Impacto de la legislación de protección del empleo sobre la productividad laboral en un modelo combinado de equilibrio general

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Cuadernos

de

economía

www.elsevier.es/cesjef

ARTICLE

The

impact

of

employment

protection

legislation

on

labour

productivity

in

a

general

equilibrium

matching

model

Domenico

Lisi

DepartmentofEconomicsandBusiness,UniversityofCatania,Catania,Italy Received12December2012;accepted26March2013

Availableonline19September2013

JEL CLASSIFICATION J24; J38; J63; J64 KEYWORDS Employment protection; Endogenouslabour productivity; Jobdestruction

Abstract ThestandardanalysisoftheimpactofEPLonlabourmarketoutcomesconcentrates mainlyonunemploymentandjobflows,disregardingpossibleeffectsonlabourproductivity. Inthispaperwemake(acomponentof)labourproductivityendogenousandanalyzehowthe presenceofastringentprotectionlegislationaffectslabourmarketinanequilibriummatching modelwithendogenousjobdestruction.Inparticular,inourstudyweimaginethatanemployed workerhastoexertefforttoproduceandthisgeneratesdisutility.Therefore,inthisframework highlabourproductivityononehandiscostlyforaworkerintermsofdisutility,andonthe otherhandmightbebeneficialintermsoflowerjobdestruction.Wefindthathighfiringcosts partiallysubstitutehighlabourproductivityinreducingjobdestructionandthis,consequently, bringsdowntheoptimallevelofproductivity.Furthermore,theimpactofEPLonunemployment isambiguousbutnumericalexercisesshowunambiguouslyhowhigherfiringrestrictionsreduce differentmeasuresofaggregatewelfare.Tosomeextent,theclearemergenceoftheseresults leadstointerestingpolicyimplicationsand,indeed,rationalizestherecentempiricalevidence ontheimpactofEPL.

CÓDIGOSJEL J24; J38; J63; J64 PALABRASCLAVE Protección delempleo; Productividadlaboral endógena;

Impactodelalegislacióndeproteccióndelempleosobrelaproductividadlaboral enunmodelocombinadodeequilibriogeneral

Resumen ElanálisisestándardelimpactodelaEPLsobrelosresultadosenelmercadolaboral se concentra sobre todo enel paro y en losﬂujos de trabajoy paro. En este documento hacemosendógena(uncomponentede)laproductividadlaboralyanalizamoscómoafectaal mercadolaborallapresenciadeunalegislacióndeprotecciónrigurosaenunmodelocombinado deequilibrioapropiadoconladestruccióndeempleoendógena.Concretamente,ennuestro estudioimaginamosqueuntrabajadorporcuentaajenadebehaceresfuerzosparaproducir y esto genera desutilidad.Por lotanto, dentro de este marco, para un trabajador la alta

E-mailaddress:[email protected]

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Destrucción deempleo

productividadlaboralescostosaentérminosdedesutilidad,perotambiénpuedeserbeneﬁciosa porloquesereﬁerealamenordestruccióndeempleo.Observamosqueelaltocostedeldespido sustituyeparcialmentelaaltaproductividadlaboralalreducirladestruccióndeempleoy,en consecuencia, estoreduce elnivel óptimodeproductividad. Además,elimpactodela EPL sobre eldesempleo esambiguo,pero loscálculosnuméricosmuestran de maneraevidente cómo lasmayoresrestriccionesdeldespidoreducendiferentes medidasdebienestarglobal. Enciertamedida,laapariciónevidentedeestosresultadosconllevaimplicacionesnormativas interesantesy,loqueesmás,racionalizalaevidenciaempíricarecientesobreelimpactodela EPL.

1. Introduction

Recent empirical evidence from European countries and the US shows that the presence of stringent employ-mentprotectionlegislation(EPL)affectssigniﬁcantlylabour productivity. In particular, cross-country (DeFreitas and Marshall,1998),diff-in-diff(MiccoandPages, 2006; Autor etal.,2006,2007;BassaniniandVenn,2007;Bassaninietal., 2009; Lisi,2013)and other studies(Riphahn, 2004;Ichino andRiphahn,2005)foundthathigherEPLhaveanegative impactonlabourproductivity.

Nonetheless,standardtheoreticalanalysisofEPLfocuses mainlyonunemployment andjobﬂows,disregarding pos-sible effects on labour productivity. In particular, both standard analysis of labour demand under uncertainty (Bentolilaand Bertola,1990; Bertola,1990;Bentolila and Saint-Paul, 1992; Bentolila and Dolado, 1994; Boeri and Garibaldi,2007)andgeneralequilibriummodels(Mortensen and Pissarides, 1994, 1999b; Garibaldi, 1998; Pissarides, 2000; Cahuc and Postel-Vinay, 2002) tend to consider an exogenous productivity, not inﬂuenced by the presence of labour-market policies. Indeed, some studies analyze the role of EPL in distorting the adjustment of employ-ment andinvestment,consequently affecting productivity (Hopenhayn and Rogerson, 1993; Saint-Paul, 1997, 2002; BartelsmanandHinloopen,2005).

Inthispaper,inthespiritofIchinoandRiphahn(2005), we concentrate more on the behavioural component of productivity.Therefore,wemake(acomponentof)labour productivityanendogenousobjectofthemodeland,then, studytheimpactofastringentprotectionlegislation.Since ourconcernistounderstandtheequilibriumimpacton pro-ductivity, unemploymentand welfare,we need toembed theanalysis intoan equilibriummodelof thelabour mar-ket. Tothisextent, thematching approachtoequilibrium unemploymentshouldrepresentthebestcandidateforthis kindofanalysis.

Inthecanonicalmatchingmodeltotalproductivityis usu-ally characterized by an exogenous common component, affectingproductivityinalljobs,andanidiosyncratic com-ponent,governed byastochastic process.Indeed,in such speciﬁcationofproductivitytheredonotseemtobeplace for workers. Differently, in our study we imagine that an employed workerhas to exert effort toproduce and this generates disutility. Following this argument, we assume

thatacomponentofproductivityisdeterminedbythelevel ofeffortexertedbyworkers.Thus,inthisframeworkhigh labour productivity onone hand is costly for a worker in termsofdisutility,andontheotherhandmightbebeneﬁcial interms of lowerjobdestruction. Since stringent protec-tionlegislationhasthesamewell-knowneffectofreducing job destruction (e.g. Pissarides, 2000), EPL might affect totalproductivityalsothroughthisbehaviouralcomponent. Therefore,thenoveltyintroducedinthispapershould con-tribute to offer a more comprehensive evaluation of the impactofEPLonlabourproductivityand,moregenerally, onlabour-marketoutcomes.

Anequilibriumisajobdestructionandjobcreationrule, alabourproductivityandalevelofunemploymentimplied bythe rational expectations behaviour of individual firms andworkersandbythematchingtechnology.Westudyhow the presence of a stringent protection legislation affects productivity,unemployment andwelfare in the aggregate steady-state.Wefindthathighfiringcostspartially substi-tutehighlabourproductivityinreducingjobdestructionand this,consequently,bringsdowntheequilibriumlabour pro-ductivity.Furthermore,theimpactofEPLonunemployment isambiguousbutnumericalexercises showunambiguously howhigherfiringrestrictionsreducedifferentmeasuresof aggregatewelfare.Tosomeextent,theclearemergenceof theseresultsleadstointerestingpolicyimplications, espe-ciallyinthelight ofthegreatdebateemergedinthelast yearsregardingEPL.Moreover,theextensionpursuedinthis paperwouldofferareasonableinterpretationtorationalize therecentevidenceonthenegativeimpactofEPLon pro-ductivity.Indeed,thisapproachtoconsiderlabourmarket outcomesandpersonneleconomicstogetherin addressing policyquestionshasalreadyturnedouttobesuccessful(see e.g.ShapiroandStiglitz,1984).

In regards to how this paper places in that strand of literature aiming to evaluate the impact of EPL, the maincontributionconsistsinintroducinglabour productiv-ity (besides unemployment and job ﬂows) in the general equilibriumevaluationofthisparticularpolicyinthelabour market.Tothisextent,thepapersharesthesamespiritof Lagos(2006).Inparticular,thatpaperproposesan aggrega-tivemodelofTFPinthematching framework,allowingto evaluatetheimpactoflabour-marketpoliciesonthegeneral aggregateproduction functionand, especially,onaverage TFP.Nonetheless,inLagos (2006)higherﬁringcostsaffect

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TFPonlybyreducing ﬁrms’jobdestructioninresponseto negativeshocks,implyingaloweraverageidiosyncratic pro-ductivityofactiveunits.Indeed,inthemodelproposedhere wewillseethatamorecomprehensive evaluationofEPL, beyondtheimpactontheaverageidiosyncraticcomponent, shouldconsideralsotheimpactonthebehavioural compo-nentofproductivity.

Ontheotherhand,thispaperisalsoclosetoDoladoetal. (2011),aimingtoevaluatetheimpactofhavinglarge differ-encesbetweenEPLforpermanentandtemporarycontracts onendogenousworkers’effortandfirms’conversionrates. Interestingly,theyfindthatanincrease infiring costsgap wouldleadtoareductioninbothfirms’conversionrateand effortexertedbytemporaryworkers.Nonetheless,asstated intheirpaper,theyfocusontemporarycontractsinsomuch asthey stillconsider productivity for permanent employ-mentexogenousand,inturn,notinfluencedbyprotection legislation.Moreover,inordertostressthemechanism link-ingfiringcoststoconversionratesandtemporaryworkers, theyworkinapartialequilibriumframeworkunderdifferent assumptions.1 _Differently, _in _this_paper _we _aim _to under-linethekeymechanism wherebyEPLcouldaffectaverage labour productivity of regular workers in a general equi-libriumframework, that is, not only by reducing average idiosyncraticproductivityofactiveunits,butalsoby substi-tutinghighlabourproductivityincontainingjobdestruction. The restofthepaperproceedsasfollows:inSection2 wedescribethebasictheoreticalframeworkandinSection 3 characterize itssteady-state. Section 4 studies qualita-tivelytheimpactofastringentprotectionlegislationonthe equilibriumlevel.InSection5weconductsomenumerical exercisetostudytheeffectonproductivity,butalsoon dif-ferentmeasureofaggregatewelfare.Section6concludes. Finally,AppendixAcontainssomeusefulderivations.

2. The

theoretical

framework

Thebasictheoreticalframeworkisthematchingapproachto equilibriumunemploymentwithendogenousjobdestruction (e.g.Pissarides,2000).Inthiseconomythereisan endoge-nouslysizedcontinuumofjobs,characterizedbyacommon component of productivity p and an idiosyncratic compo-nent x. Each product commandsin themarket a priceof px, whichevidently differs fromeach other for the pres-enceoftheidiosyncraticcomponent.Instandardversionsof thismodelpisusuallyconsideredanexogenousparameter, capturingmacroeventsthataffectproductivityinalljobs bythesameamountandinthesamedirection.Differently, inthispaperweinterpretpasthebehaviouralcomponent oflabourproductivity,withxstillrepresentingthe idiosyn-craticconditioninthemarket,duetodemandortechnology. Therefore,inourmodelwedonotconsiderpaparameter

1_In_particular,_Dolado_et_al.₍₂₀₁₁₎_work_in_a_partial_equilibrium environmentwithcertainty,implyingexogenousvacancyﬁllingand jobdestructionrates.Moreover,theyassumealineardisutilityof effort(whereashereweworkwithanincreasingdisutility),which representstheuniquecomponentofproductivity(thatis,without anystochasticidiosyncraticcomponent).Therefore,intheir frame-work neither job destruction nor labour productivity of regular workersisaffectedbyEPL.

capturingmacroshocks,becauseouraimisindeedtostudy howﬁringcostsaffectthelevelofthebehavioural compo-nentofproductivity.However,itisevidentthatthereisno difﬁcultyinincludingalsosuchparameterinourmodel.

Thestochasticprocessgoverningtheidiosyncratic com-ponent xis Poisson witharrival rate . Whenevera jump arrives,thenewlevelofxisdrawnfromthedistributionG(x) withﬁniteuppersupport ¯xandnomasspoint.ThePoisson processimpliesthatshocksarepersistent,but conditional onchangethenewdrawsareindependentbytheinitiallevel ofx.

Eachfirmhasonlyonejobthatcanbeeitherfilledand producingsomegood(stateJ(x)),accordingtothe idiosyn-craticlevelxandthebehaviouralproductivityp,orvacant and searching for a worker (state V), which costs pc per unitoftime.Firmshavefullinformationontechnologyand market condition, therefore theycreate always the most profitable job,that is, withthe idiosyncraticlevel at the upper supportof the pricedistribution.Furthermore, the Nash bargaining rule impliesalso that newjobs offer the highest wage. However, investments are irreversible and whenashockarrivesfirmshavenochoiceovertheir produc-tivity.Filledjobsnotalwaysresisttonegativeproductivity shocksand,inparticular,theyaredestroyedwheneverthe newdrawofxfallsbelowacertainlevelofreservation pro-ductivityR.Thisimpliesthateachjobhasaprobabilityof beingdestroyedequaltoG(R).Jobdestructionisnot cost-less,ratherwheneverajobisdestroyedfirmhastopaythe firingcostspF.

Respectively,each workercanbein oneoftwostates, employedandproducingsomegood(stateW(x))or unem-ployedandsearchingforajob(stateU).Employedworker receivesthewagew(x)andhastochoosehowmucheffort e to exert in the job, which determines the common component of productivity p=f(e). Even if not neces-sary,weassumealinearrelationp=e betweeneffortand productivity.2_On_the_contrary,_unemployed_worker_does_not exerteffortand beneﬁtsonlyfromz,which canbe inter-pretedeitherasunemploymentcompensationorasleisure. Wages aretheoutcome ofthe Nash bargaining,according towhich workers receive afraction0<ˇ<1 of thematch surplus, where ˇ can beinterpreted asthe workers’ bar-gaining power. Since the match surplus is conditional on idiosyncratic productivity, wages are revised whenever a productivityshock occurs. Inparticular,itis intuitivethat bothmatchsurplusandwageareincreasingfunctionofx. Followingtheprevious literature,weassumethatworkers areriskneutralandimpatient,whichimplieszerosavingand fullconsumption.Furthermore,exertingeffortgeneratesan increasingdisutility.Therefore,anemployedworkerenjoys conditionalonxtheinstantaneousutility

u(x)=w(x)− 1 2e

2_,

2_Notice_that_this_{specification}_is_without_loss_of_generality,_given thatfortheutilityfunctionbelowanadditionalparameteronthe relation p=ϕe would notbe identified,but only ␥/ϕ2 _would _be identified.

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where is the parameter governing marginal disutilityof effort(seee.g.Garibaldi,2006),whereastheinstantaneous utilityoftheunemployedworkerissimply

u=z.

Thenumberofmatchesbetweenvacantjobsand unem-ployedworkersisgovernedbyacanonicalmatchingfunction m(v,u),wherevanduarerespectivelythenumberofvacant jobsand unemployedworkers. Labourforce is normalized to1, so that in thiseconomy the numberof unemployed workers u is the unemployment rate. As standard in the literature,we assumethatthematching functionistwice continuouslydifferentiable,increasingandconcaveinboth itsargumentsandhomogeneousofdegree one,with elas-ticitystrictly between0<<1.Bylinearhomogeneity,the transitionratefromvacanttoﬁlledjobism(v,u)/v=m(1, u/v)=q(),withq()<0,where=v/uidentiﬁesthelabour markettightness.Moreover,theelasticityofq()isstrictly between−1<<0anditisrelatedwiththeelasticityofthe matchingfunction(respecttov)by=−1.Similarly, the transitionprobabilityfromunemployedtoemployedism(v, u)/u=m(v/u,1)=q(),anincreasingfunctionof.

Thus,theendogenousvariablesofthemodelarethelevel ofmarkettightness,thelevelofreservationproductivity R,thelevelofefforte and,in turn,labourproductivityp andthe level ofunemploymentu.In thenext sectionwe characterizeandderivetheirsteady-statevalues.

3. Steady-state

equilibrium

Insteady-statethechoiceofopeningavacancyand destroy-ingajobforaﬁrm,aswellasthelevelofeffortforaworker, arebased ontheir assetvalues. Indeed,these valuesare fairlysimilartothoseinacanonicalmatching model(e.g. Pissarides,2000),withthedifferenceoftheeffortlevelin theworkerutilityfunction.Therefore,theinclusionofeffort doesnotchangeheavilytheassetvalues,butitdoeschange signiﬁcantlythesubsequentsteady-stateanalysis.

From the assumptions on vacancy cost, idiosyncratic componentandfiringcosts,wehavethattheassetvalues ofavacancyandafilledjobsatisfythefollowingBellman equations: rV=−pc+q()[J(¯x)−V] (1) rJ(x)=px−w(x)+ ¯x R J(s)dG(s)−G(R)pF−J(x) (2) In(1)afirmhastopaythevacancycostperunitoftime ---pcandwithprobabilityq()matcheswithanunemployed worker,givesupthevalueofavacancyVandgetsthevalue ofafilledjobattheuppersupportofthepricedistribution J(¯x).Insteady-statevacanciesareopeneduntilallrentsare exhausted.Therefore,theequilibriumzero-profitcondition is

rV=0⇒J(¯x)= pc

q() (3)

In(2),conditionalontheidiosyncraticproductivity,aﬁrm enjoysthevalueofproductpxandpaythewagew(x),then withprobability a shock arrivesand anewlevel of xis drawnfromthepricedistributionG(x).Inthiscasetheﬁrm

hastogiveupthevalueJ(x)andgetsthenewvalueJ(s)if sisoverthereservationproductivityR,ordestroysthejob andpayﬁringcostspFincasethenewdrawsisunderR.

Similarly, from the assumptions on unemployment compensation(orleisure)andinstantaneousutilityfunction, theassetvaluesofunemployedandemployedworkersatisfy

rU=z+q()[W(¯x)−U] (4) rW(x)=w(x)−1 2e 2₊ ¯x R W(s)dG(s)+G(R)U−W(x) (5) In (4) an unemployed worker enjoys the unemployment compensationz andwithprobabilityq()matches witha vacantjob,givesupthevalueUandgetsthevalueofbeing employed at the upper support of the price distribution W(¯x).In(5),conditionalontheidiosyncraticproductivity, anemployedworkerenjoysthewagew(x)butsuffersthe effortexerted−(1/2)e2_, _then_with_probability _a _shock arrivesandanewlevelofxisdrawnfromtheprice distri-butionG(x).Inthiscasetheworkerhastogiveupthevalue W(x)andgetsthenewvalue W(s)ifsisover the reserva-tionproductivity R,orthe valueof unemployedUin case thenewdraw s is underR.Furthermore,as willbemore clearbelow,eistheeffortlevelmaximizingtheassetvalue ofbeingemployed,sincewe characterize theequilibrium underrationalexpectations.

Nashbargainingimpliesthatworkersreceiveafractionˇ ofthetotalmatchsurplus,whichisrevisedwhenevera pro-ductivityshockoccurs.However,thetotalmatchsurplusof anewjobisdifferentfromthatofanexistingjob,because onlyinanexistingjobﬁrmssaveﬁringcostsforthe continu-ationofthematch.Therefore,asstandardinthematching literature,wehave todistinguishbetweentheoutside w0 andtheinsidewagew(x).

Inthecaseofanewjobthematchsurplusis S0(¯x)=J(¯x)−V+W(¯x)−U

andthesharingruleimplies

W(¯x)−U=ˇ(J(¯x)−V+W(¯x)−U) (6) Usingtherelationp=e,thezero-proﬁtcondition(3),the asset equations for a ﬁlled job (2), unemployed (4) and employed worker (5) and the sharing rule (6), gives the outsidewageequation3

w0=(1−ˇ) z+1 2p 2 +ˇp(¯x+c−F) (7)

Differently, in the case of an existingjoba ﬁrm saves ﬁringcostsfor the continuationof thematchand, conse-quently,thematchsurpluschangesinthefollowing S(x)=J(x)−(V−pF)+W(x)−U

3_The _derivation _of _the _inside _and _outside _wage _equations can be found in the working paper version (Lisi, 2010), which can be downloaded from http://www.demq.unict.it/ db/Allegati/wp201008c1merged.pdf.

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andthesharingruleimplies

W(x)−U=ˇ[J(x)−(V−pF)+W(x)−U]

Following the same argument, we get the inside wage equation w(x)=(1−ˇ) z+1 2p 2 +ˇp(x+c+rF) (8) Eqs.(7)and(8)differonlyfor theimpactoffiringcostsF and,indeed,thisdifferenceemphasizesthestandard con-flictbetween insiders and outsiders. On one hand, inside a matchthe prospect of paying F leads firms toconcede marginallyahigherwagetoavoidthedestructionof exist-ingjobs.Ontheotherhand,outsideamatchtheexpectation ofpayingfiringcosts,whenthejobwillbedestroyed,leads firmstostartthenewmatchwithalowerwagetopartially recoup the future payment of F. Moreover, as(7) clearly showstheimpactofFontheoutsidewageishigherwhenis higher,becausetheprobabilityofjobdestructionisgreater. Thechoiceofdestroyingajobistakeninsideamatch, thereforeweusetheinsidewageequationtoderivethejob destructioncondition.Substituting(8)in(2),wegetamore explicitexpressionoftheassetvalueofafilledjobJ(x)as afunctionoftheidiosyncraticcomponent

(r+)J(x)=(1−ˇ) px−z− 1 2p 2 −ˇp(c+rF)+× ¯x R J(s)dG(s)−G(R)pF (9) From(9)we can seethat J(x) isa monotonically increas-ing function of x. This implies that thereexists a unique valuex*suchthat J(x*)=0 and,inturn, for anyxgreater (smaller)thanx*,thenJ(x)>0(J(x)<0).Inthemodel with-outfiringcosts,thisimpliesthatthereservationproductivity R,underwhichafirmdestroysajob,satisfiesthe reserva-tionpropertyJ(R)=0.Differently,withfiringcostsforafirm isoptimaltocontinueevenanegativematch,asfarasthe negativesurplusissmallerthanthecostofdestroyingajob pF.Therefore,withfiringcoststhereservationpropertyis J(R)=−pF(orW(R)=U),whichallowsustocharacterizethe reservationproductivityR.

EvaluatingthegenericassetequationofaﬁlledjobJ(x) atx=R,wehavethefollowing

(r+)J(R)=(1−ˇ) pR−z−1 2p 2 −ˇp(c+rF)+ ¯x R J(s)dG(s)−G(R)pF (10)

Now, subtracting equation J(R) from the generic asset equation (9) and, then, using the reservation property J(R)=−pF,weget

(r+)[J(x)−J(R)]=(1−ˇ)p(x−R) J(x)= (1−ˇ)p(x−R)

r+ −pF

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Finally,substituting(11)intheintegralexpressionof(10) anddividingby(1−ˇ)p,weget animplicitexpression for

Rasafunctionofmarkettightness,labourproductivityp andtheparametersofthemodel

R− z p− 1 2p− ˇ 1−ˇc+ r+ ¯x R (x−R)dG(s)+rF=0 (12) Eq.(12)istheﬁrststeady-stateconditionofthemodel.In whatfollowwewillrefertothisasthejobdestructionrule (JD),whenweemphasizetherelationbetweenRand,or asthereservation equation(RE),whenwe emphasize the relationbetweenRandp.

Thevalue of pRis thelowest acceptable priceto con-tinueajob.Moreover,from(12)wecanseethatpRislower than the reservation wage (rU=z+(ˇ/1−ˇ)pc), which isthe lowestacceptablewagefor aworker.Onereasonis thepresenceoffiringcosts,whicharepaidbyfirmsbutnot enjoyedbyworkers.Theotherreasonstandardinthis liter-atureisthepresenceoflabourhoarding,representedbythe integralexpression.Inparticular,giventheprobabilitythat theidiosyncraticproductivityxmightchangeinthefuture, forafirmisoptimaltocontinuesomenegativematchand waitforahigherprice,inordertoavoidthehiringcost.As intuitive,labourhoardingisincreasingintheprobabilityof achange.

Ontheotherhand,thechoiceofcreatingajobistaken outsidethematch;thereforeweusetheoutsidewage equa-tion and evaluate the value of a ﬁlled job at the upper support of the price distribution. Substituting (7) in (2), subtracting(10)andusingJ(R)=−pF,weget

(r+)[J(¯x)−J(R)]=(1−ˇ)p(¯x−R)+ˇpF(r+) J(¯x)= (1−ˇ)p(¯x−R)

r+ −(1−ˇ)pF

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Finally,insertingthezero-proﬁtcondition(3)in(13),we getanimplicitexpressionforasafunctionofthe reserva-tionproductivityRandtheparametersofthemodel

c q() =(1−ˇ) ¯ x−R r+ −F (14) Eq.(14)isthesecondequilibriumconditionandwewillrefer tothisasthejobcreationcondition(JC).Thelefthandside of (14)isthecostof avacancyfor theexpectedduration of ﬁllinga vacancy. The right handside is thediscounted additionalsurplus a ﬁrm getsfroma newjob.Therefore, thiscondition saysthatin equilibriumtheexpectedhiring costofanewvacancyhastobeequaltotheexpectedgain fromanewjob.

Eqs.(12)and(14)jointlydetermineRand,asillustrated inFig.1.Let usdeﬁne (12)asB(R,,p,ω)=0and(14)as D(,R,ω)=0,whereωisthesetofparameters.Then,we have ∂R ∂ =− ∂B/∂ ∂B/∂R = cˇ/(1−ˇ) (r+G(R))/(r+) >0 (15) ∂ ∂R =− ∂D/∂R ∂D/∂ = (1−ˇ)/(r+) (c/q()2)q() <0 (16) As (15) shows, thecurve JDslopes upbecausea higher increases the probability of ﬁnding a job and, thus, the opportunitycostforaworker((ˇ/(1−ˇ))c),whonow pre-tendsahigherwagetoacceptajoband,consequently,more

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R

JD

JC

θ

Figure 1 Steady-state reservation productivityand market tightness.

jobsaremarginallydestroyed.Ontheotherhand,from(16) we know thatthe curveJC slopes downbecausea higher R increases the probabilitythat a jobis destroyedG(R) and, in turn, reduces the expected gain from a new job ((1−ˇ)((¯x---R)/(r+))),solessvacanciesareopened.

So far, thejoint determinationof Rand (for a given level of labour productivity p) has followed the previous literatureand,indeed,besidesthedifferentspeciﬁcationof theworkerutilityfunction,nosigniﬁcantnoveltyhavebeen introduced. However, in our model labour productivity is notaparameter,butanulteriorendogenoustobestudied. Followingourinterpretationofpasbehaviouralcomponent of productivity, we assumed that it is determinedby the level ofeffort e exertedby theemployed workerand,in particular,thatp=e.

Thechoiceofeffortisrationallytakenbyworkerswhen theymatch witha vacantjob, therefore in equilibriume maximizesthevalue ofbeingemployedat theupper sup-port of the price distributionW(¯x).In particular, when a workertakesthischoiceheactuallyknowsthejob destruc-tionruleRand,thus,takesintoaccounttheimpactonit. Moreover,given the choice ofeffort is taken individually, thesingleworkerconsiderstheimpactonmarkettightness marginallynegligible.Fromthis,itcanbeeasilyseenthat thesameeffort levelmaximizesthe assetvalueof unem-ployment, being Ua monotonically increasing functionof W(¯x)

(r+q())U=z+q()W(¯x)

ThemaximizationofW(¯x)intheformofBellman equa-tion(5)isnotatrivialcalculus.However,usingp=eandthe reservationpropertyW(R)=U,Eqs.(4)and(5)canbesolved forthepermanentincomeformasafunctionofR,,pand theparametersofthemodel(seeAppendixA)

rW(¯x)=(1−ˇ)z+ˇp ¯ x+c−1 2p + ˇp r+ G(R(p))RR(p)+ ¯x R(p) sdGR(s)−¯x (17) R _PE RE p 2z γ

Figure 2 Steady-state reservation productivity and labour productivity.

Intuitively,sincethereisanon-zeroprobabilityofa pro-ductivity shock and, all the more so, of being fired, the permanentincomeofanemployedworkerattheupper sup-portofthepricedistributionislessthanhisinstantaneous utility.The permanentincomeform(17)allowsustotake the F.O.C.and characterize the equilibriumcondition for labourproductivityp∂rW(¯x)/∂p=0 ¯ x₊c---p₊ r+ (G(R)R₋¯x)₊pG(R)∂R ∂p+ ¯x R sdG(s) =0 (18) Eq.(18)representstheequilibriumconditionforlabour productivityp(orefforte)4_and_from_now_on_will_be_called theproductivity equation (PE). From(18), we can notice thattheoptimallevelofpdependsonRand.Differently, from(12)and(14)wecanseethatonlyREdependsonp. Therefore,forany level ofmarkettightness , PEandRE jointlydetermineRandp,asillustratedinFig.2.Theshape ofthesecurvesisabitmorecomplicatedthanJCandJD,but stillintuitive.RememberingthatwedefinedthePE(12)as B(R,,p,ω)=0and,now,definingEq.(18)asM(p,R,,ω)= 0,wehavethefollowing

∂R ∂p =− ∂B/∂p ∂B/∂R=− (z/p2₎₋₍_/2) (r+G(R))/(r+) = ⎧ ⎪ ⎨ ⎪ ⎩ >0, ∀p>2z/ =0, p=2z/ <0, _∀p<2z/ (19) 4_At_ﬁrst_sight,_the_S.O.C._for_this_maximization_problem_would dependonthevalueofparameters

∂2_rW_(¯_x₎ ∂p2 =−+ G(R) r+G(R) _z p2+ y 2

However,for averylarge setofvalues,indeed alltheplausible ones,numericalcomputationsunequivocallyshowthatthe condi-tion∂2_rW_(¯_x_)/_∂p2_<₀_is_respected.

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∂p ∂R =− ∂M/∂R ∂M/∂p = −/(r+) [G(R)+pf(R)(∂R/∂p)(1---(G(R)/(r+G(R))))] −₊(G(R)/(r₊G(R)))((z/p2₎₊₍_/2)) >0 (20) Looking at (19), labour productivity p has two opposite effectsonoptimalreservationproductivityR,the disutility-wage effect and the production effect. On one hand, a higher p increases the disutility of worker and conse-quentlythewage(−(1/2)p),thusmorejobsaremarginally destroyed. On the other hand, a higher p increases the valueofproduction(pR)andpartiallycompensatesalower x, leading to a fall in R. Nonetheless, because of the increasing marginal disutility of effort, we can establish thatwhen p is low the effecton wage is relatively small andtheeffectonproductiondominates;ontheotherhand, when p is high the disutility increases morethan propor-tionallyandthe effectonwage dominates.Therefore,RE has a standard u-shape, with a minimum in the point in whichdisutility-wageeffectandproductioneffectexactly compensate.

Similarly, reservationproductivityRaffectslabour pro-ductivity p for the continuation value effect. In fact, a marginal increase in R does not change the instan-taneous utility of worker, but certainly it does change his continuation value. In particular, a higher R not only increases the probability of being ﬁred (G(R)), shorten-ingtheexpectedperiodofemployment,butalsodecreases the probability of ﬁnding a job (q()), increasing the expected period of unemployment. Indeed, both these impacts affect negatively the continuation value and, therefore, the worker chooses p also in order to address optimally the level of R through (12). This continuation valueeffectis includedin thenumerator of(20)and itis greaterforRandp high,implyingthePEshapeshowedin Fig.2.

Thelastequationofthemodelisthesteady-state condi-tion for unemployment, the so-called Beveridge Curve. Indeed, there are different ways to derive this condi-tion, here we state it in terms of ﬂows in and ﬂows outunemployment.In equilibriumthe numberof workers whoenterunemployment(1−u)G(R) hastobe equal to the number of workers who leave unemployment uq(). Therefore, the steady-state condition for unemployment is

u= G(R)

G(R)+q() (21)

Eq.(21)istheﬁnalequilibriumconditionofthemodeland impliesthatinequilibrium,foranyvaluesofRand,thereis auniqueunemploymentrateuand,inturn,auniquenumber ofvacantjobsv.

The Beveridge Curve is often drawn in vacancy-unemployment space by a downward sloping and convex curve.Indeed,as highlightedby Mortensen andPissarides (1994),inthematchingmodelwithendogenousjob destruc-tionthepreciseshapeoftheBeveridgeCurveisambiguous. Inparticular,differentiationof(21)showsthattherearetwo

ν

BC

u

JC

Figure3 Steady-stateunemploymentandvacancies. oppositeeffects ∂v ∂u=− ∂T/∂u ∂T/∂v = −−G(R)+(1−u)f(R)((∂R/∂)(∂/∂u))+q() (1−u)f(R)((∂R/∂)(∂/∂u))−q()(1+) = −<0 0 (22)

On onehand, morevacancies increase thenumberof job matches,implyingalowerunemploymentrate,capturedby thesecondtermofthedenominator(22).Ontheotherhand, more vacancies increase the number of jobs destroyed, implyingahigherunemploymentrate,theﬁrsttermofthe denominator(22).Despitethisambiguity,sincethe empiri-calevidenceseemstosupporttheconventionalshape,itis commontoassumethatthematchingeffectisstrongerthan thedestructiononeand,thus,todrawtheBeveridgeCurve asadownwardslopingandconvexcurve.Inthisregard,the numericalsimulationofourmodelwiththeequilibrium val-uesalsoconﬁrmsthisconventionalform.Therefore,inFig.3 wedrawEq.(21)asadownwardslopingandconvexcurve. Asusual,wedrawtheBeveridgeCurvewithastraightline throughtheorigin,representingallthepossiblevaluesforv anducompatiblewiththeequilibriummarkettightness.

Inconclusion,wearereadytodeﬁnetherational expec-tationsequilibriumofthemodel:

Steady-state equilibrium --- The rational expectations equilibriumisaquadruple(R*,*,p*,u*)thatsatisﬁesthe jobdestructioncondition(12),thejobcreationcondition (14), the productivityequation (18) and theBeveridge Curve(21)impliedbytherationalexpectationsbehaviour ofindividualﬁrmsandworkersandbythematching tech-nology.

Foranyvalueoflabourproductivityp,Eqs.(12)and(14) determinereservationproductivityRandmarkettightness .Then,fromalltheseequilibriumtriples,Eq.(18)identiﬁes theuniquevalueofequilibriumproductivityp,compatible with jobcreation and jobdestruction conditions. Finally, withthe knowledge of Rand , theBeveridge Curve(21)

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identiﬁes a unique value of equilibrium unemployment u and,inturn,auniquevalueofv.

Even ifwedonotaddress rigorouslytheanalysisofthe dynamic out-of-steady-state,here we reportsome proper remarks.Theusualassumptionsinthiskindofanalysisare thatfirmsareabletoopenuporclosevacancies instanta-neouslyandthatwagecanberenegotiatedatanytime;that is,vacanciesandwagesarejumpvariables.These assump-tionsensurethatthezero-profitconditionforanewvacancy (3)andthesharingrule(8)holdoutofequilibriumaswell. Similarly, the natural assumptions to make for the other twounknownsof the modelarethat firmscan shut down unprofitablejobsinstantaneouslyandthatworkersexertthe optimaleffort atany time;that is,reservation productiv-ityandlabourproductivity arealsojumpvariables.These assumptions imply that the reservation property (12) and theoptimalproductivity(18)holdbothinandoutof steady-state.Differently,thedynamicbehaviourofunemployment, governed by the job flows in and out of unemployment, is anyhowconstrained by the matching technology,which doesnotallowjumpsinjobcreation.Therefore, unemploy-mentistheuniquestickyvariableofthemodel,becauseof thefrictioninthejobcreationprocessduetothematching technology.

Finally, from (12), (14) and (18) it can be easily seen thatneitherthejobdestructioncondition,northejob cre-ationcondition, northeproductivityequation,depend on stickyvariables.Therefore,alltheseendogenous(R,,p) donotexhibittransitionaldynamicsand,indeed,theymust beontheirsteadystatevaluesevenduringtheadjustments, allthedynamicsbeingdischargedonvacanciesand unem-ployment. Moreover, notice that market tightness is still a jump variable even if unemploymentis sticky, because ﬁrmscanadjustinstantaneouslytheoptimalvacancies dur-ingthetransitionaldynamicsofunemployment.Therefore, followingthisargumentitisnaturaltoimaginethe out-of-steady-statedynamicsasasaddlepath,withonestableroot for unemploymentand threeunstable roots for the other endogenous5_.

4. Qualitative

analysis

Inthissectionweaddressthemainquestionoftheimpactof EPLonsteady-stateand,inparticular,onendogenouslabour productivity. However,in ordertohighlight the relevance of the extension pursued in this paper, pre-emptivelywe starttheanalysisoftheimpactofFconsideringpa param-eterandonlysubsequentlyweregardpastheendogenous productivity.

Indeed,theanalysisoftheimpactofEPLonjobcreation and job destruction, considering p a parameter, retraces basically the previous matching literature.From (12) and (14)wehavethat ∂R ∂F =− ∂B/∂F ∂B/∂R =− r (r+G(R))/(r+) <0 (23)

5_A_much_more_rigorous_analysis_of_the_transitional_dynamics _in thiskindofmodelshasbeenpursuedinPissarides(1985or1990) andcanbefoundalsoinPissarides(1990).However,herewefollow thesamelineandargumentsofPissarides(2000).

R R∗ R∗∗ θ θ θ JC JD ∗ ∗∗

Figure4 Impact of ﬁring costs onreservation productivity andmarkettightness(withpﬁxed).

∂ ∂F =− ∂D/∂F ∂D/∂ =− 1−ˇ (c/q()2)q()<0 (24) As(23)and(24)show,firingcostsreduceboth Rand. The impacton Ris due to thefact that destroying a job ismorecostly,whereastheimpactonisbecause,oncea jobiscreated,firmswillpaysoonerorlaterthefiringcosts andthis reducesthe expectedprofit froma new job. To gettheequilibriumimpactweneedtoconsidertheoverall impactofF,sowedifferentiate(12)and(14),respectively asB(R∗,(R∗,F),p,F,ω)=0andD(∗,R(∗,F),F,ω)=0and weget ∂R∗ ∂F =− ∂B/∂F ∂B/∂R∗ = − (ˇq() 2 /q())+r [(r+G(R∗))/(r+)]−[ˇq()2/((r+)q())]<0(s) (25) ∂∗ ∂F =− ∂D/∂F ∂D/∂∗ =− (1−ˇ)((r/(r+G(R)))−1) (c/q(∗₎2 )q₍∗₎₋₍_cˇ/₍_r₊_G₍_R₎₎₎<0 (26) Therefore, in equilibrium firing costs reduce both job destruction and job creation. In particular, we can see thattheequilibriumimpactonjobdestruction(25)iseven stronger than the initial impact (23), because higher fir-ingcosts reduce market tightness and in turn wage, thus lessjobsaredestroyedmarginally (see(15)and (24)).On theotherhand,theequilibriumimpactonjobcreation(26) isweakerthantheinitialimpact(24),becausefiringcosts increasethedurationofjobsand thispartiallyattenuates thelossoftheexpectedprofitduetoF(see(16)and(23)). TheequilibriumimpactisillustratedinFig.4,wherehigher FshiftsJDdownandJCleft.Asthefigureshows,job destruc-tion decreases unambiguously whereas the effect on job creationwouldseemambiguous,butindeedweknowfrom (26)thatjobcreationdecreasesaswell.

Becauseofthesymmetricimpactonjobcreationandjob destruction,theimpactofﬁringcostsonunemploymentin

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JC BC u∗ u∗∗ u ν ν∗ ν∗∗

Figure5 Impactofﬁringcostsonunemploymentand vacan-cies.

matchingmodelsisusuallyambiguous,asdifferentiationof (21)shows

∂u ∂F =

f(R)q()(∂R/∂F)−G(R)q()(∂/∂F) [G(R)+q()]2 =0

The equilibriumimpactonunemploymentis illustrated inFig.5.HigherﬁringcostsshifttheBeveridgeCurveinand rotatethejobcreationlineclockwise,thereforetheimpact on unemployment is ambiguous, but vacancies decrease unambiguously.

Sofar, weconsidered p aparameter unaffectedby fir-ing costs and, basically, we obtained the same results of thepreviousliteraturewithoutsignificantnovelty. Nonethe-less,inourmodelpistheendogenouscomponentoflabour productivity, thus now we regard it as endogenous and, in particular, we allow it to be affected by a change in F. Intuitively, we expect that firing costs affect in some waythe behaviouralcomponentof productivityfor differ-entreasons.Firstly,as(7)and(8)showfiring costsaffect directlytheactual andfuturewage.Moreover,theyaffect indirectly wage through the probability of finding a job (q()).Finally,theyinfluencetheprobabilityofbeingfired (G(R)),affectingthecontinuationvalueof(17).

From(18)wehavethattheinitialimpactofﬁringcosts onoptimalproductivityisnull,thatis

∂p ∂F =− ∂M/∂F ∂M/∂p =− 0 −₊(G(R)/(r₊G(R)))((z/p2₎₊₍_/2))=0

Theeconomic intuitionofthisresultisthatﬁringcosts haveanegativeeffectontheoutsidewageandapositive effectontheinside wage,thus inexpectations thesetwo impactsonthepermanentincomeofanewworker compen-sate,asshowedby(17).Thisinterpretationismadeevident bythedifferencebetween(17)andthepermanentincome ofaworkerinsideamatch

rW(x)=(1−ˇ)z+ˇp(x+c+rF−(1/2)p)+ ˇp r+ × G(R(p))R(p)+ ¯x R(p) sdG(s)−x

whereﬁringcostscertainlyhaveapositiveeffectonwage. Therefore,alltheeffectofFonpshouldbeinducedbythe impactontheotherendogenousaffectingtheworker con-tinuationvalue.Infact,aslongasRanddonotvarythere isnochange onthecontinuationvalueandthepermanent income of a newworker, thus thereshould be noimpact on labour productivity. To get the equilibrium impactwe differentiate(18)asM(p∗,R(,p∗,F),(R,F),ω)=0andwe getthefollowing:

∂p∗ ∂F =− ∂M/∂F ∂M/∂p∗ =− (∂M/∂R)(∂R/∂F)+(∂M/∂)(∂/∂F) (∂M/∂p∗)+((∂M/∂R)(∂R/∂p∗)) =− <0 <0 (27)

Proposition1. AhigherlevelofEPLreducesthe equilib-riumlabourproductivitythroughtheimpactonreservation productivityandmarkettightness.6

Theeconomicintuitionofthisresultliesinthefollowing argument.As(12)shows,labourproductivityhasanegative impactonreservationproductivitythroughtheproduction effect,thereforeinthechoiceoftheoptimalpthe produc-tion effectinduces workers tochoosemarginally ahigher p to reduce Rand, in turn, theprobability ofbeing fired (G(R)).Indeed,whenweanalyzetheimpactoffiringcosts onreservation productivitywe can easily realizethat the effectisof thesamemagnitudeof theproductioneffect. Toseethispointletmultiply(12)bypandconcentrateon theproductioneffect andthefiringcostseffect,ignoring forawhiletheotherelements

pR+rpF=0 (28)

As(28)shows,theproductioneffectispartially substi-tuted by the ﬁring costs effect in lowering R and thus a higherF,amplifyingtherelevanceofthedisutilityeffect, inducesworkerstochoosemarginallyalowerp.Moreover, ahigherFreducesalsoandconsequentlybothoutsideand insidewage,againinducingworkerstochoosealowerp(see (24)).TheequilibriumimpactisillustratedinFig.6,when ahigherFshiftsREdownandPEleft.

Considering p the endogenous component of productivity leads us to reassess the equilibrium impact of F on job creation and job destruction. In particular, now we differentiate (12) and (14), respectively as B(R∗,(R∗,F),p(R∗,),F,ω)=0 and D(∗,R(∗,F,p(R,∗)),F,ω)=0andweget

6_At_ﬁrst_sight,_there_might_be_an_ambiguity_on_the_denominator of(27).However,bothgraphicalanalysisandnumerical computa-tionswithalargesetofvalues,indeed themostplausibleones, unequivocallyshowthat(27)isnegative.

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PE RE R R∗ R∗∗ p∗∗ p∗ p

Figure 6 Impact ofﬁring costs on reservation productivity andlabourproductivity.

∂R∗ ∂F =− ∂B/∂F ∂B/∂R∗ = − (∂B/∂)(∂/∂F)+(∂B/∂F) (∂B/∂R∗₎₊₍₍_∂B_/_∂₎₍_∂_/_∂R∗₎₎₊₍₍_∂B_/_∂p₎₍_∂p_/_∂R∗₎₎<0 (29) ∂∗ ∂F =− ∂D/∂F ∂D/∂∗= −₍_∂D_/_∂_∗₎₊₍₍_∂D((_/∂D_∂R/∂R₎₍_∂R)(_/∂R_∂/_∗∂F₎₊))₍₍+_∂D(∂D_/_∂R/∂F₎₍_∂R) _/_∂p₎₍_∂p_/_∂_∗₎ <0 (30)

from which we can easily establish the following results (29)>(25)and(30)<(26),summarized inthenext Proposition:

Proposition2. Comparedtothestandardequilibriumwith p as a parameter of the model, in the equilibrium withendogenouslabourproductivityEPLreducesevenmore jobdestruction,butreduceslessjobcreation.

Theeconomicintuitionofthisresultisthat,aswehave seenbefore(28),thepresenceofamorestringent protec-tion legislation reducesthe role of the production effect andamplifiesthatofthedisutility-wageeffect,leadingto alowerlabourproductivitywhichdecreaseswagesand,in turn, the optimal reservation productivity. Consequently, lower jobdestruction increases the expected durationof jobandpartiallyattenuatesthelossoftheexpectedprofit due to higher firing costs, leading toa smaller reduction of job creation. The equilibrium impact onR and with endogenouslabourproductivityisillustratedinFig.7.

In conclusion, regarding p as the endogenous compo-nentofproductivitychangesquantitativelytheequilibrium impactofFonjobcreationandjobdestruction,butnotthe direction.However,ﬁrstlytheextensionofthemodelwith endogenouslabourproductivityshouldbeimportantperse,

JD JC R R∗ θ∗∗ R∗∗ R∗∗∗ θ∗∗∗θ∗ θ

Figure7 Impact of ﬁring costs onreservation productivity andmarkettightness(withpendogenous).

especiallyinthelightoftherecentempiricalevidenceon theimpactofEPLonlabourproductivity.Moreover,aswill beclear inthenextsection, consideringp anendogenous objectofthemodelturnsouttobeverymuchimportantfor thequantitativeexerciseand,inparticular,forthewelfare analysisandconsequentpolicyimplicationsconcerningEPL.

5. Quantitative

analysis

Inthissectionweattemptaroughcalibrationofthemodel toevaluatequantitativelytheimpactofﬁringcostsnotonly onlabourmarketperformance,butalsoonsomemeasureof aggregatewelfare.Asstandardinthisliterature,weadopt thefollowingCobb-Douglasmatchingfunctionwithconstant returnstoscale,usuallythespeciﬁcationmostappropriate tomatchthedataonjobcreation(seee.g.Layard etal., 1991,fortheUK;BlanchardandDiamond,1989,fortheUS)

m(u,v)=Au˛_v1−˛

Furthermore,the distributionof the idiosyncratic compo-nentofproductivityistakenuniformoverthesupport[0,1],7 i.e.G(x)=(x−x_-)/(¯x−x_-)=x.Following theprevious lit-erature,the baseline parameters reportedin Table 1 are setsoastomatchsome typicalfeatures ofthe empirical

7_Usually, _in_the_literature_the_{idiosyncratic}_component_of pro-ductivityxisanadditivecomponentoftotalprice(p+x)andthe distributionis takenuniformover [x_-,¯x],withx_- beinganegative number.However,theexogenousleveloflabourproductivitypis ﬁxedsothatthetotalpriceisfairlyeverywherepositive(seee.g. MortensenandPissarides,1994,1999a,b).Differently,inourmodel wemakeapreferencefor theinterpretationoftheidiosyncratic componentasamultiplicativecomponentoftotalprice(px),thus weneedtoadoptapositivesupportforthedistribution(seeLilien, 1982;BlanchardandDiamond,1989;Pissarides,2000).Nonetheless, itisclearthatbothinterpretationsmaintainthesamemechanism underpinningthereservationproductivity.

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Table1 Baselineparameters.

A ˛ ˇ r z c [x

-,¯x] 0.15 0.5 0.5 0.081 0.03 0.35 0.05 0.5 [0,1]

Table2 ImpactofFonlabourmarketequilibrium. U JF P R ud F=0 0.212 5.5 2.29 0.87 3.03 3.83 F=1 0.205 4.9 2.09 0.77 2.57 4.15 F=2 0.197 4.3 1.92 0.67 2.15 4.55 F=3 0.188 3.7 1.76 0.56 1.75 5.03 F=4 0.176 3.1 1.62 0.47 1.39 5.65

data (e.g. Davis and Haltiwanger, 1992). To this extent, theparameters ofthe matching function areset asusual at A=0.15 and ˛=0.5. The workers’ bargaining power is setatˇ=0.5equal totheelasticityof thematching func-tion, so as to get constrained efficiency at least in the economywithoutfiringcosts(e.g.Hosios,1990).To gener-ateinthesimulationreasonablejobflows,thearrivalrate oftheidiosyncraticproductivityshockisset=0.081(see MortensenandPissarides,1994).Similarly,theworker pref-erenceparametergoverningthedisutilityofeffortissetat =0.5,whichinducesanincreasingdisutilityofeffortbut indeedgeneratesreasonablevaluesoflabourproductivity. Finally,inoursimulationweconsiderasemesterastheunit oftimeand,accordingly,wesettheinterestrateatr=0.03 (seee.g.CahucandPostel-Vinay,2002).

In order toassess the impact of firing costs on labour market performance, we compute8 _different _equilibriums ofthemodelwithFvaryingfrom0to4.Thisshouldcovera significantrange,fromthelaissez---fairecase (F=0)tothe substantialfiringrestrictionscase(F=4),wherefiringcosts aremorethanthreetimesthesemesterwage(seee.g.for ItalyGaribaldi,2006).InTable2wereporttheequilibrium valuesofunemploymentrate,jobflows,labourproductivity, reservation productivity, market tightness and unemploy-mentspelldurationfordifferentlevelsoffiringrestrictions. First,wecan seethatmorestringentfiringrestrictions reducesignificantlytheequilibriumlabour productivity.In particular, a level of firing costs equal to two times the semesterwage (F=2) is enough to reduce labour produc-tivity more than 10% respect to the laissez---faire case, whereasinthesubstantialfiringrestrictionscasethe reduc-tionisevenofthe 30%.Similarly, firingcostsreduce both reservationproductivityandmarkettightnessand,inturn, jobflows.As wecan see,jobflows inthe substantial fir-ing restrictions case are less than 60% of those in the laissez---fairecase.Nonetheless,asstandardinthesemodels (e.g.Mortensen andPissarides,1999a),theoverall impact onunemployment is positive, because the impact on job destructionovercomesthat onjobcreation.Interestingly, thedifferenceinthelevelofjobflowsbetweenthe econ-omywithlowfiringcosts(5.5−4.9)andthatwithhighfiring costs(3.7−3.1),seemstomatchreasonablytherealdata

8_Fix_point_algorithm_written_in_Matlab_available_under_request_by theauthor.

Table 3 Job creation and Job destruction with p ﬁxed (p=2.29). R(p=2.29) (p=2.29) R F=0 0.87 3.03 0.87 3.03 F=1 0.78 2.08 0.77 2.57 F=2 0.69 1.26 0.67 2.15 F=3 0.61 0.59 0.56 1.75 F=4 0.53 0.11 0.47 1.39

intheU.S.,thequintessentialfrictionlesscountry,andthe Europeancountries,wherenotoriouslyfiringrestrictionsare consistent.Finally,becauseofthedecreaseonjobcreation, higherfiringcostsincreasesignificantlytheunemployment spellduration.Inparticular,inthesubstantialfiring restric-tionscasetheunemploymentdurationincreasesmorethan 50%respecttothelaissez---fairecase.

In Table 3 we show the equilibrium valuesof reserva-tionproductivityandmarkettightnessinthemodelwithp exogenous,alongwiththeirvaluesforthecomplete specifi-cation.Inparticular,wesettheexogenousproductivitypat theequilibriumlevelgetinthelaissez---fairecase(p=2.29) andwekeeppfixed,regardlessofthevalueofF.Inthisway wemakeclearwhathappentojobcreationandjob destruc-tionwhenweallowlabourproductivitytoadjustoptimally tochangeinfiringcosts.Aswecansee,thisnumerical exer-cise confirmsexactlytheresultofthe qualitativeanalysis (see(29),(30) andFig.7). Inparticular,whenwe allowp torespondoptimallytochange inF,thisleadstoaneven stronger reduction of the equilibrium reservation produc-tivity,buttoasmallerreductionoftheequilibriummarket tightness.

Finally,toassesstheimpactoffiringcostsonthe well-beingof theeconomy, wecomputethe valueof different measures of aggregate welfare from the laissez---faire to the substantial firing restrictions case. In particular, we considertwomainmeasuresofaggregatewelfare,thefirst concerningtheproductionnetofrecruitingcosts(Y−RC), thesecondtheutilityofagents(AWF).Ourconsistent meas-uresofaggregatewelfareintheeconomyare(seeAppendix A) Y=uq()p¯x[1+(1−)(1−u−uq())]+ (1−u−uq())pE(x|x≥R)[+(1−)(1−uq())] (31) AWF=uq()rW(¯x)[1+(1−)(1−u−uq())]+ (1−u−uq())rW(E(x|x≥R))[+(1−)× (1−uq())]+urU (32)

whereE(x|x≥R)indicatestheconditionalexpectationofthe idiosyncraticproductivityxoverthetruncateddistribution oftheactiveunits[R, ¯x],thatis

E(x|x≥R)= ¯ x R xg(x)dx G(¯x)−G(R)

InTable4wereporttheequilibriumvaluesofthesetwo measuresofaggregatewelfarefordifferentlevelsofﬁring

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Table4 ImpactofFonaggregatewelfare. Y Y₋RC rW(¯x) rW(E(x)) rU AWF F=0 1.70 1.62 0.73 0.71 0.69 0.71 F=1 1.49 1.43 0.66 0.65 0.61 0.64 F=2 1.30 1.26 0.58 0.59 0.55 0.58 F=3 1.14 1.11 0.52 0.55 0.50 0.54 F=4 1.01 0.98 0.48 0.52 0.46 0.50

restrictions.Alongwiththesemainmeasuresofwelfare,we reportsomeotherindexofwell-beingintheeconomy,asthe permanentincomeofunemployedandemployedworkerin differentconditions.

Asstandardinthematchingliterature,firingrestrictions reduce unambiguously allmeasures ofaggregate welfare, regardlesswethinkthewell-beingoftheeconomyinterms of production or utility of agents.9 _This _is _not surpris-ing, since we know that under the restriction ˛=ˇ the laissez---faireeconomygetstheconstrainedefficiency.More interestingisthesizeofthereductionofproduction.In par-ticular, amiddle level of firingrestrictions is sufficientto yield a production 25% lowerrespect tothe laissez---faire case,whereasinthesubstantialfiringrestrictionscasethe productioniseven40%lower.Indeed,despitethenegative impactofEPLonaggregatewelfarebeingwellknown(see e.g.CahucandPostel-Vinay,2002),suchworryingreduction inproductionisnotstandard:

Proposition3. Comparedtothestandardmatchingmodel with p exogenous, in the equilibrium with endogenous labourproductivity EPL reducesevenmore the aggregate welfare,regardlessweconsiderthewell-beingofthe econ-omyintermsofproductionoraggregateutility.

Nonetheless,hiddenunderthisresultthereisexactlythe negativeimpactofﬁringrestrictionsonlabourproductivity, whichnotonlyreducesthetotalproductionoftheeconomy, butalsothesurplusfromjobmatches and,therefore, the utilityofagents.Unsurprisingly,theinclusioninthe analy-sisofthiselementenrichesthepicture ofourmodeland, certainly,tellsusanalarmingresultweshouldworryabout.

6. Conclusion

The matching model studied in this paper revealed that, indeed,theleveloflabourproductivityintheeconomycan beinﬂuencedbylabourmarketpoliciesusuallyimplemented by governments. Stimulated by the recent empirical evi-dence,we focusedonEPLandshowedthatahigherlevel ofﬁringrestrictionspartiallysubstitutehighlabour produc-tivity in reducing job destructionand this, consequently,

9_For_what _concern _the_welfare_measure _in_terms_of_utility_we shouldrememberthatweassumedriskneutralandimpatient work-ers,whichimplieszerosavingandfullconsumption.Thisisusually doneinthisliteratureinordertoavoidtosolvingtheconsumption problem,sothatwecanworkwiththemaximizedBellmanequation toderivethesteady-stateofthemodel.Nonetheless,such limita-tionshouldbesomewhattakeninmindwhenwethinkaboutthe policyimplicationsofourresults.

brings down the optimal level of productivity. Further-more,theresponseofproductivitytoEPLreasonablyaffects thelevelof productionand, infact,numerical simulation of the model showed that a higher level of ﬁring costs shouldinduceaconsistentreductiononproduction,beyond thestandard reductionfound in the literature.Moreover, despite the reduction on the disutility of effort, higher EPLreducesunambiguouslyourmeasuresofaggregate wel-fare(AWF),inducingaworseningonthewell-beingofboth employedandunemployedworkers.Therefore,inthelight of the predominant role of labour productivity growth in drivingtheincomegrowthinthelasttwentyyears(OECD, 2003,2007), theresults ofthis paperbringafurther ele-mentinsupportoftheconsolidatedvoiceoftheliterature forareductionofEPLespeciallyinEuropeancountries.

To conclude, the extension of the endogenous labour productivitypursuedinthis paperallowsustorationalize within the already fruitful matching approach the well-established empirical evidence on the impact on EPL on labourproductivity,whichindeedassumestheappearance of a macro-stylized fact in the European economiesand, thus,shouldbeexplainedin amacro modelof thelabour market. On the other hand, the inclusion of the optimal workers’responsetopoliticaltoolsshouldrepresenta pos-itiveelementforanyotherpolicyevaluation.Inparticular, includingbothoptimal agents’ responses andmarket out-comes, the matching approach might turn out to be the idealframework toaddress crucial questionsusually ana-lyzedinmicroeconomiccontexts,butthatcertainlypresent signiﬁcantmacroimplications.

Acknowledgements

The author would like to thank Robert Shimer, Roberto Cellini,JeremyLise,ananonymousrefereeandparticipants invariousconferencesandseminarsfor helpful comments andsuggestions.Theusualdisclaimerapplies.

Appendix

A.

A.1. Workerpermanentincomeattheupper supportofthepricedistribution(17)

Thereare differentways in which thepermanent income equation(17)can bederived usingtheequilibrium condi-tions; we show one of these which allow us to establish differentinterestingrelations.

Firstfromtheassetvalueofunemployedworker(4)we havethat

U= z

r+q()+ q()

r+q()W(¯x) (33)

Fromthe assetvalue of employed worker(5) we have that (r+)W(x)=w(x)−1 2p 2₊ ¯x R W(s)dG(s)+G(R)U (34)

(13)

Evaluating(34)attheuppersupportoftheprice distri-butionandatthereservationproductivity

(r+)W(¯x)=w0− 1 2p 2₊ ¯x R W(s)dG(s)+G(R)U (35) (r+)W(R)=w(R)− 1 2p 2₊ ¯x R W(s)dG(s)+G(R)U (36)

Nowsubtracting(36)from(35)andusingthereservation propertyW(R)=Uweget (r+)[W(¯x)−W(R)]=ˇp(1−R)−ˇpF(r+)W(¯x)− U=ˇp 1−R r+ −F (37) Substituting(33)in(37)weobtain rW(¯x)=z+(r+q())ˇp 1−R r+ −F (38) Similarly,subtract(36)from(34)toget

W(x)−U=ˇpx−R r+

andnowsubstitute(33)anduse(38)toobtain rW(x)=rW(¯x)−rˇp 1−x r+−F (39) Thisexpression interestinglysaysthatwhenﬁringcosts arelowthepermanentincomeofagenericworkerisalways lowerthanthatofanewworker,thedifferencebeingdue tothedifferentleveloftheidiosyncraticproductivity. How-ever, when ﬁring costs are high the advantage of being alreadyinsideamatch,leadingtoahigherwage,overturns therelationinfavourofthegenericworker(seeTable4).

Finally, inserting (39) in the integral expression of the assetvalueofanewworkerweget

rW(¯x)=w0− 1 2p 2₊ ¯x R W(¯x)−ˇp 1−s r+−F × dG(s)+G(R)U−W(¯x)=w0− 1 2p 2₋ G(R)W(¯x)−U+ ˇp r+× ¯x R sdG(s)−(1−G(R)) +ˇpF(1−G(R)) and now using (37) and substituting the outside wage equation(7)givesus(17) rW(¯x)=(1−ˇ)z+ˇp ¯ x+c− 1 2p + ˇp r+ G(R(p))R(p)+ ¯x R sdG(s)−¯x

Similarly,inserting(39)intheassetvalueofthegeneric workergiveshispermanentincome.

A.2. Totalproduction(31)andaggregatewelfare function(32)

Inequilibriumthereare(1−u)producingworkers,who dif-fer only for the level of the idiosyncratic productivity x. Amongtheseuq()workersareintheﬁrstperiodof employ-ment,thereforeproduceattheuppersupportoftheprice distribution ¯x. Instead, the other (1−u−uq()) workers wereemployedalreadythepreviousperiodandindeedtheir level ofxis notthesame for allofthem. Inparticular, a fractionfacedaproductivityshockandchangedthelevel of x in a newvalue between ¯x and R,whereas the com-plement(1−)maintainedthesameleveloftheprevious period.In turn, amongtheseoldworkers maintaining the level of x, a fraction uq() entered two period ago and therefore produce at the upper support of the price dis-tribution ¯x,whereasthe others(1−uq())entered more thantwoperiodagoandindeedweshoulddistinguishagain between those whofaced a productivity shock and those whonotandsoforth.Therefore,thetotalproductionis Y =uq()p¯x+(1−u−uq()){pE(x|x≥R)+

(1−)[uq()p¯x+(1−uq()){pE(x|x≥R)+ (1−)[uq()p¯x+(1−uq())...]}]}

As intuitive, the precise computation of the level of idiosyncratic productivity of producing workers in steady state is troubling, due to the recursive computation. Nonetheless,giventhatouraimistoevaluatetheimpactof ﬁringrestrictionsontotalproduction,itwouldbeharmless tomakean assumptiontosimplifythe computationwhich affectsin thesame waythe valueof production between thelaissez---faireandthesubstantialﬁringrestrictioncase. Obviously, more an employed worker is old higher is the probabilitythathefacedaproductivityshockandchanged his level of x. For simplicity, in (31) we assume that all workersolderthantwoperiodsfacedaproductivityshock. Therefore,ourmeasureoftotalproductionis

Y =uq()p¯x+(1−u−uq()){pE(x|x≥R)+

(1−)[uq()p¯x+(1−uq())pE(x|x≥R)]} whichaftersomeeasyalgebragivesus(31).

Moreover,tocheckifourassumptionisreally harmless for ourpurpose, werepeatedasimilarnumericalexercise ofTable4assumingthatallworkersolderthanthreeperiods faced a productivity shock. As expected, we did not get any sizabledifferenceon the impactof ﬁring restrictions onoutput.

Similarly,theaggregatewelfarefunctionistheweighted sum of utility of the different workers in steady state, knowingthattheutilityofworkerdependsonthe idiosyn-cratic component of productivity. Following the identical argumentmentioned before,inequilibrium theaggregate welfarefunctionis

(14)

AWF=urU+uq()rW(¯x)+(1−u−uq()){rW(E(x|x≥R))+ (1₋)[uq()rW(¯x)₊(1₋uq())rW(E(x_|x_≥R))]_}

whichaftersomeeasyalgebragivesus(32).

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