Treating Equals Unequally: Incentives in Teams,Workers' Motivation and - PDF document

Treating Equals Unequally: Incentives in Teams,Workers' Motivation and Production TechnologySebastian KubeRo'i Zultan DISCUSSION PAPER SERIES zur Zukunft der Arbeit January 2009 Treating Equals Unequally: Incentives in Teams, Workers’ Motivation and Production Technology Sebastian Goerg University of Bonn Sebastian Kube Max Planck Institute for Research on Collective Goods and IZA Ro’i Zultan Max Planck Institute for Economics Discussion Paper No. 3959 January 2009 IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 E-mail: iza@iza.org opinions expressed here are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but the institute itself takes no institutional policy positions. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. 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IZA Discussion Paper No. 3959 January 2009 ABSTRACT Treating Equals Unequally: Incentives in Teams, Workers’ Motivation and Production Technology The importance of fair and equal treatment of workers is at the heart of the debate in organizational management. In this regard, we study how reward mechanisms and production technologies affect effort provision in teams. Our experimental results demonstrate that unequal rewards can potentially increase productivity by facilitating coordination, and that the effect strongly interacts with the exact shape of the production function. Taken together, our data highlight the relevance of the production function for organization construction and suggest that equal treatment of equals is neither a necessary nor a sufficient prerequisite for eliciting high performance in teams. JEL Classification: C92, D23, D63, J31, J33, J41, M12, M52 Keywords: team incentives, equity, production function, social preferences, laboratory experiment, discriminating mechanism, mechanism design Corresponding author: Sebastian Kube Max Planck Institute for Research on Collective Goods Kurt-Schumacher-Str. 10 53113 Bonn Germany E-mail: kube@coll.mpg.de ThegeneralmodelasdescribedinWinter(2004)featuresnrisk-neutralagentswhoworkonaproject.Eachagentidecidessimultaneouslywhethertowork(ei=1)orshirk(ei=0).Exertingeortisconnectedwithcostsc,withcbeingconstantacrossallagents.Individualeortisassumedtobenon-observableandnon-contractible.Instead,agents'rewardsarecon-tingentonthesuccessoftheproject,i.e.,agentsreceiveindividualrewardsb=(b1;:::;bn)iftheprojectsucceedsand0otherwise.Theprobabilityp(k)oftheproject'ssuccessisspeciedasafunctionofthenumberkofagentsexertingeort,mappingtheeortprolesto[0;1].Inthissense,p(k)canbeinterpretedastheproject'stechnologyorproductionfunction.Weassumep(k)tobestrictlyincreasingink.Dependingontheexactspecicationofp(k),theproductionfunctioncanbemodeledtohavein-creasingordecreasingreturnstoscale.Byincreasingreturnstoscalewemeanthattheproductionfunctionisoneofcomplementarity,i.e.,thatp(k+1)�p(k)increasesink;whereasaproductionfunctionofsubstitutabil-ityhasdecreasingreturnstoscale,i.e.,p(k+1)�p(k)isdecreasingink(k2[0;:::;n�1]).4Inthefollowing,arewardvectorbissaidtobestronglyincentive-inducingifitinducesallagentstoexerteortasauniqueNashequilibrium,anditisoptimalifitdoessoatminimalcostofrewards.Themechanismissym-metricifrewardsareconstantacrossallagents.Itcanbeshownthatsuchasymmetric,optimal,stronglyincentive-inducingmechanismexistsifandonlyiftheproductionfunctionisoneofsubstitutability.Contrarily,aproductionfunctionofcomplementarityimpliestheoptimal,stronglyincentive-inducingmechanismtobefullydiscriminatingevenifallagentsareperfectlysym-metric! (1972),NalbantianandSchotter(1997)orIrlenbuschandRuchala(forthcoming),usuallyfocussesontheproblemoffree-ridersandprovidesmeanstoorganizeanddisciplineselshworkers.Complementingthislineofresearch,ourpaperpointstothedicultiesthatcanariseifincentiveschemesoriginallydesignedforselshagentsareappliedtoother-regardingagents;thus,interestingly,inoursetupitistheabsenceofselshagents,andnottheirpresence,thatconstitutesapotentialsourceofineciencyforworkteams.4Forthesakeofsimplicityweonlyconsiderthetwoextremecasesofincreasingordecreasingreturnstoscalehere.Ingeneral,theproductionfunctioncouldtakeanyform,aslongasitsatisestheassumptionofp(k)beingstrictlyincreasingink.2 eortundertheproductionfunctionofcomplementarity,notwithstandingtheunequaltreatmentofequals.Contrarily,thesymmetricrewardschemesig-nicantlyhamperseciency,demonstratingthatequaltreatmentofequalsisnotnecessarilyaprerequisiteforelicitinghighperformanceinteams,andthatunequaltreatmentcanfacilitatecoordinationwithintheworkforce.Theinsightsgainedfromourexperimentareofsignicantimportanceforresearchonoptimalmechanismdesigningeneral,butespeciallyinthecontextofworkcontractsandorganizations.AsWinterputsit:Alargenumberofmodelsinpersonneleconomicsestablishesthatunequaltreatmentofunequalagentsmayhavemajorincentiveadvantages.Theparticularim-portanceofdemonstratingtheoptimalityoftreatingequalsunequallyisthatitpotentiallyimpliesanadditionalgainforinequalityineachofthesemod-els(Winter(2004),p.766).Wecomplementthisassertionbyascertainingitinanempiricalway.Inthisregard,wecontributetothequestionofequalityversusinequal-ity,whichisattheheartofthedebateinorganizationalmanagement.Inter-nalinequityisthoughttohaveatendencytoleadtomoraleproblemsandtointerferewithteamwork(cp.AkerlofandYellen1990,MilgromandRoberts1992,orBewley1999,chapter6),whereasequalwagesareusuallyassoci-atedwithpositiveeects(e.g.,increasedpeermonitoringorlowertransac-tioncosts,seeKnezandSimester2001orPrendergast1999).However,asLazear(1989,p.561)putsit,..itisfarfromobviousthatpayequalityhastheseeects.Forexample,equalwagesdonotaccountforheterogeneityinagents'abilityandperformance,andpaymentisnotlinkedtotheindivid-ual'smarginalproduct,whichinturncanleadtofree-ridingamongselshagents(cp.Holmstrom1982).Moreover,aswedemonstrateinoursetup,equalrewardsmakeithardtoformexactbeliefsabouttheothers'eort.Incontrast,theasymmetrythatiscreatedbyunequalrewardshasthepotentialtofacilitatecoordinationwithintheworkforce,becauseitreducesstrategicuncertaintyabouteachothers'actions.Inreal-lifeorganizations,thisdiscriminationisoftenimplementedthroughnon-monetaryrewards,e.g.,prestige,orbyusingarticialclassicationsor(job)titlesforseeminglysimilartasks,e.g.,`ProjectHead'or`TeamCap-4 withholdeorttopunishandenforceprincipalstopayhigherwagesinthefuture,whichtousnotonlyseemsdiculttoreconcilewithreal-worldwork-relationships,butadditionallyisoutsidethescopeofWinter'smodel.Fourth,tothebestofourknowledgewearethersttopayattentiontotheimportantroleoftheproductionfunctioninalabormarketsetting.8Ourndingthatagents'behaviorissensitivetotheshapeoftheproductionfunctionshouldbetakenintoaccountinfutureempiricalresearchontheinteractionbetweensocialpreferencesandrewardschemes.Theremainderofthispaperisorganizedasfollows:Inthenextsection,wedescribetheexperimentaldesignandderivetheoreticalpredictions.Sub-sequently,theexperimentalresultsarepresentedanddiscussedinSection3,andSection4concludes. 8Normannetal.(2007)examinetherelationbetweenproductionfunctionandtheexistenceoflarge-buyers'discounts.6 constant(individualrewards,costs,productionfunctionandgroupcompo-sition).Thiswasdonetoallowforpossiblelearningtotakeplace.Afterourexperiment,subjectshadtocompleteasocialvalueorientationtest12andasocio-economicquestionnaire.Thecomputerized13experimentswererunin2007attheBonnEconLabattheUniversityofBonn.Participantswererandomlyrecruitedviaemailinvitationoutofapproximately3000personsfromtheBonnEconLab'ssub-jectpool(includingmostlyundergraduatestudentsfromalargevarietyofelds).Foreachtreatment,werantwosessionswith18subjectseach;to-talling12independentmatchinggroups(allperiods)or36independentde-cisions(onlyrstperiod)pertreatment.Unfortunately,inonesessionintreatment444COM,only15subjectsshowedup,sothatwearemissingoneofthetwelveindependentobservationsinthistreatment.Asessionlastedap-proximately70minutes.Subjectswerepaidfortheirdecisionandtheirbeliefintherstperiod,andadditionallyforonerandomlyselectedperiod(whichwasconstantacrossallsubjectswithinasession)outofthesubsequentveperiods.Onaverage,subjectsearnedapprox.7Euro.2.2BehavioralPredictionsInthissectionwederivethepossibleequilibriaundertheclassicalassump-tionsofagentsbeingfullyrational,self-centered,money-maximizing,andrisk-neutral14.Aswillbeseen,thedegreeofeciency,denedasthesumofagentsexertingeortinequilibrium,issensitivetotheproductionfunc-tionandtotherewardmechanism.Subsequently,wedemonstratehowthepredictionschangeonceweintroduceagentswhoareadditionallymotivated 12The`ringtest'isdescribedforexampleinGriesingerandLivingston(1973)orLiebrand(1984);seealsoBeckenkamp(1995)foranearlyapplicationinEconomics.13TheexperimentwasprogrammedinPascalusingRATimagebyAbbinkandSadrieh(1995).ThequestionnaireandtheringtestwereconductedusingzTreebyFischbacher(1999).Screenshotsoftheprogramcanbefoundintheappendix.14OurgameasdescribedinSection2.1canberewritteninaprobabilisticway,whichistheinterpretationusedbyWinter(2004).Weinsteadoptedforadeterministicrepre-sentationtoimposerisk-neutralityoverthenaloutcomeoftheproject,i.e.,topaytheexpectedvalueofalotteryratherthantoactuallyimplementthelottery.Thisallowsustoabstractfromsubjects'individualriskpreferences.9 Figure1:Player'spayofunctionbytypeanddecision Inbothtreatments,thepayosforthe5-typeplayersfromworkingdominatethepayosfromshirking,andsothepossibilityofzeromatchedagentsworkingcanbeeliminatedfortheotherplayers.Nowworkingdominatesshirkingforthe4-typeplayersundercomplementarity,whiletheoppositeistrueforthe3-typeplayersundersubstitutability.Theremainingplayerinbothtreatmentnowmaximizesherpayobyworking.Thustheequilibriaarederivedthroughrepeatedeliminationofdominatedstrategies.Thetwopureequilibriaoftheegalitariantreatment444COMarerevealedbythecrossoverofthepayofunctionsofthe4-typeplayerundercomplementarity.Notethatthegainfromworkingcanbeseentoincrease(diminish)undercomplementarity(substitutability).previousone.Foranygiveneortsum,thenumberofunitsproducedisalwaysequalorhigherundersubstitutabilitythanundercomplementarity.However,in345SUBthediscriminatingrewardschemeisnotoptimalany-more,becausethethreshold-orderisreversedunderaproductionfunctionofsubstitutability(i.e.,X02:6,X1=3:6andX2=4:5).Thus,thelow-rewardplayershirksinequilibrium,whiletheothertwoplayerswork;andallplayersholdcorrespondingbeliefs.Thepayostructureofthegameandtheequilibriaderivationareillustratedingure1.Infact,Winter(2004)showsthatthetotalcostsofanoptimal,stronglyincentive-inducingrewardschemearealwayslowerundercomplementarity11 insteadof(310;310;310));whichissomethingthat(notonly)aninequality-aversesubjectwouldneverprefer.Takentogether,ifsubjectsaremotivatedbyequityconsiderationsinsteadofbeingself-centeredandmoney-maximizing,inthesymmetrictreatmentwecannotnecessarilypredictalowereciencythaninthediscriminatingtreatmentanymore.Alreadyameageramountof(uncertaintyabout)equal-itypreferencesreversestheinitiallylowamountofstrategicuncertaintyin345COM,whereasthesymmetricmechanismin444COMisratherrobustinthisrespect.Thisisrecapitulatedinthefollowingtable,whichliststhepos-sibleequilibriainpurestrategiesforself-centeredsubjectsintherstrow,andinthesecondrowtheequilibriathatmightadditionallyemergeinthepresenceofequity-considerations: Treatment 345SUB 345COM 444COM productionfunction substitutability complementarity rewardmechanism discriminating symmetric self-centered (0,1,1) (1,1,1) (1,1,1),(0,0,0) inequality-averse (0,0,1) (0,0,0),(0,0,1),(0,1,1) noadditionalequ. 13 sumtest,Prob�jzj=:0004).In345COM,6outof12(9/12)groupsexertfulleortinallperiods(allbutoneperiod),whereasthesameisneverobservedin345SUB.Thedierenceineciencybetween345COMand345SUBispredictedtostemfromadierenceinthebehaviorofthelow-rewardtypeinequilibrium.AscanbeseeninFigure2,theaverageeortlevelofthelow-rewardtypein345SUBissignicantlylowerthanthatoftheothertwotypes(22.2%vs.81.9%and91.7%,signed-ranktest,Prob�jzj=:0074and:0039).Itisalsosignicantlylowerthantheeortlevelofthesametypeinthecomplementaritytreatment(22.2%vs.88.9%,rank-sumtest,Prob�jzj=:0001).Subjects'individualbeliefsareinlinewiththending.In345COM,medium-andhigh-rewardplayersbelievethatthelow-rewardplayerwillworkin85%ofallcases,whilein345SUBthelow-rewardplayerisexpectedtoworkinonly33%ofallinstances(rank-sumtest,medium-reward:Prob�jzj=:0004,high-reward:Prob�jzj=:0007).Theeortlevelsofthemedium-andhigh-rewardtypesin345COM(88.9%and97.2%)donotdierfromthecorrespondinglevelsthatweobservein345SUB.Overall,whenstandardequilibriumpredictionsdictateeortexer-tion,theobservedeortlevelsareover80%.Intheonecaseinwhichtheequilibriumstrategyistoshirk,indeedalmost80%ofthedecisionsaretoshirk.Comparingthesumsofeortpermatchinggroupintherstroundandthelastround,wendnoindicationofasignicanttimetrend(signed-ranktest:345COMProb�jzj=:65;345SUBProb�jzj=:31).17Thebehaviorintherstroundrevealsasimilarpictureasabove.Again,thenumberoflow-rewardplayerschoosingtoexerteortismuchhigherin345COMthanin345SUB(16.7%vs.75%;Fisher'sexacttestp=:012).Fortheothertwoplayertypesthedierencesacrosstreatmentsareonlymarginalandstatisticallyinsignicant(medium-rewardtype:91.7%vs.91.7%,p=1;high-rewardtype:100%vs.91.7%,p=1).Takentogether,underadiscriminatingrewardschemetheeortprovi- 17Cp.thecorrespondingtime-seriesdatainFigures3and4intheappendix.15 costoftherewardmechanismconstant,theobservedmeaneciencyintherstperiodislowerunderthesymmetricrewardmechanism(78.9%)thanunderthediscriminatingone(88.9%),albeitnon-signicant(rank-sumtest,Prob�jzj=:1552).Overthecourseoftheexperiment,thedierencegrowslargerandsignicant(averageeciencyoverallperiodsof72.2%vs.91.7%,rank-sumtest,Prob�jzj=:0649;cp.Figure2).Onaverage,everyrewardtypeinthediscriminatingtreatmentprovidesmoreeortthantheplayersinthesymmetrictreatment.Only3outof11groups(4/11)exertfulleortinallperiods(allbutoneperiod),comparedto6outof12(9/12)groupsin345COM.Moreover,thestandarddeviationofgroupecienciesissig-nicantlyhigherin444COMthanin345COM(0:233vs.0:158,Conover'ssquared-rankstest,Prob�jzj=:0143).Noticethatthedierenceisnotanartifactresultingfromthehighdegreeofeciencyin345COM(whichputsaboundonthevariance),asthegroupecienciesin345SUB,inwhichtheoveralleciencyissimilartothatin444COM,showanevenlowerstandarddeviationof0:068(cp.Figure6intheAppendix).Ourresultsuggeststhatequaltreatmentofequalsdoesnotnecessar-ilypromotefulleortprovisionwithinateamofagents.Apotentialrea-sonfortheobserveddierenceineciencybetweenthesymmetricandthediscriminatingmechanismmightbetheintroductionoftheadditional`all-shirk'-equilibriumintreatment444COM.Eventhoughitispayo-andrisk-dominatedbythe`all-work'-equilibrium,themultiplicityofequilibriaintro-ducesstrategicuncertainty(cp.vanHuycketal.(1990)).20Playersformu-latingbeliefsareuncertainwhethertheotherplayersintheirgroupwillworkorshirk,whichisvisibleinourdata:83%expectbothotherplayerstoworkin345COM,whereasonly62%dosoin444COM(rank-sumtest,Prob�jzj=:0979).Thistranslatesintoloweciencyratesandahighvarianceofgroupecienciesin444COM,suggestingthatstrategicconsider-ationsshapedbytherewardmechanismarecrucial,andoutweighpossibleequitypreferencesofthesubjects.21Theasymmetryoftherewardmech- 20Notethatstrategicuncertaintyshouldalsobepresentin345COM(cp.Section2.2),because`all-work'and`all-shirk'arepotentialequilibriaonceweallowforequityconsid-erations.Yet,weobservealmostfulleciencyinthistreatment.21Onemightconsiderthattheresultmaybedrivenbyadierenceinthesubjectpop-17 inpractice.First,theyclearlypointtotherelevanceoftheproductionfunc-tionfororganizationconstructionafactorwhichhassofarreceivedlittleattentionintheliterature.Designing(production)tasksinawaythatmakesworkers'eortscomplementsratherthansubstitutesmayleadtoamajorcostadvantage.Insofaraspeerpressureconstitutesacomplementarityineortexertion,thestrengtheningofsocialtiesamongsttheworkforcealonemighthaveastrongimpactonproductivity.Second,andcloselyrelated,isourndingthatunequaltreatmentofequalsdoesnotnecessarilyhampereciency.Whenevertheorganizationaltechnologyisoneofcomplementarity,i.e.,whenevertheimpactofaworker'sinputincreasesinthesizeoftheothers'input,theusageofadiscriminatingrewardschememightbepotentiallyeciency-enhancing.Themainreasonforthisisthatasymmetricrewardsfacilitatecoordination,becauseworkerscananticipatethatthosewhohavehighstakesathandwillcertainlyexerteortwhichinturnincentivizestheotherworkerstoexerteortaswell.Considerthatdiscriminationmustnotnecessarilybeinmonetaryterms,butmightalsotaketheformofhierarchies.Whileavastbodyofliteratureinpersonneleconomicsalreadypromotestheimplementationofhierarchies(e.g.,LazearandRosen(1981)),ourresultssuggestthathierarchiesmightenhanceperformancedespitetheabsenceoftheexistingliterature'susualassumptionsofmonitoringorauthorityrelations.Inthisregard,wemoregenerallycontributetotheongoingresearchonbehavioralphenomenainorganizations.AsJamesKonow(2000)putsit:Manyofthesuccessesofeconomicscanprobablybeattributedtoitspushingtheassumptionofself-interesttotheextreme.Toproceedfurther,however,itmaybenecessarytoincorporatericherbehavioralassumptionsthatincludefairnessandothermoralstandards.(Konow(2000),p.1089).Whileweagreeinprinciple,itshouldbeaddedthatitisadditionallynecessarytoidentifythesituationsinwhichbehaviorisinlinewiththeclassicalmodelwhichisultimatelyanempiricalquestion.Onlythencanwereallyunder-standhowtomodelthericherbehavioralassumptionsinawaytoadvanceEconomics.Theresultsinthispapershouldnotbetakenasargumentsagainsttheim-19 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AppendixA:InstructionsThisistheEnglishtranslationoftheinstructionsusedintreatments345COMand444COM.Intreatment345SUB,thetableandexampleswereadjustedtottheproductionfunction.Welcometothisdecision-makingexperiment.Pleasereadthefollowingin-structionscarefully.Theexperimentwillbeconductedanonymously,thatistosayyouwillnotlearnwithwhomoftheotherparticipantsyouareinteracting.Pleasekeepinmindthatfromnowonandthroughouttheex-perimentyouarenotallowedtotalktotheotherparticipants.Ifyouhaveanyquestions,pleasegiveasignalwithyourhandandwewillcometoyou.DuringtheexperimentyoucanearnTaler.Howmuchyouearndependsonyourdecisionsandthedecisionsoftheotherparticipantsinyourgroup.AttheendoftheexperimenttheseTalerwillbeconvertedtoEuroatanexchangerateof80Taler=1EURO.TheEuroamountwillbepaidouttoyou.Youwillbecalledtocollectyourearnings.Pleaseturninallinstructionsheetswhenyoucollectyourearnings.Inthisexperimentyouwillberandomlydividedintogroupsofthreepersons.Togetherwithtwootherparticipantsyouformagroup.Eachparticipantdecideswhetherhewantstoworknormalorhard.Themoreparticipantschoosetoworkhard,themoreunitsofgoodswillbeproduced. Number(#)ofhardworkingparticipants 0 1 2 3 Producedunitsofgoods 20 40 65 100 Examples:Incasethatallparticipantsofthegroupworknormal,20unitswillbeproducedaltogetherinyourgroup.Ifyouworkhardandanotherparticipantinyourgroupworkshardaswell,65unitswillbeproducedaltogetherinyourgroup.etc...goodForeachunitofgoodsproduced,youreceiveacertainamountofTaler.AtthebeginningoftheexperimentyouareinformedhowmanyTaleryouearnperunitproduced.Additionally,youlearnhowmanyTalerperunittheothertwoparticipantsinyourgroupearn.Examples:Inthebeginningoftheexperimentyouaretoldthatyoureceive5Talerforeachunitproduced.In25 Playertype 345COM 345COM vs. vs. 345SUB 444COM 3 .0001 n.a. 4 n.s. n.a. 5 n.s. n.a. Means .0004 .0649 Table2:Comparisonofmeanecienciesbyplayertypesbetweendierenttreatmentswithtwo-sidedrank-sumtest. Figure3:Eortperrewardtypeovertimein345COM29 Figure4:Eortperrewardtypeovertimein345SUB Figure5:Eortperagentovertimein444COM30