Information and Human Capital Management

HeskiBar-Isaacy

IanJewittzDecember2008

ClareLeaverx

Abstract

Employeesdi¤erbothintermsofgeneralhumancapitaland…rm-speci…chu-mancapital(ormatchwithaparticular…rm).Currentemployerstypicallyhaveaccesstomoreinformationabouttheiremployeesthanrivalemployers.Thisin-formationasymmetrya¤ectsthedistributionofwages,turnoverrates,pro…ts,andtheextentofallocativeine¢ciencyinthelabourmarket.Webeginbyexploringtheimplicationsofdi¤erentinformationstructuresandhighlightthatinformationa¤ectsboththeextentanddistributionofadverseselection.Wethensupposethat…rmscana¤ecttheinformationthattheyortheirrivalsobserve,therebyendoge-nizingtheextentandnatureofasymmetricinformationbetweencurrentandrivalemployers.Inparticular,wehighlightthatdi¤erentinformationstructuresthatleadtosimilaradverseselectioncandi¤erintheirallocativee¢ciency.Usingthisobservation,wedetailhowoptimalinformationmanagementpoliciesvaryacross…rmswithdi¤erenthumancapitalmanagementpriorities,andhowthesedecisionsa¤ectaggregatelabourmarketoutcomes.

Keywords:humancapital,informationdisclosure,regressiontothemean,adverseselection,turnover,wagedistribution,humanresourcemanagement.

Wearegratefultoextremelyhelpfulparticipantsatnumerousseminarsandconferencesforhelp-fulcommentsandsuggestions.Speci…cthanksareduetoRicardoAlonso,PatrickBolton,JimDana,CatherinedeFontenay,JanEeckhout,IgnacioEsponda,JuanJoséGanuza,IlloongKwon,LarryKranich,AlessandroLizzeri,JimMalcomson,AdrianMasters,MegMeyer,ArijitMukherjee,KevinMurphy,OghuzhanOzbas,JoePerkins,BarbaraPetrongolo,HeikkiRantakari,MikeRyall,ArminSchmultzer,JoelShapiro,JoelSobel,MargaretStevens,EricvandenSteen,GianlucaVi-olante,DennisYaoandMikeWaldman.Theusualdisclaimerapplies.Updatedversionswillappearathttp://www.economics.ox.ac.uk/Research/workpapers.asp.y

SternSchoolofBusiness,NewYorkUniversity.heski@nyu.edu.z

Nu¢eldCollegeOxford,CMPOandCEPR.ian.jewitt@nuf.ox.ac.uk.x

DeptofEconomicsandTheQueen’sCollegeOxford,CMPOandCEPR.clare.leaver@economics.ox.ac.uk.

󰀃

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JELClassi…cation:D82,J24,L21.

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1Introduction

Twocentralandestablishedthemesinlabourtheoryareadverseselectionandthedistinc-tionbetween…rm-speci…candgeneralhumancapital.However,typically,thesethemeshavebeenconsideredseparately.Thispaperbeginsbyintroducingmatch-speci…cvalueinastandardmodelofadverseselection,buildingonalargeliteratureinitiatedbyWald-man(1984)andGreenwald(1986).Speci…cally,rivalemployersobservesomestatisticaboutaworker’sproductivityandmakewageo¤ers.Havingobservedtheseo¤ers,thecurrentemployerdecideswhethertoretaintheworker(matchingthehighestoutsideo¤er)ortoreleaseher.

Allowingfor…rm-speci…cmatchesintroducesaregressiontothemeane¤ectinthemodel.Thisarisesbecausethecurrentemployer’sbestestimates—basedonherpri-vateinformation—ofaworker’sproductivityifretainedwithinthe…rm(retainedhumancapital)andifreleasedtojoinanother…rm(generalhumancapital)arenotperfectlycorrelated:sometimesworkerswillbeexpectedtobemoreproductiveifretainedandsometimesmoreproductiveifreleased.Inthiscontext,regressiontothemeanimpliesthatworkerswithhighretainedproductivityarelikelytohavelowerproductivityelse-where,converselyworkerswithlowretainedproductivityintheir…rstemploymentareexpectedtohavehigherproductivityelsewhere.Thisprovidesareasonforsomeworkerstoswitchjobspurelyonthegroundsofe¢ciency.Acontributionofthepaperistoexplorehowthis‘legitimate’reasonforjobturnoverinteractswiththeotherfundamen-talforce,adverseselection,underdi¤erentinformationstructures(thatis,assumptionsabouttheinformationheldbycurrentandrivalemployers).

Incharacterisingthee¤ectofaninformationstructure,itisusefultofocusontheextentofadverseselectionthatariseswhenoutsideemployersdrawinferencesfromthecurrentemployer’sretentiondecision.Whenoutside…rmshaveinformationthateliminatestheneedtomakethisinferencethereisnoadverseselection.Forexample,thiswillbethecaseisoutsideemployershavethesameinformationasthecurrentemployeraboutaworker’soutsideproductivity(orgeneralhumancapital).Equally,iftheoutsideemployershavethesameestimateasthecurrentemployerofinsideproductivity,thenpublicinformationis…nerthanthatcontainedintheretentiondecision,soonceagainthereisnoadverseselection.Note,however,thatwhilethesetwoinformationstructuresorregimesinducethesameadverseselection(andhencethesameexpectedwage),theydi¤erintheire¢ciencyinallocatinglabour.

Moregenerally,inassessingdi¤erentinformationstructures,wede…nethequantityofadverseselectionateachrealisationofthestatisticobservedbyoutside…rmsasthe

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di¤erencebetweenthewageiftherewerenoprivateinformationanditsequilibriumvalue.InSection3.3,inourjointnormalspeci…cationofthemodel,weshowthatinformationstructuresconsistingofagarbledreportofthecurrentemployer’sbestestimateofoutsideproductivity(i.e.generalhumancapitalplusrandomnoise)generateanamountofadverseselectionthatisindependentoftherealisation.However,weidentifyotherinformationstructuresforwhichadverseselectionisimposedmoreheavilyonthoseworkerswhomitise¢cientforthe…rmtoretain.1Ourgoalistoanalyzetheimpactofdi¤erentinformationstructuresonaveragewages,…rmpro…tsandretentiondecisions.

Forapplication,itisimportanttoconsiderhowdi¤erentinformationstructuresmightarise.First,itisnaturalthatthenatureofproduction,ortheindustrymightleadtoexogenouslydi¤erentinformationstructures.Trivial,butillustrativeexamples,includethattheinformationavailabletopotentialemployersaboutsportsmen,actors,andmusiciansisquitedi¤erenttotheinformationonprivateinvestigators,orspies.Similarly,theinformationaboutprogrammersthatoutsidersobservecandi¤erdramat-icallydependingonwhethertheprojectisopensourceorclosedsource(asdiscussedforexampleinLernerandTirole(2005),Spiegel(2005),andinanapproachperhapsclosesttothispaper,BlatterandNiedermayer(2008)).

Further,variedinformationstructuresmightariseendogenouslythrough…rms’de-cisions.Speci…cally,weanalyze…rms’strategicchoiceswhentheycommittotheinfor-mationavailabletopotentialrivalemployers.Forexample,…rmsmightcrediblycommit(eithercontractually,oroftenthroughreputationalconcerns)astohowmuchtimeaprogrammercanspendonopensource,ortheextenttowhichaconsultantorlawyerhasdirectaccessandcontactwithclients,publicizethattheworkerisindeedemployedatthe…rm,forexample,throughawebsite,oreveninstituterulesandrestrictionsonso-cialinteractions(Leibeskind,1997).Morebroadly,choicesoverproductiontechnologies(suchaswhethertorequireteamorsoloproduction)andthedesignoforganization(in-cludinglayersofhierarchyandpromotioncriteria)willa¤ecttheinformationstructure.Here,weabstractfromconsideringdirectcostsinsuchchoicesand,instead,treatthe…rmasdirectlychoosingthenatureofthesignalobservedbyrivalpotentialemployers.

Usingourcharacterizationofthee¤ectsofdi¤erentinformationstructures,itisrelativelystraightforwardtocharacterize…rm’spreferredinformationpolicies.Ourre-sultsherearedrivenbyasimpletrade-o¤:policiesthatbestenable…rmstoexploittalent(bycapturinggeneralhumancapitalrents)makeithardtoattractemployees,andviceversa.Equilibriumpoliciesthereforere‡ecttherelativeimportancetothe…rm

Inthelanguageofauctiontheory,biddersobserveacombinationofcommonandprivatevaluations,ratherthan,e.g.,agarblingofthecommonvaluation.

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ofattractingversusexploitingtalent.

Toexploretheseideas,weextendthemodelbysupposingthat…rmscompetetohireworkersineachoftwoperiods.Inthe…rststage,no…rmholdsaninformationaladvantage.Firmscangaininformationaladvantagethrough…rstperiodemploymentanddependingoninitialcontractswhichconsistnotonlyofawageo¤er,but,also,adisclosurepolicy(leadingtoaparticularinformationstructure).Havingchosena…rstperiodemployer,workersgenerateperformancestatisticswhichareprivatelyobservedbytheiremployer,aswellasacquiringskillsthatarevaluableinsecondperiodproduction.Thesecondperiodthenproceedsexactlyasabove,outside…rmsobservesomestatisticofthisinformation(arisingfromthedisclosurepolicytowhichthe…rstperiodemployerhadcommitted)andthenmakesecondperiodwageo¤ers.Havingobservedtheseo¤ers,…rstperiodemployersdecidewhethertoretaintheirworkers(matchingthehighestoutsideo¤er)ortoreleasethem.Workersthenengageinsecondperiodproductionandthegameends.

Notethatinthe…rstperiodcompetitionbetween…rms,…rmsattractworkersbothdirectly,through…rstperiodwages,andindirectly,throughthefuturecareers(asex-pressedbytheexpectedsecondperiodwages)thattheyo¤er.Thesecareerprospects,inturn,arisefromthegeneralskillsandtrainingthatareo¤eredinthe…rm(which,forthemostpart,wetreatasexogenous)andfromthedisclosurepolicychosen.Disclosurepolicies,however,donotsimplyimplytransfersofsecondperiodsurplusbetweenem-ployeesand…rstperiodemployers,sincedi¤erentdisclosurepoliciesvaryintheextentofsurplus-destroyingallocativedistortionthattheyintroduce.Wecanquantifythisexplicitlyusingourcharacterizationofinformationstructuresthatassociateswitheachpossibledisclosurepolicyapairofoutcomes:expectedfutureearningsfortheworkerandexpectedfuturepro…tsforthe…rm.

Thusthedisclosurepolicyforour…rmscorrespondstothebestchoicefromthesetoffeasiblewage,pro…tpairs,bearinginmindthat…rstperiodwagescantransferfuturepro…ttoworkersbut,becauseofcreditconstraints,notnecessarilyfuturewagestopro…t.Firmsfacingcompetitiontoattractworkers(competitive…rms)willseektomaximisee¢ciency(thesumoffutureearningsandfuturepro…tswhicharetransferredtotheworkerascurrentwages).Incontrast,‘technologicallyadvantaged’…rmsfacelimitedcompetitionandtransformworkerrentintopro…tsviaadverseselection(skill-augmenting…rms).

Theseresultshaveimplicationsforlabourmarketoutcomes.2InSection5.2.1,

Acemoglu(2002)stressesthattechnologicalchangesarelikelytoalterthewaysinwhich…rmsorganiseproductionandconsequentlyimpactonlabourmarketoutcomes.Thecurrentpaperendorses

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wecalculatehowwagedistributionsandlabourturnoverratesrespond,viainforma-tionmanagementpolicies,totechnologicalchangesintheskill-augmentingsector.Adeclineineitherthemeanofestimatedgeneralhumancapitalformationormeanmatchquality,oranincreaseinthevarianceofestimatedmatchquality,increasestherateoflabourturnoverintheskill-augmentingsector.Interestingly,sinceanincreaseinthevarianceofanestimatecanbeinterpretedasanimprovementininformation,thissug-geststhatobservedincreasesinlabourturnovercouldstemfromimprovedinformationacquisitionwithin‘innovative’…rms.Turningtothedistributionofwages,anincreaseinthe“skill-gap”(theexpectedhumancapitaldi¤erencebetweentheskill-augmentingandcompetitive…rms)increasesinequalityandskewsthedistributionofwageintheskill-augmentingsectortotheleft,whileanincreaseinthemean,orareductioninthevariance,ofestimatedmatchqualityincreasesinequalitybuthaslittleimpactonskewness.

RelatedLiteratureAsnotedabove,ouranalysisdrawsonthefamiliarconceptsofadverseselectionandregressiontothemean(thelatterinducingmatchquality).3Theseconceptshavebeenwidelyappliedinthelaboureconomicsliterature,althoughtypicallyseparately.Thenotionofmatchquality,buildingonBecker’sdistinctionofspeci…chumancapital,wasintroducedbyJovanovic(1979)whoshowsthatanon-degeneratedistributionofworker-…rmmatchvaluesleadstoworkerturnoverasinformationaboutmatchvaluesaccruesovertime.Inemphasisingthedynamicsofthelearningprocess,Jovanovicabstractsfromgeneralhumancapitaland(hence)adverseselectionaspects.Incontrast,Waldman(1984)andGreenwald(1986)focusessquarelyonadverseselection,highlightingthatthisforcecanleadworkerstoearnlessthantheirmarginalproductsandhasimplicationslabourturnover.4Indeed,inGreenwald’smodel,thereisnoturnoverunlessthereisapossibilitythatseparationsoccurforexogenousreasons.Weshowthatintroducinganon-degeneratedistributionofmatchqualityintoamodelofgeneralhumancapitalformationcounterbalancestheforcesofadverseselection.Evenwhen…rmshold

thisviewanddetailssuchamechanism.3

Adverseselectioncan,ofcourse,betracedbacktoAkerlof(1970).RegressiontothemeanpredatesevenGalton(1885)who…xedtheideainwhatKoenker(2001)calls“Arguably,themostimportantstatisticalgraphiceverproduced.”Galton’sgraphicrelatedchildandparentalheight.Tallparentstendtohavetallchildren,thoughnotsotallasthemselves.Similarlyforshortparents.Ofcourse,weareconcernedwithproductivityin…rstandsubsequentemploymentsratherthanheightsofparentsandchildrenbuttheprincipalisthesame.4

Thefactthatworkersearnlessthantheirmarginalproductsgivesrisetothepossibilityof…rm-sponsoredhumancapitalinvestments.ThisideaisdevelopedinmanysubsequentpapersincludingKatzandZiderman(1990),ChangandWang(1996)andAcemogluandPischke(1998).AcemogluandPischke(1999)provideareviewthatemphasisestheroleofexogenousmarketfrictions.

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privateinformationrelatingtogeneralhumancapital(theGreenwaldcase),ourmodelendogenouslygeneratespositivelabourturnover.

Inthissense,ourpaperisrelatedtoLi(2006)whoalsoseekstoexplainjobmobilityinthepresenceofasymmetricinformationoverworkerproductivity.Limodelsthewagedeterminationprocessasa…rstpriceauction.ThiscreatesabiddingsituationsimilartoMilgromandWeber’s(1981)analysisofthe‘mineralrights’modelinwhichthereisasingleinformedbidderandanumberofuninformedbidders.Inthissetting,theuninformedbiddersadoptamixedstrategywhichgeneratespositiveturnoverandanon-degeneratedistributionofwages.ThoughinLi’ssettingthereisnomatch-speci…ccomponentofproductivityandnoe¢ciencyconsequencesofturnover.Inourmodel,wagesaredeterminedviaasecondpriceauctionandturnoverarisesfromthenon-degeneratedistributionofmatchquality.Notably,thisgivesane¢ciencyrationaleforturnoverthatisabsentinLi(2006).Afurtherdi¤erenceisthatLiassumestheinformationstructuretobeexogenously…xed.

Eeckhout(2006)alsostudiesasettingwherecurrentemployers(exogenously)havesuperiorinformationtooutsiderstoexamineimplicationsforturnoverandwages.Inhismodelthereisgraduallearning,asinJovanovic(1979),butovergeneralhumancapitalratherthanmatchquality.Thisapproachcontrastswithourmodelwhereinformationasymmetriesareendogenousandthereispersistenceinmatch-speci…cvalues(thelatterleadstoourregressiontothemeane¤ect).Afurtherdi¤erencearisesinthewage-determinationprocess.InEeckhout’smodelwagesaredeterminedviaasecondpriceauctionwithtwoheterogenousbidders—anincumbentandachallenger,eachofwhomhaveprivateinformation(see,also,Pinkston2008).Inourmodel,wagesarepinneddownbythebehaviourof(interim)identicaloutside…rms.This“competitivefringe”assumptiongreatlysimpli…estheanalysis.

Althoughweabstractfrominternalorganisationcostsofinformationmanagementinordertofocusontheadverseselectionvse¢ciencytrade-o¤mostdirectly,ourpaperrelatestoasigni…cantorganisationaleconomicsliteratureinwhichinternalorganisationcostsplayamajorrole.Waldman(1984)(andmorerecentlyDeVaroandWaldman(2005)),Ricart-i-Costa(1988)andBlanesiVidal(2007)arguethat,sinceadversese-lectioninthelabormarketcana¤ectwages,5retentionratesandtherebypro…ts,…rmswillhaveincentivestodistort(respectively)promotion,taskassignmentordelegationdecisions.Theseareexampleswhereorganisationaldesignispartlymotivatedbyhuman

GibbonsandKatz(1991)presentempiricalsupportfortheeconomicsigni…canceofsuche¤ects.Morerecently,Schönberg(2007)…ndsevidenceofadverseselectionforcollegegraduates,whileHuandTaber(2005)…ndamarkede¤ectforwhitemales.SeealsoKahn(2008).Finally,Pinkston(2008)presentsevidenceanddiscussesgradualasymmetriclearningbetweendi¤erentpotentialemployers.

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capitalmanagementissuesand,furthermore,impactsthroughinformation‡owstothelabourmarket.6

Finally,ourpaperisalsocloselyrelatedtoagrowingliteraturestudyinginformationdisclosure(see,e.g.,CalzolariandPavan(2006),Mukherjee(2008),KochandPeyrache(2005)andAlbanoandLeaver(2005)).Likethecurrentpaper,thisliteraturehighlightsthatanemployer’sinformationmanagementpolicycanformpartofoverallcompensationasitin‡uencesanemployee’sfuturecareerprospects.7(SeealsoKimandMarschke(2005)andLewisandYao(2006)whoexplorethisideainthecontextofresearchers).Though,manyofthesepapershighlightcareerconcernandmoralhazardaspectsomittedinouranalysis;ourpaperfocusesonthedetailedimplicationsforwagesandturnoversofabroaderrangeofinformationstructuresthanistypicallyconsidered(forexample,AlbanoandLeaver(2005)consideronlyfullytransparentandfullyopaquestructures).Moreover,thispaperinallowingforvariationinbothgeneralhumancapitalandmatchvalues,allowsforconsiderationofe¢cientturnoverandforricherinformationstructurethanmanyoftheseworkswhicheitherforceallworkerstomove…rmsbetweenthe…rstandsecondperiod(KochandPeyrache,2005)andCalzolariandPavan,2006)orassumethattheworkerisalwaysmoreproductiveintheoutside…rmbya…xedamount(Mukherjee,2008).

2AModelofInformationStructuresandLabourMarketOutcomes

ConsideracurrentemployerIwhoprivatelyobservesavector-valued‘teststatistic’QI.ThevectorQIshouldbethoughtofaseverythingthe…rmknowsaboutitsworker.Inparticular,informationinQIwillallowthecurrentemployertoestimateYII,thevalueofaworker’soutputwhenretainedin…rmI,andYII0thevalueofheroutputwhenreleasedtoadi¤erent…rmI0.ItisconvenienttothinkofthecurrentemployersinformationQIassimplygivenbyYIthevectorofproductivities.Thisnotationissomewhatcumbersome,butprovesusefulintheextensionofthemodelinSection4.

Whilethecurrentemployer,orinside…rm,observesQI,rivalemployersobservea

Burguet,CaminalandMatutes(1999)takeadi¤erentpathusingsimilaringredients.Theyarguethatincertainindustries,speci…callyprofessionalsports,characterisedbyextremevisibilityofperfor-mance,incentivesarecreatedforrestrictivelabourpractices—suchastransferfees.7

CalzolariandPavan(2006)allowforgeneraldisclosurepolicies,anddonothavealabourmar-ketapplicationspeci…callyinmind.Theydonotconsiderthepossibilityofretentionandassumeamonopsonistemployerinthesecondperiod,leadingtosomewhatdi¤erente¤ectsandconsiderations.

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di¤erentstatisticTI=TI(QI).Note,weassumethatinside…rmsalwayshaveavailableanyrelevantinformationthatoutsideemployershold.8

EmploymentWageDeterminationOutside…rmscompetetohiretheworkerandmake“takeitorloseit”employmentwageo¤ers.Theemployertheneithermatchesthebesto¤ermadetotheworkerorreleasesthisworkertojoinoneofthehighestoutsidebidders.Equivalently,thereisanascendingopenauctioninwhich…rmsbidupwagesuntilallbutone…rmdropsoutofthebidding.

Asnotedabove,analternativethatdoesdeliversomewhatdi¤erentresultsispro-posedbyLi(2006).Li’s…rstpriceauctionmodelwouldappeartobeappropriateincaseswhere…nalwageo¤erscanbemadebyeithersideofthemarket,butnotcrediblycommunicatedtotheothersidebeforethewageroundmustbeconcluded.

2.1SimplifyingAssumptions

Inordertosimplifytheanalysisoftheemploymentwagedeterminationprocess,weimposethefollowingassumptiononthejointdistributionofteststatisticsandproduc-tivities.

Assumption1.Foranypairof…rmsI0andI00;(QI;YII0)and(QI;YII00)haveidentical

distributions.Outside…rmsareinterimidentical:theyalltakethesameviewoftheworker’slikelyoutputintheir…rm(thoughtherealizationsindi¤erent…rmsmayturnouttodi¤er).Giventhisassumption,wecanuniquelyde…ne

GI=E[YII0jQI],I=I0:

def

TherandomvariableGIisthecurrentemployer’sbestestimateoftheworker’svalueinanoutsideemployment(hergeneralhumancapital).Sincethecurrentemployerholdsalloftheinformationrelatingtothisworkerintheeconomy,GIisalsothequantitythat

Notethat,foragiveninformationstructure,alltheinformationrequiredtodeterminewagesandretentiondecisionscomprisestheinformationheldbyrivalemployersTIandtheinside…rm’sbestestimateoftheworker’sproductivityinthe…rmRI=E[YIIjQI].Itfollows,thatwhileitisconvenienttoassumethatthe…rmobservesQI,therewouldbenolossinassumingthatthe…rmobservesonlyTIandRI.Thislowerinformationrequirementfortheincumbent…rmmightbeamorepalatableassumptionandviewedasconsistentwithourmaintainedinterpretationofthedisclosedstatisticTIasarisingthroughthe…rm’sorganizationaldesign.

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outside…rmsseektoestimatewhenmakingtheiremploymentwageo¤ers.Similarly,wecande…ne

RI=E[YIIjQI].

def

TherandomvariableRIisthe…rstperiodemployer’sbestestimateoftheworker’svalueinthecurrent,insideemployment(herretainedhumancapital).9

GIwillgenerallydi¤erfromRI.ExperienceQI=qmayrevealthataworker…tsespeciallywellwith…rmI(E[YIIjQI=q]>E[YII0jQI=q])or,equally,thattherehasbeenabadmatch.Di¤erencesbetweenGIandRIwillplayanimportantroleinouranalysis,withthestatisticalpossibilityofabadmatchendogenouslygeneratinglabourturnover.Itisnaturaltoadoptaframeworkinwhichthismatchingmanifestsitselfthroughregressiontothemean:workerswhoperformwell(badly)intheirinitialemploymentwilltendtoperformworse(better)iftheyswitchjobs.Thiscorrespondstoanassumptionthattheregression‘line’E[GIjRI=x]hasaslope(derivative)everywherebetweenzeroandone,implying,forinstance,thatCov(GI;RI)󰀇0andCov(RI󰀂GI;RI)󰀇0:Infact,wewillmakeasomewhatstrongerassumption.

Assumption2.Foreach…rmI,thepairofrandomvariables(RI󰀂GI;GI)area¢liated

withdensitylogconcaveineachvariabletakenseparately.Thisassumptionleadstothefollowingconvenientproperties,asprovenintheAppendix.

Remark1Assumption2impliesthat,E[GIjRI=r],r󰀂E[GIjRI=r],andE[GIjRI󰀂GI=r]areallincreasinginr.Foranyw2R;E[GIjRI󰀆w]󰀆E[GI]andE[GIjRI󰀇w]󰀇E[GI].

Regressiontothemeanintroducesa“genuinereasonforsale”whichcounterbalancesthestandardAkerloflemonse¤ectandtendstoprotectthemarketforexperiencedworkersfromcompletecollapse.Givenregressiontothemean,intheabsenceofanyfurtherinformationdisclosure,anoutside…rmneednotconcludethatanyworkeritcanhireatagivenwagewillgeneratealossatthatwage;rather,areleasedworkermaysimplyhavebeenabadmatch.Afurtherimplicationofregressiontothemeanisthate¢ciencyintheallocationoflabourrequiresapositiveturnoverofworkers;tomaximiseproductivity,aselectionofworkersshouldswitchjobs.

OuranalysisallowsQItocontainYIIandYII0butcertainlydoesnotrestonthisassumption;allthatisrequiredisthat…rmIknowssomethingaboutitsworker’slikelyinsideandoutsideproductivitythatother…rmsmightnot.

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3.1

Analysis

WageDeterminationandDe…nitions

WithAssumption1inhand,characterisingwagesisrelativelystraightforward.Sinceoutsideemployersareinterimidentical,employmentwageswillbesetinBertrandcom-petition,andhenceequaltheexpectedproductivityofaworkerinanoutside…rmcon-ditionalonthepubliclyavailableinformation.Thisinformationincludestheeventthattheworkerisreleasedbyhercurrentemployer.10Theequilibriumemploymentwagewhenaworkerisemployedby…rmIandTI=TI(QI)=tisrealisedisde…nedimplicitlyby

wTI(t)=E[GIjTI=t;RI󰀆wTI(t)],(1)wheneversuchawTI(t)exists.11ThenotationwTI(t)denotesthewagepayableunder

disclosurepolicyTI=TI(QI)whenTI=tisrealised(weuseTItodenoteboththedisclosurepolicyandtherandomvariablethatitgenerates);wTI(TI)thereforedenotestherandomwagewhichwillbegeneratedbythedisclosurepolicy.Wewillwritetheexpectedemploymentwageas

WTI=E[wTI(TI)]:

(2)

Theexpectedpro…t,isequaltooutputlessemploymentwagesintheeventthattheworkerisretained(whichoccursifthepro…tsfromdoingsoarepositive),whichwewriteas

󰀅TI=E[(RI󰀂wTI(TI))+],(3)where(x)+denotesxwhenpositive,zerootherwise.

Next,wede…nethedegreeofadverseselectionwhenTI=tisrealised

ASTI(t)=E[GIjTI=t]󰀂E[GIjTI=t;RI󰀆wTI(t)].

(4)

ThequantityASTI(t)measureshowmuchlowertheemploymentwageiswhenoutside…rmsconditionontheemployer’sretentionbehaviourinadditiontotherealisationTI=

TherelevanceofthiseventtoemployersbiddingforGI(commonvalues)andthepossibilityofawinner’scurseisfamiliarfromauctiontheory.11

Atthislevelofgenerality,wecannotruleout(perverse)caseswheretheimplicitfunctiontheoremfails.Insuchcases,theequationdoesnotde…nethefunctionwTI;however,theconditionisstillrequiredtohold.Also,itispossiblethatthereisnowsuchthatw=E[GIjTI=t;RI󰀆w],inwhichcasewesetwTI(t)=infsuppGI.

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t.Expectedadverseselectionequalstheexpectedshortfallinemploymentwagesfromoutsideproductivity,

E[ASTI(TI)]=E[GI]󰀂WTI:(5)Finally,itisconvenienttointroducenotationforthefeasibleset,󰀇(󰀂I).Thissetis

themainobjectofouranalysisandconsistsoftheexpectedwage-pro…tpairs(WTI;󰀅TI)thatcanbeachievedforagivensetofdisclosurepolicies,󰀂I.

Weproceedintwostages.First,inSection3.2,weestablishsomebenchmarkresultsunderourgeneraldistributionalassumptionsfor(GI;RI)butwithahighlyrestrictedsetofinformationstructures.Speci…cally,wefocusonthecasewhere󰀂I=fGI;RI;?Iginwhichoutside…rmsobservetheexpectedproductivityoftheworkerGI,therealisedproductivityoftheworkerintheircurrentemployment(morestrictly,theestimateoffutureproductivitywithinthe…rm),orsimplynothing.Mostoftherelatedliteraturealsorestrictsattentiontothesepolicies.Ouranalysisclari…estheforcesatworkand…xessomegeneralfeaturesofthefeasibleset.Then,inSection3.3,wespecialisetothejointnormalcase.Thisallowsustoexplicitlytracethroughtheimpactofarichsetofalternativeinformationstructuresonlabourmarketoutcomes.

3.2

3.2.1

GeneralDistribution,RestrictedInformationStructures

InformationStructures,󰀂I=fGI;RI;?Ig

Hereweconsiderthefollowingthreemoreorlessnaturalinformationstructure.1.GI󰀂disclosure,outside…rmsobserve…rmI’sbestestimateoftheworker’sgeneralhumancapital:TI(QI)=E[YJIjQI]=GI.122.RI󰀂disclosure,outside…rmsobserve…rmI’softheworker’sproductivityifretainedwithinthe…rmTI(QI)=E[YIIjQI]=RI.3.?I󰀂disclosure,13outside…rmsobservenoadditionalinformation:TI(QI)=?I.

Notethatthesameresultswouldbeachievedifoutside…rmsobservealloftheavailableinformationinthevectorQI.Throughoutwerestrictourattentiontooutside…rmsobservingscalarinformationstatistics.13

Weretainthesubscriptsince,below,weallowfordi¤erenttypesofcurrentemployerwhomaybemoreorlesse¤ectiveintransferringgeneralhumancapitaltotheworker.

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3.2.2WagesandPro…tsGI󰀂disclosure

wGI(GI)=E[GIjGI;RI󰀆wG(GI)]=GI:

(6)

Noticethatthereisnoadverseselectionundergeneraldisclosure:ASGI(g)=0.Thisisbecause,havingobservedGI=g,outside…rmshavenoreasontopayattentiontotheemployer’sretentionbehaviour.TakingexpectationsovertherandomvariablewGI(GI),theexpectedemploymentwageissimplyexpectedgeneralhumancapital

WG=E[GI]:

RI󰀂disclosure

wR(RI)=E[GIjRI;RI󰀆wR(RI)]=E[GIjRI]:

(8)(7)

Again,thereisnoadverseselection,ASRI(r)=0;inthiscase,becausethedisclosedstatisticRI=rsupplies…nerinformationthantheeventthattheworkerisreleased,RI󰀆wR(r).However,thereisnowregressiontothemean,withr󰀂E[GIjRI=r]increasinginr.Intuitively,outside…rmsanticipatethatlow(high)valuesof…rmIretainedproductivitymaybeduetoanegative(positive)matchandthatproductivityinanewmatchwilltendtoregresstotheex-anteexpectedvalue.Bythelawofiteratedexpectations,theexpectedemploymentwageisstillequaltoexpectedgeneralhumancapital

WR=E[(E[GIjRI])]=E[GI]:(9)

?I󰀂disclosure

w?I=E[GIjRI󰀆w?]:

(10)

Thereisnowadverseselection,AS?I>0:However,incontrasttoAkerlof’s(1970)

lemonsmodelorGreenwald’s(1986)applicationtothelabourmarket,w?IdoesnotcollapsetothelowersupportofGI(evenintheabsenceofaminimumwage)becauseoutside…rmsanticipatethatlowvaluesof…rmIproductivitywillpartlyberedressedbyregressiontothemean.

Usingtheabovewagecomparisons,wenowstatetworesultswhichcomparetheinformationstructuresfGI;RI;?Ig.

Proposition1.Forany…rmI,GI󰀂disclosuregeneratesmaximumexpectedsurplus:

13

Proof.UnderGI-disclosure,wGI(GI)=GIandso,from(3),󰀅GI=E[(RI󰀂GI)+]:Summing󰀅GIandWGIgivesE[GI]+E[(RI󰀂GI)+]whichisclearlythemaximumachievableexpectedsurplus.

UnderGI-disclosureacurrentemployerreleasesitsworkerwheneverRI󰀆GI:Sincethisimpliesthattheworkerisreleasedifandonlyifthereisanegativematch,labourisalwayse¢cientlyallocatedacross…rms.Thesamecannotbesaidofthetwootherinformationstructures.UnderRI-disclosure,…rmIreleasesitsworkerwheneverRIi.RI-disclosuregeneratesWRI=WGI;󰀅RI󰀆󰀅GI;ii.?I-disclosuregeneratesW?I󰀆WGI;󰀅?I󰀇󰀅GIwith

W?I+󰀅?I󰀆WRI+󰀅RI󰀆WGI+󰀅GI:

Proof.TherankingofexpectedemploymentwagesW?IToestablish󰀅?I󰀇󰀅GI,notesinceE[GI]󰀇w?;itisimmediatethat󰀅?I=E[(RI󰀂w?)+]󰀇E[(RI󰀂E[GI])+]:Itsu¢cesthereforetoestablishE[(RI󰀂E[GI])+]󰀇E[(RI󰀂GI)+]:

TheresultfollowsbecausethevariationinGItendstocancelthevariationinRI

andconvexfunctions‘like’variation.Moreprecisely,notethatE[RI󰀂E[GI]jRI󰀂GI=x]󰀂E[RI󰀂GIjRI󰀂GI=x]=E[GI󰀂E[GI]jRI󰀂GI=x]isincreasinginxbyAssumption2.Thisfact,togetherwiththeequalityofmeans,impliestherandomvariableE[RI󰀂E[GI]jRI]isriskierthanE[RI󰀂GIjRI]:Usingtheconvexityof(x)+givestheresult.

ToestablishW?I+󰀅?I󰀆WRI+󰀅RInotethatunderRI󰀂disclosure,…rmIretainstheworkerintheeventE[RI󰀂GIjRI]󰀇0:HencetheRI󰀂disclosureallocationsolvesthefollowingoptimalallocationproblem

maxE[E[RI󰀂GIjRI]p(RI)];

14

0󰀅p(󰀃)󰀅1

wherepisanyprobabilityofretentionbasedonRI:The?I󰀂disclosuree¢ciencylevel

E[(RI󰀂GI):1fR󰀇w?g]=E[E[RI󰀂GIjRI]:1fRI󰀇w?)]

issmallerbyrevealedpreference.

Theset,󰀇(fGI;RI;?Ig)oftheexpectedwagesandpro…tsthatcanbegeneratedbythedisclosurepolicesGI;RI;?I,asderivedinPropositions1and2,isillustratedinFigure1,wheredownwardslopinglinesdepictpointsofequalexpectedsurplus.Whenoutside…rmsobserveGI,thisgenerateshigherexpectedsurplusfor…rmIthanwhentheoutside…rmsobserveRIbecause,asnotedabove,itresultsinmoree¢cientreten-tionbehaviour.Bertrandcompetitionbetweenoutside…rmsensuresthatthisexpectedsurplusissplitbetween…rmIanditsworker.Sincetheexpectedemploymentwageisthesameinbothcases,…rmImustbestrictlyworseo¤underRI-disclosurebyvirtueofthe“smallerpie”.Ine¢cientretentionbehaviourcreatesaneven“smallerpie”whenoutside…rmshavenoinformation.Intuitively,adverseselectiondepresseswagesandcausesexcessrecruitmentrelativetoRI-disclosure.Akeydi¤erencenowisthat,al-thoughexpectedsurplusissmaller,theworkerreceivesasmallershare.Proposition2tellsusthatadverseselectiondrivestheexpectedemploymentwageW?Isu¢cientlyfarbelowWGItoleave…rmIbettero¤.

Figure1:WagesandPro…tsfor

󰀂I=fGI;RI;;Ig.

Noticethat,under?I-disclosuretheadverseselectionthatdrivesdownwagesisamelioratedbyregressiontothemean.FirmIwould,therefore,enjoyhigherpro…tsiftheregressiontothemeane¤ectwere“turnedo¤”.Infact,thebestinformation

15

structurefromFirmI0sperspectivewouldbeonewhichinducessevereadverseselectionforanyworkeritwishestoretain(butnotforonethe…rmwishestoreleasesincethiswouldavoidup-fronttransferswhenthe…rmmustattracttheworkerinitially).WeshowhowaninformationstructurealongtheselinescanariseinSection3.3.2,below,whereweconsiderinformationstructuresthatcombineRIandGI.

3.3JointNormalDistribution,ArbitraryDisclosurePolicies

Forany…rmI,therandomvariables(GI;RI)arenowassumedtobejointnormallydistributed.Insomeofwhatfollows(namelywherewecalculatewages),wewillalsoassumethatGIand(RI󰀂GI)areindependent.Toavoidconfusion,wewilltermtheformercase‘jointnormality’andthelatterthe‘independentjointnormal’model.3.3.1

Jointnormalinformationstructures

Wealsolimittheset󰀂Iofinformationstructuresthatweconsider,toinformationstructuressuchthat(GI;RI;TI)arejointnormallydistributedwithTIscalar.Thisas-sumptionrulesoutmixedstructures(e.g.thatoutside…rmsobserveGIwithprobabilitypandRIwithprobability1󰀂p),conditionalstructures(e.g.observeRIifGI󰀇0)andpartitionalstrategies(e.g.observeeitherthatGI󰀇0orGI<0).Itdoes,however,closethemodelinanaturalway.

With(GI;RI;TI)jointnormal,aconvenientparameterisationisintermsofthelinearcombinationTI=aGI+bRI+cXI,whereXIisaunitvariance,independentnoisetermavailableviaQI.SincetherandomvariableTIcanalwaysberescaledtohaveanychosenmeanandvariancewithoutalteringitsinformationcontent,onlytwooftheparametersa,b,andcarefree.Itisconvenienttoseta=1󰀂b,implyingthatdisclosurepoliciesarecharacterisedbythetwoparametersbandc:

TI=(1󰀂b)GI+bRI+cXI:

(11)

Theaboveparameterisationsimpli…esthecharacterisationofthefeasibleset.How-ever,itwillalsobeusefultomapfromtheseparameterstotheirassociatedregressioncoe¢cients.Inwhatfollows,wewillusetwosimpleandtwomultipleregressioncoe¢-cients.Thesimplecoe¢cientsareonTIintheregressionofGI(RI)onTI,whichwedenoteby󰀃GITI(󰀃RITI).NormalisingVar(GI)=1,denotingVar(RI󰀂GI)by󰀆2,and

16

assumingCov(GI;RI)=1,thesecoe¢cientswriteas

󰀃GITI=

and

󰀃RITI

1

1+b2󰀆2+c2

1+b󰀆2

=.1+b2󰀆2+c2

Themultiplecoe¢cientsareonTI(RI)inthemultipleregressionofGIonTIandRI;whichwedenoteby󰀃GITI:RI(󰀃GIRI:TI)andwriteas

󰀃GITI:RI

and

󰀃GIRI:TI

(1󰀂b)󰀆2

=

(1+󰀆2)(1+b2󰀆2+c2)󰀂(1+b󰀆2)2(1+b2󰀆2+c2)󰀂(1+b󰀆2)

:=

(1+󰀆2)(1+b2󰀆2+c2)󰀂(1+b󰀆2)2

ThethreeinformationstructuresdiscussedinSection3.2areeasilystatedundereitherparameterisation.GI-disclosurecorrespondstob=c=0,giving󰀃GITI=󰀃RITI=1=󰀃GITI:RI=1and󰀃GIRI:TI=0.RI-disclosurecorrespondstob=1,c=0,giving󰀃GITI=1=(1+󰀆2)and󰀃RITI=1withtheremainingcoe¢cientsunde…ned.14Fi-nally,?I󰀂disclosurecorrespondstoc!1,giving󰀃GITI=󰀃RITI=󰀃GITI:RI=0and󰀃GIRI:TI=1=(1+󰀆2).However,inadditiontooutside…rmsobservingGI,RIorXI,ourframeworkinformationstructuresthatcombinetheserandomvariables.Itisworthhighlightingthefollowingcases:

1.GarblingGIwithb=0;c=0(󰀃GITI:RI,󰀃GIRI:TI>0).2.Nogarbling:LinearcombinationsofGIandRI

(a)Weighting(RI󰀂GI),withb>1;c=0(󰀃GITI:RI<0;󰀃GIRI:TI>0).(b)WeightingGI,with1>b>0;c=0(󰀃GITI:RI>0;󰀃GIRI:TI<0).(c)Di¤erencingGIandRIwithb<0;c=0(󰀃GITI:RI;󰀃GIRI:TI>0).

Undereachofthesecases,…rmI’sretentionbehaviourconveysinformationandsothereisadverseselectionforoutsidersinrecruitment,ASTI(t)=0.

14

AsingularityoccursatTI=RI:

17

3.3.2WagesandPro…ts

Our…rstresultexpresseswTI(t)intermsoftheregressioncoe¢cients,theconditionalstandarddeviationoftherandomvariable[RIjTI=t],denotedby󰀆RIjTI,andtheunitnormalhazardfunctionh.15

Proposition3.Underjointnormality,theequilibriumemploymentwagesatis…es

wTI(t)=󰀃GITIt󰀂󰀃GIRI:TI󰀆RIjTIh

󰀇

󰀃RITIt󰀂wTI(t)

󰀆RIjTI

󰀈

󰀈

(12)

where…nite.Equilibriumadverseselectionthereforesatis…es

ASTI(t)=󰀃GIRI:TI󰀆RIjTIh

Proof.SeeAppendix.

TheemploymentwagefunctiontakesaparticularlysimpleformforgarblingsofGI,i.e.disclosuresofGIplusnoise.Inthiscase,adverseselectionisconstantandequilibriumemploymentwagesequalexpectedoutsideproductivityconditionalonlyonTIlessthisconstant.ToseethisnotethatifTIissuchagarbling,sinceRI󰀂GIisuncorrelatedwithGI;itisuncorrelatedwiththegarblingTI;hence󰀃(RI󰀂GI)TI=0,andtherefore󰀃RITI=󰀃GITI:Substitutingthisintothewageequationyields

ASTI(t)=󰀃GIRI:TI󰀆RIjTIh

󰀇ASTI(t)󰀆RIjTI

󰀈

,forallt,

󰀇

󰀃RITIt󰀂wTI(t)

󰀆RIjTI

:

(13)

whichimplicitlyde…nesASTI(t)asaconstant.Wecanwritethisconstantas

ASTI(0)=󰀆RIjTIk(󰀃GIRI:TI):

(14)

wherek(x)istheiterationk(x)=xh(xh(:::)),thisevidentlyhasa…xedpointatzero,theonlyotherisatapointwedenotek󰀉0:302.Itfollowsthat

Corollary1.Underjointnormality,forTIanygarblingofGI,theequilibriumem-ploymentwagesatis…es

wTI(t)=󰀃GITIt󰀂k󰀆RIjTI󰀉󰀃GITIt󰀂0:3󰀆RIjTI:

(15)

15

󰀂󰀃2

Theconditionalstandarddeviationwritesas󰀃RIjTI=((1+󰀃2)󰀂1󰀂b+(1+󰀃2)b)1=2:

18

Theamountofadverseselectionis,unsurprisingly,increasingin󰀆RIjTIwhichisameasureofhowmuchuncertaintyislefttobeattributedtotheretentiondecision.AsTIgarblesGImore,󰀆RIjTIincreases.

Ingeneral,forinformationstructuresotherthangarblingsofGI,ofcourse,adverseselectionisnotindependentoftherealiseddisclosure.Note,however,that,foranygiveninformationpolicy,thesignofadverseselectionisconstantforallrealizationsoftheinformationavailabletooutside…rms,t(ithasthesamesignas󰀃GIRI:TI).MoreoverattherealisationTI=0,equation(14)remainsvalidforanydisclosurepolicyforwhichthereis…niteadverseselection.Hence,atthemeanrealisationofthedisclosedstatistics,realisedwagesarerankedaccordingtotheconditionalstandarddeviations󰀆RIjTI.

Proposition3solvesfortheemploymentwageintermsofacalculablefunction.Giventhisfunction,retentiondecisionsandthecurrentemployer’spro…tscanalsobecalculatedforeveryinformationstructurein󰀂I.16Werefertotheupperboundaryofthesetofwagesandpro…ts,󰀇(󰀂I),asthee¢ciencyfrontier,sinceonthisboundarythereisnoinformationstructurethatyieldsthesameexpectedwagefortheworkerwithoutreducingthe…rm’sexpectedpro…t.Ournextresult(calculatedusing(12)withGIand(RI󰀂GI)assumedindependent)showsthatthee¢ciencyfrontierdoesnotconsistofpolicieswhichgarbleGIwithnoise,ratherGIiscombinedwithRI.

Result4.Intheindependentjointnormalmodel,forany…rmI,thee¢ciencyfrontier

oftheset󰀇(󰀂I)isgeneratedbythedisclosurepoliciesTI=(1󰀂b)GI+bRI;withb<1;c=0:

1.With1>b>0;expectedemploymentwagesWTIaregreaterthanE[GI]:2.Withb=0;expectedemploymentwagesequalE[GI]:3.Withb<0;expectedemploymentwagesarelessthanE[GI]:4.Apolicywithb=1;c=0isonthelowerboundaryoftheset.

5.Apolicywithb>1;c=0inducesextremeadverseselection,expectedemploy-mentwagesarein…nite.

Itisworthpausingtodiscussfeaturesofthesetofwage,pro…tpairsthatdi¤erentinformationstructurescangenerateand,inparticular,itse¢ciencyfrontierplottedinFigure2(forvaluesofb2[1=3;󰀂4=3]).We…rstconsiderwhatisrequiredforan

AllcalculationshereandforResults8and9,andFigures2,3,5and6areavailablefromtheauthorsasMathematicaNotebook…les.

16

19

informationstructuretodrivetheexpectedemploymentwagebelowE[GK],andthenhowagivenreductioninWTIcanbeachievedmoste¢ciently.

Figure2:TheE¢ciencyFrontier,plottedfor

GI󰀈N[0;1]andRI󰀈N[0;1].

TodrivetheexpectedemploymentwagebelowE[GI],theexpectedadverseselec-tionmustbepositive.From(13),ASTI(t)ispositiveonlyif󰀃GIRI:TI>0;givingasimpleandintuitivecondition.FirmI’sretentiondecisionwillcreateadverse(ratherthanpos-itive)selection—i.e.depresswTI(t)=E[GIjTI=t;RI󰀆wTI(t)]belowE[GjT=t]—ifandonlyifalowervalueofRIisbadnewsforGIgivenTI:

Onemightthinkthatthisconditionwillholdwheneverretentionbehaviourisinformative.AsFigure3illustrates,thisisnotthecase;thereareinformationstructuresthatleadtoanexpectedwagefortheworkerthatliesaboveE[GI],thatisthereispositiveratherthanadverseselection.Theunifyingfeatureoftheseinformationstructureswith󰀃GIRI:TI<0isthatGIiscombinedwithRI,withmoreweightonGI.17Ofcourse,asFigure2alsoillustrates,therearemanyinformationstructuresthatdosatisfythisconditionandhencedrivetheexpectedemploymentwagebelowE[GK].Indeed,ofthefourtypesof‘combined’structureslistedattheendofSection3.3.1,above,onlythethird(weightingGI)failsincreatingadverseselection.Thequestionisthereforewhysomeoftheseinformationstructuresaremoree¢cientthanothers,andinparticularwhythefourthtype(di¤erencingGIandRI,withb<0andc=0)tracesoutthee¢ciencyfrontierbelowE[GI]?

Withnonoise(c=0),anyb2(0;1)willgeneratepositiveselection.Withnoise,therangeofpoliciesbecomesmoretightlyboundedabove0andbelow1.

17

20

Toseetheanswer,notethat,evenwhentwoinformationstructuresgeneratethesameexpectedemploymentwage,thedistributionofadverseselectionovertmayvary.Figure3illustrates,depictingtwoinformationstructuresthatgeneratethesameex-pectedadverseselection(theareaunderbothquantilefunctionsis󰀉0:47)butwithverydi¤erentdistributions.AgarblingofGI(policyC)depresseswagesuniformly:ASTIis

p

constantateveryquantileofTI=GI+5=2XI.Incontrast,di¤erencingRIandGI(policyD)imposesalotofadverseselectionatlowquantilesofTI=3=2GI󰀂1=2RIandlittleadverseselectionathighquantiles(andindeednoneatp=1).Thisise¢cient,aslowquantilesareassociatedwithgoodmatches,whilehighquantilesareassociatedwithbadmatches.Sincethisinformationstructuredepresseswagesmostwhenretentionise¢cientandleastwhenretentionisine¢cient,itgeneratesahighersurplusthantheinformationstructurewherewagesaredepresseduniformly(inFigure2thewage-pro…tpairassociatedwithpolicyCliestotheleftofthepairassociatedwithpolicyD).

Figure3:AdverseSelectionofQuantilesofTIplotted

forGI󰀈N[0;1]andRI󰀈N[0;2].

TheabovelogicexplainswhygarblingGI,the…rsttypeofinformationstructure,islesse¢cientthandi¤erencingGIandRI,thefourth,andindeedwhyagarblingofadi¤erencedestimateofinsideandoutsideproductivity(b<0;c=0)liesinsidethee¢ciencyfrontier.Allthatremainsistoconsiderthesecondtypeofpolicy(weightingRI󰀂GIwithb>1;c=0).Thereasonwhythistypeofpolicyfailstotraceoutthee¢ciencyfrontierissimple.ByweightingthedisclosurestatistictowardsRI󰀂GI,thatismatchquality,theinformationstructureeliminatesregressiontothemean.Thisleavesadverseselectiontohitwithfullforce,depressingwagesnotsimplybelowE[GI]butasfarasthelowersupport.

21

Thislogicalsohighlightsthestrengthofcertaininformationstructuresoutsidethesetofjointnormallydistributedinformationthatweareconsideringhere.Inparticular,apolicywhichdisclosesGIwheneverRI󰀂GI<0anddisclosesRIotherwise,inducesnoallocativeine¢ciency—thoseworkersexpectedtobemoreproductiveatother…rmsarereleased—butinducesfulladverseselection,drivingthesecondperiodwageasfarasthelowersupportofGIonthoseworkerswhoaree¢cientlyretained.

Havingdiscussedhowdi¤erentinformationstructuresa¤ectexpectedwagesandpro…ts,wenowextendthemodel,endogenizingtheinformationstructuresassociatedwithdi¤erent…rmsandtracingoutimplicationforlabourmarketoutcomes.

4ATwoperiodmodeloflabourmarketcompetition

Inthissection,weextendthebasicmodelpresentedabove.Wesupposethattherearetwoperiodsofemployment.Inthe…rstperiodallpotentialemployersholdthesameinformationaboutpotentialemployees.Employeesareattractedto…rms,notonlybythewageso¤ered,butalsobythecareerprospectsthata…rmo¤ers.Thesecareerprospectsarisefrom(exogenous)variationintheextenttowhich…rstperiodemploymentata…rmaugmentsanemployee’sgeneralhumancapital,andendogenousvariationthrougha…rm’sstrategicchoiceofaninformationdisclosurepolicy,whicha¤ectstheinformationavailabletorivalemployerscompetingfortheworkerinthesecondperiodofemployment.

Speci…cally,weconsideraneconomythatconsistsofN…rms(eachwithasinglepositionavailable)andMWetaketheviewthatcertain…rms,typicallyinnovativeorinsomeotherwayprivileged,naturallyenableworkerstoacquiremoreskills.Assuch,wedonotassumethatE[GI]=E[GI0]forallI;I0.Rather,wemakethenextsimplestassumptionwhichistodistinguishbetween“skill-augmenting”and“competitive”…rms.Whenwewishtoinvokethisdistinctionwewillrefertoatypicalskill-augmenting…rmas…rmKandatypicalcompetitive…rmas…rmJ(Icontinuestodenoteageneric…rm).

Assumption3.ThereareN1…rmsintheeconomy.Competitive…rmsareexchangeable:foreachpairofcom-22

petitive…rmsJ;J0;(QJ;YJI)isequalindistributionto(QJ0;YJ0I):Foreachskill-augmenting…rmK;(GK;RK)hasthesamedistributionsas(GJ+󰀃K;RJ+󰀃K)forsome󰀃K>0:Inotherwordsskill-augmenting…rms,simplyadd󰀃Ktothegeneralhumancapitaloftheiremployees.

JustasAssumption1simpli…essecondperiodlabourmarketcompetition,As-sumption3simpli…es…rstperiodlabourmarketcompetition.Skill-augmenting…rmsareadvantagedandinshort-supply,andwill(therefore)allhireoneworkerattheprevailingwage.ThisleavestheremainingN󰀂N1exchangeable…rmstoBertrandcompetefortheM󰀂N1freeworkers.ItisthisBertrandcompetitionthatdeterminestheprevailingwage.Ourconcernwillbetoexplorehowtheemploymentpoliciesofdi¤erent…rmsvarywiththesizeoftheskillgap.Weremarkthattheskillgapistreatedhereasexogenousbutinanaturalvariantofthemodelitcouldarisefrom…rmschoosingtoinvestingeneralhumancapital,asbrie‡ydiscussedinSection6.

Whendiscussinglabourmarketoutcomes,itwillbeofinteresttoconsideravari-antofAssumption3inwhichN1isavariableparameterwhichmayexceedthenum-berofworkersM.Inthisevent(correspondingtoahighdemandforlabourintheskill-augmentingsector),theemploymentwagewillbesetbyskill-augmenting…rmsthemselves.

Assumption30.ThereareN1exchangeableskill-augmenting…rmsandN󰀂N1ex-changeablecompetitive…rmsintheeconomy.Foreachskill-augmenting…rmK;theskillgap󰀃=E[GK]󰀂E[GJ]ispositive.Assumption30di¤ersfromAssumption3inthatalltheskill-augmenting…rmsareiden-tical.ThiswillservetomakewagesettingBertrand-competitiveinthecasewhereN1>M.

FirstPeriodContractsItremainstodescribe,…rstperiodcompetition:TheN…rmscompetetohireaworkerinthe…rstperiodthroughpubliclyobservablecontracts.Foragiven…rmI,acontractspeci…es:

1.AtrainingwagewI󰀇0.Theworkeriscreditconstrained.

2.AdisclosurepolicyTI=TI(QI)fromasetofpossibledisclosurepolicies(orinfor-mationstructures)󰀂I.Equivalently,havingcharacterizedthesetoffeasiblesecondperiodwage,pro…tpairsthatcanbegeneratedgiventhesetofdisclosure󰀂I,itisconvenienttothinkofthe…rmaschoosingsuchapair(WTI;󰀅TI)fromthefeasibleset󰀇(󰀂I).

23

Notethatweassume…rmscannotdisclosewhattheydonotknowandwedonotallow…rmstomanipulatethestatisticsthattheydisclose.Webelievethesenotonlytobeusefulassumptionsfortractability,butplausibleoneswhenweinterprettheinforma-tiondisclosedtooutside…rmsasarisingfromchoicesaboutorganizationaldesignandtheorganizationofproduction(forexample,ontheextentandcompositionofteam-workratherthansoloproduction,theextentofhierarchyandthelevelofindividualdiscretion).18Moreover,reputationconcerns(andthedesiretohireotherworkersinthefuture)mightalsoallow…rmstomakecrediblecommitmentsaboutmoredirectdisclo-surepolicies(suchasconsulting…rmschoosingwhetherornottocitejuniorsinvolvementin…nalreports,ordecisionstogivethemmoreorlessaccesstoclients).Notethatwhilemanyoftheseexamplesconcerndiscreteratherthancontinuousscalardisclosurestatis-tics,similareconomicforcesshouldbepresent,andourassumptionsondistributionsaswellasthedisclosedstatisticareanalyticallyconvenient.

5Analysis

Oursimplifyingassumptionsenableustocharacteriseequilibriapiecemealbysolvingtwomaximisationproblems,oneforarepresentativecompetitive…rmJandanotherforaskill-augmenting…rmK.Note,thatforagivendisclosurepolicyTI,thesecondperiodisidenticaltothemodeldescribedinSection2.Inparticular,theexpectedsecondperiodwageisgivenby(2)andexpectedsecondperiodpro…tby(3).

Workersinassessing…rstperiodcontractstakeintoaccountboththewageo¤eredand,also,theexpectedsecondperiodwage.This,inturn,dependsontheidentityofthe…rm(andtheextentofgeneralhumancapitalthatsheanticipatesacquiringinthetrainingperiod)andthedisclosurepolicytowhichthe…rmcommitsthroughthecontract.

Competitive…rmsattempttohireoneoftheM󰀂N1‘free’workersinthe…rstperiod.Sincetheyface…ercecompetition,theyattractworkersbytransferringasmuchsurplusaspossibletotheworker(uptothezeropro…tconstraint).Theytransfersurplusmosteasilythroughahigher…rstperiodwage.Speci…cally,byo¤eringtopaytheirentireexpectedsecondperiodpro…tintrainingwages:wJ=󰀅TJ.Thus,theproblemfacingacompetitive…rmJwhenchoosingadisclosurepolicyissimplyoneofexpectedsurplus

Notethatsuchchoicesoverorganizationdesignsarelikelytoinvolveproductivecosts.Weabstractfromthesehere,though(totheextentthattheyareeasilyquanti…ed)theycanbeeasilyincorporatedintothemodel.

18

24

maximisation

(WTJ;󰀄TJ)2󰀅(󰀂J)

max

WTJ+󰀅TJ.

(16)

Following,Proposition1,thisismaximizedbychoosingGJ-disclosurewhenthisdisclo-surepolicyisavailable.

Thisbehaviourbycompetitive…rmspinsdownaworker’soutside-option.Anyworkerturningdownatrainingcontractataskill-augmenting…rmcanreceiveWTJ+󰀅TJ

󰀈,theproblemfacingatacompetitive…rm.Denotingthisequilibriumoutside-optionbyU

askill-augmenting…rmK(orindeedanyother)canbewrittenas

max

󰀈+(U󰀈󰀂WT)󰀂;WTK+󰀅TK󰀂UK

(17)

(WTK;󰀄TK)2󰀅(󰀂K)

󰀈>WT,thewhere(x)󰀂denotesxwhennegative,zerootherwise.NoticethatwhenUK

󰀈󰀆WTitmaximandin(17)di¤ersfromthatin(16)onlybyaconstant,andwhenUK

coincideswith(3);the…rmchoosesthetrainingwageanddisclosurepolicytomaximizeitssecondperiodpro…ts.

Overall,wede…neanequilibriumasanarrayoftrainingcontractsforcompeti-tive…rmsfwJ;TJgJeachsatisfyingsurplusmaximisation(16),andanarrayoftrainingcontractsforskill-augmenting…rmsfwK;TKgKeachsatisfying(workerparticipationconstrained)pro…tmaximisation(17).Themaximisationproblemsareentirelystraight-forward,givenourcharacterizationofthefeasibleset󰀇(󰀂I).

5.1

EquilibriumContractsandLabourMarketOutcomes:Gen-eralResults

Here,wecanusethecharacterizationofsecondperiodwagesandpro…tsfromSection3.2.2.Inadditiontousingthesetocharacterisecontracts(whicharetypicallyhardtoobserve),wearealsointerestedintheirconsequencesforobservablelabourmarketoutcomes.Thefollowingalldependheavilyonthedisclosurepolicyandarethereforecharacterisedalongsideequilibriumcontractsfordi¤erent…rmsJ;K:1.Probabilityoflabourturnover;

2.Unconditionalwagedistributionforworkers;

3.Conditionalwagedistributionsforretainedandreleasedworkers.

Thefollowingresultholdsregardlessof󰀂J(providingGJ-disclosureisinthisset).

25

Proposition5.Foreachcompetitive…rmJwithGJ2󰀂J;

i.Contracts:Theo¤eredcontractsfeatureGJ-disclosureandatrainingwageofwJ=

󰀅GJ.ii.Labourmarketoutcomes:LabourturnovertakesplacewithprobabilityPr[RJThedistributionofemploymentwagesisidenticaltothedistributionofGJ:IfGJand(RJ󰀂GJ)areindependent,thedistributionofwagesisthesameforbothretainedandreleasedworkers;ifGJand(RJ󰀂GJ)area¢liatedthedistributionofwagesforretainedworkers…rstdegreestochasticallydominatesthatforreleasedworkers.Proof.Acompetitive…rmJchoosesGJ-disclosuresincethismaximisesexpectedsurplus.Bertrandcompetition(zeropro…ts)ensuresthatwJ=󰀅GJ=E[(RJ󰀂GJ)+].Thelabourmarketoutcomesfollowimmediatelyfromthechoiceofdisclosurepolicy.Proposition5isintuitive,themorestrikingresultswillappearwhenwecontrastwiththesituationofskill-augmenting…rms.

󰀈=E[GJ]+E[(RJ󰀂GJ)+]:Thisobser-Behaviourbycompetitive…rmspinsdownU

vation,togetherwithProposition2,enablesustosolvethemaximisationproblemin(17),andhencecharacterisetheequilibriumbehaviourof,andresultinglabourmarketout-comesfor,skill-augmenting…rmswithavailabledisclosurepolicies󰀂K=fGK;RK;?Kg.Proposition6.Foraskill-augmenting…rmKwith󰀂K=fGK;RK;?Kg;1.IfE[GK]issmall(E[GK]󰀆E[GJ]+E[(RJ󰀂GJ)+]su¢ces);then󰀈󰀂E[GK];0g:i.Contracts:GK-disclosureandatrainingwageofwK=maxfU

ii.Labourmarketoutcomes:LabourturnovertakesplacewithprobabilityPr[(RK󰀂GK)<

0]:ThedistributionofemploymentwagesisidenticaltothedistributionofGKand,ifGKand(RK󰀂GK)areindependent,isthesameforbothretainedandreleasedworkers.2.IfE[GK]issu¢cientlylarge,(E[GK]>E[GJ]+E[jRJ󰀂GJj]su¢ces);then󰀈󰀂W?;0g:i.Contracts:?K-disclosureandatrainingwageofwK=maxfUK

ii.Labourmarketoutcomes:Labourturnovertakesplacewithpositiveprobability(less

than

Pr[(RK󰀂GK)<0]):ThedistributionofemploymentwagesisdegenerateatW?K26

󰀈,thenGK󰀂disclosuremaximisessurplusandthetrainingProof.IfE[GK]󰀆U

󰀈󰀂E[GK]justmeetstheworkerparticipationconstraint.ThereforethiswagewK=U

policymaximises…rmKexpectedpro…tsubjecttotheworkerparticipationconstraint.

󰀈,thenGK󰀂disclosurewithtrainingwageswK=0remainse¢cientbutIfE[GK]>U

theworkerreceivessomeofthesurplusinexcessoftheparticipationconstraint.Ina

󰀈ispositivebutsmall,thesurpluspaidtotheworkerneighbourhoodwhereE[GK]󰀂U

remainslessthanthee¢ciencylossofswitchingtoanotherdisclosurepolicy.

󰀈ispositiveandlargeenough,theextrasurpluspaidtotheworkerunderIfE[GK]󰀂U

GK󰀂disclosurewillexceedthee¢ciencylossundernulldisclosure.Toverifythisconsider

󰀈(b)w?pro…tishigherundernulldisclosure,trainingwagesaresetatzero.Incase(b)…rm

󰀈󰀂w?)󰀇E[RK󰀂w?]󰀂U󰀈+w?=E[RK]󰀂U:󰀈Hence,pro…tisE[(RK󰀂w?K)+]󰀂(UKKK

󰀈󰀇E[(RK󰀂GK)+]:Equivalently,E[RK󰀂GK]+E[GK]󰀂U󰀈󰀇itsu¢cesthatE[RK]󰀂U

󰀈󰀇󰀂E[(RK󰀂GK)󰀂]=E[(GK󰀂RK)+]:SubstitutingE[(RK󰀂GK)+],orE[GK]󰀂U

󰀈E[GK]󰀇E[GJ]+E[(RJ󰀂GJ)+]+E[(RK󰀂GK)+]:Theresultfollowssince,byforU;

Assumption3,RJ󰀂GJandRK󰀂GKhavethesame(symmetric)distributions.Figure4displaysthesituation.Supposetheworker’soutside-optionisatthelevelofpointA(aboveWGK).Inthiscase,eventhehighexpectedemploymentwageunderGK-disclosure,failsto(strictly)satisfytheworker’sparticipationconstraint.Tohiretheworker,askill-augmenting…rmKmustsurrenderexpectedpro…tbypayingapositivetrainingwage.ItwilladoptapolicyofGK-disclosure,sincethismaximisesthe“pie”and,withtheworker’sshare…xed,leavesthelargestpossibleshareforthe…rm.

Figure4:DisclosurePoliciesgivenReservation

UtilityConstraints.

27

Alternatively,supposetheworker’soutside-optionisatthelevelofpointB(belowbutintheneighbourhoodofWGK).Inthiscase,theexpectedemploymentwageunderGK-disclosuremorethanmeetstheworker’soutside-option.Theidealstrategyfor…rmKwouldbetoo¤eranegativetrainingwagethatheldtheworkertoheroutside-option

󰀈.However,givenworkercreditconstraints,andincreasedexpectedpro…tbyWGK󰀂U

thisisnotpossible.Withthe…rmunabletoclawbackrentviathetrainingwage,switchingtoadisclosurepolicythatgeneratesadverseselectionstartstolookattractive.Unfortunatelyforthe…rm,switchingto?K󰀂disclosuredestroyssurplus.Onceithas

󰀈󰀂W?)bypayingapositivecompensatedtheworkerfortheshortfallinutility(UK

trainingwage,theremaininglevelofexpectedpro…tislessthanthatachievableunderGK-disclosure;i.e.inFigure2,pointBliestotheleftof󰀅GK.Incontrast,supposetheworker’soutsideoptionisatthelevelofpointC(somedistancebelowWGK).Nowthe…rmwillchoose?K-disclosure.Inthiscasetherenttoberecoupedislargeenoughtojustifythedestructionofsurplus;i.e.pointCliestotherightof󰀅GK.

Proposition6takesarestrictedsetofpolicesforcomparison.This,itshareswithmostofthedisclosureliterature.Theimplicationsforlabourmarketoutcomesareratherstark,especiallyinthatthedistributionofwagesforworkersintheK…rmsbecomesdegenerate.Wenowallowforawiderclassofdisclosurepolicies,again,byspecialisingtoajointnormaldistribution.

5.2EquilibriumContractsunderjointnormality

WereturntotheframeworkofSection3.3andsupposethatthe…rmcanchooseanydisclosurepolicyoftheform(11).19Westartbystatingthat…rmsneveradoptdisclo-surepolicieswhichinduceanegativeconditionalcorrelationbetweenestimatesofinsideproductivityandoutsideproductivity.Intuitively,thismakessensesinceifsuchanega-tivecorrelationwerepresent,thentheeventthataworkerisnotretainedbecomes‘goodnews’regardingtheoutsideproductivityoftheworker.Thisistheoppositeofawinners’curseandthepositiveratherthanadverseselectione¤ectwouldservetodriveupthewageo¤ersofcompetingemployers,makingitmoreexpensivetoretainworkers.This,ine¤ect,transferssurplusfromthe…rmtotheworker;however,the…rmcantransfersurplusdirectlythrough…rstperiodwages,ratherthanthroughadisclosurepolicythatdestroysoverallsurplusbymisallocatingtheworker.

Asvariousseminarparticipantshavepointedout,thisclassofpoliciesmaybebroaderthanmightbefeasiblyimplementedthroughorganizationdesign.Inthiscase,theanalysisherecanbeviewedashighlightingeconomicmechanismsandsuggestingforcesatworkwhen…rmschoosefromrestrictedand(perhapsdiscrete)disclosurepolicies.

19

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Proposition7.Underjointnormality,neithercompetitivenorskill-augmenting…rms

everchooseadisclosurepolicywith󰀃GIRI:TI<0:Proof.Thefactthateachcompetitive…rmJchoosesGJ-disclosurefollowsfromProposition1.Supposetheskill-augmenting…rmchooses󰀃GKRK:TK<0.Thenexpectedsecondperiodpro…tis

E[(RK󰀂wTK(TK))+]=E[(RK󰀂E[GKjTK]󰀂ASTK(TK))+]

󰀆E[(RK󰀂E[GKjTK])+]󰀆E[E[(RK󰀂GK)+jTK]]=E[(RK󰀂GK)+];

wherethe…rstinequalityfollowsfromASTK(TK)󰀆0andthesecondfollowsfromap-plicationofJensen’sinequality.Adisclosurepolicywith󰀃GKRK:TK<0thereforeleadstolowerexpectedsecondperiodpro…tthangeneraldisclosure.

Finally,wecanuseourcharacterizationofthefeasiblesetofwage,pro…tpairsfromResult4,tocharacterizethedisclosurepolicieschosenbyskill-augmenting…rmsis

󰀈=E[GJ]+E[(RJ󰀂GJ)+].describedasfollows,whereU

Result8.Intheindependentjointnormalmodel,foraskill-augmenting…rmK,󰀈su¢ces),thencontractsareGK-disclosureanda1.IfE[GK]issmall(E[GK]󰀆U

󰀈󰀂E[GK];0g:trainingwageofwK=maxfU󰀈su¢ces),thencontractsareadisclosurepolicyTK=2.IfE[GK]islarge(E[GK]>U

(1󰀂b)GK+bRK;withbdecreasinginE[GK];andatrainingwageofwK=0.Thisresultfollowsdirectlyfromthecalculationofthee¢ciencyfrontier.Itishelpfultocomparetheequilibriumcontractschosenbyaskill-augmenting…rmwhen󰀂KisjointnormalwiththecasediscussedinSection5.1where󰀂K=fGK;RK;?Kg:The…rstpartoftheresultissimplyarestatementofthe…rstpartofProposition6:ifthegeneralskillsacquiredat…rmKareexpectedtobelow,then…rmKchoosesGK-disclosuretomeettheworker’sreservationutilityinthemoste¢cientmannerpossible.However,if…rmKisadvantaged,sothatthegeneralskillsacquiredat…rmKareexpectedtoexceedtheworker’sreservationutility(aspinneddownbythecompetitivefringe),thenthe…rmwillswitchtoapolicythatgeneratesadverseselection.Ofcourse,itisinthe…rm’sinteresttodepresswagesase¢cientlyaspossibleandsothedisclosurepolicywillbea(noiseless)di¤erenceofinsideandoutsideproductivity.Asthesizeoftheskillgapincreases,…rmKclawsbackrentfromtheworkerbyincreasingexpectedadverseselection(decreasingbfurtherbelowzerotherebyincreasing󰀃GKRK:TK).

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5.2.1ComparativeStaticsofLabourMarketOutcomes

Thissectiontracesthemapfromtechnologicaldi¤erences,viahumancapitalmanage-mentpoliciesthroughinformationmanagementtolabourmarketoutcomesatthelevelofthe…rm.

WithVar(GK)normalisedto1,thetechnologicalpositionofaskill-augmenting…rmKischaracterisedbythreeparameters:expectedgeneralhumancapitalformationE[GK];expectedmatchqualityE[RK󰀂GK]andthevarianceofmatchqualityVar(RK󰀂GK).Thefollowingresultdescribeshowchangesintheseparametersimpactonlabourmarketoutcomesintheskill-augmentingsector(holdingthetechnologicalpositionofthecompetitivesector…xed).

Result9.Intheindependentjointnormalmodel,󰀈su¢ces),1.IfE[GK]issmall(E[GK]󰀆U

i.theprobabilityoflabourturnoverisindependentofE[GK]andVar(RK󰀂GK)and

isdecreasinginE[RK󰀂GK];ii.thedistributionofemploymentwagesisidenticaltothedistributionofGK:󰀈su¢ces)2.IfE[GK]islarge(E[GK]>U

i.theprobabilityoflabourturnoverisincreasinginVar(RK󰀂GK)anddecreasingin

E[GK]andE[RK󰀂GK];󰀈butisnolongernormal,withii.thedistributionofemploymentwageshasmeanU

inequalitydecreasinginVar(RK󰀂GK)andincreasinginE[GK]andE[RK󰀂GK]:Notethatthemodelandthisresultassumethateach…rmhasasingleworker,buttheyaresuggestiveontherelationshipbetweenwagedispersionandperformanceatthe…rmlevel.Speci…cally,skill-augmenting…rmsareabletoearnpro…tsthroughtheirrareabilitytoaugmenthuman-capitalandsoshouldbeobservedasmorepro…table.Thispro…tabilityarisessincetheyareabletoextractsomerentsfromworkers,…rstbydrivingdowntrainingwagesleadingtogreaterwageinequalitybetween…rst-andsecond-periodworkers,butalsothroughchoosinginnovativedisclosurepoliciesthatcompresssecond-periodemploymentwages,suggestingreducedsecond-periodwagedispersion.20

Empirically,however“…rst”and“second”periodshavenotbeendistinguished,whichmayaccountformixedempiricalresults(See,forexample,Martins(2008)andLallemand,Plasman,andRycx(2007)andthesummaryoftheliteraturetherein).Typically,theliteraturehaspositedthatwagedispersion

20

30

Result9isillustratedinFigures5and6(plottedforE[GJ]=E[RJ󰀂GJ]=0;

p+󰀈Var(GJ)=Var(RJ󰀂GJ)=1,implyingU=E[(RJ󰀂GJ)]=1=2󰀅).Westartby

discussingtheconsequencesoftechnologicalchangesintheskill-augmentingsectorforlabourturnover.

󰀈,labourOuranalysisofthegeneralmodelestablishedthat,forvaluesofE[GK]󰀆U

turnoveroccurswithprobabilityPr[RK󰀈Askill-augmenting…rmwillrespondtechnologicalchangethatincreasesE[GK]aboveU:

byadjustingitsdisclosurepolicy(decreasingb)toclawbacktheassociatedrentfromitsworker.Theadverseselectionassociatedwiththischangeinorganisationaldesigndepresseslabourturnover.

Asonemightexpect,labourturnoveralsodecreaseswithachangeintechnologythat‘improvesmatching’(E[RK󰀂GK]).Here,however,endogenousorganisationaldesigndampensthee¤ect.Figure5Panelbillustratesbyplottingtheturnoverrate

󰀈theturnoveragainstE[RK󰀂GK];holdingE[GK]=Var(RK󰀂GK)=1.IfE[GK]󰀆U

rateisequaltoPr[(RK󰀂GK)<0]whichisevidentlydecreasinginE[RK󰀂GK]:

󰀈,however,…rmKwillseektoimposeadverseselection.SupposethatWithE[GK]>U

E[RK󰀂GK]declinesbelow1butthat…rmK(sub-optimally)leavesitsdisclosurepolicy…xedatb󰀉󰀂0:37.LabourturnoverincreasesbutataslowerratethanPr[(RK󰀂GK)<0](comparethemiddleandthehighestlineintheFigure).Inotherwords,adverseselectionmutesthee¤ectofadeclineinE[RK󰀂GK]onlabourturnover.Thisdampening

󰀈(thee¤ectbecomesstrongerif…rmKadjustsitsdisclosurepolicytokeepitsworkeratU

bottomlineintheFigure).AsE[RK󰀂GK]declines,regressiontothemeanamelioratesadverseselection.Largerdeviations(morenegativeb)fromGK󰀂disclosurearethereforenecessarytogeneratesu¢cientadverseselectionandtheseadjustmentsdepresslabourturnoverfurtherbelowPr[(RK󰀂GK)<0].

mayexplain…rmperformanceandfocusesonworkere¤ort,inparticular,contrastingtheincentivesandwagedispersionthatariseintournaments(asinLazearandRosen,1981)withthecollaborationthatarisesfromfairnessandlowwagedispersion(AkerlofandYellen,1990andFehrandSchmidt,1999)ortheincentivesforin‡uenceactivitiesandrent-seekingthatmaybeprevalentwithhighwage-dispersion(Milgrom,1988andMilgromandRoberts,1990)orsabotageintournaments(Lazear,19).Ourresults,suggestthat…rmperformanceandtheextentofwage-dispersionmaybotharisefromtheextenttowhicha…rmhasanadvantageoveritsrivalsinaugmentinggeneralhumancapital(orprovidingaplatformforasuccessfulcareer).

31

Figure5:TheProbabilityofLabourTurnover.

32

Figure5PanelcillustratestheimpactofVar(RK󰀂GK);holdingE[GK]=1;

󰀈,…rmKwillseektoimposeadverseselection.E[RK󰀂GK]=0:Again,withE[GK]>U

SupposethatVar(RK󰀂GK)declinesbelow1butthat…rmK(sub-optimally)leavesitsdisclosurepolicy…xedatb󰀉󰀂0::LabourturnoverdecreasesfurtherbelowPr[(RK󰀂GK)<0](comparethebottomandhighestlineintheFigure).Thise¤ectismuted,

󰀈(themiddlelinehowever,if…rmKadjustsitsdisclosurepolicytokeepitsworkeratU

intheFigure):Sincepoorerinformationaboutmatchqualityreducestheregressiontothemeane¤ect,adverseselectionhitsharder.Smallerdeviations(lessnegativeb)fromGK󰀂disclosurearenecessarytogeneratesu¢cientadverseselectionandthisdepresseslabourturnoverlessbelowPr[(RK󰀂GK)<0].

Turningtothedistributionofemploymentwagesat…rmK:forvaluesofE[GK]󰀆󰀈,thedistributionofemploymentwagesisidenticaltothedistributionofGK.GivenourU

assumptionthatGKand(RK󰀂GK)areindependent,thedistributionsforretainedandreleasedworkersareidentical.ForhighervaluesofE[GK];…rmKadjustsitsdisclosure

󰀈SinceadverseselectionispolicytokeeptheexpectedemploymentwageequaltoU:

greateratlowerquantilesofTK(recallFigure3),thedistributionofemploymentwagesisnolongernormal,butbecomesnegativelyskewed.

p

Figure6Panelaillustrates.WithE[GK]=1=2󰀅,…rmKchoosesGK󰀂disclosureandsothedistributionofemploymentwagesfollowingtrainingat…rmKsimplyre‡ects

p

thedistributionofgeneralhumancapital(i.e.N[1=2󰀅;1]).IfE[GK]=2but…rmKchoosesGK󰀂disclosure,thenthedistributionofemploymentwagesistranslatedtoN[2;1].Ofcourse,itisoptimalforthe…rmtoalteritsdisclosurepolicy,inthiscaseto

󰀈and,withb󰀉󰀂2.ThisadjustmentdrivesthemeanemploymentwagebackdowntoU

adverseselectionhittinghardestonthelowTKquantiles,skewsthedistributiontotheleft.

TheremainingpanelsinFigure6holdexpectedgeneralhumancapitalformation…xedandvarythedistributionofmatchquality(RK󰀂GK).SupposethatE[GK]=Var(RK󰀂GK)=E[RK󰀂GK]=1andthat…rmKchoosesadisclosurepolicywithb󰀉󰀂0:37.IfE[RK󰀂GK]declines,sothattheexpectedretainedhumancapitalislower,but…rmK(sub-optimally)leavesitsdisclosurepolicy…xedthenthereislessad-verseselection.AsPanelbillustrates,thischangeinadverseselectionbothcompresses,andincreasesthemeanof,thedistributionofemploymentwages.Sincetheexpectedemploymentwagenowexceedstheworker’sreservationutility,itisoptimalforthe…rmtoalteritsdisclosurepolicy,heretob󰀉󰀂1:51.Thisadjustmentreintroducesadverseselectionandskewsthedistributionofemploymentwagestotheleft.

33

Figure6:TheDistributionofEmploymentWages.

34

Finally,considertheimpactofachangeinVar(RK󰀂GK):SupposethatE[GK]=Var(RK󰀂GK)=1,E[RK󰀂GK]=0andthat…rmKchoosesitsoptimaldisclosurepolicywithb󰀉󰀂0::IfVar(RK󰀂GK)declinesbut…rmK(sub-optimally)leavesitsdisclosurepolicy…xedthereismoreadverseselection.AsPanelcillustrates,thischangeinadverseselectiondisperses,anddecreasesthemeanof,thedistributionofemployment

󰀈,itisoptimalforthe…rmtoalteritsdisclosurewages.SincetheexpectedwageisbelowU

policy,nowtob󰀉󰀂0:30.Thisadjustmentremovesadverseselection,reducingtheleftskewnessofdistributionofemploymentwages.Indeed,asPanelcmakesclear,theoveralle¤ectofadecreaseinthevarianceofRK󰀂GKresemblesamean-preservingspreadinwages.

Notethatonecaninterpretanincreaseinthevarianceofanestimateasanim-provementininformation.Thisfollowssinceconditioningonextrainformationproducesameanpreservingspreadofconditionalexpectations:E[YKK󰀂YKJjQK;Q0K]isameanpreservingspreadofE[YKK󰀂YKJjQK].AnincreaseinVar(RK󰀂GK)thereforefollowsfromtechnologicalchangesthatgive…rmKabetterideaofworkermatchquality.Im-provementsininformationaboutmatchqualitythereforecompresswagedistributions.Thiscontrastswithimprovementsininformationaboutgeneralhumancapital(when…rmsarecompetitive).

6ConcludingRemarks

Thispaperhasmadetworelatedcontributions.First,wehaveintroducedamodelwhereworkersmayvaryinboththeirgeneralabilityandtheirmatchwithparticular…rms.Inthiscontext,weconsideredtheimplicationsofdi¤erentinformationstructuresonwagesandpro…ts,highlightingthatinformationstructureshaveimplicationsnotonlyforthedistributionofsurplusbetweenanemployerandworker,but,also,fortheaggre-gatesurplusthroughthepossibilityofmisallocation.Second,wecharacterisedoptimalinformationmanagementpolicies.Thesepoliciesaredeterminedaccordingtowhethertheemployerisconstrainedprincipallybytheneedtoattractworkers(participationconstraints)orbyaninabilitytofullyleverageacquiredgeneralhumancapitaltalent(creditconstraints).AshasbeenrecognisedsinceAkerlof(1970),thedistributionofinformationcanhavestriking,apparentlydisproportionate,e¤ectsonmarketoutcomes.Ouranalysishasalsohighlightedthat,whereorganisationalresponsestotechnologicalchangeimpactthroughinformation‡ows,theconsequencesforwagesandturnoverratesmayappeartobedisproportionatelylarge.

Thereareseveralnaturalextensionsthatmightbeconsideredbeyondgeneralizing

35

theresultstootherwagedeterminationprotocols,othertypesofdisclosurepolicy,ordi¤erentdistributionalassumptions.Inparticular,webrie‡ydiscussbroadeningthestrategicdecisionsavailabletoemployerstoincludeadditionaldecisionsontrainingandinformationacquisition.

First,itisnaturaltoendogenizetheextenttowhicha…rmaugmentshumancapitalinthetrainingperiod.Ifa…rmcancommittoprovidealeveloftrainingwhichwouldsupplementaworker’snaturalabilitythenintheinitialperiodofcompetition,…rmswouldcompetebyo¤eringwages,andcommittingtobothadisclosurepolicyandtraining.Aslongastrainingise¢cient(thatis,aslongasthesecondperiodproductivityitgeneratesisgreaterthanthe…rstperiodcost)thenthemostcost-e¤ectivemeanstoattractworkersisbyprovidingmoretraining.Atsomepoint,however,thismightinvolveworkerpayingforthesegeneralskillsup-front,asproposedbyBecker(19).Ofcourse,thisisimpracticalwhenthesumsinvolvedaresigni…cant,especiallyforcreditconstrainedworkersattheoutsetoftheircareers.Nevertheless,inthemannerdescribedinSection5,theworkercane¤ectivelypledgeexpectedsecondperiodwagesbyagreeingtoacontractwithaninformationdisclosurepolicythatleadstohigherexpectedsecondperiodwages.

Incontrasttoourresultsabove,evenwhenall…rmsareidentical,theymaychoosetorestricttheinformationthatisreleasedwhenallowingforatrainingdecision.Again,competitionamong…rmssuggestthat…rmsseektocreateasmuchsurplusaspossibleandtransferittoworkersinordertoattractthem.However,inSection5,theonlyleverthata…rmpossessestogeneratemoresurplusistoreleaseinformationthatallowsfortheworkertobee¢cientlyallocatedinthesecondperiod.Whenthe…rmshaveatrainingdecision,trainingispotentiallyanotherleverwithwhichtocreatesurplus.Ifthee¢cientleveloftrainingissuchthatitwoulddrivetheworker’strainingwagetothepointwheretheworker’s…rstperiodcreditconstraintbinds,thenthereisatrade-o¤betweenprovidingmoree¢cienttrainingandtransferringsurplustothe…rmtocompensateforthistrainingwhichmightrequiretheworkeragreeingtoan(ine¢cient)informationdisclosurepolicythatallowsthe…rmtoearnsomeadditionalsecondperiodrents.21Equivalently,Becker(19)hasarguedthatworkersmustpayforgeneralhumancapitalandcreditconstraintsmightthereforeleadtounderprovision;herewearguethatagreeingtoaninformationdisclosurepolicymightbeasecond-bestmeansofallowing

Notethatthisparagraphhighlightstrainingforgeneralhumancapital.Sincedisclosurepoliciesthatallowthe…rmtoearnhighersecondperiodrentsmightalsoleadtoretentionlevelswhichare,fromtheex-postperspectivewhenmatchrealizationsarerealized,ine¢cientlyhigh,theymightalsolead…rmstoprovidemorespeci…ctraining.Empirically,therefore,onemightobserve“complentarities”betweengeneralandspeci…ctraining,eventhoughthereisnotechnologicallinkbetweenthem.

21

36

theworkertopayfortraining.

Thisdiscussioncomplementsaliteratureoninformationfrictionsandtraining(forexampleKatzandZiderman(1990),orAcemogluandPischke(1999)foranoverview)whichhastypically,assumedthat…rmscannotcommittotrainingpolicies,insteadtreatinginformationfrictionsasexogenous.Inthesepapers,exogenousinformationfrictionsallowthecurrentemployertocapturesomereturnforgeneraltrainingandsoleadtotrainingprovision.Hereinstead,wepositthereversecausality:training(whentheworkeriscreditconstrainedandcannotpayforit)leadstoworkertoagreetoinformationpoliciesthatallowthe…rmtoearnareturnonitstraininginvestment.22

Finally,wehave,ofcourse,takenasomewhatnarrowviewoforganisationaldesign,evengivenourexclusivefocusoninformationmanagement.Inparticular,wehaveab-stractedfromendogenousinformationacquisition;forexample,through…rms’decisionsontheextent,natureandfrequencyofappraisal.23Forthepurposesofinducingadverseselection,acquiringmoreinformationwitha…xedamountdisclosedisakintodisclosinglesswitha…xedamountacquired.Inotherwords,…rmscanmanageinformationsimplybygettingtoknowtheirworkersbetter.Skillaugmentingandcompetitive…rmswillgenerallytakeaverydi¤erentview.Forcompetitive…rms,informationprivatelyac-quiredabouttheirworker’sgeneralhumancapitalbecomesahotpotato—somethingtobepassedontothemarketasquicklyaspossible.Incontrast,forskill-augmenting…rms,incentivestoacquireprivateinformationaboutworkerproductivityaremorenuancedandonewouldexpecttoseedeliberatepoliciesdesignedtogeneratesuchinformation.Thesedi¤erentialincentivesarelikelytoaccentuatetheincreasedwageinequalityforskill-augmenting…rmsidenti…edinthepaper.

References

[1]Acemoglu.D.(2002)“TechnicalChange,InequalityandtheLaborMarket,”Journal

ofEconomicLiterature,40(1):7–72.[2]Acemoglu,D.andPischke,J.-S.(1998)“WhyDoFirmsTrain?TheoryandEvi-dence”,QuarterlyJournalofEconomics113(1):79–119.

Intheparagraphsabovewehaveassumedthatthe…rmcancommittotraining,butevenwhenitcannot,workerswillunderstandthat…rms’equilibriumtrainingpolicieswilldependontheinformationstructuretotheextentthatthesetrainingpoliciesin‡uencethedistributionofadverseselection.23

ExogenouschangesininformationacquisitionwereconsideredinSection5.2.1,wherewecalculatedtheimpactofachangeinthevarianceofRK󰀂GKandGKonlabourturnoverandthedistributionofemploymentwages.

22

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Appendix

ProofofstatementinAssumption2.Thestatementis:E[GIjRI=r],r󰀂E[GIjRI=r]andE[GIjRI󰀂GI=r]areallincreasinginrand,foranyw2R;E[GIjRI󰀆w]󰀆E[GI]andE[GIjRI󰀇w]󰀇E[GI].LetSI=RI󰀂GIanddenotethedensityof(SI;GI)asf(s;g):Thedensityof(RI;GI)isthereforef(r󰀂g;g)itfollowsthatfroma¢liationandlogconcavitythatbothf(s;g)andf(g;r󰀂g)areTP2,i.e.both(SI;GI)and(RI;GI)area¢liated.ThisimpliesE[GIjRI=r]andE[RI󰀂GIjRI=r]areincreasinginrasrequired.Also,forallw,E[GIjRI󰀆w]󰀆E[GI].

ProofofProposition3.Bythelawofiteratedexpectations

wTI(t)=E[GIjTI=t;RI󰀆wTI(t)]=E[E[GIjTI=t;RI]jTI=t;RI󰀆wTI(t)]:Usingtheregressionequation

E[GIjTI=t;RI]󰀂󰀄G=󰀃GT:R(t󰀂󰀄T)+󰀃GR:TRI

and󰀄T=0;wehave

wTI(t)=E[󰀄G+󰀃GT:Rt+󰀃GR:TRIjTI=t;RI󰀆wTI(t)]

=󰀄G+󰀃GT:Rt+󰀃GR:TE[RIjTI=t;RI󰀆wTI(t)]:

Sincetheconditionalrandomvariablehasanormaldistribution:[RIjTI=t]󰀈NE[RIjTI=wecanwrite[RIjTI=t]intermsofastandardnormalrandomvariableZ:

[RIjTI=t]󰀅E[RIjTI=t]+󰀆RjTZ.

UsingZ,

wTI(t)=󰀄G+󰀃GT:Rt+󰀃GR:TE[RIjTI=t;RI󰀆wTI(t)]

=󰀄G+󰀃GT:Rt+󰀃GR:TE[RIjTI=t]+󰀃GR:T󰀆RjTE[ZjZ󰀆

󰀅

t];󰀆2RjT

󰀆

,

wTI(t)󰀂E[RIjTI=t]].

󰀆RjT

UsingtheregressionequationE[RIjTI=t]󰀂󰀄R=󰀃RT(t󰀂󰀄T)and󰀄R=0,wehavewTI(t)=󰀄G+t(󰀃GT:R+󰀃GR:T󰀃RT)+󰀃GR:T󰀆RjTE[ZjZ󰀆

wTI(t)󰀂E[RIjTI=t]

]

󰀆RjT

41

orusingCochrane’sidentity󰀃GT=󰀃GT:R+󰀃GR:T󰀃RT,

wTI(t)=E[GIjTI=t]+󰀃GR:T󰀆RjTE[ZjZ󰀆

Notingthatsince󰀇0(x)=󰀂x󰀇(x),

Rz

󰀂1wTI(t)󰀂E[RIjTI=t]

]:

󰀆RjT

󰀇(x)dx󰀇(z)󰀇(󰀂z)

===h(󰀂z)=󰀂

󰀆(z)󰀆(z)1󰀂󰀆(󰀂z)

0

Rz

󰀂1x󰀇(x)dx

=󰀂E[ZjZ󰀆z]

󰀆(z)

givestherequiredexpressionforwTI(t).

42