for the characteristicsthat are categorical;for example, X2 = 1 for blacks and 0 for whites. For each continuouscharacteristic (wage,income, or age), x consistsof a set of variablesthat, whenweighted by the estimatedcoefficients, form a continuous,piecewise linear function of the characteristic.Each coefficientbi or -Ti should be interpretedas approximatelythe proportionalchange in the correspondingprobability associatedwith xi = 1 ratherthan xi = 0. Thus 62 is approximatelythe proportionby whichthe probabilitythat a blackwill becomeunemployed exceedsthe probabilitythat a white will become unemployed.The exact interpretationof thesecoefficients is obtainedby evaluatingthe expressions just given. Data for this studywere obtainedfrom the Surveyof EconomicOppor- tunity(SEO), conducted by the U.S. Bureauof the Censusin the springof 1967,and referto 1966experience. All individualsliving in the twelvelarge standardmetropolitan statistical areas identified in the SEOwere included, exceptthose unableto work, those employedin the constructionindustry or the armed forces, and those for whom data on unemploymentwere

3. "Wages, Income, and Hours of Work in the U.S. Labor Force," in Harold W. Watts and Glen G. Cain, IncomeMaintenance and LaborSupply: Econometric Studies, Monograph Series, University of Wisconsin, Institute for Research on Poverty, forth- coming. 748 BrookingsPapers on EconomicActivity, 3:1972 missing.Separate results were obtainedfor men and for women. The co- efficientstogether with their estimatedstandard errors are presentedin TablesA-1 and A-2. Theseestimates were based on 9,766 men and 12,287 women, contributing432,974 and 567,728 weekly observations,respec- tively, to the estimationof a, and 13,990 and 12,040 observationsto the estimationof A.

Table A-1. Coefficients for Weekly Probabilities of Entering and Leaving Unemployment for Men, by Selected Characteristics, 1966 Parameterof Parameterof probabilityof becoming probabilityof leaving Characteristic unemployed,a unemployment,y Constant -6.13 -1.85 (0.14) (0.15) Color Black 0.56 -0.32 (0.06) (0.07) White 0 0 Children None 0.19 0.16 (0.10) (0.11) Preschool only 0 0 School age only 0.14 0.00 (0.11) (0.13) Both ages 0.17 0.11 (0.11) (0.12) City of residence Baltimore 0.07 0.17 (0.12) (0.13) Chicago -0.37 0.52 (0.11) (0.13) Cleveland 0.03 0.02 (0.16) (0.17) Detroit 0.36 0.09 (0.10) (0.12) Houston -0.12 0.34 (0.15) (0.17) Los Angeles 0.36 -0.08 (0.09) (0.09) New York 0 0 Philadelphia -0.02 0.11 (0.12) (0.13) Pittsburgh 0.63 -0.11 (0.15) (0.16) RobertE. Hall 749 Table A-1 (Continued) Parameterof Parameterof probabilityof becoming probabilityof leaving Characteristic unemnployed,a unemployment,y St. Louis 0.32 -0.12 (0.14) (0.16) San Francisco 0.55 -0.11 (0.10) (0.11) Washington,D.C. -0.40 0.38 (0.13) (0.14) Wage rate per hour (dollars) 0 0.50 0.15 (0.82) (0.96) 1.50 0.24 -0.24 (0.14) (0.16) 2.00 0.12 -0.10 (0.13) (0.14) 3.00 0 0 4.00 -0.28 -0.11 (0.26) (0.34) 10.00 -16.46 6.19 (9.44) (12.53) Annual family income per adult (dollars) 0 -1.30 0.45 (0.46) (0.49) 2,00 -0.05 0.02 (0.11) (0.12) 4,000 0 0 7,000 -0.40 -0.37 (0.18) (0.20) 10,000 0.20 -0.34 (0.40) (0.53) 40,000 -4.75 -9.60 (6.27) (14.58) Age (years) 15 -0.40 0.83 (0.15) (0.17) 22 0.40 0.23 (0.12) (0.14) 30 0 0 45 -0.30 0.14 (0.12) (0.13) 65 -0.33 -0.09 (0.13) (0.14) 98 -4.61 1.22 (0.91) (0.99) 750 Brookings Papers on Economic Activity, 3:1972 TableA-1 (Continued) Parameterof Parameterof probabilityof becoming probabilityof leaving Characteristic unemployed,a unemployment,y Type of worker Not reported -0.62 -0.99 (0.09) (0.09) Privatewage or salary 0 0 Government -0.77 -0.12 (0.14) (0.11) Self-employed Salaried 0.13 1.00 (0.36) (0.53) Not salaried -0.79 0.19 (0.18) (0.20) Marital status Married 0 0 Not married 0.60 -0.14 (0.08) (0.08) Source: Derived from the Survey of Economic Opportunity conducted by U.S. Bureau of the Census, Spring 1967. The data cover twelve standard metropolitan statistical areas, identified by the largest cities under "City of residence." The numbers in parentheses are estimated standard errors.

Table A-2. Coefficientsfor Weekly Probabilitiesof Enteringand Leaving Unemploymentfor Women,by SelectedCharacteristics, 1966 Parameterof Parameterof probabilityof becoming probabilityof leaving Characteristic unemployed,a unemployment,y Constant -7.45 -1.02 (0.27) (0.32) Color Black 0.75 -0.40 (0.07) (0.07) White 0 0 Children None 0.03 0.01 (0.09) (0.10) Preschool only 0 0 School age only -0.03 0.01 (0.10) (0.12) Both ages -0.05 0.32 (0.11) (0.12) City of residence Baltimore -0.35 0.06 (0.14) (0.15) Robert E. Hall 751 Table A-2 (Continued) Parameterof Parameterof probabilityof becoming probabilityof leaving Characteristic unemployed,a unemployment,y City of residence(cont.) Chicago -0.43 0.07 (0.11) (0.13) Cleveland 0.27 -0.10 (0.14) (0.16) Detroit 0.11 -0.37 (0.11) (0.12) Houston 0.07 0.44 (0.15) (0.18) Los Angeles 0.19 -0.13 (0.09) (0.10) New York 0 0 Philadelphia -0.04 -0.25 (0.11) (0.12) Pittsburgh 0.15 -0.32 (0.19) (0.20) St. Louis 0.36 -0.29 (0.14) (0.16) San Francisco 0.37 -0.20 (0.10) (0.11) Washington,D.C. -0.47 0.17 (0.12) (0.13) Wage rate per hour (dollars) 0 -1.19 -1.23 (0.46) (0.53) 1.50 0.31 -0.91 (0.23) (0.28) 2.00 0.49 -1.09 (0.26) (0.30) 3.00 0 0 4.00 -0.46 -1.61 (0.86) (0.93) 10.00 16.97 1.00 (3.79) (3.61) Annual family income per adult (dollars) 0 -0.45 0.43 (0.37) (0.42) 2,000 0.22 0.00 (0.11) (0.12) 4,000 0 0 7,000 -0.09 -0.43 (0.19) (0.22) 10,000 -2.17 -0.89 (1.08) (1.45) 752 Brookings Papers on Economic Activity, 3:1972 TableA-2 (Continued) Parameterof Parameterof probabilityof becoming probabilityof leaving Characteristic unemployed,a unemployment,y Income (dollars)(cont.) 40,000 6.71 -0.52 (1.16) (1.25) Age (years) 15 -0.04 0.49 (0.14) (0.16) 22 0.51 0.04 (0.12) (0.13) 30 0 0 45 -0.30 -0.06 (0.12) (0.14) 65 -0.44 -0.19 (0.15) (0.16) 98 -4.74 0.13 (1.07) (1.30) Type of worker Not reported 0 0 Private wage or salary 1.22 0.38 (0.07) (0.07) Government 0.45 0.30 (0.11) (0.12) Self-employed Salaried 2.51 0.28 (0.39) (0.44) Not salaried 0.77 0.60 (0.27) (0.30) Marital status Married 0 0 Not married 0.22 -0.06 (0.06) (0.07) Sources: Same as Table A-1. The numbers in parentheses are the estimated standard errors. Robert E. Hall 753

~~APPENDIX B~~

GeographicalDifferences in Unemployment, Turnover,and Wage Rates*

THE THEORY STARTS in the following way: I considerthe behavior of workersand employersin a singlecity. Both may considermoving to other cities,workers because of higherwages or lowerunemployment rates, em- ployersbecause of lowerwages or moreproductive workers. I will assume that unemployedworkers follow reasonablestrategies in trying to find work, and that, as a result,there is a probability,b, of findingwork each week. To some extent,this probabilityis withinthe control of the unemployedworker, although this shouldnot be takento mean that unemployment is somehowvoluntary. I will assumethat b is a stablefunction of two measuresof conditionsin the market,the unemploymentrate, u, and the vacancyrate, v: b = B(u, v). Similarly,employers trying to fill jobs are assumedto have a probability, r, of fillinga given vacancyeach week, againassumed to be a function of u and v: r = R(u, v). In addition,each workeris assumedto have a probability,q, of quitting each week, while employershave a probability,y, of laying off a given workereach week.In equilibrium,the unemploymentrate in this systemis

~~u- q+y q +yj+,b and the vacancyrate is~~

~~= qq+y q + y + r~~

* My debt to the thinking of CharlesC. Holt will be apparentto all readersof this appendix. See appendix of Charles C. Holt and others, The Unemployment-Inflation Dilemma:A ManpowerSolution (Urban Institute, 1971), pp. 94-102. 754 Brookings Papers on Economic Activity, 3:1972 The effectivewage elsewherein the economyis assumedto be fixedexoge- nouslyat the level w. In orderthat workersin this city haveno inducement to emigrate,and that workerselsewhere have no inducementto immigrate, effectivewages here and elsewheremust be equal:

(1 - u)w = w. I will referto this as the conditionfor workerequilibrium. The similarcondition for employerequilibrium is that effectivelabor costs hereand elsewheremust be equal.I assumethat the net productivity, f(r, q), of workersin a givenlabor market depends on the cost of recruiting, as measuredby the probabilityof fillinga job, r, and on the quit rate, q. Net productivityis higherwhen r is higher,since in that case it is cheaper to replaceworkers who havequit and also possibleto lay off workersin the event of a brief reductionin demand.If unit labor cost elsewhereis x, the equilibriumcondition for employersis w f(r, q) X. Quits and layoffs depend on conditions in the market. I will assume that the quit rate dependson the cost of findingnew work: q = Q(b); and that the layoff rate dependson the cost of fillingjobs: y = Y(r). In principle,y should also dependon the quit rate, but nothing essential is lost by makingthis simplerassumption. Since the quit and layoff rates depend on the rates of job findingand job filling,which in turn dependon the underlyingmeasures of conditions, u and v, it is possibleto writethe unemploymentrate as a functionof itself and the vacancyrate: U Q(B(u, v)) + y(R(u, v)) Q(B(u, v)) + y(R(u, v)) + B(u, v) This can be solved to get v as a function of u: v = g(u). The functiong(u) tells what vacancyrate is necessaryto achievethe quit rate,layoff rate, and rateofjob findingthat areconsistent with the specified unemploymentrate, u. It may slope upwardor downward.In general,a Robert E. Hall 755 higher unemploymentrate is associatedwith a lower quit rate, a higher layoff rate, and a lower rate of job finding.If the first of these dominates the other two, a higherlevel of vacancieswill be necessaryto balance a higheremployment rate. Otherwise,vacancies will be lower when unemploymentis higher. The equilibriumcondition for employerscan now be writtenin termsof the wage level and the unemploymentrate: w f(R(u, g(u))), Q(B(u, g(u))) Unless the quit rate is very sensitiveto the rate of job finding,R(u, g(u)) will be an increasingfunction of u (recruitingis easier in a marketwith higherunemployment) and Q(B(u, g(u))) wil be a decreasingfunction of u (sincejobs are harderto find when unemploymentis higher).Both of these considerationsmake workersmore productivewhen the unemployment rate is higher.This relationcan be summarizedby a function, h(u) = f(R(u, g(U))), Q(B(u, g(u))), which is increasing in u. Full equilibriumin the market requires that worker and employer equilibriumhold together.In the diagramof Figure 1, this takes place at the intersectionof the schedules

~~w = 1 _ and w = xh(u).~~

~~Differencesamong Cities~~

Supposefirst that cities differin theirattractiveness to workers,and that this differencecan be measuredby a variable,a, which enters the equilibriumcondition for workersin the followingway: (1 - u)w = w- a. Workerswill not leave an attractivecity with a high valueof a even though the effectivewage there is lower than elsewhere.This is a simpleapplica- tion of the principleof equalizingdifferences. Similarly, suppose that cities differin productivityfor reasonsapart from conditions in theirlabor markets. I definea measure,z, which shiftsthe net productivityof workersso as to make the equilibriumof employersthe following: w = [h(u) + z]x. 756 Brookings Papers on Economic Activity, 3:1972 Differencesin climateamong cities are likelyto affectboth theirattractiveness and productivity;for example, in warmercities both workersand employerspay less for heating.On this accountI would expect a positive relationbetween a and z. On the other hand, many differenceswill affect only workersor only employers,so thereneed not be any strongsystematic relation between a and z. Rather than attempt to create a theory that dependson measurementsof a and z, I will treatthem as randomvariables and ask what relationbetween wages and unemploymentis likely to be observedin the face of randomdifferences of the sortjust described. Nothing much is lost and a great simplificationgained by considering the following linearizedversions of the two conditionsfor equilibrium:

~~w = (1 + u -a); w = (ho +hlu+z)X. The slope of the observedrelation between w and u inducedby differences in a and z is' OfW+ (I -0)hifc, where~~

~~0 = x2 + XW g2o2 + 2XWpo7a?7z + f20-2~~

and o-Xis the standarddeviation of z, o-a is the standarddeviation of a, and p is their correlation.Several conclusions follow from this formula.First, if thereare no differencesin productivityamong cities (o- = 0), then 0 = 0 and the slope is hix, exactlythe slope of the equilibriumcondition for employers.Similarly, if thereare no differencesin attractivenessamong cities (oa = 0), observed points trace out the equilibrium condition for workers. Otherwise,the observedrelation is differentfrom either equilibrium condition. If 0 lies between0 and 1, the observedslope must lie betweenthe slopes of the two equilibriumconditions. Since both are positive,the observedrelation must slope upward. A glanceat the formulafor 0 showsthat it will alwaysbe positiveand less than one if a and z are positivelycorre- lated(which I findlikely), and will in fact behavewell for negativep as long as p exceedsa certainlower limit.

1. I will not burdenthe readerwith the details. See Franklin M. Fisher, The Identi- ficationProblem in Econometrics(McGraw-Hill, 1966), Chaps. 1-3. By slope I mean the ratio of the expectedvalue of u*w to the expectedvalue of u2. Commentsand Discussion

AaronGordon: This paperfalls into two parts.The firstis a usefulstudy of the contributionof laborturnover to unemployment,both in the aggregate and amongdifferent sectors in the labor force.The seconddeals with geographicaldifferences in wages and unemploymentand is much more con- troversial.In this part of the paper, I am convincedneither by Hall's analyticalmodel nor by his reportedstatistical results. The findingsin the firstpart are interesting. On the wholethey contribute to our understandingof how unemploymentis generatedand why its level is differentfor differentsegments of the labor force. Hall computesthe weekly probabilityof a person becomingunemployed, and of a person leavingunemployment. Unfortunately, the data do not permithim to dis- tinguishunemployment arising from layoffs or quitsfrom that arisingfrom entering or reenteringthe labor force. That informationis particularly importantfor youths and marriedwomen. I foundit difficultto acceptHall's resultsfor teenagers.He findsthat the probabilityof becomingunemployed in a givenweek is no greaterfor male teenagersthan for 30-year-olds.In addition,he finds that male teenagers spend a smallerfraction of the year unemployedthan do personsof any other age group except those in their forties. That flatly contradictsall otherevidence on this problemwith whichI am familiar.The fact that the currentpopulation survey may give particularlyunreliable evidence on teenage unemploymentis certainlyrelevant but can hardlybe the entire answer.Finally, one point to which not enough attentionis paid is the effect of occupation,which is particularlyimportant in unemployment differencesby age and sex. In the latterpart of the paper,dealing with geographicaldifferences in unemploymentand real wages,the statisticalfindings are presentedwithin 757 758 Brookings Papers on Economic Activity, 3:1972 the frameworkof what is called a theory of equilibrium.This theory is static and, in effect, assumesperfect competition in productmarkets and local labor markets.Production of goods and servicesis subjectto dimin- ishingmarginal productivity in the shortrun, whilein the long run marginal and averageproductivity of labormay rise,but only throughtechnical change.All employersand workersare profitmaximizers. Labor and capital are free to move geographically.The corollaryto these assumptionsis that realwages must fall as employmentexpands, except as the production functionshifts in the long run. If my descriptionis even approximatelycorrect, I fail to see the connection betweenthis model and the world from which the actual data are taken. Hall assumesthat there are permanentgeographic differentials in unemploymentrates. Judgingby the officialfigures for unemploymentin the twentylargest standard metropolitan statistical areas since the begin- ning of the 1960s,that assumptiondoes not hold up. A numberof the SMSAs did, indeed, retain approximatelythe same ranking,having the secondhighest or the tenthhighest or the twelfthhighest rate of unemployment, but not all of them. In Hall's sample,Chicago has the lowestunem- ployment rate. Although it had one of the lowest unemploymentrates throughoutthe 1961-71period, its rate was higherthan that of severalof the other twenty largest metropolitanareas in 1961 and in most of the otheryears up to 1971.Detroit had the highestunemployment rate in 1961 and again in 1970and 1971,but was near the medianduring the 1964-67 period. St. Louis was below the medianin 1964 and 1965and above it in 1967. I was unable to standardizethese rates for changesin the various dimensionsin the 1Thorforce as Hall did. But I assumethat this does not mattermuch for %iiui1gesover a periodas short as twelveyears. In Figure2, the positiveslope is not verydefinite, and the standarderrors on the regressioncoefficients confirm this uncertainfit. If Detroit and San Franciscowere excluded,would the regressionhave any positive slope at all?This seemsto me a weakempirical basis for the model, or even for an ad hoc generalizationthat high realwages and high unemploymentalways go together-now, ten yearsago, or twentyyears ago. TableA-1 in the ap- pendixreinforces these observations.Four out of the elevencoefficients for the SMSAsfor the probabilityof becomingunemployed are smallerthan their standarderrors. For the probabilityof leaving unemployment,six coefficientsare smallerthan theirstandard errors and only threeare equal Robert E. Hall 759 to twice their standarderrors. The correlationsare better for the other characteristicsmeasured than for the ones on geographicallocation. I missedany referenceto differencesin occupationaland industrialpat- terns of employmentamong the standardmetropolitan statistical areas that mighthave somethingto do with observedunemployment differences. And finally,in his discussionof deflatingwages by city, Hall ignoresthe differencebetween the deflatedwage conceptsthat are relevantfor employersand for employees.The employeris concernedwith product wage in determiningprofitability. Presumably it is the real wage that attracts the worker. On a local or regional basis, product wages would be ex- tremelydifficult to determine.

CharlesHolt: I think Robert Hall has made an importantcontribution with this paper.He has combinedthe dynamicsof turnoverin the labor marketand a competitivemodel of prices and wages into a static theory of wage differentials.The importanceof this accomplishmentis that most theoryup to this point has come out with an equilibriumprice, while Hall comes out withtwo mechanismsfor allocatingresources in theseimperfect markets:One is the wage offeredand the otheris the availabilityof jobs. That both of these are importanthas long been recognized;but Hall has made real progressin puttingthem together in a model that has extremely fruitfulimplications. And his insight should carry over to other kinds of differentialsbesides the one on whichhe reports. On more specificpoints: The fact that Hall'smodel of productivityrises whenunemployment rises is clearlya long-termstatic phenomenon. It certainly is not true cyclically,where labor productivityincreases as employment rises. As the empiricalwork advances,we must round out Hall's modelby fullyincorporating it into a dynamictheory reflecting this cyclical behavior. The first part of the paper contains a good deal of discussionof the probabilitiesof becoming unemployedand of leaving unemployment. Hall's work suggeststhat ratios of these probabilitiesbetween different groups in the labor force are stable. One has to keep in mind that these ratioswere observedfor 1966.Some of them, like the black-whiteunem- ploymentratio, are knownto be relativelystable. More recentwork, however, demonstratessystematic variation in others. These ratios certainly should not be taken as parameters. 760 Brookings Papers on Economic Activity, 3:1972 In some of his inferencesabout policy, Hall may have been premature. One has to be carefulnot to concludethat this paperimplies unemployment is a good thing simply on the basis of social efficiencyarguments. Before we use an efficiencyargument alone, we must look carefullyat questionslike, Who is unemployed?What are the economiccosts of unemploymentin termsof suicide,divorce, crime? What is the impactof unemploymenton incomedistribution? What will be the impacton futurelabor forceparticipation of youngpeople suffering high levelsof unemployment? These kinds of issues have to be much more thoroughlyexplored before we can begin to think about the policy implicationsof Hall's analysis. In Figure 1, two curves-the worker equilibriumand the employer equilibrium-aredepicted. The discussionpoints out that they mightcross in one of two ways,depending on whichis steeper.The policyimplications of this sound paradoxical:Increasing mobility may increaseunemployment, and labor subsidiesmay increaseunemployment. The difficultyhere is that one kind of intersectionis unstableand the other-the one drawn in Figure 1-is stable.In that case, mobilityand subsidieswould produce the kind of resultsone wouldanticipate. On the otherhand, with the slopes shown,the forcesrestoring equilibrium once it is disturbedare not strong. And this raisesthe chancesthat othervariables, such as unioninfluence or flows of workersinto differentmarkets, would be important. Vacancystatistics for the cities could be addedto Table 4. They are in the analysisnow and appearin the appendix.We know quite a lot about the functionalform in which vacanciesenter the analysisand even about the size of the parametersto be expected.The log of both Hall's alphaand his beta variableswould be linearlyrelated to the vacancyrate and the unemploymentrate. I am puzzledby Hall's denial of a connectionbetween unemployment and wages operatingthrough labor mobility.On discoveringstrong equi- libriumpatterns of unemploymentand wages acrosscities, Hall seemsin- clinedto acceptthe equilibriumas necessarilya good thing. Reallocating workersfrom marketsthat have more workersthan are neededto others that have fewerthan could be absorbedmight decreasethe total level of unemploymentand increaseoutput without increasing inflation. Hall recognizesthat when the ratioof vacanciesto unemploymentis high, quitswill be relativelyhigh. Many of those quittingwill not pass through unemploymentat all. Yet this process of changingjobs is an important part of the mechanismproducing a creepinginflation process. RobertE. Hall 761 In the discussionof social costs and benefits,Hall considersa "tax on employersfor the socialcost of withdrawingworkers from the pool of idle workers."It is importantto recognizethat, althoughhe stressesdynamic turnoverin his analysisgenerally, here he refersto a reductionin the stock of workers,not the grossflow of new hiresfrom the stock. The overallthrust of this paperunderlines once againthe limitationsof aggregatedemand policy in treatinginflation and unemploymentand the need for effectivepolicy measuresto improvethe structureof the labor market.

RobertHall: In replyto some of Aaron Gordon'scomments, let me first reiteratethat in the comparisonof citiesthat I make, I am talkingabout a long-run equilibriumcomparison rather than transitorydifferences in unemployment.Treating them as long-rundifferences across cities, we are lookingat caseswhere the capitalstock and the level of employmentare in equilibriumfor purposesof comparingone city with another.I certainly do not believemy productivityarguments apply in a cyclicalcontext. Thereis one importantmisunderstanding, I believe, in his criticismof my basic model. I do not assumedecreasing marginal or averageproduct of labor in the long run. High unemploymentdoes not necessarilyimply low employment,because I considerthe size of the labor force free to vary.In the model, the relationbetween unemployment and productivityoperates not throughthe level of employmentbut directlythrough the personnel policies of employers. The resultson teenagersdo pose a seriousproblem. However, I do not think we can take the officialdata from the CurrentPopulation Survey as the finalword and say that everystudy ought to reproducethose statistics. The monthlysurvey statistics have some seriousproblems. We know about the rotationgroup problem: The answerto how muchunemployment there is varies considerablydepending on how many months the respondents havebeen in the surveysample, and this problemis especiallysevere among teenagers.Unemployment is a state of mind, and the mere act of asking about it seemsto have a considerableeffect on the answer.Regarding the resultsfor teenagersin this paper,I am workingon the problemwith what I believewill be muchbetter data, so I have not giventhe subjecttoo much attentionhere. I am uncomfortableabout the issues of adjustingfor occupationaldif- ferences,but not quite surewhat to do. The moderntheory of discrimina- 762 Brookings Papers on Economic Activity, 3:1972 tion is reallyone of occupationalcrowding. It does not assumethat people are not paid the marginalproducts, but ratherthat women are crowded into certainkinds of occupationsand are paid their marginalproducts in those occupationseven though they may not be the best occupationsfor them. If this is the case, introducingdummy variablesfor occupation would show substantialeffects. But I would not be sure how to interpret them. I would ratherhave this kind of occupationaleffect show up as a differencebetween men and womenrather than as an occupationaldiffer- ence. But I admitto some uncertaintyabout exactlyhow best to proceed. I did have some resultsstandardizing for occupations.They do not affect the basic conclusionsof the paper; but they do affect the comparison betweenmen and womenthat is reportedhere. As to equilibrium,in my model, basicallyit is a conditionin which no unexploitedopportunities remain through which individualscan make themselvesbetter off. I think the kind of theory I have talked about is robust with respectto some of the imperfectionsin markets that may exist, and that concernAaron Gordon. Holt makes the basic point that the parametersI estimatedapply for 1966and that theycan be expectedto changethrough time. All of the work I have done shouldbe thoughtof as a functionof time, observedat a par- ticularpoint in time. The parametersI reportcharacterize the economy only for the 1966cross-section.

~~GeneralDiscussion~~

Therewas considerablecriticism of the role playedby the unemployed as a laborreserve in Hall's model. CharlesSchultze described the model as an economyin whichthe presenceof unemployedhungry workers reduces quits,making it possibleto have more layoffsand to scheduleproduction better.Through this mechanism,a net increasein productivityis achieved by increasingunemployment. But Hall then removesthis effectby arguing that it is necessaryto pay enough unemploymentcompensation to make sure that workersare not hungry-that, indeed, they are indifferentbe- tween employmentand unemployment.And similarly,Schultze argued that there was a big differencebetween having 3 million unemployedac- tively seekinga job and 3 millionunemployed not scramblingfor a job at all. Hall repliedthat it was not the hunger of unemployedworkers but RobertE. Hall 763 their mere availabilitythat permittedmore efficientpersonnel policies by firmsin a slack labor market.Arthur Okun noted, however,that if unemploymentcompensation were approximately equal to wages,people would takejobs less rapidly,assuming there were any costs to searchingfor a job; on the other hand, he pointed out, despite specificexamples to the con- trary,unemployment compensation currently replaces only a smallfraction of lost wages. From mid-1969to mid-1972,for example,unemployment compensationpayments increased by $3.5 billion (annualrate) as unem- ploymentrose by 2 million people. Hall agreedthat incentiveconsidera- tions impliedthat the level of unemploymentcompensation ought to be a parameterin the model helpingto determinethe socially optimallevel of unemploymentand compensation,but he felt that otherwisehis analysis remainedappropriate. RobertSolow pointed out the uncertaintyabout where equilibrium would occurin Hall'stype of model.Only a smallchange in the slope of the equi- libriumlocus betweenemployees and employerswould lead to largerdif- ferencesin unemploymentrates. If Hall's model is taken literally, zero unemploymentwould be optimalwhen the slope was flat. If therewere a noticeableslope, the marginalproductivity of unemploymentwould be very high, and implausiblyhigh unemploymentrates, along with large unemploymentcompensation payments, would be calledfor. R. J. Gordon thought that Hall's regressioncould support two differentstories. The firstis the one he has told, in whichall workersare homogeneous;in tight labor marketsemployers need a large personneldepartment, which reduces productivity.The other story is that in low-unemploymentecono- mies, the employerscrapes the bottom of the barrel, employingpeople with low ability. This situation reduces the averageproductivity of all workersbut imposesno social cost becausethe productivityof the people hired earlieris not affected.Hall agreedthat his regressionslopes could containsome of this second effect. WilliamPoole questionedthe assumptionof externalitiesto unemployment. He noted that, if unemploymentcompensation did not exist, in competitivelabor markets wages would be higherin occupationsthat have predictableseasonal patterns of unemploymentthan in occupationsthat did not, so that, allowingfor the valueof leisure,annual earnings would be the same. He arguedthat this same effect should operatebetween Hall's high- and low-unemploymentmarkets and would not give rise to ex- ternalities.Hall replied that he did not argue that externalitieshad to 764 Brookings Papers on Economic Activity, 3:1972 exist. He could imaginea labor marketoperating as Poole described,in which the private returnsto remainingunemployed equaled the social returnsbecause the workerwould do all the work of findingthe job. How- ever, the empiricalresults suggest that this is not true. Some evidence exists that suggestsan externalitysuch that employershave a role in the processof findingwork. In its extreme,this theory of unemploymenthas all unemployedworkers sitting around idle exactlyas if they wereidle on the job. Theyare providing a usefulservice by makingthemselves available to employersbut they are not being compensatedfor it. Poole questioned whether,if such externalitiesdo exist, therewould not be more firmspro- vidingtemporary workers to otherfirms that had fluctuatingemployment needs. Hall repliedthat the externalityis global becausethe unemployed workeris functioningas a reserveacross a wide varietyof alternativeem- ployers.Thus thereis no way to internalizeit completelyexcept by collective action acrossthe whole society.That is why the governmenthas to be responsiblefor maintainingthe appropriatelevel of employmentand compensatingunemployed workers just as they would be compensated withinthe firm. R. J. Gordon pointed out that the results for differentdemographic groupsare veryhard to interpretwhen participation rates vary as much as they do. So long as the probabilityof leaving unemploymentincluded probabilitiesfor both droppingout and findingwork, the resultscould not be comparedacross groups. He noted that this might help explain the unusual results for teenagers,since their low unemploymentdurations reflectedperiods spent out of the work force ratherthan unemployed. HymanKaitz noted that differentcities had markedlydifferent employ- mentpatterns, a factthat might influence Hall's intercity comparisons. They differ noticeablyin the participationrates of secondaryworkers in the labor force and in the proportionof workerslooking for part-timework. Sinceall the evidencesuggests that unemploymentis a thresholdphenome- non andthat smalldifferences in circumstancesor habitscan pusha person over the threshold,unemployment measures for differentcities might not be exactlycomparable. Kaitz also noted that annualsurveys of work ex- periencehave shown respondentsto be quite reliable in recallingtheir employment,but less so in recallingunemployment. This may be behind some of the discrepancyin the teenageunemployment results reported by Hall comparedwith the results from the monthly CurrentPopulation Survey.