英文【世界银行】Optimal Public Sector Premium,Talent Misallocation,and Aggregate Productivity

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PolicyResearchWorkingPaper10963

OptimalPublicSectorPremium,TalentMisallocation,andAggregateProductivity

EvidencefromtheMiddleEastandNorthAfrica

FranciscoParroJesicaTorres

WORLDBANKGROUP

MiddleEastandNorthAfricaRegionOfficeoftheChiefEconomist

October2024

PolicyResearchWorkingPaper10963

Abstract

Thispaperdevelopsatractablegeneralequilibriummodeltoquantifytheaggregateproductivitygainsfromadjustingthepublicsectorpremiumandthesizeofthepublicsectortotheiroptimallevels.Intheframework,theoptimalsizeofthepublicsectoriscontingentontheefficiencylevelofpublicgoodsinincreasingtheproductivityoftheprivatesector.Themodelalsoincorporatesanendogenousdecisionbetweenmarketandnon-marketactivitiesforwomen.ThemodeliscalibratedusingdatafromtheArabRepublicofEgypt,acountrythatexhibitsadisproportionateshareofworkers,andwomenespecially,inthepublicsector.Thefindingsshowthat,underaconservativevaluefortheefficiencyofthepublicsector,aligningthepublicsectorpremiumwithitsoptimallevel,thusloweringtheshare

ofemploymentinthepublicsector,resultsinaggregateefficiencygainsof12percentforoutputperworkerand8percentfortotalfactorproductivity.Forlowervaluesoftheelasticityofprivateoutputtopublicgoods,theproductivitygainsarealmosttwiceaslarge.Theoptimalpremiumispos-itiveforwomenandapproacheszeroformen,preventingashiftofmid-high-levelskilledwomenfromthepublicsectortonon-marketactivitiesandalsoacontractionofthemaleentrepreneurialsector.Notably,areducedfemalepublicsectorpremiumfostersgreaterfemalelaborforcepartic-ipationinmarketactivitiesthroughanexpansionofthefemaleentrepreneurialsector,whichincreasesthedemandforproductionlaboranddriveswagesup.

ThispaperisaproductoftheOfficeoftheChiefEconomist,MiddleEastandNorthAfricaRegion.ItispartofalargereffortbytheWorldBanktoprovideopenaccesstoitsresearchandmakeacontributiontodevelopmentpolicydiscussionsaroundtheworld.PolicyResearchWorkingPapersarealsopostedontheWebat

/prwp

.Theauthorsmaybecontactedatfrancisco.parro@uai.clandjtorrescoronado@.

ThePolicyResearchWorkingPaperSeriesdisseminatesthefindingsofworkinprogresstoencouragetheexchangeofideasaboutdevelopmentissues.Anobjectiveoftheseriesistogetthefindingsoutquickly,evenifthepresentationsarelessthanfullypolished.Thepaperscarrythenamesoftheauthorsandshouldbecitedaccordingly.Thefindings,interpretations,andconclusionsexpressedinthispaperareentirelythoseoftheauthors.TheydonotnecessarilyrepresenttheviewsoftheInternationalBankforReconstructionandDevelopment/WorldBankanditsaffiliatedorganizations,orthoseoftheExecutiveDirectorsoftheWorldBankorthegovernmentstheyrepresent.

ProducedbytheResearchSupportTeam

OptimalPublicSectorPremium,

TalentMisallocation,andAggregateProductivity:EvidencefromtheMiddleEastandNorthAfrica*

FranciscoParrotJesicaTorres‡

Keywords:Misallocation;publicsectoremployment;aggregateproductivity;femalelaborforceparticipation.

JELClassiication:E6;H3;J2;O1.

*WehavebenefitedfromhelpfulcommentsandsuggestionsfromRobertaGatti,AartKraay,DanielLed-erman,CesarCalderon,andRaulMoralesLema.Thefindings,interpretations,andconclusionsexpressedinthispaperareentirelythoseoftheauthors.TheydonotnecessarilyrepresenttheviewsoftheWorldBankanditsaffiliatedorganizations,orthoseoftheExecutiveDirectorsoftheWorldBankorthegovernmentsthey

repe.rsidadAdolfoIb´a˜nez,SchoolofBusiness.Email:francisco.parro@uai.cl

‡TheWorldBank.Email:jtorrescoronado@

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1Introduction

Inmanycountries,thestructureofwagesandlaborlawlegislationdiffersbetweenpublicandprivatesectoremployees.Forexample,vastevidenceshowsthatapublic-privatewagegapexists(Tansel,2005;Postel-VinayandTuron,2007;Depaloetal.,2015;CalvalcantiandRodriguesdoSantos,2021;Abdallahetal.2023;amongothers).Insomecases,thepensionsystemalsodiffersbetweentheprivateandpublicsectors(CalvalcantiandRodriguesdoSantos,2021).Moreover,manycountrieshavelaborlegislationthattranslatesintomoresecurejobsinthegovernmentthaninprivatefirms(ClarkandPostel-Vinay,2009;OECD,2011;Piketty,2014;Heetal.,2018;CalvalcantiandRodriguesdoSantos,2021).1Thesefactsraisesomequestions:Isthepublicsectortoolarge?Arepublicsectorworkersbeingoverpaid?Byhowmuch?Whataretheefficiencygainsfromadjustingthepublicsectorpremiumtoitsoptimallevel?Whatistheoptimalsizeofthepublicsector?

Thispaperdevelopsatractablemodeltoquantifytheaggregateproductivitygainsfromadjustingthepublicsectorpremiumandthesizeofthepublicsectortotheiroptimallevels.Oureconomymodeldeliverstheoptimalpublicsectorpremium,andthustheoptimalsizeofthepublicsector,asafunctionoftheefficiencylevelofpublicspending.Toaccountforpotentialnon-pecuniarybenefitsthatmightattractworkerstothepublicsector(suchasmorejobstability,fewerhoursworked,prestige),wedonotrefertothepremiumasawagepremium.Keyaspectsofourmodelaretheexistenceofahome-productionsectorandthedemandformanagerialtalentinthepublicsector.2Ourpaperthenhelpsshedlightonthetrade-offsinvolvedinthepublicsectordemandfortalent,andhowthepublicsectorpremiumaffectsaggregateoutputandproductivity.

Severalexamplescanbefoundofmanagerialskillsappliedinthecontextofthepublicsectortoeffectivelyleadorganizationsandservetheneedsofthepopulation.Someoftheseskillsincludeeffectivecommunication,strategicplanning,budgetingandfinancialmanagement,policydevelopmentandimplementation,teamleadership,conflictresolution,adaptabilityandflexibility,amongothers.Publicsectormanagersendowedwithmoreoftheseskillsproducemoreofagivenpublicgood.Incontrast,thelackofmanagerialskillsinthepublicsector

1Weusethetermspublicsector,publicfirm,andgovernmentinterchangeably.

2Forbackgroundliteratureonthehome-productionsector,seeBecker(1964),Becker(1965),Benhabibetal.(1991),AguiarandHurst(2007),Beenetal.(2020),amongothers.

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translatesintoaverypoorproductionofpublicgoods.Therefore,thepublicsectorneedstoattracttalentedmanagers.However,thesetypeofagentscanalsousetheirmanagerialskills(effectivecommunication,strategicplanning,teamleadership,etc.)torunbusinessesprivately.Inotherwords,managerialskillsarealsovaluableintheprivatesectortorunprivatebusinesses.Then,thegovernmentmustpaypotentialpublicsectormanagersawagehighenoughtocompensatethemforthepotentialearningstheycouldobtainrunningtheirownfirms.Thesepotentialearningswouldbewellabovetheproductionlaborwageforindividualsendowedwithmoremanagerialskills.Consequently,apremiumarisesinthepublicsectortoincentivizesomeindividualswithmanagerialtalenttoleavetheirprivateactivitiesandacceptmanagerialrolesinthepublicsector.Becausemanagerialtalentcanalsobeattractedtothepublicsectorthroughnon-pecuniarybenefits,wedefinethepublicsectorpremiumasthepackageofmonetizedorpecuniarybenefitsreceivedbypublicsectormanagersrelativetothewagepaidtoproductionworkers.

Inourmodel,publicgoodsenhancetheproductivityofprivateactivities(e.g.,publicinvestmentininfrastructure)andtalentmustbeallocatedbetweenthepublicandprivatesectors.Alowpublicsectorpremiumattractslesstalenttothegovernment,whichlowerstheamountofpublicgoodsthatboostprivateoutput,butexpandstheprivatesectorandresultsinalargernumberoffirms.Ontheotherhand,ahighpublicsectorpremiumattractsmoretalenttothepublicsectorbutshrinkstheprivatesector.Fewerfirmswouldproducebutwithalargeramountofthepublicgood.Thistrade-offsuggeststheexistenceofanoptimalpremiumandanoptimalsizeforthepublicsector.Importantly,thisoptimalpremiumdependsonhowintensivelythepublicgoodenhancesprivatesectorproductivity.Thehighertheelasticityofprivatesectoroutputtothepublicgood,thehighertheoptimalpremiumandthelargerthesizeofthepublicsector.

Weconsideraneconomypopulatedbywomenandmen,eachendowedwithunitsofmanagerialskill.Theeconomyconsistsofthreesectors:theprivatesector,thepublicorgovernmentsector,andthehomeproductionsector(onlyamongwomen).Individualsmakedecisionsregardingemploymentineithertheprivateorpublicsector.Additionally,womenhavetheoptiontoengageinhomeproduction.Intheprivatesector,individualsmaychoosetooperatetheirownbusinessesorworkasproductionworkersforawage.Inthepublicsector,

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individualsareemployedforawage,eitherasproductionworkersormanagers.Managerialrolesinthepublicsectorreceiveagender-specificpremium.Inequilibrium,themostskilledwomenoperatebusinessesintheprivatesector,mid-highskilledwomentransitionbetweenmanagerialrolesinthepublicsectorandhomeproduction,mid-lowskilledwomenengageinproductionathome,whiletheleastskilledjointheproductionlaborforce.Regardingmen,thelowest-skilledindividualsworkasproductionworkers,somewithmid-skillsassumemanagerialrolesinthepublicsector,andthemostskilledrunprivatebusinesses.

WecalibratethemodeltomatchdatafromtheArabRepublicofEgypt.Thiscountryisaninterestingcasestudysinceitexhibitsadisproportionateshareofworkersinthepublicsector.Publicsectoremploymentiscloseto22%oftotalemployment(18%formenand42%forwomen),about7percentagepointshigherthantheaverageof108non-MENAeconomies.3Manyoftheseemployeesarehighlyeducated:amongworkerswithcollegeeducation,around25%ofmenandtwo-thirdsofwomenworkinthepublicsector.Eventhoughthemodelstructureissimple,weshowthatitiscapabletomatchseveralfeaturesoftheallocationoftalentintheEgyptianeconomy.Moreover,thetractabilityofthemodelallowstoeasilyextendtheanalysistoseveralotherdevelopingeconomies.

Wecomputeaggregateproductivitygains,intermsofoutputperworkerandtotalfactorproductivity(TFP),fromadjustingthecurrentpublicsectorpremiumandthesizeofthepublicsectortotheiroptimallevels.Weshowthatreducingthepublicsectorpremiumfromthecurrenttotheoptimallevelwouldyieldaggregategainsof12%foroutputperworkerand8%forTFPifEgyptexhibitstheelasticityoftheprivatesectortopublicgoodsoftheaveragedevelopedeconomy(0.1,BomandLigthart2014).Thelowerthevalueofthiselasticity,thehighertheproductivitygainsinourbaselineeconomyfromreducingthecurrentpublicsectorpremiumandthecurrentshareofpublicsectoremployment.

Inaddition,weshowthat,inEgypt,anoptimaltalentallocation(assuminganelasticityofprivatesectoroutputtopublicgoodsofγ=0.1)requiresadecreaseintheaveragepublicsectorpremiumfrom22%to13%,butthepremiumwouldremainpositiveforwomenandclosetozeroformen.Thiswagestructurereducesthesizeofthepublicsectorfrom22%toabout8%,andfostersfemaleentrepreneurialactivities.Moreover,comparedtoawage

3MENA:MiddleEastandNorthAfrica.SeeInternationalLaborOrganization(ILO)and

.eg/2020/08/31/public-sector-employment-mena-comparison-world-indicators/

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structurewherethepremiumisequalizedacrossgenders,itpreventsasignificanttransitionofmid-highskilledwomenfromthepublicsectortothehomeproducersector,andalso,acontractionofthemaleentrepreneurialsector.Furthermore,weshowthatalowerfemalepublicsectorpremium(andalowershareofpublicsectoremployment)promotesfemalelaborforceparticipationinmarketactivities.Thelatterstemsfromtheexpansionofthefemaleentrepreneurialsector,whichincreasesthedemandforproductionlaboranddriveswagesup.Consequently,low-skilledwomenareincentivizedtotransitionfromthehomeproducersectortotheproductionlaborforce.Then,thenumberoflow-skilledhomeproducerscontracts,morethancompensatingfortheslightincreaseinthenumberofmid-highskilledwomenleavingthepublicsectorandstartinghomeproductionasaresultofthelowerpublicsectorpremium.Thisresultthenreversesthedirectionofcausalitybetweenthedemandfortalentinthepublicsectorandfemalelaborforceparticipationtypicallyofferedintheliterature(Assadetal.2020).

Theliteraturefrequentlyassociatestheexistenceofapublic-privatewagepremiumwithanoverpaidpublicsector(e.g.,CalvalcantiandRodriguesdoSantos,2021).Oncesuchevi-denceisdocumented,thesestudiesperformacounterfactualanalysisthatinvolvesanarbitrarydecreaseofthepublic-privatewagepremiumfromitsbenchmarkvalue.Moreovertheseframe-worksdiscard,bydesign,thehome-productionsector.Ourpaperdiffersfromthattypeofanalysisinthreedimensions.First,ourmodelallowsustoderiveanoptimalpublicsectorpremium.Inotherwords,weshowthattheexistenceofapublic-privatewagepremiumdoesnotnecessarilyreflectanoverpaidpublicsector.Second,ourcounterfactualanalysisisnotarbitrary;wecomputetheefficiencygainsofbringingthecurrentpublicsectorpremiumtoitsoptimallevel.Third,oureconomymodelincludeshomeproductioncarriedoutbywomen.Thus,fewerincentivesforwomentojointhepublicsectormightresultintheirtransitiontotheprivatesectororthehomeproductionsector.Eachofthesealternativesimpliesadifferentpooloftalentinvolvedinmarketactivitiesand,thus,bringsdifferentconsequencesintermsofefficiencylevels.

Therestofthispaperisorganizedasfollows.Section2developsourframework.Section3showsthecomparativestaticsofourmodel.WepresentourcalibrationstrategyinSection4.Section5documentstheresultsfromsomecounterfactualexperiments.Sections6presentstheoptimalpublicsectorpremium.WeoffersomeconcludingremarksinSection7.

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2Model

Consideraneconomypopulatedbywomenandmen,eachendowedwithsunitsofmanagerialskill(ortalent)andoneunitoftime(inelasticallysupplied).The(given)skilldistributionG(s)isthesameforwomenandmen,withdensityg(s)andsupportintheintervalS=[s,s].Thereisamassoneofeconomicallyactiveindividualswhoproducegoodseitherinthemarketorathome.Womenandmenaccountforfractionsϕfandϕmofthispopulation,respectively,withϕf+ϕm=1.

Therearethreesectorsinthiseconomy:theprivatesector,thepublicorgovernmentsector,andthehomeproductionsector.Agentschoosewhethertoworkintheprivateorpublicsector.Womeninadditionhavetheoptionofusingtheirtalentandtimetoproduceathome.Intheprivatesector,individualscanruntheirownfirmorbecomeproductionworkersandearnawage;inthegovernment,individualsworkforawageeitherasproductionworkersormanagingothers.Thesemanagerialpositionsinthepublicsectorreceiveagender-specificpremium,whichwetakeasgiven.

2.1Privatesector

Intheprivatesectorthereisacontinuumoffirmsorbusinessesoperatedbyentrepreneurswithheterogeneousmanagerialtalent.Eachproductionunitproducesahomogeneousgoodcombininglaborl,capitalk,andmanagerialskillsaccordingtothefollowingtechnology:

y=s1-ηe(kαl1-α)ηe,(1)

whereηe∈(0,1)isthespan-of-controlparameterandα∈(0,1)denotestheshareofcapitalinthevariablefactors.4AsinGonzalezandParro(2022),thelaborofwomenlfandmenlmarecombinedusingaCESaggregatorwithanelasticityofsubstitutiongivenbyσ:

σ

l=[(lfmσ-1.(2)

4Ourequilibriumconceptinvolvesasteadystateandnotabalancedgrowthpath.Hence,wenormalizeaggregateproductivitylevelstoone,whichappliestotheprivate,public,andhome-productionsectors.

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Entrepreneursmaximizeprofits,takingwagesandtherentalpriceforcapitalservicesasgiven.Themaximizationproblemofatype-ientrepreneur,fori∈{f,m},withtalentsis:

-wfl-wml-Rki,(3)

whereRistherentalpriceforcapitalservices,lthedemandforfemaleproductionlaborbya

type-ientrepreneur,lthedemandformaleproductionlabor,kithedemandforcapital,and

wiisthewageoflabortype-i.

Thefirst-orderconditionsofthemaximizationproblemresultinthefollowingsystem(seetheAppendix):

yi(s)=Φes,(4)

(5)

(7)

(8)

where

Notethatηe<1impliesdiminishingreturnsinvariableinputs,whichresultsinanon-degenerateendogenoussizedistributionofproductionunitsintheeconomy.Notealsothatinequilibriumentrepreneurialprofitsarelinearinskill:

πi(s)=(1-ηe)Φes(9)

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Thetotaloutputproducedintheentrepreneurialprivatesectoris:

Ye=GγyE,(10)

whereyEdenotesthesumofproductionacrossentrepreneurialprivateactivities,Gcorrespondstothepublicgoodproducedbythegovernment,andγdenotestheelasticityofaggregateprivateproduction,Ye,tochangesinthesizeofthepublicgoodG.5

2.2Publicsector

InthepublicsectorthereisasinglepublicfirmthatproducesagoodGthatincreasestheproductivityintheprivatesector.Thepublicfirmcombinesmanagerialtalent,productionlabor,andcapitalaccordingtothefollowingtechnology:

G(Zp)=Z-ηp(KL-κ)ηp,(11)

whereZpistheaggregateamountofmanagerialtalentattractedtothegovernment,Lpdenotesaggregateproductionlabor,Kpistheaggregatecapital,andηp∈(0,1)isthespan-of-control

parameter.Femaleproductionlabor,L,andmaleproductionlabor,L,arecombinedasin

theprivatesectorandwiththesameelasticityofsubstitutionσ:

σ

Lp=[(L

Toattractmanagerialtalentintothepublicfirm,thegovernmentpaysagender-specificpremium,τfandτm,onthecompetitivewagesofproductionworkerswfandwm.Noticethatthispremiumisnotofferedtowageworkersinthepublicfirm.Inotherwords,whileproductionworkersearnthesamerateinthepublicandprivatesector,type-imanagersinthegovernmentearnapremiumτiinexcessofthewagerate.Definition1formallystateswhatconstitutesamanagerialpositionwithinthepublicfirm.

5Theonlyroleofthepublicgoodinthiseconomyistocomplementprivatesectorproduction.Thatis,weabstainfrompotentialwelfareimplicationsandassumethatthegoodisnotconsumedorvaluedbyworkers.Giventhattheobjectiveofthepaperistounderstandtheeffectsofpublic-privatetalentallocationonaggregateproductivity,thisisareasonableassumption.

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Definition1.Ifanagentoftype-ifori∈{f,m}ishiredbythegovernmentandearnsawage(1+τi)wi,thenthisagentisinamanagerialpositioninthepublicfirm.

Inthemaximizationproblemofthepublicfirm,weassumethegovernmenttakesthe

premiumsτfandτmasgiven.LetI(s;τi)=1beanindicatorforatype-iagentwithskills

who,givenτi,ishiredbythepublicfirm.Thenthesupplyofmanagerialtalenttothepublicsector,andthereforethesizeofthepublicgood,willdependonthepremiumonmanagerialpositionsofferedbythegovernment:

Takingasgivenτfandτm,themaximizationproblemofthepublicfirmis:

where

arethemassoffemaleandmalemanagerialtalenthiredbythepublicfirm.Theseindividualstakeamanagerialpositioninthegovernmentandearnawage(1+τi)wi,whiletherestofpublicworkersareemployedasproductionlaborandearnwi.

Thefirstorderconditionsofthemaximizationproblemresultinthefollowingpublic

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demandforinputsandsizeofthepublicgood(seetheAppendix):

G(Zp)=ΦpZp,(15)

(16) (17)

where

Analternativesetupofthepublicsectorproblemcouldhavethepremiumsτfandτm

determinedexogenouslytogetherwiththefactorsZp,Kp,L,andL.Webelievethatour

setupisabetteralternativethatoffersalowerboundontheproductivitylossesfromalargepublicsectorsincethegovernmentisoptimallysettingthequantityandcombinationofinputs,andthereforetheamountofthepublicgood,giventhepublicsectorpremiums.Discipliningthepublicsectorwiththegovernmentbudgetconstraint,forexample,wouldintroduceunnecessarycomplicationstoourmodel.Indeed,theoptimalsizeofthepublicsectorisalsoafunctionofthedistortionarytaxesneededtofundit.Sincethisproblemhasalreadybeendealtwithintheliterature,wechoosetoabstainfromthismargintofocussolelyontheallocationoftalent.6

2.3Homeproduction

Onlywomenworkinthehomeproductionsector.Inotherwords,thehomeproductionsectorconsistsofallactivitiesperformedbywomenwhodonotparticipateinthelabormarketand,thus,choosetoproduceathome.Homeproductionrequiresspecificskillsandfemalelabor,as

6Asitisstandardinthemacro-developmentliteratureonproductivitylossesfromdifferentregulations,theimplicitassumptionisthatthegovernmentisfundingthepublicfirmwithnon-distortionarylump-sumtaxes.

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outlinedbythefollowingtechnology:

h(s)=s1-ηh(l)ηh+h,(20)

wherehisalevelofhouseholdproductionthatanywomancanproduceatzerocost.Conse-quently,moretalentedorskilledwomenwillproducemoreofthehomegoodcomparedtolesstalentedwomen.

Themaximizationproblemofa(female)homeproducerwithtalentsis

−wfl(21)

Werefertof(s)asthe(net)valueofhome-producedgoodsorvalueofhomeproductionforawomanwithskills.Thefirst-orderconditionsofthemaximizationproblemresultinthefollowinghomeoutputandhomedemandforinputs:

h(s)=Φhs+h(22)

(23)

where

Moreover,thevalueofhome-production(forwomenonly)isalinearfunctionofskill:

f(s)=(1−ηh)Φhs+h(24)

TotaloutputinthehomeproductionsectorYhresultsfromaggregatingtheactivitiesofwomenwhoproduceathome.

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2.4Occupationalchoices

Tosolveforthesortingoftalentacrossbothoccupationsandsectorsweneedtoassumeanallocationrulebetweenmanagerialpositionsandwage-workingpositionsinthepublicfirm.Assumption1statesthishiringrule:

Assumption1.Thehiringruleofmanagerialtalentinthepublicfirmissuchthatthegovern-mentacceptstohireanagentiwithskillssforamanagerialpositionif,andonlyif,πi(s)≥wi.

TheallocationruleinAssumption1statesthatthegovernmentcanobservetheskillofjobapplicantsandselectsmanagerialtalentbycomparingtheprofitsthatanagentwouldgenerateasanentrepreneurtotheproductionlaborwage.Iftheformerexceedsthelatter,thegovernmentacceptstheagent’sjobapplicationforamanagerialpositioninthepublicfirmandpaysapremiuminexcessoftheproductionwagerate.Managerialpositionsinthepublicfirm—thosethatearnthepublicsectorpremium—arethenexclusivelyfilledwithworkerswiththehighestmanagerialtalent.Somecountrieshavestringentregulationsonthetypeofpositionpublicsectorworkerscanoccupyintermsofformaleducationdegreesandexperience,whichisinlinewiththeallocationruleinAssumption1(seeforexampletheEstatutoAdministrativoforChile)7.Moreover,assumingthatthemosttalentedpublicsectoremployeesbecomepublicsectormanagerswhilethelesstalentedbecomepublicsectorproductionworkersisarelativelyconservativescenariothatoffersalowerboundfortheproductivitylossesfromalargepublicsector.Alternativeallocationrulesinsidethepublicfirm(forexample,ifthelessskilledindi-vidualsweretobecomepublicsectormanagers)wouldresultinloweramountsofthepublicgood.

Agentsselecttheoccupationthatmaximizestheirearnings.Mencomparetheirprofitsasentrepreneursπm(s),theirearningsasproductionworkerswm(whetherinthepublicortheprivatesector),andtheirearningsasmanagersinthegovernment(1+τm)wm(althoughthesepositionsareonlyavailableforthemostskilledmen).Inequilibrium,amaleentrepreneurearns

profitsgreaterthanthewageofferedbythegovernmentformanagerialtalent.LetI(s;τi)be

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https://www.dt.gob.cl/portal/1626/articles-117137_galeria_36.pdf

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anindicatorforatype-iagentwithskillsswhooptimallybecomesanentrepreneur.Then,(

NoticethatamanforwhomI(s;τm)=1wouldbeeligibleforamanagerialpositionin

thepublicfirm,butthepremiumpaidbythegovernmentisnotsufficientlyhightorewardhis(relativelyhigh)talent.Inthiscase,theagentwouldchoosenottobecomeamanagerinthepublicfirmandwouldinsteadprefertousetheirmanagerialtalentintheprivatesector.

Thepremiumofferedbythegovernmentwouldattractsomemenwhopossessenoughtalenttobecomeentrepreneursintheprivatesector.Asentrepreneurs,theseindividualswouldbecapableofgeneratingprofitsexceedingtheproductionlaborwagebutlessthanthewagepaidbythegovernm