stiglitz equilibrium unemployment as discipline

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American Economic Association

Equilibrium Unemployment as a Worker Discipline DeviceAuthor(s): Carl Shapiro and Joseph E. StiglitzSource: The American Economic Review, Vol. 74, No. 3 (Jun., 1984), pp. 433-444Published by: American Economic Association

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Equilibriumnemployments a Worker isciplineDevice

ByCARL SHAPIRO AND JOSEPHE. STIGLITZ*

Involuntarynemploymentppears o bea persistenteature f manymodem abormarkets. he presence f such unemploy-ment aises he uestionfwhywages onotfall oclear abormarkets.n this aperweshowhowthe nformationtructuref em-ployer-employeeelationships,n particularthe nabilityf employerso costlesslyb-serveworkers'n-the-jobffort,anexplaininvoluntary nemployment's an equi-

libriumhenomenon.ndeed,we show hatimperfectonitoringecessitatesnemploy-mentnequilibrium.

The intuitionehind ur results simple.Under theconventionalompetitiveara-digm,nwhich ll workerseceivehemarketwage and there s no unemployment,heworst hat can happen to a workerwhoshirksnthe ob is that e sfired. incehecan mmediatelyerehired,owever,epaysnopenalty or ismisdemeanor.ith mper-fectmonitoringnd full mployment,here-

fore, orkers ill hoose oshirk.To inducetsworkersot oshirk,he irmattemptsopaymore han he goingwage";then,f a workers caught hirkingnd isfired, e willpay a penalty.f it paysonefirmo raise tswage, owever,twill ayallfirmsoraise heir ages.When hey ll raisetheirwages, he ncentiveotto shirkgaindisappears.ut s allfirmsaise heir ages,their emand orabordecreases,nd unem-ploymentesults.With nemployment,venif ll firmsaythe amewages, worker asan incentiveotto shirk. or, fheis fired,

an individualwill not immediatelybtainanotherob. The equilibriumnemploymentrate mustbe sufficientlyargethat t paysworkerso work ather han o take heriskofbeing aught hirking.

The dea that he hreatffiringworkeris a methodf disciplines notnovel.Guil-lermoCalvo (1981) studied staticmodelwhichnvolves quilibriumnemployment.2No previous tudieshave treated eneral

marketquilibriumith ynamics,owever,or studied hewelfare ropertiesf suchunemploymentquilibria.nekey ontribu-tionof thispaper s thatthepunishmentassociated ith eing iredsendogenous,sitdepends n the quilibriumate f unem-ployment. ur analysis husgoes beyondstudies f nformationnd ncentivesithinorganizationssuchas ArmenAlchian ndHaroldDemsetz, 972, ndthemore ecentand growingiteraturen worker-firmela-tionsas a principal-agentroblem) o in-

quireabout the equilibriumonditionsnmarkets ithhesenformationaleatures.Thepaper losestn spirito ours s Steven

Salop 1979) n which irmseduce urnovercostswhen hey aisewages;here he avingsfrom igher ages reon monitoringosts(or, at thesame evelofmonitoring,romincreasedutput ueto ncreasedffort).sinthe aloppaper, he nemploymentn thispaper is definitelynvoluntary,nd notof the standard earch heoryype PeterDiamond, 981, or xample).Workersaveperfectnformationbout ll ob opportuni-ties n ourmodel, ndunemployedorkersstrictlyreferowork twagesessthan heprevailing arketwage ratherhanto re-mainunemployed);hererenovacancies.

*WoodrowWilson chool of Public and Interna-tionalAffairs,nd Departmentf Economics,espec-tively, rincetonniversity,rinceton,J 08540.Wethanketer iamond, eneGrossman,dLazear, teveSalop, nd MikeVeallfor elpfulomments.inancialsupport romheNational cience oundations appre-ciated.

'By involuntarynemploymentemean situationwhere n unemployedorkers willingo work or essthan hewagereceived yanequallykilledmployed

worker,et o ob offersreforthcoming.

2In his 1979 paper,Calvo surveyed variety fmodels funemployment,ncludingishierarchicalirmmodel alsowith tanislawWellisz,979).There re anumberf mportantifferencesetweenhatwork ndthis aper,ncludinghe pecificationf themonitoring

technology.433







434 THE AMERICAN ECONOMIC REVIEW JUNE 1984

The theorywe develophas several m-portantmplications.irst,we showthatunemploymentenefitsand otherwelfarebenefits)ncreasehe quilibriumnemploy-ment ate,butfor reason uite differentfromhat ommonlyutforthi.e., hat ndi-vidualswill have insufficientncentivesosearch orobs). In ourmodel, he xistenceofunemploymentenefitseduces he pen-alty" ssociated ith eing ired. herefore,to induceworkersotto shirk, irmsmustpayhigher ages. hesehigher ages educethedemand orabor.

Second,themodel explainswhy wagesadjust lowlyntheface faggregatehocks.

A decrease n the demandfor aborwillultimatelyausea lowerwage nda higherlevel of unemployment.n the transition,however,hewage decreasewillmatch hegrowthn theunemploymentool, whichmaybe a sluggishrocess.

Third,we show that the market qui-libriumwhich mergess not, n general,Paretooptimal,wherewe have takenex-plicitlynto ccounthe osts ssociated ithmonitoring.here xist,n otherwords,n-terventionsn themarkethatmake veryone

better ff.n particular, e show hat hereare circumstancesn whichwagesubsidiesare desirable. here re also circumstanceswhere hegovernmenthould ntervenenthemarkety supplyingnemploymentn-surance,ven f all firmsrationally)o not.A (small) urnoverax s desirable, ecausehigh turnoverncreases he flow of jobvacancies, nd hence the flowout of theunemploymentool, making he threat ffiringess evere.

Additionally,urtheory rovides redic-tions about the characteristicsf labormarkets hich ause thenatural ate i.e.,equilibriumevel)of unemploymento berelativelyigh:high ates f abor urnover,highmonitoringosts,highdiscount atesforworkers,ignificantossibilitiesorwork-ers ovaryheir ffortnputs,rhigh osts oemployerssuch s brokenmachinery)romshirking.

Finally, ur heoryhows owwagedistri-butionsfordentical orkers)anpersistn

equilibrium.irmswhich ind hirkingar-ticularlyostlywill offer igher ages han

other irmso. The dual rolewagesplaybyallocatingabor ndprovidingncentivesoremployee ffortllowswage dispersion opersist.

Although e havefocused ur nalysis nthe abor market,t shouldbe clearthatsimilarnalysis ould pply oothermarkets(for xample, roduct rcreditmarkets)swell.Thispaper anbe viewed s ananalysisof a simplifiedeneral quilibriumodel fan economyn which here re importantprincipal-agentincentive)roblems,ndinwhich the equilibrium ntails quantity con-straintsjob rationing). s in all suchprob-lems, t s importantoidentifyhat s ob-

servable,nd, basedonwhat s observable,what are the set of feasible ontractualarrangementsetweenhepartieso the on-tract.Undercertain ircumstances,or n-stance,workersmight ssue performancebonds ndthismight lleviate heproblemswithwhichwe areconcernedn thispaper.In Section II wediscuss heroleofalterna-tive ncentiveevices.

In thehighlyimplified odel ponwhichwe focushere, ll workersreidentical,llfirmsre dentical,ndthus,nequilibrium,

all paythe amewage.Theassumptionhatall workersre the same s important,e-cause it implies hatbeingfired arries ostigma thenextpotentialmployernowsthat heworkersnomore mmoralhan nyotherworker; e onlynfershat he irm orwhich heworker orkedmusthavepaid awage ufficientlyow that tpaidtheworkerto shirk).We have made thisassumptionbecausewewished oconstructhe implestpossiblemodel ocussingimplyn ncentiveeffects,nwhichdverse electiononsidera-tionsplayno role. n a sequel,wehopetoexplore he mportantnteractionsetweenthetwo fundamentalnformationroblemsof dverse electionndmoral azard.3

Theassumptionhat llfirmsrethe ameis not ritical or he xistencefequilibriumunemployment.irm heterogeneityill,however,ead to a wagedistribution.f the

3Otherstudies avefocusednquantityonstraints(rationing) ith dverse-selectionroblems.ee Stiglitz

(1976), CharlesWilson1980),AndrewWeiss 1980),andStiglitzndWeiss 1981).







VOL. 74 NO. 3 SHAPIRO AND STIGLITZ: EQUILIBRIUM UNEMPLOYMENT 435

damagethata particularirmncurs s aresult f a worker ot performingp tostandards larger, he firmwill have an

incentiveo pay theworker higher age.Similarly,fthe ost fmonitoringdetectingshirking)or firms large, hatfirmwillalso paya higher age.Thus, venthoughworkersre all identical, orkersordiffer-entfirms illreceive ifferentages.Thereis considerablevidencehat,n fact, iffer-entfirms o pay differentages o workerswho ppear o be quite imilarfor xample,more capital intensive irms ay higherwages).The theorywe develophere mayprovide artof the xplanationf this he-

nomenon.In Section,wepresenthe asicmodelnwhichworkers re riskneutral. uit ratesand monitoringntensitiesre exogenous.welfarenalysis f theunemploymentqui-libriums provided.n Section I, we com-ment n extensionsf the nalysiso situa-tionswheremonitoringntensitiesnd quitrates reendogenous,nd where orkersrerisk verse. ectionII compares heroleofunemployments an incentive evicewithothermethodsfenforcingisciplinen the

laborforce.

I. TheBasicModel

Inthis ection eformulatesimplemodelwhich aptures he ncentiveoleofunem-ployments describedbove. xtensionsndmodificationsf this asicmodel reconsid-ered nsubsequentections.

A. Workers

There rea fixed umber, , of denticalworkers,ll of whomdislike uttingortheffort,utenjoy onsumingoods.We writeanindividual'snstantaneoustilityunctionas U(w, ),wherewis thewage eceivednde s the evel feffortntheob. Forsimplic-ity,we shall assume heutilityunctionsseparable;nitially,e shall lsoassume hatworkersreriskneutral.With uitable or-malizations,e can thereforeewritetilityas U = w- e. Again, forsimplicity, e as-

sume hatworkersanprovideither inimalefforte = 0),or somefixed ositiveevel f

e > O.' Whena workers unemployed,ereceives nemploymentenefitsf -w ande = 0).

Each workers inoneoftwo tates t anypointin time:employed r unemployed.There s a probability perunit ime hatworker illbe separatedrom is ob due torelocation,tc.,whichwillbe taken s exog-enous. xogenouseparationsause workerto enter he unemploymentool. Workersmaximize he expected resent iscountedvalue of utility ith discountate r> O.'The models set n continuousime.

B. TheEffortecisionof Worker

Theonly hoiceworkers akesthe elec-tion of an effortevel,whichs a discretechoicebyassumption.f a workererformsat thecustomaryevelof effortorhis ob,that s, ifhe does notshirk, e receiveswageofwandwill etain is ob until xog-enousfactorsausea separationo occur.fhe shirks,here s someprobability (dis-cussed elow), erunit ime,hathewillbecaught.6f he is caughthirkingewillbefired,7ndforced o enterhe nemployment

pool.Theprobabilityerunit ime f cquir-ing a job while n the unemploymentool(whichwe call the ob acquisitionate, nendogenousariablealculatedelow) eter-mines he xpectedengthftheunemploy-ment pellhe must ace.While nemployedhe receives nemploymentompensationf-w also discussedbelow).

4Including fforts a continuousariable ould otchange he ualitativeesults.

5That s,we assumendividualsre nfinitelyived,and havea purerateof timepreferencef r. Theymaximize

W= EJ u(w(t),e(t))exp(- rt)dt,

wherewe have mplicitlyssumedhatndividualsanneitherorrowor end.Allowingn exponentialeathratewould ot lter he tructurefthemodel; eitherwould orrowingn the isk-neutralase.

6Fornow we takeq as exogenous;ater t willbeendogenous. he assumptionf a Poissondetectiontechnology,ikea number f the other ssumptionsemployedn theanalysis,s madeto ensure hat he

model as a simpletationarytructure.7Thiswill e firm'sptimalolicyn equilibrium.







436 THE AMERICAN ECONOMIC RE VIEW JUNE 1984

The workerelects n effortevel omaxi-mize his discounted tility tream.Thisinvolvesomparisonfthe tilityromhirk-ing with he utility romnot shirking,owhichwe now turn.We defineVE, s theexpected ifetime tility f an employedshirker,E as the xpectedifetimetilityfan employed onshirker,nd VuKs theexpected ifetime tility f an unemployedindividual. he fundamentalssetequationfor shirkers given y

(l) rVEs= W + ( b+ q)(V,,- VEs),

while or nonshirker,t s

(2) rVEN=w-e + b(Vu-VV

Each of these quationss of theform in-terest ate imes sset alue quals low ene-fitsdividends) lus expected apitalgains(or losses)."8Equations 1) and (2) can besolved orVESndVEN:

(3) VES=w+(b+q)VJK

(4) N= (w-e)+bVU(4) VE r+b

The worker ill hoosenot o shirkfandonly f VEN VE.We call this heno-shirkingcondition NSC), which,using (3) and (4),can bewrittens

(5) w>rVu+(r+b+q)e/q=aW.

Alternatively,he NSC also takes heformq(VEs V") e. This highlightshe basic im-

plicationf heNSC: unlessheres a penaltyassociated ith eing nemployed,veryonewill shirk.n otherwords,f an individualcould mmediatelybtain mploymentfterbeing fired,V"K VEs, nd the NSC couldnever e satisfied.

Equation5) has several aturalmplica-tions. f thefirm ays a sufficientlyighwage, hen heworkers illnotshirk. hecriticalwage,w', s higher

(a) thehigherhe equiredfforte),(b) thehigherhe xpectedtilityssoci-

atedwith eing nemployedV,),(c) the ower heprobabilityf being

detectedhirkingq),

(d) thehigherherateof interesti.e.,therelativelyoreweights attached o theshort-runainsfrom hirkinguntil ne iscaught)omparedo the ossesncurredhenone seventuallyaught),

(e) thehigherhe xogenousuitrateb(if one is going o have to leave thefirmanyway,nemights well heat nthe irm).

C. Employers

There reM identical irms,=1,..., M.

Each firm as a productionunction i=f(Li), generatingn aggregate roductionfunctionf Q = F(L).9 HereLi is firm'seffectiveaborforce;we assume workercontributesneunit f effectiveabor f hedoes not shirk.Otherwise e contributesnothingthis s merelyor implicity).here-fore irmsompetenofferingage ackages,subject o theconstrainthat heirworkerschoosenotto shirk.We assume hatF'(N)> e,that s,fullmploymentsefficient.The monitoringechnologyq) is exoge-

nous. Monitoringhoices yemployersreanalyzedn the ollowingection.Weassume

8Aderivationollows:aking u sgivennd ookingat a short imenterval0, ]wehave

VE= wt (1- rt)[bt, + (1- bt)VE],

since heresprobabilitytof eavingheobduringheinterval0, t] and since e 1- rt.SolvingforVE, wehave

VE wt (1- rt) btVu [1 - (1-rt)(l- bt)] .

Takingimitss t 0 gives 1). Equation2) can bederivedimilarly.

9Thats,

F(L) maxEf (Li)(Li I

such that Li = L. Thisassumes hatnmarketqui-librium,abor sefficientlyllocated,s it will e n thebasicmodel f this ection. he modificationsequiredformore eneralases,when ifferentirmsace iffer-

ent critical o-shirkingages,wv, r havedifferenttechnologies,re traightforward.







VOL. 74 NO.3 SHAPIRO AND STIGLITZ: EQUILIBRIUM UNEMPLOYMENT 437

thatother actorsforexample, xogenousnoise or the absenceof employee pecificoutputmeasures)revent onitoringf ffort

via observingutput.A firm's agepackage onsists f a wage,w, and a level of unemploymentenefits,-w.10achfirmindstoptimalofirehirkers,since theonly otherpunishment, wagereduction, ouldsimply nduce the disci-plinedworkero shirkgain.

It is notdifficultoestablishhat ll firmsofferhe mallestnemploymentenefitsl-lowed say,by law).11 his follows irectlyfrom heNSC, equation5). An individualfirm as no incentiveo set Tv ny higher

thannecessary.n increasen -w aisesVuand hence equires higherw tomeet heNSC. Therefore,ncreasesn-wost hefirmboth irectlyhighernemploymentenefits)and ndirectlyhigher ages). ince hefirmhas no difficultyttractingabor in equi-librium),t sets w s small s possible. encewe can interpretwn whatfollowss theminimumegal evel,whichs offeredon-sistentlyy ll firms.

Having fferedheminimumllowablew,an individual irm ays wages ufficientoinduce employeeeffort,hat is, w= iw tomeet heNSC. Thefirm'sabordemand sgivenby equating he marginal roduct flabor to thecost of hiringn additionalemployee. his costconsists fwagesandfuturenemploymentenefits.or TV 0,12the abordemand s given imply y f'(Li)= w, with ggregateabordemand fF'(L)= W.

D. Market quilibrium

Wenow turn o thedeterminationf the

equilibriumage nd employmentevels. etus firstndicate euristicallyhe actors hichdeterminehe quilibriumage evel.

If wages revery igh,workers illvaluetheirobs for wo easons:a) thehighwagesthemselves,nd b) the orrespondinglyowlevel femploymentdueto owdemand orlabor t highwages)whichmpliesong pellsofunemploymentnthe vent f osing ne'sjob. In such situationmployersillfindtheycan reducewageswithout emptingworkerso shirk.

Conversely,f the wage is quite low,workers illbe tempted o shirk or tworeasons: a) lowwages mply hatworkingsonlymoderatelyreferredo unemployment,and b)highmploymentevelsat owwagesthere s a largedemandfor abor) implyunemploymentpells ueto being ired illbe brief.n such situation irms illraisetheir ages o satisfyheNSC.

Equilibriumccurswhen achfirm,akingas givenhewages ndemploymentevels tother irms,indst optimal o offerhe oingwagerather han differentage.The keymarket ariablewhich eterminesndividualfirmehaviorsVu, he xpected tilityfanunemployed orker.We turnnow to thecalculationfthe quilibriumu.13

Theasset quation orVu,nalogouso 1)and 2), sgiven y

(6) rVu=W+a(VE-VV),

where is theob acquisitionate ndVE istheexpected tilityfan employed orker

(which qualsVEj n equilibrium). e cannow solve 4) and 6) simultaneouslyorVEandVu oyield

(7) rVE= (w e)(a+br)+b

(w - e)a + i(b + r)(8) rVu a + b + r

l'More complexmploymentontracts,or xample,wages ising ith eniority,rediscussednSectionII.With our assumptionsf stationaritynd identicalworkers,mployersannot mproven the implem-ploymentrovisionsonsideredere.

"We are mplicitlyssuminghat he firmannotoffer only oworkers ho uit. his s sobecausehefirman always ire worker howishes o quit, nd twould e optimal or he irmo do so.

12For w 0 theexpected ost of a workers thewage ostfor he xpectedmploymenteriod f 1/b,followed y w for heexpected eriod funemploy-ment, /a. Thisgeneratesabor emand iven y

frLi = w +b(-

+)/ .

13Wehave lreadyhownhat ll firmsfferhe ameemploymentenefitsw, o Vu s ndeed single umber,i.e., n unemployederson'stilitys ndependentfhispreviousmployer.








SubstitutingheexpressionorVu i.e., 8))intothe NSC (5) yields heaggregate SC

(9) w>-w+e+e(a+b+r)/q.Notice hat he ritical agefornonshirkingisgreater:a) the mallerhedetectionrob-ability ; (b) the arger he ffort; (c) thehigher hequitrateb; (d) thehigherheinterestater; (e) thehigher heunemploy-mentbenefitTv); and (f) thehigher heflows utofunemployment.

We commentedbove on thefirst ourproperties;he ast wo re lsounsuiprising.If theunemploymentenefits high, he

expectedtilityfanunemployedndividualishigh, ndthereforehe unishmentssoci-ated with eingunemployeds low. To in-duce ndividualsot toshirk, higher agemustbe paid. If a is theprobabilityfobtainingjob perunit ftime, /a is theexpectedurationfbeing nemployed.helonger heduration,hegreaterhepunish-ment ssociated ith eing nemployed,ndhence he mallerhewage hat srequiredoinduce onshirking.

The rate a itself an be related omore

fundamentalarametersf themodel,n asteady-statequilibrium.n steady tate heflow ntohe nemploymentool s bL whereL is aggregatemployment.he flow ut sa(N - L) (per unit time)whereN is thetotal abor upply. hesemust e equal, obL = a(N- L), or

(10) a = bL/(N- L).

Substitutingora into 9), the aggregateNSC, wehave

(11) w?e+ v+ (( bNL) +r)

=e +w + (e/q)(b/u + r)-w,

where u= (N - L)/N, the unemploymentrate.Thisconstraint,he ggregateSC, isgraphedn Figure . It is immediatelyvi-dent that no shirkings inconsistentith ull

employment.f L = N, a = + x, so anyshirking orkerwould mmediatelye re-

WAGESAw

NO HIRKINGEGION

Wv+e+qbrSCbrq ~~~~~NSCII1)

w+ee

EMPLOYMENTN L

FIGURE 1. THE AGGREGATENO-SHIRKING CONSTRAINT

hired.Knowinghis,workers ill hoose o

shirk.The equilibrium age and employmentlevel re now easy to identify.ach (small)firm, aking he aggregateob acquisitionrate a as given, inds hat t must ffer tleast the wage w'. The firm'sdemand forlabor hen eterminesowmanyworkersrehired t thewage.Equilibriumccurswherethe ggregateemand or abor ntersectsheaggregate SC. For -w 0, equilibriumc-curswhen

F'(L) = e + (e/q)(bN/(N - L)+ r).

Theequilibriums depictednFigure .14 tis importantounderstandheforces hichcause E to be an equilibrium.romthefirm's ointof view, here s no point nraisingwages sinceworkers re providingeffortnd thefirman getall the abor twants t w*.Lowering ages, n theotherhand,wouldnduce hirkingnd be a losingidea."5

Fromtheworker's oint f view,unem-ployments involuntary:hosewithout obswould e happy o work tw*or ower, utcannotmake credibleromiseottoshirkatsuchwages.

'4Aggregateabor emands F'(L) onlywhenw 0(see fn. 2).

15Wehaveassumed hatoutput s zerowhen nindividualhirks, utwe need onlyassumethata

shirker'sutputs sufficientlyow thathiringhirkingworkerss unprofitable.








AGGREGATE

w AGGREGATELABOR DEMAND /

ww

W~~~~~~~~~~~~~~~~~ I ~~~~~F'(L

l Iv+e -

___ __ ___ __ ___ _ _ i - L EMPLOYMENTN L

FIGURE 2. EQUILIBRIUM UNEMPLOYMENT

Notice hat he ype funemploymentehave haracterizedere s very ifferentromsearch nemployment.ere, ll workersndall firmsre dentical.heresperfectnfor-mation bout ob availability.here s adifferentnformationroblem: irmsre as-sumedquite easonably,nourview)nottobe able to monitor he activities f theiremployeesostlesslyndperfectly.

E. Simple omparativetatics

Theeffectfchangingarious arametersofthe roblem ay asily edetermined.snoted bove, ncreasinghe quitrate b, ordecreasing hemonitoringntensity, de-creasesncentiveso exert ffort.herefore,thesehangesequiren ncreasenthewagenecessaryat each levelofemployment)oinduce ndividualsowork, hat s, theyhifttheNSC curve pwardssee Figure ). Onthe ther and, heyeave hedemand urvefor aborunchanged,nd hence theequi-libriumevel f

unemploymentnd the qui-librium age rebothncreased.ncreasesnunemploymentenefits ave thesame m-pactontheNSC curve,uttheylsoreducelabordemand s workersecomemore x-pensive,o theyauseunemploymentorisefor wo easons.

Inward hiftsn the abordemand ched-ule createmoreunemployment.ue to theNSC, wagescannotfall enough o com-pensate or hedecreasedabordemand. hetransitiono thehighernemploymentqui-

libriumwill not be immediate: age de-creases y ndividual irms ill nly ecome

NSC'A NSC1

WAGES /w

l ro/ l

F'(L) I

'___________________

'- - EMPLOYMENTL' L N L

FIGURE. COMPARATIVETATICS

Note:A decreasen themonitoringntensity, or an

increasen thequitrate b, leads to higher ages ndmore nemployment

attractives theunemploymentool grows.This provides n explanationf wage slug-gishness.

F. Welfare nalysis

In this ection e study hewelfare rop-erties ftheunemploymentquilibrium. edemonstratehat heequilibriums notingeneralParetooptimal,when nformationcosts reexplicitlyccounted or.

Webeginwith he ase where heownersof thefirmsre the ame ndividualss theworkers,nd ownerships equallydistrib-uted mongN workers.hecentral lanningproblems to maximize he xpected tilityof therepresentativeorker ubject o theNSC andthe esourceonstraint:

(12) max (w-e)L + w(N-L)w,w,L

subject o w> e + w+ (e/q)((bN

/(N-L)) + r) (NSC)

subject o wL + w(N- L) < F(L)

(Feasibility)

subjecto w O.








Sinceworkersrerisk eutralt s easy ocheck'6 hat heoptimumnvolves w t theminimumllowable evel,which s assumed

to be 0. The reason s that ncreasesn -wtightenheNSC, so allpaymentshould emade nthe ormfwrather .

Setting w 0, theproblem implifieso

(12') max(w-e)Lw, L

subject o w> e + (e/q)((bN/(N-L)) + r);

and wL<F(L).

The set ofpointswhich atisfy he con-straintss shaded n Figure4. Iso-utilitycurves rerectangularyperboles.o long sF'(L) > e, these re steeperhan he verageproductocus,so the optimum ccursatpointA where heNSC intersectshe urvew= F(L)/L, that s,wherewages qual theaverage roduct f labor. n contrast,hemarketquilibriumccurs t E where hemarginalroduct f abor urve,w= F'(L),intersectsheNSC (Figure ). Observe hatin the case of constant eturns o scale,F'(L)L = F(L), so the equilibrium s opti-mal.

Wages houldbe subsidized, singwhat-ever pure)profitsan be taxedaway.Anequivalent ay o view he ocial ptimumsa tax on unemploymento reduce hirkingincentives;hewealth onstraintn theun-

INDIFFERENCECURVES NSC

WAGES w=APLw wAPL

F(L)/L

L+e

F'L)

EMPLOYMENTN L

FIGURE 4. SOCIAL OPTIMUMATA

employedequireshatv> 0, orequivalentlythat rofitsfteraxes enonnegative.17heoptimumanbeachievedytaxingway llprofitsnd financing wagesubsidy f T,

shown n Figure4. The "natural" unemploy-ment ate s toohigh.

In thecase where he workersnd theownersredistinctndividuals,he axpolicydescribed bove wouldreduceprofits,n-creasewages, ndincreasemploymentev-els. While t wouldncreaseggregateutput(netofeffortosts), uch taxpolicywouldnotconstitute Pareto mprovement,inceprofits ouldfall.Forthis eason,he qui-libriums Pareto ptimal n this ase,eventhought fails to maximize et nationalproduct.We thushave theunusualresultthat hePareto ptimalityfthe quilibriumdepends pon he istributionfwealth. hestandardeparationetween fficiencyndincome istributionoes notcarry vertothismodel.

It shouldnotbe surprisinghat heequi-

libriumevelofunemployments ingeneralinefficient.ach firm ends o employ oofewworkers,ince tseestheprivateostofan additional orker s w,while he ocialcost s only , which s lower.On theotherhand,when firm ires nemoreworker,tfails o take ccountf the ffecthis as onVu byreducing hesize of theunemploy-ment ool).This ffect,negativexternalityimposed y onefirm n otherss it raisests

16Formally,

Y2= (w- e)L+ -w(N- L)

+ A[w - e - -w (e/q)(bN/(N - 1)+ r)]

+ It F(L)- wL -vw(N - L)].

Differentiatingith espectfwand-w ields

Y,=L+A-iL?0 and=O if w>O.

.-=(N-L)-A-[L(N-L)?O and=O if -w>O.

Weknoww> Oby heNSC, so ' =O, i.e.,L(1- p)+A= 0. Therefore,inceA> 0, t > 1. But then2'w = (N

- L)(1- g)- A< 0. This implies hatW 0.

17The onstraintw 0 canbe rewritten,sing he

resourceonstraint,s F(L)- wL 0 , .e., v ? 0.








levelof employment,ends o lead to over-employment.n the implemodel resentedso far, heformerffectominates,nd the

natural evelof unemployments toohigh.Thiswillnotbe truen more eneralmodels,however,s we shall ee below.

II. Extensions

In this ection e describe ow he esultsderivedbove remodifiedrextended henwe relax some of the simplifyingssump-tions.We discuss hree xtensionsn tum:endogenousmonitoring,isk version,ndendogenousumover.etailed erivationsf

theclaimsmadebelow reavailablen ourearlier orkingaper.

A. EndogenousMonitoring

When mployeesan select hemonitoringintensity, they antrade ff tricter oni-toringata cost)with igher ages smeth-ods ofworker iscipline.n general, irms'monitoringntensities illnot be optimal,due to theextemalitiesetween irms e-scribedbove. ngeneral,t snotpossible oascertain hetherhe quilibriumntails oomuch rtoo ittle mployment.n the ase ofconstantretumsto scale (F(L) = L), how-everwhiched toefficiencyith xogenousmonitoring),he ompetitivequilibriumn-volves oo muchmonitoringnd toomuchemployment.

The results notas unintuitives it firstseems: achfirm elieves hat heonly n-strumentt itscontrolor educinghirkingis to ncreasemonitoring.heres,however,

a second nstrument:y reducingmploy-ment, orkersre nduced ot o shirk. hisenables ocietyosaveresourcesn monitor-ing (supervision).hese gainsmorethanoffsethe ossfromhe educedmployment.

It s straightforwardo see how his olicymay e mplemented.ffirmsan be nducedto reduce heirmonitoring,elfare illbeincreased. ence a tax on monitoring,iththeproceeds istributed,ay, s a lump umtransfero firms, ill eave theno-shirkingconstraint/national-resourceonstraintn-

affected,utwill educemonitoring.

B. RiskAversion

With isk eutrality,he ptimumnd the

marketboth involve w= 0. Clearly w =0cannot e optimalf workersrehighly iskaverse nd may e separatedromheirobsforexogenouseasons.Yet themarket l-waysprovideswv 0 (or the egal minimum).The proof bovethatwP 0 carries ver othe aseof risk-averseorkers.

When equilibriumnvolvesunemploy-ment,firms ave no difficultyttractingworkersnd hence ffer = 0, sincew> 0merely educes he penalty f beingfired.WhenotherfirmsfferwP 0, this rgument

is onlystrengthened:nemployed orkersare even asier o attract.t is strikinghatthemarket rovides o unemploymenten-efitsvenwhenworkersrehighlyiskverse.Clearlyhe ocial ptimumnvolves > 0 ifrisk versionsgreat nough. hismaypro-vide a justificationormandatory inimumbenefitevels.

C. Endogenous urnover

In general firm's mploymentackagewill nfluencehe urnoverate t experiencesamongts mployees.ince he umoveratebaffectsherate fhiringutof theunem-ploymentool, nd henceVu,t affectstherfirms'o-shirkingonstraints.ecause f hisexternality,irms' hoicesof employmentpackageswillnot ngeneraleoptimal.histype fextemalitys similaro searchxter-nalitiesnwhich,or xample,nesearcher'sexpected tilityepends n the numberrmix f searchersemainingnthemarket.n

the urrent odel, olicieswhich iscouragelabor tumoverre attractives theymakeunemploymentore ostlyo shirkers.

III. Alternativeethods or heEnforcementfDiscipline

Thispaperhas exploredparticular ech-anism or he nforcementfdiscipline:n-dividuals ho redetectedhirkingrefired,and in equilibriumhe evel of unemploy-mentssufficientlyargehathis hreaterves

as an effectiveeterrento shirking.he








question aturallyriseswhetherhere realtemative,ess costly, r more ffectiveis-ciplinemechanisms.

A. Performanceonds

The most irectmechanismy which is-ciplinemight e enforceds throughheposting y workers f performanceonds.Underthis rrangementhe workerwouldforfeithe bond if thefirm etected imshirking.ne problem ith his olutionsthatworkers aynothave hewealthopostbond."8 morefundamentalrobleih iththismechanisms that hefirm ouldhave

anincentiveo claim hat heworkerhirkedso that t couldappropriatehe bond.As-suming,uiterealistically,hat hird artiescannotasily bserve orkers'ffortindeed,it is usuallymore costlyfor outsidersoobserve orkernputs han or he mployerto do so),theres nosimple ay o disciplinethe irm romhis ype fopportunism.

Havingrecognizedhisbasic point,t iseasyto seethat numberfother lausiblesolutions ace he amedifficulty.or exam-ple, considern employmentackagewhich

rewardsffortyraising ages ver ime orworkers ho havenot been found hirking.This s n fact quivalento givingheworkera levelwage tream,uttaking ackpart fhis earlier ayments s a bond,which sretumedohimater. herefore,y he boveargument,hefirm illhave n incentiveofireheworker hen e s about o enter he"payoff' period n whichhe recovers isbond.This is theequivalento thefirm'ssimplyppropriatinghebond. t is optimalfor the firm o

replace expensive eniorworkersy nexpensiveunior nes."9

Clearlyhefirm'seputations anhonestemployeran partiallyolvethisproblem;the mployers mplicitlyenalized or iring

a workerfthis endersim ess ttractiveoprospectivemployees. et thisreputationmechanismmaynot workespeciallywell,since prospectivemployeesftendo notknow the employer'secord,nd previousdismissals ayhavebeen egitimateit s notpossibleforprospectivemployeeso dis-tinguishegitimaterom nfair arlier is-missals,fthey re aware fthemt all). Ifthereputation echanisms less thanper-fect,twillbe augmentedytheunemploy-mentmechanism.

B. OtherCostsofDismissal

Unemploymentnthemodel bove ervesthe role of imposing osts on dismissedworkers.fother osts f dismissalre suffi-ciently igh,workers ayhave n incentiveto exert ffortvenunder onditionsf fullemployment.xamplesof such costs aresearch osts,moving xpenses,ossof ob-specific uman apital, tc. nmarkets herethese osts re substantial,heroleofequi-

librium nemployments substantiallyi-minished.heeffectehave dentifiedbovewill stillbe present, owever, heneffortlevels are continuousariables: ach firmwill till ind hat mployeefforts increas-ingwithwages, o wageswillbe bid upsomewhatbove heir ull-employmentevel.The theoryredictshatnvoluntaryas wellas frictional) nemploymentateswill behigheror lasses fworkers hohave owerjob switchingosts.

'8This s especiallyrue f detections difficultlowq) so thatn effectiveondmust e quite arge. ven fworkersould borrow o post the bond, o long asbankruptcys possible, he ncentivesor voiding e-faultingn thebond renotdifferentromhe ncen-tives o avoidbeing aught hirkingythefirmn theabsence fa bond.Note once gain he mportancefthewealthistributionndetermininghenature f theequilibrium.f all ndividualsnheritlarge mountfwealth,hen hey ould ost onds.

'91ncompetitivequilibrium,he veragediscount-ed) valueof thewage must e equal to the average

(discounted)alue f hemarginalroductf heworker.If theres a bonusfornot hirking,nitiallyhewagemust e below he alue f hemarginalroduct.t s asiftheworker ere osting bond the differencee-tween ismarginalroductnd thewage), nd as suchthis chemes susceptibleo preciselyhe ameobjec-tions aised gainst osting erformanceondings.heemployer as an incentiveo appropriatehe bond.Sinceworkers now his, hiss not viable ncentivescheme. or a finetudynwhichirms'eputationsre

assumed o functiono as to make his cheme iable,see Edward azear 1981).







VOL. 74 NO.3 SHAPIRO AND STIGLITZ: EQUILIBRIUM UNEMPLOYMENT 443

C. Heterogeneousorkers

The strongestssumptione havemade s

thatof identicalworkers. his assumptionruled utthepossibilityhat iring workerwould arryny tigma. uch stigma ouldserve s a discipline evice, venwithfullemployment.20n reality, f course, m-ployers o makewageoffershich re con-tingentn employmentistory.uchpoliciesmake sense when firms ace problems fadverseelection.

We recognizehatworkers'oncern boutprotectingheir eputationss effective,ili-gentworkers ayprovideneffectivencen-

tive or disciplinedaborforce.2' hapiro'searlier1983) nalysis f reputationn prod-uctmarketshowed, owever,hat or epu-tations o be an effectivencentive evice,theremust e a cost o the ossofreputation.It is our conjecture hat,underplausibleconditions,venwhenreputationsre im-portant,quilibriumill ntail omeuseofunemployments a disciplineevice or helabor orce,t east orower-qualityorkers.An mportantine fresearchs the tudyflabormarketsn which dverse elections

well as moralhazardproblemsre present.In this ontext,urmodel hould rovideusefulcomplemento the more commonstudies f dverseelectionn abormarkets.

IV.Conclusions

Thispaperhasexploredhe ole f unem-ployment,r ob rationing,s an incentivedevice.We have rguedhatwhent scostlyto monitor ndividuals,ompetitivequi-

librium illbe characterizedy unemploy-ment, ut hat henaturalate funemploy-ment o engenderedillnot n general eoptimal.Wehave dentifiedeveral orces t

work, omewhich end o make hemarketequilibriumnemploymentate oohigh,ndothers hich end omake t too small. ach

firm ails to take ntoaccount heconse-quences f tsactions n the evelof moni-toring nd wageswhich therfirmsmustundertaken orderto avoid shirking yworkers.Although hese externalitiesremuch ikepecuniaryxternalities,hey reimportant,ven n economies ith largenumberffirms.22sa result, ehave rguedthat heres scopefor overnmentnterven-tions,both withrespect o unemploymentbenefitsnd taxes r subsidiesnmonitoringand labor turnover, hichcan (if ap-

propriately esigned) ead to Pareto m-provements.The type f unemploymenttudied ere s

not the only or eventhe most mportantsource funemploymentnpractice.Webe-lieve t s,however,significantactorntheobservedevelofunemployment,speciallyin lower-paid,ower-skilled,lue-collar c-cupations.t maywell be more mportantthan frictionalr searchunemploymentnmanyabormarkets.

20See ruceGreenwald1979)for simplemodel nwhich hosewho re n the used abormarket"re nfacta lower uality han those n the "new" labormarket.

21Thisuggestsnce again hat urresultsmaybemostsignificantn labor markets or ower-qualityworkers:n suchmarketsmploymentistories reutilizedess nd workerslreadyabeled s below ver-

age inquality ave ess to lose fromeing abeled ssuch.

22For a moregeneral iscussion f pecuniary,rmore eneralmarket ediatedxternalities,ithppli-cations oeconomies ith mportantdverse electionandmoral azard roblems,eeGreenwaldnd Stiglitz(1982).

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