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Heterogeneous Labor, Minimum Hiring Standards, and Job Vacancies in Public Employment Ronald G. Ehrenberg Cornell University,
[email protected]
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Heterogeneous Labor, Minimum Hiring Standards, and Job Vacancies in Public Employment Abstract
[Excerpt] Although a government employer may be the only employer of a particular class of employees in an area (say firemen), it does not necessarily follow that the government agency possesses monopsony power, as current or potential employees can find employment in alternative occupations in the private sector. Moreover, a model is presented in this paper that indicates that the existence of persistent vacancy rates for a class of employees is compatible with there being a greater number of applicants than there are positions, at a wage rate that is predetermined either through a legislative process or collective bargaining. In particular, if applicants vary in quality, then under certain conditions a rational government employer will choose to employ fewer employees than his assumed predetermined authorized employment level. That is, the employer will choose an optimal equilibrium positive vacancy rate. Keywords
public employment, hiring, heterogeneous labor, monopsony, vacancies Comments
Suggested Citation Ehrenberg, R. G. (1973). Heterogeneous labor, minimum hiring standards, and job vacancies in public employment [Electronic version]. Journal of Political Economy 81(6), 1442-1450. Required Publisher Statement © University of Chicago Press. Reprinted with permission. All rights reserved.
This article is available at DigitalCommons@ILR: http://digitalcommons.ilr.cornell.edu/articles/632
Communications
HeterogeneousLabor,MinimumHiring Standards,and Job Vacancies in
PublicEmployment
Ronald G. Ehrenberg University of Massachusetts, Amherst
I.
Introduction
The existenceof substantial,persistent,and widespreadjob vacancies or shortagesamong certain classes of urban governmentemployeesis well established,with attentionrecentlybeing focusedon shortagesof policemen and registerednurses.1Several authors have attemptedto explain thisphenomenonby postulatingthat local governments can be consideredas monopsonists in the marketsforjob classesforwhich they are large employers.2As is well known,a monopsonystructureimplies thatjob vacancieswill be observed. Althougha governmentemployermay be the only employerof a particularclass of employeesin an area (say firemen),it does not necessarilyfollowthat the government agencypossessesmonopsonypower,as currentor potential employees can find employmentin alternative occupationsin the privatesector.Moreover,a model is presentedin this paper that indicatesthat the existenceof persistent vacancy rates fora class of employeesis compatiblewith therebeing a greaternumberof applicantsthan thereare positions,at a wage rate thatis predetermined eitherthrougha legislativeprocessor collectivebargaining.In particular, if applicantsvary in quality, then under certainconditionsa rational Research was partially supported by a grant from the Manpower Administration, 1> . Departmentof Labor. I am gratefulto Richard Kihlstromand a refereefortheir commentson an earlierversion. I See, for example, Devine (1969, 1970), Altman (1970), Moskow (1970), and Yett (1970). 2 See Devine (1969, 1970), Altman (1970), and Yett (1970). I442
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governmentemployerwill choose to employfeweremployeesthan his assumed predeterminedauthorized employmentlevel. That is, the employerwill choose an optimalequilibriumpositivevacancyrate. As might be expected a priori,the vacancy rate that resultsfrom our model is a functionboth of the "value" of the public serviceto the communityand the cost of public employees.However,contraryto the implicationsofthetextbookmonopsonymodel,it is shownthatincreasing the wage rates of public employeesmay actually increase ratherthan decreaseobservedvacancy rates.Thus, on the theoreticallevel, it is not at all clear thatincreasingthewagesofpublicemployees(relativeto those in theprivatesector)is theappropriateway to reduceurban government manpowershortages. Afterdevelopingthemodelin thenextsection,we applyitin an attempt to explain variationsin vacancy rates across police departmentsfor a sample of over400 United Statescitiesin 1967. Preliminary evidenceon thewage-vacancyrelationship is obtained,and it appearsthatempirically one can also not concludethatincreasingthe wages of public employees would help to reduce manpowershortagesin urban governments. II.
A Model of Equilibrium Job Vacancies3
We assumethateitherthrougha politicalprocessor by someothermeans a governmental agencyis allocated an authorizedemployment level and, abstractingfrom the internalwage structure,informedof the fixed wage rate per employeethat theycan pay. At this exogenouslydeterminedwage, the agencyis assumedto attractmorepotentialapplicants than it has authorizedvacant positions.Suppose the quality level of applicantsvaries,and therecruitment divisionmustaccept or rejecteach applicant as he presentshimself,ratherthan cumulatingall applicants and thenselectingthe best. Given a stochasticdistribution of applicants by quality,one approach thatthedecisionmakerscan followis to choose a setofminimumhiringstandardsor a minimumacceptablequalitylevel, so as to maximizetheexpectednetgain to society.Implicitlyand rationally,thisapproachmaycreatean expectedpositivenumberofvacancies.4 3 The analysispresentedbelow draws heavilyon the methodologyused by Mortensen (1970) and severalpapers in the Phelps (1970) volume. 4 This type of approach seems to be quite similar to that which is oftenfollowedby governmentagencies. For example, considerthe situationin which all applicants who achieve above a specifiedminimumscore on an examinationare placed on an "appointment list" with the order of appointmentsto be based upon test scores. A persistent positivequeue of acceptable applicantscan be thoughtof as negative"vacancies" in this context. Note also that an implication of this approach is that publicized minimum standards may discourage some applicants fromapplying; consequently,the observed numberofapplicantsis nota good measureofthepotentialnumberofapplicantsthatthe agencyfacesat the specifiedwage rate.
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we considerforsimplicitya single-periodmodel in More specifically, of altering whichlabor turnoveris ignored.We also ignorethe possibility recruiting expenditures either by of applicants the quality distribution or by trainingexpendituresonce an applicantis employed.Let W and E the specifiedwage rate anidauthorizedemployment denote,respectively, level givenfromthepoliticalprocess,and let P denotethevalue per unit of the public serviceto society. Applicants are assumed to be heterogeneouswith qi (where 0 < qi ? 1) beingtheserviceflowfromtheithapplicant.Althoughthequality of each applicant can be ascertainedwith certaintyonce he presents officeis a randomvariable himselftheflowofapplicantsto therecruiting q* is designatedas situation, suppose Given this with distribution (q). f the minimumacceptable qualitylevel. That is, all applicantsexceeding this minimumhiring standard will be employed; all others will be rejected.Then the expectedqualityof an accepted applicantis givenby A(q*), where d qqf (q) dq A(q*) = J* f' ff(q) dq
A'(q*) > 0.
and
(1)
Let M be the total numberof applicantsto the agency.This number is assumedto be greaterthanthe numberof available positions,assumed here to be the entireauthorizedemploymentlevel (E). The probability that any one of these applicantsmeets the minimumquality standard q* is then n(q*)
=
(2)
{f(q). Jq*
The number of applicants who satisfythis standard, X, is thus a random variable distributedbinomiallywith expectationn(q*)M. Let B(X, n, M) denote the relevantbinomialprobabilitydensityfunction.5 Then the numberactuallyemployed,Y, is a randomvariablesuch that
X, El
if X < E, if X> E.
(3)
givenby The agency'sexpectedemployment level, N, is therefore N
E
=
0
XB[X, n(q*), M] + E I -
E
20
B[x, n(q*), M]
(4)
An increasein the minimumacceptable quality level, q*, obviously
decreases n(q*) thatany applicantwill meetthestandard. theprobability Cruciallyone can show that a decrease in this probabilityleads to a 5 Where B(X, n, M)
=
X) ( )X(1n
1445
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decrease in the expected employmentlevel.6 Hence, increasesin the minimum acceptable quality level cause expected employmentto decrease: N'(q*) < 0. (5) The expected value of the net gain to societyfromemployingthe particularclass of public employeesis givenby G = PA(q*)N(q*) + VW[E - N(q*)].
(6)
The firstterm representsthe expected value of the public service, theexpectednumberof"qualityunits"ofpublicemployees[A(q*)N(q*)] multipliedby the value per unit. The second termrepresentsthe value to societyoffundsthatcan be utilizedelsewherebecauseall oftheagency's authorizedpositionsare not filled.This is equal to the expectednumber of vacant positions(E - N) multipliedby the wage cost per man and the value to societyof a dollar spentin alternativeuses (V). Note that equation (6) can be rewritten
G = [PA(q*) - WV]N(q*) + WVE.
(6a) in thismanner,it is clear thatthe termin Withtheequation rewritten bracketsrepresentsthe expectednet value to societyof each employee that the agency hires.Consequently,in orderforany employeesto be hired,the termin bracketsmustbe positiveforsome value ofq*. If we assume that an interiorsolutionexists,the first-order necessary conditionto maximizeequation (6a) requiresthatthe minimumacceptable qualitylevel be chosento satisfy [PA(q*) - WV]N'(q*) + PA'(q*)N(q*) = 0.
(7)
of thisconditionis straightforward. The interpretation An increasein the minimumacceptable quality level increasesthe expected quality level, and hence the expectednet value of the serviceflowper man of thoseapplicantsaccepted. On the otherhand, it resultsin a decreasein the expectednumberof acceptable applicants.The agencymustchoose the minimumqualitylevel such that the net impactof thesetwo effects is to maximizethe expectedvalue ofthe net gain to society. Totallydifferentiating equation (7) and makinguse ofthesecond-order necessaryconditionforequation (7) to have yielded a local maximum, we findthat7 as>O. 8W
e < O. aP
a
eV
> O.
(8)
6 A formal proofofthisproposition is availableon request.I am indebtedto Richard Kihlstrom forhelpingto construct theproof. 7 The second-order conditionis thatB(q*) = [PA(q*) - WV]N"(q*) + necessary 2PA'(q*)N'(q*) + PA"(q*)N(q) < 0. Furthermore, aq*/aW= VN'(q*)JB(q*)> 0, aq*IaP = -A(q*)N'(q*)/B(q*) < 0, aq*IaV = WN'(q*)/B(q*)> 0.
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That is, an increasein the wage cost of public employeesor thevalue of fundsin alternativeuses, ceteris paribus,leads to increasesin the minimum acceptable quality level, while an increasein the value per unit of the public serviceleads to a decrease. The rationalefortheseeffects shouldbe obviousand need not be discussedhere. The minimumacceptable quality level is not directlyobservable.In practiceit may consistofa vectorofhiringstandardssuch as educational requirements,physical and mental health characteristics, test scores, and residencerequirements.Note, however,that the agency'sexpected vacancyrate is givenby mR= 1I
(9)
()
Differentiating equation (8) withrespectto each parameterthenyields directly[since N'(q*) < 0]: AVR aW
0
0 VR aPa
0 0
V RV (IR) 0
EV
An increasein thewage costofpublic employeesor thevalue of funds in alternativeuses and a decrease in the value per unit of the public serviceall lead to an increasein the expectedvacancy rate. Crucially, then,increasingthe wages of public employeesto reduce the number ofvacancieswould be a self-defeating policy. If the governmentagencydoes have monopsonypowerin the market forits potentialemployees,thisconclusionmust,of course,be modified. In thecontextofour model,monopsonypowerreflects eitherthenumber of applicantsto the agencyincreasingor the qualitydistribution of the applicantsshifting upward in responseto a ceteris paribusincreasein the agencywage.8 Whilethenetimpactofthesetwoeffects maybe todecrease the expected vacancy rate when the agency wage increases,a priori thereis no reason to conclude that the net impact of theseeffectsplus the previouslydiscussedone would be negative.Hence, until empirical evidenceis presentedon the net relationshipbetweenpublic employees' wagesand vacancyrates,thereshouldbe no presumption thatincreasing thewages of public employeeswould prove to be an effective methodof reducingthe numberofjob vacanciesin public sectoragencies. 8 Throughout,we continueto assume that the wage rate is predeterminedand is not necessarilyequal to that wage which a profit-maximizing monopsonistwould choose. Thus it remainsmeaningfulto speak of increasingthe wage rate. The quality distributionof applicants could shift,withoutthe number of applicants changing,if the increasein high-qualityapplicantsis offsetby a decrease in the number of previouslylow-quality applicants. The latter group may withdrawfrompotential applicant statuswhen theyobserve the higherminimumstandardsthat accompany an increasein the wage rate.
COMMUNICATIONS
III.
1447
Empirical Analysis
This section presentspreliminaryevidence on the public employee wage-vacancyrelationshipas we apply the model of the previoussection in an attemptto explainvariationsin vacancyratesacrosspolice departmentsfora sample of over 400 United States citiesin 1967.9 Table 1 presentsthe resultsof regressions in which two measuresof the departmentvacancy rate were regressedon severalalternativemeasuresof the wage costs of police, a measure of the frequencyof recruitment, and severalsociodemographic variablesdesignedto act as proxyvariablesfor thevalues to thecommunityofpolice servicesand offundsin alternative uses. The sociodemographicvariablesare includedprimarilyas control variables.Since in most cases theywould be expected to have similar impactson the value of police protectionand the value of otherservices (e.g., fireprotection),we cannot a priori predictthe signs that their coefficients shouldhave.'0 Given thecrudenatureofthedata, theresults presentedhereshouldalso be consideredonlysuggestive. Equations (1)-(4) utilizeas a dependentvariable VI, a dichotomous variablethattakeson thevalue ofunityifthepolice departmentis below authorizedstrength, and zero otherwise." Inasmuch as some vacancies are caused bydisequilibrium phenomenaand someare caused bypositions thattheexplanatory beingauthorizedbut notfunded,it is notsurprising power of the estimatedequations is quite low (with R2 less than .1 in all cases). Nevertheless, thecalculatedF-statistics indicatethatstatistically significantrelationshipsexist between the dependentand independent variables.Furthermore, regardlessof whetherwe use as the measureof wage coststhe police patrolmen'sentrancesalary (WI), average annual earningsofpolice department employees(W2), or theanalogousvariables adjusted for city price level differences(W3 and W4), we observe a significantpositiverelationshipbetween the vacancy dummy variable
9 The sample consistsof 419 cities with population greaterthan 25,000, for which police departmentvacancy data were reportedin the 1967 MunicipalYear Book. Over 75 percentof the citiesin the sample reportedthattheirpolice departmentswere below authorized strength,with the mean vacancy rate across all of the cities being over 5 percent. IO The city crime index might appear to be a good proxy for the value of police services. However, this may be simultaneouslydeterminedwith the police vacancy rate, and the accuracy of crimereportingvarieswidely acrosscities. I1 The customarydisclaimersthat: (a) the qualitativenatureofthedependentvariable implies that the disturbanceswill be heteroskedastic, and hence the estimatesare not minimum-variance estimates;(b) the predictedvalues of thedependentvariable may fall outsidethe (0, 1) range; and (c) the disturbancesare nonnormal,hence the significance testsshould be consideredonly as heuristictests,are all applicable here. In addition to the resultspresentbelow, regressions in which all variableswere in linear formwere also estimated,and the resultsdifferonly marginallyfromthosereportedin the paper.
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and police wage costs.' 2 Ceterls paribus,the higher the wage, the greater the probability that the police department will have vacancies. Equations (5)-(8) utilize V2, the actual police department vacancy rate, as the dependent variable. I 3In contrast to the results above, here we observe either a negative relationship between the wage level and vacancy rate (W1 and W3) or an insignificantpositive one (W2 and W4). Given the contradictorynature of the two sets of results,it is clear that one should not claim that the available evidence indicates that increasing police employees' wages would unambiguously reduce police department vacancy rates.14 IV.
Conclusion
This paper has presented an alternative explanation, based upon a stochastic quality distribution of applicants, for the existence of job vacancies or shortages among public employees. Contrary to the implication derived from the textbook monopsony model, increasing the wages of public employees, a priori,would not necessarilyprove to be an effective means of reducing these shortages. Empirical estimationof the relationship between police wages and police department vacancies in 1967 for a sample of 419 United States cities lends support to this conclusion. References
Altman,S. "The Structureof NursingEducation and Its Impact on Supply." In Empirical Studies in Health Economics,edited by H. Klarman. Baltimore:
JohnsHopkinsPress,1970. Devine, E. "Manpower Shortagesin Local GovernmentEmployment."A.E.R. Proc. 59 (May 1969): 538-46. en Analysisof Manpower Shortagesin Local Government. New York: Praeger,
1970.
Ehrenberg, R. The Demand for State and Local Government Employees.Lexington,
Mass.: Heath, 1972.
12 using an The moneywage variables were adjusted forcity price level differences estimatedcity price level variable, developed by the author, that is based upon the Bureau of Labor StatisticsIndexes of Comparative Living Costs for 44 metropolitan and nonmetropolitanareas (U.S., Bureau of Labor Statistics,1970). Details of the variable's constructionare available fromthe author. 13 In addition, equations (5)-(8) were estimatedforthe subsetof cities with positive vacancy rates to avoid potential biases due to the significantnumber of zero vacancy observations(Goldberger 1964, p. 252). The results,however,were virtuallyidentical withthosereportedin the text.Equations (5)-(8) werealso reestimatedusinga dependent variable which assumed that all police departmentvacancies occur among uniformed employees,i.e., an estimateof the vacancy rate among uniformedemployees.Again the resultswere virtuallyidenticalwith thosereported. 14 For brevity,since theyare not our centralconcern,we have omittedall discussion of the nonwage variables. In any case, mostdo not have unambiguous of the coefficients interpretations.
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JOURNAL OF POLITICAL
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Goldberger,A. Econometric New York: Wiley, 1964. Theory. InternationalCityManagersAssociation.1967 MunicipalYearBook.Washington: Internat.CityManagersAssoc., 1967. Mortensen,D. "Job Search, the Duration of Unemploymentand the Phillips Curve." A.E.R. 60 (December 1970): 847-61. Moskow, M., et al. CollectiveBargainingin Public Employment. New York: Random
House, 1970.
Phelps, E., et al. Microeconomic Foundationsof Employment and InflationTheory.New
York: Norton,1970. U.S., Bureau of Census. County and CityData Book-1967. Washington:GovernmentPrintingOffice,1970. U.S., Bureau of Labor Statistics.Handbook ofLaborStatistics-1970.Washington: GovernmentPrintingOffice,1970. Yett, D. "The Chronic 'Shortage' of Nurses: A Public Policy Dilemma." In Studiesin HealthEconomics, edited by H. Klarman. Baltimore:Johns Empirical HopkinsPress,1970.
