DISCUSSION PAPER SERIES - PDF document

DISCUSSION PAPER SERIES Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor Does the Welfare State Make Older Workers Unemployable? IZA DP No. 4440 September 2009 Gilles Saint-Paul Does the Welfare State Make Gilles Saint-Paul Toulouse School of Economics, Birkbeck College and IZA Discussion Paper No. 4440 September 2009IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 E-mail: iza@iza.org Anyopinions 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. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author. IZA Discussion Paper No. 4440 September 2009 Does the Welfare State Make Older Workers Unemployable? This paper discusses the specificities of the labor market for older workers. It discusses the implications of those specificities for the effect of labor market institutions on the employability of those workers. It shows that while unemployment benefits indexed backwards and hiring costs are likely to harm these workers more than the average worker, the converse is true for employment protection, provided it is uniform across workers and not specifically higher for older workers. It provides some evidence on the impact of labor market institutions on older workers by comparing their outcome in the United States and France. It discusses how the welfare state can be reformed in order to improve outcomes for older workers. JEL Classification: J23, J24, J26, J31 Keywords: older workers, labor market institutions, employment, employment protection, welfare state, pensions, retirement Corresponding author: Gilles Saint-Paul GREMAQ-IDEI Université des Sciences Sociales Manufacture des Tabacs Allée de Brienne 31000 Toulouse E-mail: gilles.saint-paul@univ-tlse1.fr olderworkerslessthanyoungerones.Sections2and3discusstheseissuesfromatheoreticalpointofview.Section4compareslabormarketoutcomesforolderworkersintwocountries:arigidone(France),anda‡exibleone(theUS).Itthendiscussestheroleofrigiditiesbyrelatingtheempirical…ndingstotheprecedinganalyticaldiscussion.Section5drawsthepolicylessonsfromourexercise.2Whyisthelabormarketforolderworkersspeci…c?Therearethreecharacteristicsofolderworkersthatpresumablyhaveanimpactontheirlabormarket.Themostimportantoneisthattheirremainingcareertimeissmall:theyareexpectedtoleavetheirjobandretirefairlysoon.Thisisincontrasttoayoungerworkerwhocanbeexpectedtoremainwiththe…rmformorethanadecade.Aswewillsee,thisobviousfacthasprofoundimplicationsfortheemploymentofolderworkers.Thesecondcharacteristicisthattheirproductivityis(likely)falling.Whilethisisplausibleitisnotobvious,buthasbeendocumentedbyanumberofstudies.Inparticular,Kotliko¤andGhokale(1992)estimateanage-productivitypro…leforvariouscategoriesofworkersbydisentanglingaworker’swagefromhismarginalproductivity–theideaisthatdeferredpay-mentsforincentivereasonscreatesuchawedge.Insuchaworld,aworker’smarginalproductivitypro…leovertimeisdi¤erentfromhiswagepro…le.Theformercanneverthelessbeestimatedbyusingthefactthatundercompe-tition,nonetpro…tsshouldbegeneratedbyhiringanadditionalworker.Hence,thepresentdiscountedvalueoftheworker’smarginalproductshouldbeequaltothatofhiswages,andKotliko¤…ndsthatundersomecondi-tionsthiscanbeusedtorecovertheage-productivitypro…le.Hisresultsarestriking.Theyimplythatformostcategoriesofworkers,productivitypeaksataroundage45,thenfallstolevelsthatareestimatedtoathirdofthatpeakatage65.Sinceitistypicallyfoundthatcompensationriseswithagethroughoutthelifecycle,these…ndingsimplythatrelativetotheirproductiv-2 ity,olderworkersare"overpaid",whiletheywere"underpaid"duringtheirprimeage.This…ndingisconsistentwiththetheoreticalliteraturewhicharguesthat…rmsusedeferredcompensationasanincentivedevice(Lazear,1990).Otherstudies(surveyedine.g.Skirbekk(2003))relyondirectmea-suringofhowabilityevolveswithage.Theycon…rmthe…ndingsofKotliko¤andGhokale,althoughbydesigntheycannotexpressthemasamonetaryequivalent.Figure1,takenfromAvolioandWaldman(1994),showshowdi¤erentmeasuresofabilityevolvewithage.Theyallpeakaround20-25,suggestingthatifproductivityincreasesfrom25to45,itisduetoexperienceratherthanability.Third,relativetoyoungerworkers,olderworkershaveahumancapitalwhichismorespeci…ctotheircurrentjob/…rm,andlessgeneral,i.e.lesstransferabletoother…rmsandothersectors.Thisisbecausetheyhavespentagreaterfractionoftheirlifeacquiringthosespeci…cskillsthroughlearning-bydoingrelativetoacquiringmoregeneralonesintheeducationalsystem.Empirically,onewaytomeasurethate¤ectistolookatthewagelossofdisplacedworkersintheirfuturejobs,whichshouldbegreater,thegreaterthespeci…ccomponentoftheirhumancapitalinthejobtheylost.Indeed,existingstudies(Ruhm(1991),Jacobsonetal(1993)Cohenetal(1997)RosoliaandSaint-Paul(1998))often…ndalargelossforolderworkers.However,suchalossmayalsore‡ectgreaterrentsratherthangreaterspeci…cskills,especiallyinlightoftheaboveargumentthatdeferredcompensationgeneratessuchrentsforolderworkersforincentivereasons.Wereturntothatissueinourempiricalstudybelow.Thesethreekeycharacteristicsofolderworkershaveanumberofimpli-cationsfortheworkingofthelabormarketandespeciallyforhowtheimpactoflabormarketinstitutions,suchasthosewhichprevailinEurope,onthoseworkers.Letusdiscusstheseimplications.Ifworkerswereo¤eringtheirservicesinapurespotmarket,theywouldbepaidtheirmarginalproductateachpointintime.Wewouldthenobservewagespeakingataround45andthenfallingtoreachpossiblymuchlowerlevelstowardtheendofone’scareer.However,aspointedabove,thisisnotwhatwesee,sincewagesgoupwithage.Ifweassumethatthisdiscrepancyis3 duetoincentiveproblems,weseethatolderworkerswholosetheirjobloseanimportantrent.Thatis,whiledeferredpaymentsarenotdirectlyallocativeatthelevelofthe…rm/workerpair(thetimingofpaymentsisdisconnectedfromthatoftheworker’smarginalproduct),theyarenotneutralwhenoneconsidersmobilitytoanotherposition,whichismorecostlyandthereforemoredeterred,thegreatertheworker’swagerelativetohisproductivity–andthereforethegreaterhisage.Thisiscompoundedbythelossofspeci…chumancapital,andalsobyathirde¤ect,whichisthatgiventheshortexpectedtenureinanypositionthattheywill…nd,thereislittleroomforengagingindeferredcompensation.Insomesense,thatisfortunate,becauseitmakesitlesslikelythattheemployerlowersthewageuponhiringtoincreaseitlater.Atthesametime,italsomeansthattheolderworkersaremorelikelytoendupinjobswhereincentiveproblemsarelessimportant.Thisistruenotonlybecausedeferredcompensationismoredi¢cultbutmoregenerallybecauseitismoredi¢culttousepaytoelicitincentivesforworkerswithshortexpectedtenure1.Overall,thismeansthatolderworkers,unlesstheyarestillemployedata"lifelong"position,aremorelikelytobeemployedinthe"secondary"sectorofjobsthatareeasilymonitoredandthustypicallyinvolvelessautonomyandresponsibility,andalsolowerwages2.Asecondimplicationisthatunemploymentbene…tsarelikelytobemoredamagingtotheemploymentrateofolderworkersthattothatofyoungerworkers.LjunqvistandSargent(1998)haveanalysedtheconsequencesforaggregateunemploymentofthefactthatunemploymentbene…tsareindexedbackwardonwages.Thisbackwardindexationimpliesthattheunemployedwillbeespeciallypickyifthedistributionofjobo¤ersisassociatedwithlowerwagesthantheprecedingone.Theyshowthatattimesof"turbulence",i.e.intensesectoralreallocation,joblossesareassociatedwithlossesof…rm-andsector-speci…chumancapital,sothatthewagesthattheunemployedcangetinthenewsectoroftheeconomy,wheretheyareyettolearnthetrade,are 1Thisisageneralpredictionofthe"shirking"modelofe¢ciencywages(seeShapiroandStiglitz(1984)).2SeeSaint-Paul(1996).4 lowcomparedtotheirpreviousones,andthereforelowcomparedtotheirunemployentbene…ts.Thisiswhy"turbulence"hasalargeadverseimpactonunemploymentincountrieswithgenerous,backward-indexed,unemploymentbene…ts;ontheotherhand,thee¤ectismuchsmallerincountrieswheresuchbene…tsarenotgenerous.Theirargumentisespeciallysalientfortheolderworkers.Ourdiscussionaboveimpliesthatevenintheabsenceof"turbulence",thewagestheycanclaimafterhavinglostajobarelikelytobesubstantiallysmaller,becauseofthedeferredcompensatione¤ect,thelossofspeci…chumancapitale¤ect,andthegreaterlikelihoodofworkinginthesecondarysector.Furthermore,astheirproductivityfallswithage,thewedgebetweentheirreservationwage–asdeterminedbytheirbene…tlevel–andtheo¤erstheygetislikelytogrow.Thuswenotonlyexpectalowerexitratefromunemployment,butalsoastronger"durationdependence"–thephenomenonbywhichexitratesfromunemploymenttendtofallwiththelengthoftheunemploymentspell3.Wewillreferbelowtothise¤ect–thefactthatunemploymentbene…tspushtheresevrationwageofolderworkersuprelativetothewagestheycanexpectontheirfutureo¤ers–astheentitlemente¤ect.Third,hiringand…ringcostswilla¤ecttheemployabilityofolderwork-ersdi¤erentlyfromyoungerworkers.Thisisanimportantquestionbecausealargefractionofthosecostsareregulatory–especiallythe…ringcoststhatarecreatedbyemployentprotectionlegislation.Furthemore,employ-mentprotectionispaidspecialattentioninthedebateoverthemarketforolderworkers.Somecountries(e.g.France,asdiscussedbelow)havespe-cialprovisionsthatincreaseemploymentprotectionbeyondacertainage.Furthermore,inmostcasesentitlementsareincreasingwithtenure,whichautomaticallybene…tsolderworkers.Ifwe…rstconsider…ringcosts,weseethattheirdeterrente¤ectonem-ployabilityislowerforolderworkers.Thereasonisthat,shouldthe…rmconsiderlayingo¤theworker,itcanwaitforhisretirementinsteadofpay-ingthe…ringcost.Thatvalueofwaitingisobviouslymuchhigherifthe 3Unfortunately,myownattemptsto…ndsuchastatisticallysigni…cante¤ectintheFrenchcasefailed.5 workerisyoung.So,somewhatparadoxically,a…ringcostthatwouldbeim-poseduniformlyonallworkerswouldmakeolderworkersmoreemployablerelativetotheyoungerones.Ofcourse,thestoryisentirelydi¤erentif…ringcostsgoupwithage.In-deed,mostEuropeancountrieshaveemploymentprotectionlegislationsthatbecomemorestringentasthetenureoftheworkerincreases.Thisislikelytobecorrelatedwithage.Furthermore,anumberofcountriesimposeaddi-tionaltaxesonlayo¤sforolderworkers.Anotableprovision,forexample,istheFrenchso-called"Delalande"contribution,whichimposesanadditional…ringtaxonworkerswhoareolderthan50.Followingstandardeconomics,weexpectsuchataxtoreduceboththehiringratesandthe…ringratesofthiscategoryofworkers.Furthermore,itisalsolikelythattheexpectationofthetaxwillreducethehiringrateforworkersyoungerthan50,andisalsolikelytoincreasetheirlayo¤rateas…rmsmaywanttoanticipateonafuturelayo¤decisionconcerningthoseworkerstoavoidpayingtheadditionaltax.Behageletal.(2008)usechangesintheDelalandetaxtoestimateitse¤ectonthehiringrateofolderworkers.Inparticular,in1992thesystemwaschangedsoastoexempt…rmsfrompayingthetaxwheneverworkerswereolderthan50atthetimetheywerehired.Clearly,thiswasmeanttoo¤setthenegativee¤ectsofthetaxuponhiring;butatthesametimeitmeantthatthosehiredafter50lackedtheextraprotectionoftheothers.Thiswouldimplythatworkershiredafter50wouldbelaido¤beforeworkersofthesameagehiredpriortothatage,thusreinforcingthedualnatureofthelabormarket.Inanycase,theestimatesofBehageletalbasedonthatnaturalexperimentcon…rmthepresumptionthatimposingextraprotectiononaselectedgroupofworkershasasubstantialnegativeimpactontheirhiringrate.They…ndthatthereformincreasedthejob…ndingrateofthe50+group,relativetoyoungerworkers,by0.5percentagepointsonamonthlybasis.Thisisalargee¤ect.Forexample,withamonthlyjoblossrateof0.1%andjob…ndingrateof1.5%,wegetanunemploymentrateinsteadystateequalto0.1/1.6=6.25%.Ifwenowreducethemonthlyjob…ndingrateby0.5%,theunemploymentratejumpsto10%.Thee¤ectisacompoundof"direct"e¤ects–thereturnfromhiring6 somebodyisloweriftherearegreater…ringcosts–andsubstitutione¤ects–Ipreferthelow…ringcostapplicantthehighone.Whileitisdi¢culttodisentanglethetwokindsofe¤ects,theauthors’resultssuggestthatstrongsubstitutionisatwork:thereformnotonlyreducedthegapinhiringratebetweenth50-andthe50+agegroups,itinverteditssign:afterthereform,itwaseasierto…ndajobforaworkeraged51thanaworkeraged49.Finally,theauthorsarealsoabletoestimatethee¤ectoftheDelalandetaxonlayo¤s;they…ndthatitreducesthelayo¤rate.Theyalso…ndaslightpositivee¤ectonthelayo¤ratebeforeage50butitisverysmallandstatisticallyinsigni…cant.Turningnowtohiringcosts,weseethattheyhaveastrongere¤ectonaworker’semployability,theolderthatworker.Thisisbecausethehiringcostislessdamagingtothe…rm,thelongerthedurationofthejoboverwhichthe…rmcanrecoupit.Clearly,thatdurationislowerforolderworkers.Thusauniformhiringcostsreducedthedemandforolderworkersrelativetoyoungerones.Thelowerexpecteddurationofthejobreducesthetotal(discounted)valuetothe…rmofemployingtheworker:thisiswhatwewillcalltheendgamee¤ect.Asaresultthe…rmiswillingtopaylesstoemploytheworker,implyingthatolderworkersaregoingto…ndjobsinsectorswheretrainingandrecruitmentcostsarelow.Below,Iwilldocumenttheendgamee¤ectbothinthecontextofasmalltheoreticalmodelandofanempiricalcomparisonbetweenFranceandtheUnitedStates.Thisisinaccordancewiththerestoftheliterature.Forexample,inarecentpaper,Hairaultetal.(2008)capturethee¤ectsofhiringcostsinasearch-matchingmodel,andtheydocumentapositiverelationshipbetweentheageofretirementandtheemploymentrateofolderworkers.ThispositiverelationshipisdepictedonFigure2.Theysupplementthiswitheconometricevidencebyconstructingaworker-speci…cvariablewhichmeasuresthedistancetoretirementandshowthatthisvariablehasapositivee¤ectontheprobabilityofbeingemployedinaFrenchdataset,controllingfortheusualvariables.7 3LessonsfromasimplemodelWhilesomeoftheaspectsdiscussedaboveareeasytograsp,aformalmodelmaybeusefulinordertounderstandtheinterplaybetweenhiringand…ringcostsandtheendgamee¤ect.Inthissection,Iconsidersuchamodel.AssumetimeiscontinuousandthatthedurationofhumanlifeisT:Whenhired,workersareinahighproductivitystateandproducea‡owofoutputy=yH:Letsdenotetheworker’sage.Withprobabilityp(s)perunitoftime,theworkersfallsintoalowproductivitystatesuchthaty=yLyH:Theworkerremainsinthatstateuntilheleavesthejoborretires.Inprinciplep(s)canvarywithage,andcouldre‡ectthehump-shapeddependenceofproductivitywithrespecttoagedocumentedbyKotliko¤andGhokaleandothers.Wagesare…xedandequaltow:Tohireaworkera…rmmustpayahiringcostH:Furthermore,a…ringcostFmustbepaidandweallowittobetime-dependent.Morespeci…cally,the…ringcostisassumedtobeequaltoF0forssandF1F0forss:IfF1=F0weareinthespecialcaseofa…ringcostwhichisindependentofage.Firmsmaximizethepresentdiscountedvalueofpro…ts,underaconstantrealinterestrateequaltor:Theyhaveworkersofdi¤erentagesarrivingrandomly,andforeachworkerdecidewhetherornottohirehim.Clearlygiventheconstantreturnstoscaleimplicitinourassumptionsregardingtheprocessforproductivity,allthesehiringdecisionsareindependentfromoneanother.Wewanttocharacterizethehiringanddismissaldecisionsof…rmsde-pendingontheageoftheworker.Fortheproblemtobeinteresting,itmustbethatyLwyH:Otherwise,onewouldeithernothireanybodyornot…reanybody.Letusthenassumethatthisinequalityholds.We…rstcharacterizethedismissaldecision.Foraworkerofages&#x-277;ssuchthaty=yL;the…rmcankeephim8 untilretirementwhichyieldsa(negative)presentdiscountedpro…tequaltoK(s)=ZTs(yL�w)e�r(t�s)dy=yL�w r�1�e�r(T�s)
:(1)Ontheotherhand,the…rmcangetridoftheworkerrightaway,whichinvolvesanimmediatecostequaltoF1andthusanetpro…tequaltoF(s)=�F1:Thusthe…rmwillkeeptheworkerifandonlyifw�yL r�1�e�r(T�s)
F1:Foraworkerinthelowstatewithagess;thetwooptionsarethesame:keeptheworkeruntilretirementandgetapro…tK(s)givenbytheRHSof(1),vs.…retheworkerrightawayandhaveapro…tF(s)=�F0:Theintermediaryoptionofkeepingtheworkertogetridofhimimmediatelypriortotheriseofthe…ringcostatagescannotbeoptimal.Itwouldyieldanetpro…tequaltoW(s)=Zss(yL�w)e�r(t�s)dy�F0e�r(s�s)=yL�w r�1�e�r(s�s)
�F0e�r(s�s)=�F0+F0+yL�w r�1�e�r(s�s)
:(2)Clearly,forthatoptiontodominateimmediatedismissal,wewouldneedthatW(s)��F0;implying,byvirtueof(2),thatF0�w�yL r:Butsincew�yL risthepresentdiscountedvalueoflossesforalowproductivityworkerthatwouldstayforever,thislatterinequalityinturnimpliesthatthe…rmwillbebetter-o¤keepingtheworkeratagesratherthangetridofhim.Inshort,ifthe‡owequivalentoflossesisgreaterthanthe…ringcost,thenimmediatedismissalisoptimal;otherwise,waitinguntiltheworkerretiresisoptimal.Theintermediateoptioncannotbeoptimalunlessthelossesthemselvesaretime-varyingwhichwehaveruledoutinourmodelforsimplicity.9 Figure3plotsthe"dismissal"frontierFFinthe(s;yL)plane:itgivesthelowestvalueofyLsuchthatthe…rmpreferstokeeptheworker,asafunctionofage.Itisdownardslopingandhasaverticalasymptoteats=TandyL=�1;re‡ectingthefactthat…rmsaremorelikelytowait,theoldertheworker.Thestepats=sre‡ectstheincreasein…ringcostswhenonepassesthatagethreshold.TheintersectionofthisfrontierwithahorizontallineattheactualvalueofyLdeterminesacriticalage,~s;afterwhichtheworkerwillnotbe…redifhefallsinthelowproductivitystate.Conversely,allworkersyoungerthanthatwillbe…rediftheyfallinthelowproductivitystate.Thecriticalagemaybelargerthan,equalto,orsmallerthan,theregulatorythresholds:Itwillbeexactlyequaltoitforawholerangeoflowproductivitylevels,duetotheverticalportionofFFats=s:Tighteningemploymentprotectionlegislation–increasingF0,F1;orboth—shiftsthedismissalfrontierdownandlowersthecriticalage.ThisisillustratedonFigure4.Whilethemodelrulesoutany"preventive"dismissalinanticipationofthethresholdforlow-productivityworkers,thismayhappenforhigh-productivityworkers.InAppendix1Isolveforthe…rm’smaximumex-pecteddiscountedpro…tinthecasewherepisconstantandintheregimewhere~s�s:ItisshownthatforF0smallenoughandF1andwlargeenoughwithintheparameterzonecompatiblewiththisregime,itisindeedoptimalto…rehighproductivityworkersimmediatelybeforetheyreachthecriticalages:Thenextstepistocharacterizethehiringdecision.Todoso,IneedtocomputeJH(s);thevaluetothe…rmofemployingaworkerofagesinthehighproductivitystate.Thisinturngivesusthe"employabililty"ofaworkerofages:IfitisgreaterthanthehiringcostH;thenanapplicantofageswillbehired,otherwisetheapplicantwillbeturneddown.Therefore,thegreaterthevalueoftheworkerJH(s);themoretheworkerisemployable.ThevariationofJH(s)withsisanalysedintheAppendix,andtherearethreepossibilities:1.ThesimplestcaseiswhenJH(s)fallswithsalongthelifecycle.This10 isthecasedepictedonFigure54.Workersarealwayslessemployablewhentheygetolder.Typically,thisismorelikelytooldwhenpissmall,yHislarge,F1issmall,andw�yLissmall.Firingcoststhendonotplayabigroleinthe…rm’shiringdecisions:oneisnotverylikelytofallintothelowproductivitystate,thelossesmadeinthatstatearenotverylarge,thepro…tsmadeinthehighproductivitystatearelarge,andthelevelofthe…ringcostislow.Thepro…leofemployabilitythenresemblestheonethatwewouldgetintheabsenceofemploymentprotection;itisdecreasingsimplybecausewhentheworkerisolderthe…rmexpectstoreappro…tsfromtheworkeroverashorterperiodoftime.2.InthesituationshownonFigure65,employabilitygoesupuntilitreachesamaximumage^s;whichisgreaterthan~s;meaningthatthemostemployableworkersarenot…redwhentheyfallintothelowproductivitystate.Thissituationprevailsif…ringcostsareimportant,thusifpislarge,F1large,yHsmallandw�yLlarge,andalsoiftheincremental…ringcostforolderworkers,F1�F0;issmall.Insuchasituationthepossibilityofhavingtoine¢cientlyretaintheworker,orgetridofhimandpaythe…ringtax,shouldproductivityfall,playsanimportantrole.Thisgivesapremiumtoolderworkerswhoarenotexpectedtostaylong,andthisinturn,throughforward-lookingexpectations,generatesanupward-slopingpatternofemployabilityuptoage^s:Theprocesshaslimits,though,sincehighproductivityworkerswhoaretoooldstaytoolittletimeinthe…rmtogeneratealargeNPV:thevalueofthejobeventuallyfallstozeroassincreasesbeyond^s:3.InthesituationdepictedonFigure7,employabilityisM-shaped6.Thatis,itfallsuntilonereachesthethresholdages;thengoesupuntilage^s;andthenfallsagain.Thissituationprevailsinthesamecircumstancesastheprecedingone,exceptthatthegapF1�F0isnowlarge.Thismeansthatworkersgetlessandlessemployablewhentheyapproachthethreshold. 4This…gurehasbeendrawnforT=50;s=35;w=1;yH=2;yL=0:5;F0=0:5;F1=1:5;r=0:05;p=0:1:5This…gurehasbeendrawnforT=50;s=35;w=0:8;yH=1:5;yL=0:5;F0=2:8;F1=3;r=0:05;p=0:1:6This…gurehasbeendrawnforT=50;s=35;w=0:8;yH=1:5;yL=0:5;F0=0:5;F1=3;r=0:05;p=0:1:11 However,afterthat,ageisagainapositivefactorsinceitreducesthelikeli-hoodofhavingtopaythe…ringcost.Butthisisagaineventuallydefeatedbythevanishingoftheindividual’sremainingprofessionallife.Finally,itisalsousefultocomparethepro…leofemployabilityfordi¤erentlevelsofemploymentprotection.ThisiswhatisdoneonFigure8,wherethreesituationsarecompared:a"‡exible"onewithno…ringcost,a"rigid"onewithauniform…ringcostequalto150%oftheannualwage,andanasymetricalonewitha…ringcostequalto100%ofthewagebefores=35andto200%ofthewagetherafter.Thegraphcon…rmsthatrigiditiesreduceemployabilitymostlyforyoungandprime-ageworkersratherthanolderworkers,andthatthestepreducesemployability,relativetoauniformsystem,aheadofthedatethesteptakesplace(bysome…veyearsinthissimulation).4Howdoolderworkersfareina‡exiblevs.arigidlabormarket?Anempiricalcom-parisonbetweenFranceandtheUS.InthissectionIperformanempiricalcomparisonoftherelativeemployabilityofolderworkersina"‡exible"labormarket(theUnitedStates)anda"rigid"one(France).Tokeepthediscussionshort,Ionlyconsiderthosedimensionswherethetwocountriesaresigni…cantlydi¤erent.However,acompletesetofgraphsandtablesisavailableintheworkingpaperversionofthisarticle.4.1Employmentrates:theendgamee¤ectThe…rstvariableIlookatistheemploymentrate.Thisvariablere‡ectsbothlaborsupplyandlabordemand,andthereforecapturesdi¤erentforcesfromindicatorslikeunemploymentorunemploymentduration,whichtellussomethingaboutthefunctioningofthelabormarket.Anemploymentratecanbeloweitherbecauseunemploymentishighorbecauselaborsupplyislow,andthelattercanbeloweitherbecauseofdistortionsorbecauseoftaxes.Ontheotherhand,itisoftenarguedthattheincentivestoregister12 asunemployedarelowifunemploymentbene…tsarenotgenerousenough,whichblursthedistinctionbetweenbeingunemployedvs.outofthelaborforce.Wecannotsolvetheseissuesherebutwecanlookatbothindicators.Cohenetal.(1997)haveshownthatforsu¢cientlynarrowlyde…ned(bysexandeducation)cells,employmentratesareparadoxicallyslightlyhigherinFrancethanintheUSforprime-ageworkers.Thus,mostofthelowerperformanceofFranceoverallcomesfrom(i)nonprime-ageworkers(ii)thecompositione¤ectduetolowereducationallevelsinFrance.Morerecentdatafromthe2005USCPSandthe2005Frenchlaborforcesurveycon…rmsthose…ndigs:employmentratesaremarginallyhigherinFranceforprime-agedmen.Butforolderworkers,thepictureisreversed.Whileemploymentratesareunderstandablymuchlowerinthe60-65agerange–sincetheo¢cialretirementageinFranceis60–theyarealsolowerinthe55-60range7.ThisisreportedinTable1:employmentratesforthosecatgoriesofworkersarealllowerinFrancethanintheUS1,andthecategorieswheretheolderworkersareleastemployedinFrancerelativetotheUS,arelowandmedium-skilledmen.Tohavesomeclueabouthowtointerpretthese…ndings,wecanrefertothemodelabove.Itimpliesthatemployabilityfallssharplyasonenearsretirementage(seeforexample…gure8).Thustheloweremployabilityofthe56-60agegroupinFrancecomparedtotheUSisprobablyduetotheearlierretirementageinFrance.Whenthatagewasbroughtdownto60thee¤ectonemploymentforpeopleimmediatelybelowthatagewasnottakenintoaccount–thesenumberssuggestitissubstantial.Wehavealsoseenthatemploymentprotectionlegislationrunsintheoppositedirection,bymakingtheolderworkersrelativelymoreemployable.Thusthenumberssuggestthatthise¤ectisnotstrongenoughtoo¤settheendgamee¤ect. 7Forwomen,thepictureismorecomplex.Forhigh-schooldrop-outs,employmentratesaresubstantiallyhigherinFrance,implyingthateventhe55-60rangehasahigheremploymentratethanitsUscounterpart.Thesameistrueforcollegegraduates,butthatisnowduetothefactthatemploymentratesarevirtuallyidenticalacrossallactegories,exceptofcoursethe60-65agerange.Forhighschoolgraduatesandcollegedropouts,thepatternisthesameasformen:higheremploymentratesforprime-ageworkersinFrance,butmuchloweronesforthe55-60range.13 4.2Unemployment:themid-lifediscountWenowturntounemploymentrates(Table2).These…guresarefairlylowforolderworkers;forworkersolderthan60inFrance,veryfewareactivelylookingforajobandunemploymentrates(notreported)areverylow.Themoststrikingfeaturehereisassociatedwithmatureratherthanolderworkers:ThereisasharpriseinunemploymentrateformenwithatleastahighschooldegreeinFranceduringtheirforties.Wewillrefertothisasthemid-lifediscount.ThisphenomenondoesnottakeplaceintheUnitedStates.Itismostsalientfortheintermediateskillsgroup,kickinginat41forhighschoolgraduatesand46forworkerswithsomecollege.Itismilderandchie‡ylimitedtothe41-46agegroupforcollegegraduatesandvirtuallynon-existentforhighschooldropouts.SincethemidlifediscountoccursinFranceandnotintheUS,itisnaturaltoassumethatitisduetolabormarketrigidities.Whileinstitutionssuchastheincreaseinemploymentprotectionwithtenureandtheexistenceofastepatacertainagemayplayarole,abiggerrolecanpresumablybeascribedtotheentitlemente¤ect,aswehavediscussedabove.At45workersenjoytheirpeakproductivity,whichincludesagreatdealofjob-speci…chumancapital,andinadditionderivelargerentsfromdeferredcompensation.Thustheentitlemente¤ectislikelytobelargeforthisgroup.Thishypothesisissomewhatcon…rmedbythefactthatthephenomenonisabsentforhigh-schooldropouts.Theyaremorelikelytoworkineasilymonitoredroutineornoncognitivetasks,whichreducestheroleforincentivepaymentschemes,includingdeferredcompensation.Andthescopeforlearningbydoinginthosejobsislower,whichsuggestsa‡atterevolutionofproductivityduringone’scareer.Therefore,atmid-lifetheseworkers’wagesarelikelytobelessdi¤erentfromtheirmarginalproduct(inboththeircurrentandfuturejobs)thanforotherworkers,whichmakestheentitlemente¤ectofbackwardindexationofunemploymentbene…tslesssalient.Interestingly,themid-lifediscountdoesnotseemtoa¤ectwomen.In-stead.theyexperienceabnormallyhighunemploymentrateinFrancecom-paredtotheUSduringtheirfertileyears,between25and45.Thisispresum-14 ablytheresultofgenerousprovisionsformaternityleaveinFrance,whichreducesthedemandforwomeninthoseages.Thee¤ectmaybesostrongastodwarfthemid-lifediscount.Butthemid-lifediscountisalsolikelytobesmallerforwomenonaverage,sincetheyarebothlesslikelytoengageincontinuouscareers(thusacquiringlessspeci…chumancapital)andmorelikelytoworkinthe"secondary"sector.4.3LabormarkettransitionsTheprecedingdatagivesusastaticpictureofthelabormarket.Wealsowanttoknowhowtheolderworkersfareinadynamicsense.ForthiswecomparethetransitionratesbetweenFranceandtheUS.Astylisedrepresentationofthesetwoeconomiesholdsthatbecauseofrigidities,boththejoblossandthejob…ndingratesarelowerinFrancethanintheUS.Thisisindeedwhattheearlierliteraturefound,e.g.Cohenetal.Howeveritalsofoundthatsomegroups,liketheyoung,wereusedasabu¤erof‡exibilityandthattheirjoblossrates,inparticular,weremoresimilartotheUS.Wewanttoknowifthisstylizedvisionholdsformorerecentdata,andinparticularhowtheolderworkersfare:aretheyusedina"‡exible"orina"rigid"way.Oneissueisthatlabormarket‡owsarequitesensitivetothebusinesscycle.Andthebusinesscyclewasnotthesamein2005inFranceandtheUS.WhileunemploymentwasfallingintheUS,itwasstillrisinginFrance;itstartedtofallin2006.Therefore,weperformthecomparisonoftransitionratesfortwomoresimilaryears,keeping2005forFrancebutusing2002fortheUnitedStates.I…rstdiscussaggregatetransitionratesbyageandthendisaggegatethembysexandeducation.Istartwiththejoblossrate.Inrelationtotheabovediscussionaboutthemeasurementofemploymentandunemployment,therearetwowaystomeasureit:onecanusethe‡owfromemploymenttounemployment,oralternativelythe‡owfromemploymenttonon-employment(thesumofunemploymentandnonparticipation).Ideally,the…rstoneshouldcapture15 involuntaryjoblosses,andthesecondoneaddsvoluntaryones.Inpractice,thedistinctionisblurredbythehighincentivestoregisterasunemployedinFrance(eveninthecaseofavoluntaryquits),andthelowonesintheUS.SoIlookatbothmeasures.Figure9depictstheemployment-to-unemployment‡owinbothcountries.AstrikingfactisthatthismeasureofthejoblossrateisnotlargerintheUS.Themeasuresaresimilarforprime-age,higherinFrancefortheyoung,andlowerfortheolderworkers.Thissuggeststhatolderworkers,despitereformslikethe1992adjustmenttotheDelalandecontributionmentionedabove,…rmlyremainintheprotectedsector.Incontrast,theyoungnowhaveajoblossrateevenhigherthanintheUnitedStates.Figure10showsthejoblossrate,includingtheemployment-to-nonparticipation‡ow.Thepictureissomewhatmoreconsistentwithconventionalwisdom:thejoblossrateishigherintheUSforprime-ageworkers;itissimilarinbothcountriesfortheyoung;anditisnowhigherinFranceforolderworkers.Thisisclearlyduetothe‡owtononparticipation,andthereforermostlycapturestheroleofretirementandearlyretirementschemes.Thisisnotsurprising,butthenumbersaretelling:theysuggestthatforthe56-60agegroups,whohavenotreachedtheo¢cialretirementageyet,theseschemesaccountforsome15%oftherelevantworkforceretiringeachyear,ascomparedto10%intheUnitedStates.Inowturnonthejob…ndingrates,thatarereportedonFigure11.Thedataarestriking.Overall,job…ndingratesaretwentypercentagepointsgreaterintheUnitedStatesthaninFrance,say50%vs.30%yearly.Andthegapwidensastheworkersgetolder,risingtothirtypercentagepointsforthe51-55agegroup,whilethejob…ndingratefallstoaverysmall5%peryearforthe56-60agegroupinFrance.Thisleadsustoreconsidersomewhattheexistenceofthemid-lifedis-count:itdoesnotshowupaslargeunemploymentforolderworkersbecausetheincidenceofunemployment(theemployment-unemploymenttransitionrate)amongthoseworkers,islow.Butifwelookatthedurationofunem-ployment(theinverseofthejob…ndingrate),we…nditisextremelylowforthoseworkers;andwealsohaveseenthattheincidenceissomewhat16 arti…callylowbecauseofthelargerateatwhichtheywithdrawfromtheworkforce.Boththesupplysideandthedemandsideconspireingeneratingalowjob…ndingrateforolderworkers:onthesupplyside,thereistheentitlemente¤ect.Onthedemandside,wehavetheendgamee¤ect.Notehoweverthatifweusethejob…ndingrateofthe60-65agegroupintheUnitedStatesasameasureoftheendgamee¤ectina‡exibleeconomy,wedo…ndthatitexists,howeveritaccountsforsayareductioninjob…ndingratesfrom55%ayearto40%ayear.Thisissubstantial,butnotcomparabletothemassivecollapseinjob…ndingrateexperiencedbyFrenchworkersastheyreach55.Thegapisnotlikelytobeexplainedbytheentitlemente¤ectalone:itisprobablyaslargeforthe46-50group(otherwisethemid-lifediscountwouldnotarise),andyetthisgrouphasamuchhigherjob…ndingrate.Anadditionalfactorprobablycomesfromtheminimumwage.Onecouldtrytotestforthisbylookingatmoredisaggregateddata,howeverthatisdi¢cultforthejob…ndingratesincethereareveryviewunemployedworkersinmanysexxagecells.Butthescantevidencethatwehavesuggeststhatthejob…ndingratesareespeciallylowfortheolder,lowskilledworkers.Indeed,intheFrenchlaborforcesurvey,thevastmajorityoftheunemployedabove50arehigh-schooldropouts.Forthesmallnumberofolderunemployedworkerswithgreaterskills,thejob…ndingratesaretypicallysubstantiallyhigher,althoughtherearesofewobservationsthatweshouldbecautiousindrawinganyconclusion.Overall,thesedatagiveapictureofasubstantialexcessprotectionforjoblossinFranceforolderworkers,withthecounterpartofextremelylowjob…ndingratescomparedtoothergroups.4.4WagesWenowturntotheanalysisofwages,startingwiththeevolutionofwagesoverthelifecycleinbothcountries.Figure12depictsthetimepro…leofwages,foreacheducationalgroup,17 inFrance8.We…ndatypicalpatternofwagesrisingwithage,andtherateofincreaseshowsnosignofslowingdown.Oneexceptionishighschooldropouts,whohaveapretty‡atpro…leandexperienceaslightfalltowardtheendoftheircareer(consistentwithmyargumentaboveregardingtheentitlemente¤ectbeingweakerforthoseworkers).Figure13showsthewagepro…leforeacheducationalcategoryforthe"‡exible"US.Weseethatthereisahump-shapedpatternandthatitistypicallymorepronounced,themoreeducatedtheworker.Infact,forhigh-schooldropouts,wagesareessentially‡atovertime:thereseemstobenohumancapitalaccumulation,andnodepreciationthereof.Thissharpcontrastbetweenthetwocountriessuggestthatwage-settinginstitutionsinFranceleadtoreturnstoagethataresubstantiallytoohighrelativetothemarketoutcome:wagesshouldeventuallybefalling,despitethetendenciestodeferredcompensationandhumancapitalaccumulation,andinaccordancewiththedirectevidenceonproductivity.Thefallshouldstartataround50(whichispreciselytheagewheretheDelalandecontri-butionkicksin).ButinFrancetheincreasecontinues.Forexample,intheUS,malecollegegraduatesaged61-65earn10%lessthanthoseaged45-50.InFrancetheyearn33%more.Takenatfacevalue,thissuggeststheyare43%overpaid.Consequently,oneneedsaverylargeincremental…ringcosttoo¤setthehighincentivesof…rmto…rethem,andonewouldneedasharpreductionintheirunemploymentbene…treplacementratiotobringtheirreservationwageinlinewithwhattheycouldearninafuturejob.4.5WagelossesAlotofthediscussionabovearoundthee¤ectsofunemploymentbene…tsandtheirretrospectiveindexationonwagesrevolvesaroundtheexistenceofhighrentsforolderworkers.Wehavearguedthatthoserentsmayoriginateintheirdisproportionateaccumulationofjob-speci…chumancapitalaswellastheuseby…rmsofdeferredcompensationinordertoelicitincentives.Thereareothersourcesofrentsaswell:Theymayoriginateinacollective 8Forspacereasonthedataareagaincon…nedtomen.Asimilarpatternarisesforwomen.18 bargainingstructurethatwouldimposeanagepro…leforearningsdiscon-nectedfrommarketforces.Or,itmaybethatolderworkershavehadmoretimetoacquirerents,forexamplebyinvestinginsecuringajobintheunion-izedsector.InthissectionIprovidesomeevidencebylookingatthewagelossesofdisplacedworkers.Intheory,therentofaworkershouldbede…nedasthe(expected)presentdiscountedvalueofhisincomestreamunderhiscurrentjob,minushisex-pectedpresentdiscountedvalueofincomeshouldhebecomeunemployed.Underacompetitivelabormarket,thedi¤erencebetweenthetwoshouldbezero.Inpractice,tomeasurethatwewouldneedtoknowthedetailsoftheprocessesgoverningincomebothunderemploymentandunderunemploy-ment.Whilethisisnotinprincipleunfeasible,itisrepletewithproblems,soweuseinsteadthedi¤erencebetweentheageearnedfollowinganunem-ploymentspellandthewageofsimilarworkerswhohavenotexperiencedthatspell.Thisisonlyanimperfectmeasureoftherentbecauseitrestsonthewagesofthoseworkerswhodo…ndjobs.Thistendstoreducethewagelossascomparedtotherent,sincewageo¤ersthatarebelowthereservationwagearerejected,whichtendstoincreasethedurationofunemployment,thusdepressingthevalueofbeingunemployed.Thusthetruerentmaterial-izesnotonlyinthefuturewagebutalsointhedurationofunemployment,andthatpart–whichclearlyisa¤ectedbylabormarketinstitutions–isnotre‡ectedinourmeasureofwageloss.Nevertheless,ifanythingthisleadsourmeasuretounder-estimatetherentinthe"rigid"(=highunemploymentduration)countrycomparedtothe‡exible(=lowunemploymentduration)country.Thusifwe…ndasubstantialwagelossforolderworkersintherigidcountry,thisisanunderstatementoftheproblemgeneratedforthoseworkersbythebackwardindexationofunemploymentbene…ts.Toestimatethee¤ectofage,IestimateanearningsfunctiontowhichIaddagedummiescrossedwithadummyequalto1iftheworkerhasexpe-riencedanunemploymentspellintheprecedingyear.Twocommentsareinorder:First,thisapproachconstrainstheestimatedwagelosstobethesameacrosseducationalcategories;thisisadrawbackbutitsavesondegreesoffreedom.Second,theestimatesmaybebiasedifthereisacorrelationbe-19 tweenunobservedabilityandthelikelihoodoflosingone’sjob;tocorrectforthistheliteraturehasusuallylimitedtheanalysistojoblossesthataresupposedlyexogenoustotheworkers’unobservedability,suchasthosedrvenbyplantclosing.Here,however,thiswouldsubstantiallyreducethenumberofavailableobservations.Notehoweverthatmycomparisonbetweentwocountriesremainsvalidaslongasthebiasesinducedbyunobservedhetero-geneityareassumedtobethesame;furthermore,theestimatesarequitesimilartothoseoftheliterature,suggestingthebiasissmall9.Table3reportstheresultsformenandwomen.InbothFranceandtheUnitedStates,theestimatedwagelossissubstantialandofthesameorderofmagnitudeasfoundbytheearlierliterature.Thelossissigni…cantlyhigherintheUnitedStatesthaninFrance,whichisatvariancewithsomeoftheearlier…ndings10.Finally,therentseemsincreasingwithageinFrance,butintheUSitishighestforthe41-50agegroup.Inanutshell,Table3tellsusthatrents(asmeasuredbywagelosses)aregreaterintheUSthaninFrance,andthattheyrarehump-shapedwithageintheUSbutincreasingwithageinFrance.Howcanwemakesenseofthoseresults?Inbothcountries,rentsaregreaterforolderworkersoverall.Thisisconsistentwithourdiscussionaboveasboththee¤ectofdeferredcompensationandthatofspeci…chumancapitalaccumulationtendtogenerateanupwardpro…leofrents.Thedi¤erencesbetweentheUSandFrancearemoredi¢culttounderstand.Ifonlythesetwomarketforceswerepresent,wewouldexpecttogetthesameresultsinthetwocountries.Rigiditiesobviouslyintroducedi¤erencesbetweenthetwocountries,butitisnotstraightforwardtopredicttheire¤ect11.One 9Itshouldbeaddedthattheplantclosingapproachhasproblemsofitsown:Totheextentthatwageshaveaplantspeci…ccomponent(whichwouldbetrueifwageformationobeyedsomerent-sharinglogic),theyarelikelytobecorrelatedwiththelikelihoodofplantclosing.Andsuchacorrelationwillalsoariseifworkersofsimilarunobservableabilitytendtoworkinthesameplants,asthetheoryofassignmentpredictsundercomplementaritybetweenworkerquality.10Notably,Cohenetal.(1997).11Notethatthetheoreticalpredictionregardingthecomparisonofwagelossesbetweenrigidand‡exiblecountriesisambiguous.Ontheonehand,greatergenerosityofunem-ploymentbene…tspushedthereservationwageup:thistendstoreducethewagelossfromdisplacement,andatthesametimetolengthenthedurationoftheunemploymentspell.20 interpretationisthatintheUS,wherewagesaremorein‡uencedbymarketforcesandwageinequalityisgreater,thereturntospeci…chumancapitalisgreater,implyinggreatere¤ectsonwageswhensuchhumancapitalislostordepreciated12.Atthesametime,collectivebargaininginFranceforcesanupwardpro…leofrentswithage.Onnet,thisgeneratesgreaterrentsintheUSexceptfortheagecategorywherethelattere¤ectisstronger,i.e.theolderworkers.5ConclusionandpolicyperspectivesAboveIhavearguedthatanumberoffeaturesofEuropeanlabormarketinstitutionsareparticularlyharmfulfortheelderly.Thisbringsthekeyquestion:howshouldpolicyhandletheseissues?Atemptinganswerwouldbetoincreaseemploymentprotectionfortheelderly,whichhasindeedoftenbeendone.Whyisthattempting?Becausetheendgamee¤ectisafundamentalcharacteristicofthelabormarketfortheelderly.Onecanreduceitsstrengthbyeliminatingregulatorycomponentsofhiringcosts—whateverthejusti…cationforsuchcosts,theexistenceoftheendgamee¤ecttellsusthattheyparticularlyharmolderworkersandsuggestssuchregulationsshouldbealleviatedforthem.Butthebulkofhiringcostsareintrinsicandnotgeneratedbyregulation.Thusitistemptingtosaythatnoderegulationofhiringcostswillworkandthattheonlythingonecandoistohavehigheremploymentprotectionforolderworkers.Yetthisisfarfromsatisfactory,foratleastthreereasons.First,wehaveseenabovethattherearereasonstobelievethatdi¤erentialemploymentpro-tectionprovisionsgeneratestrongsubstitutionse¤ects.Second,thiswould Ontheotherhand(thiswouldbeapparentfromadynamicsearchmodel),theprobabilityof…ndingajobislowerinarigidcountry,whichmakesitmorecostlyfortheworkertoturndownano¤er;thispushesthereservationwagedown.SomesimulationsreportedinSaint-Paul(2000)suggestthatthetwoe¤ectscouldeaslycanceleachother,deliveringasimilarwagediscountina‡exibleandarigidcountry.12Notethatthehump-shapedpatternofwagelossesintheUSmimicksthatofwages.Thisisconsistentwithourinterpretationprovidedthat(i)asubstantialfractionoftheevolutionofwagesoverthelifecycleisaccountedforbyspeci…chumancapital,and(ii)asubstantialfractionofthatspeci…chumancapitalislostwhentheworkerlosesisjoband/orduringthesubsequentunemploymentspell.21 leadtolockingolderworkersintheirjobsforalongtime,whichisprobablyudesirablefromtheviewpointofallocativee¢ciency.Third,nomatterhowhighemploymentprotectionis,therewillalwaysbeamassofunemployedolderworkers,ifanythingbecausetheiremployerwentbankruptorbecausetheyhadtoresignduetosomeadversepersonalshocksuchashavingtomove.Clearly,thesewouldbeparticularlyharmedbydi¤erential…ringcostsforolderworkers.ThisisindeedtherationaleforthewaivingoftheDela-landecontributionforworkershiredafter50discussedabove,butitbegsthequestionofhowtohandletheendgamee¤ect.Toresolvethistension,itisusefultostartrecognizingthattheendgamee¤ectisgenuineinthatitissimplysociallyine¢cienttopayhighhiringcostsforaworkerwhowillretirefouryearsafterbeinghired.Thisshouldruleoutpoliciesthatsubsidizethehiringofolderworkers;ifolderworkershavetochangejobs,itmustbeinactivitieswherehiringcostsarenottoohigh.Togetagraspofhowane¢cientpolicywouldlooklike,wemayspecu-lateonhowthelabormarketforolderworkerswouldoperateinaworldofperfectlycompetitivelabormarkets.Insuchaworld,olderworkerswouldbemorelikelytosticktotheircurrentjobbecauseoftheendgameprob-lem.Thismeansthattheywouldhavetobearwithwagecutsinresponsetoproductivityfallingwithageandinresponsetonegativeshockstothatproductivity.Butsomeofthemwouldneverthelesslosetheirjobsandtheymighteitherworkinsectorswithlowhiringcosts,thatareprobablynotpayingmuch,ordecidetousetheiraccumulatedwealthtoretire.Thuswewillsee(i)decliningwageswithage,(ii)asusbstantialwagelossuponun-employment(re‡ectingthedevaluationofspeci…chumancapitalassociatedwithjobloss),(iii)lowerjoblossrates,(iv)useofpersonalsavingstomakeupforwagelosses,and…nally(v)retirementcontingentonhavinganadverselabormarketshock.Ironically,wecouldmakethepointthat,totheextentthatthewagesofolderworkersare"toohigh"relativetothatbenchmarkinEurope,institu-tionslikeadditionalemploymentprotectionandpre-retirementareexactlywhatisneededtoreplicatethecompetitiveoutcomeintermsofemployment22 patternsdespitethatwagesgivethewrongsignals.However,thisadmin-istrativesolutiondoesnotguaranteethattherightpeopleareallocatedtothesituationsofcontinuingintheirjobandretiring,and,moreworryingly,thethirdtierofolderworkers–thosewhomovetolow-productivityjobs–iseliminatedaltogether,beingpushedintopre-retirementschemesorotherwelfareprograms.Onewaytoimproveonthatwouldbetomovetoasystemofmore‡exiblewagesandlessgenerousunemploymentbene…ts(andinparticularreconsidertheirbackwardindexationonwages),whileintroducingacompen-sationsystemthatallowsolderworkerstosupplementtheirlaborincome.Anattractivesolutionistoletthemfreetochoosetheirretirementageinanactuariallyfairway,whiledisconnectingentirelythepaymentofpensionsfromlabormarketparticipation.Thus,thosewhoseetheirwagefallingatsay58,couldstartdrawingtheirpension,eitherinpartorfully,andcu-mulateitwiththeirlaborincome.Anotherapproachwouldbetoreplacegenerousunemploymentbene…tsbya"wageinsurance"schemethatwouldsupplementtheincomeofolderworkersiftheyhavelosttheirjobandendupinalow-payingjob.Thiswouldnotbeofgreathelptotheunemployed,butevidencefromanglo-saxoncountriessuggeststhatatlowbene…tlev-els,unemploymentdurationislow,sothatsubstantialinsuranceisderivedfromhighjob…ndingrate.Furthermore,asystemofunemploymentsup-portaccountcouldbeintroduced,whichwouldamounttoeasingthecreditconstraintontheunemployed.Onecommonworryisthatincreasingtheretirementagedoesnotwork,becauseolderworkershaveaverylowjob…ndingrateandarethus"unem-ployable".Totheextentthatthisisduetotheendgamee¤ect,ouranalysissuggeststhatthemerefactofraisingtheretirementagewillincreasethejob…ndingrateforworkersinagivenagecategory.Ontheotherhand,theendgamee¤ectcannotbeeliminatedanditwillnowapplytotheolderworkerswhoareatthesamedistancefromretirement;sincethoseareevenlessproductive,thee¤ectwillbeevenstronger,whichreinforcesmyclaimthatcumulatingpensionswithworkmustbeanimportantfeatureofanyworkablepensionreform.23 Shouldtheemploymentoftheolderworkersbesubsidized,asisthecaseintheNetherlands?Euwalsetal.(2008),inanextensivediscussionoftheDutchsystemanditsreformprospects,arguethatthisisprobablycounter-productive.Inadditiontotheethicalproblemsoftaxtreatmentslinkedtoindividualcharacteristics,inapuremarketoutcometheemploymentrateofolderworkerswouldnaturallybelowerthanforprime-ageones.Theonlydis-tortionthatexacerbatesthatisthebackward-indexedunemploymentbene…t,butthenitmakessensetoreconsiderthedesignofunemploymentbene…ts.Andthereissomecontradictionbetweentheattempttoimprovethe…nanc-ingofpublicpensionsbyworkinglonger,andatthesametimeintroducinganotherredistributiveschemeinfavoroftheelderly.Thewageinsurancesystemproposedaboveisnotasperverselyredistrib-utiveastheDutchsubsidy,especiallysinceitmaybene…tyoungerwork-ersandolderonesalike(butthelatterwouldbene…tmore),andwouldbecompensatedbylowerunemployentbene…ts(whichwouldalsobebetterinbudgetaryterms).Andallowingtocumulatepensionsisevensimplerand…nanciallyanddistributivelyneutral–overall,thegoalsofthosesystemsistoallowconsumptionsmoothingalongthelifecycleandacrossstatesofnature,inthefaceof…nancialmarketimperfections,andthatiswhatunem-ploymentsupportaccountsandactuariallyfairaccesstopensionsprovide.Euwalsetal.agreewiththisbutseemmorecautiousaboutsuchunemploy-mentsupportaccounts,basedontheviewthatcreditconstrainsarenotsoimportantintheNetherlands.Ifthisistrue,thenunemploymentsupportaccountsareoflittlevalue,but,ashownbyHasslerandRodriguez-Mora(1998),soisunemploymentinsurance:giventherelativelylowdurationofunemploymentspellsina‡exiblelabormarket,borrowingandlendingallowworkerstoachieveagreatdealofinsuranceontheirownintheabsenceofunemploymentbene…ts.Fewcountrieswouldconsiderreducingemploymentprotectionforolderworkers.YetEuwalsetal.(2009)pointtoaDutchstudywhichshowsthatthiscouldreduceunemploymentdurationforolderworkersconsider-ably.Furthermore,theeconomiccaseforincreasingemploymentprotectionwithage/tenureisnotstrong.Currentsystemsofadditionalemployment24 protectionforolderworkersareaveryimperfectattemptatprovidingcon-sumptionsmoothinginlightoflowerre-employmentprobabilitiesforolderworkers.Butoncemoree¢cientinstrumentssuchasthosesuggestedaboveareputinplace,themeritofemploymentprotectionrestsatbestonwhetherthereisadiscrepancybetweentheprivatecostoflaborasperceivedbythe…rmandthetruesocialopportunitycostoflabor.Thegreatertheformerrelativetothelatter,thegreatertheincentivestoine¢cientlydismisstheworker.Employmentprotectionisoftenunderstoodasataxtocorrectsuchadiscrepancy(SeeforexampleBlanchardandTirole(2006)).Abovewehavediscussedthreesourcesofhighwagesforolderworkers.Oneisspeci…chumancapitalaccumulation;itincreaseswagesbecauseitsreturnaretyp-icallysharedbetweentheworkerandthe…rm,notthebecausethe…rm’sperceivedcostofemployingtheworkerhasincreased.Anotherisacollec-tivebargainingstructurewhichismorebindingforolderworkers.Itmayindeedincreasethewedgebetweentheprivateandsocialopportunitycostoflabor,butthenonemayequallyconsiderachangeincollectivebargaining.Finally,thereisthee¤ectofdeferredpayments.Butsuchpaymentsarenotallocative:InLazear’s(1990)model,forexample,theirtimingisdeterminedbyincentiveconsiderations,whiletheseparationdecisionisdeterminedbyacomparisonoftheworker’sproductivityandtheprivateopportunitycostofwork.Therefore,inthatsetting,greaterwagesfortheelderlypersedonotgenerateexcesssiveincentivesfordismissalsrelativetootherworkers.Hencethereisnocompellingreasontoargueforadditionalemploymentprotectionforolderworkers.REFERENCESAvolio,B.J.andD.A.Waldman(1994).“VariationsinCognitive,Per-ceptual,andPsychomotorAbilitiesAcrosstheWorkingLifeSpan:Exam-iningtheE¤ectsofRace,Sex,Experience,Education,andOccupationalType.”,PsychologyandAging,Vol.9,No.3,pp.430-442.Behaghel,Luc,BrunoCréponandBéatriceSédillot(2008),"Theperversee¤ectsofpartialemploymentprotectionreform:ThecaseofFrencholderworkers",JournalofPublicEconomics92,696–721Blanchard,OlivierJeanandJeanTirole,"TheOptimalDesignofUnem-25 ploymentInsuranceandEmploymentProtection:AFirstPass",JournaloftheEuropeanEconomicAssociation,vol.6,n1,2007,p.45-77.Cohen,Daniel,ArnaudLefrancandGillesSaint-Paul(1997),"FrenchUnemployment:Atransatlanticperspective",EconomicPolicyEuwalsRob,RuuddeMooij,andDanielvanVuuren(2009),"RethinkingRetirement:Fromparticipationtowardsallocation",CPBworkingpapern80,DenHaag.Hairault,Jean-Olivier,FrançoisLangotandThepthidaSopraseuth,(2008)"DistancetoRetirementandOlderWorkers’Employment:TheCaseForDe-layingtheRetirementAge",mimeo,UniversityofParisIJacobson,Louis,LaLonde,Robert,andSullivan,DanielG,(1993)."Earn-ingsLossesofDisplacedWorkers,"AmericanEconomicReview,83(4),685-709.Kotliko¤,LawrenceandJ.Gokhale(1992),"EstimatingTheAge-ProductivityPro…leUsingthePresentValueofLifetimeEarnings",QuarterlyJournalofEconomicsLazear,Edward,“JobSecurityProvisionsandEmployment,”QuarterlyJournalofEconomics105:3(August1990):699-726.Ljunqvist,LarsandThomasSargent(1998),"TheEuropeanUnemploy-mentDilemma",JournalofPoliticalEconomy,106,3,514-550Rosolia,AlfonsoandSaint-Paul,Gilles(1998),"Thee¤ectofunemploy-mentspellsonsubsequentwagesinSpain",workingpaper,UniversitatPom-peuFabraandCEPR.Ruhm,Christopher(1991),“AreWorkersPermanentlyScarredbyJobDisplacements”AmericanEconomicReview,Vol.81,No.1,319-24.Saint-Paul,Gilles(1996),DualLaborMarkets.CambridgeMA:MITPress———————-(2000),"L’anatomieduchômageenEspagne;unecom-paraisonaveclaFranceetlesEtatsUnis",EconomieetStatistique,332/333,159-167Shapiro,Carl,andStiglitz,JosephE.(1984)."Equilibriumunemploy-mentasworkerdisciplinedevice".AmericanEconomicReview74:433-44.26 Skirbekk,Vegard(2003),"Ageandindividualproductivity:aliteraturesurvey",MaxPlanckInstituteworkingpaper.27 APPENDIXInthisAppendix,wesolveforthevalueofthe…rmunderaconstantp:Wealreadyknowthatinthelowproductivitystate,thevalueofthejobtothe…rmisequaltoJL(s)=yL�w r(1�e�r(T�s))fors�~s;andtoJL(s)=�F(s)fors~s;withF(s)=F0ifssandF(s)=F1ifs&#x-381;s:Letusfocusontheregimewhere~s&#x-381;s:WethenhavethatF1=w�yL r(1�e�r(T�~s)):(3)ConsidernowJH(s);thevalueofemployingaworkerofagesinthehighproductivitystate.TheBellmanequationfors�~sis(r+p)JH(s)=yH�w+pyL�w r(1�e�r(T�s))+dJH(s) ds:(4)Thesolutionofthisdi¤erentialequation,whoseterminalconditionisJH(T)=0;isJH(s)=yH�yL r+p�1�e�(r+p)(T�s)
+yL�w r(1�e�r(T�s)):(5)ThelasttermissimplyJL(s);the…rsttermistheexpectedpresentdis-countedvalueoftheadditionalpro…tsmaderelativetothelowproductivitystateaslongastheworkerremainsinahighproductivityone.Notealsothatthisequationalongwith(3)impliesthatJH(~s)=yH�yL r+p�1�e�(r+p)(T�~s)
�F1:(6)Forss~s;theBellmanequationis(r+p)JH(s)=yH�w�pF1+dJH(s) ds:Theterminalsolutionofthisdi¤erentialequationisgivenby(6).Conse-quently,thesolutionisJH(s)=yH�yL r+p�1�e�(r+p)(T�s)
+yL�w r+p(1�e�r(T�s)e�p(~s�s))�pF1 r+p:(7)28 Considerthedecisionto…reahighlyproductiveworkerjustbeforeages:ThiswillbeoptimalprovidedJH(s)�F0:Thisismorelikelytohold,thelowerF0andthegreaterF1:ThesmallestpossiblevalueofF0iszero,andthelargestonecompatiblewiththisregimeistheonesuchthat~s=s;i.e.F1=w�yL r(1�e�r(T�s)):Substitutinginto(7),weseethatinsuchacasetheinequalityJH(s)�F0=0holdsprovidedyH�yL r+p�1�e�(r+p)(T�s)
w�yL r(1�e�r(T�s)):Themaximumadmissiblevalueofwisw=yH;anditcanbecheckedthatatthispointthisinequalityholds,sinceforanya�0theexpression1�e�az zfallswithz:Finally,forsstheBellmanequationis(r+p)JH(s)=yH�w�pF0+dJH(s) ds;(8)andtheterminalconditionisavalue-matchingconditionwith(7)ats=s:Wegetthefollowingsolution:JH(s)=yH�yL r+p�1�e�(r+p)(T�s)
+yL�w r+p(1�e�r(T�s)e�p(~s�s))�pF0 r+p�p(F1�F0) r+pe�(r+p)(s�s)(9)Equations(5),(7)and(9)de…netheage-pro…leofthe…rm’snetexpectedpro…tsfromemployingaworkerinthehighproductivitystate.IfJH(s)�H;thenanyworkerofageswouldbehired.Ifthatinequalityfails,thentheworkerwouldnotbehired.Theseformulasarevalidintheparameterzonewhere~s�s;orequivalentlyF1w�yL r(1�e�r(T�s)):Di¤erentiatingtherelevantformulaforJH(:)inthethreezones,wegetthefollowing:1.Ifs�~s;wehavethatJ0H(s)_(w�yL)�(yH�yL)e�p(T�s):2.Ifss~s;thenJ0H(s)_(w�yL)�(yH�yL)e�p(T�~s):3.Finally,ifss;thenJ0H(s)_(w�yL)�(yH�yL)e�p(T�~s)�er(T�s)ep(~s�s)p(F1�F0)29 Consequently,if(w�yL)(yH�yL)e�p(T�~s);orequivalentlyw�yL(yH�yL)1�rF1 w�yLp=rthenJ0H0throughout.Ifthisinequalitydoesnothold,thentherearetwopossibilities:-If(w�yL)�(yH�yL)e�p(T�~s)&#x]TJ/;༕ ;.9;U T; 12;&#x.425;&#x 0 T; [00;er(T�s)ep(~s�s)p(F1�F0);thenH0&#x]TJ/;༕ ;.9;U T; 12;&#x.425;&#x 0 T; [00;0fors^s=T+1 plnw�yL yH�yLandH0�0fors�^s:-If(w�yL)�(yH�yL)e�p(T�~s)er(T�s)ep(~s�s)p(F1�F0);thenH00forss;H0&#x-277;0forss^s;andH0&#x]TJ/;༕ ;.9;U T; 34;&#x.166;&#x 0 T; [00;0fors&#x]TJ/;༕ ;.9;U T; 34;&#x.166;&#x 0 T; [00;^s:Forthesakeofcompleteness,letusalsodescribethesolutionifF1&#x]TJ/;༕ ;.9;U T; 34;&#x.166;&#x 0 T; [00;w�yL r(1�e�r(T�s)):Inthiscase,workerssuchthats�sarenot…redwhenfallingintothelowproductivitystate,andwehavetwofurtherpossibilities:A.IfF0w�yL r(1�e�r(T�s));thenallworkerssuchthatsslosetheirjobwhentheirproductivityfalls.ThenJHisgivenby(5)foralls&#x-277;s:Forss;itfollowstheBellmanequation(8)withtheterminalconditionJH(s)=yH�yL r+p�1�e�(r+p)(T�s)
+yL�w r(1�e�r(T�s)):ThesolutionisJH(s)=yH�yL r+p�1�e�(r+p)(T�s)
�pF0 r+p�1�e�(r+p)(s�s)
+yL�w r(r r+p+p r+pe�(r+p)(s�s)�e�r(T�s)e�p(s�s)):B.IfF0�w�yL r(1�e�r(T�s));thenworkerswhofallintothelowstateareretainedi¤s�~s;with~snowsolutiontoF0=w�yL r(1�e�r(T�~s));(10)and~ss:Foralls&#x-308;~s;JH(s)satis…estheBellmanequation(4)withtheterminalconditionJH(T)=0:Henceitisagaingivenby(5).Foralls~s;itsatis…es(8)withterminalconditionJH(~s)=yH�yL r+p�1�e�(r+p)(T�~s)
�F0:30 ThesolutionisJH(s)=yH�yL r+p�1�e�(r+p)(T�s)
�F0 r+p�p+re�(r+p)(~s�s)
+yL�w r+p�1�e�(r+p)(~s�s)
:31 life cyle; source: Avolioand Waldman (1994) ss countries. Source: Hairaultet al. (2008) syLFigure 3: the firing frontier s* syLFigure 4: effect of tighter employment protection s* s~ Figure 9: E-�U transitions0,01,02,03,04,05,06,07,08,021 to 2525 to 3031 to 3536 to 4041 to 4546 to 5051 to 5556 to 6061 to 65 France United States Figure 10: E�--non E transition0,05,010,015,020,025,030,035,040,021 to 2525 to 3031 to 3536 to 4041 to 4546 to 5051 to 5556 to 6061 to 65 France United States Figure 11: job finding rate0,010,020,030,040,050,060,070,021 to 2525 to 3031 to 3536 to 4041 to 4546 to 5051 to 5556 to 6061 to 65 France United States Figure 12: median wage, France, men0,05,010,015,020,025,030,035,021 to 2525 to 3031 to 3536 to 4041 to 4546 to 5051 to 5556 to 6061 to 65 High School dropouts High school Some college College graduates Figure 13: median wage, USA, men0,05,010,015,020,025,021 to 2525 to 3031 to 3536 to 4041 to 4546 to 5051 to 5556 to 6061 to 65 High School dropouts High school Some college College graduates High school Some college College degree Country France USA France USA France USA France USA 56-60 47.9 (1.5) 61-65 8.6 (1.1) Table 1 – Employment rates of older workers by educational levels, men, US and France. High school Some college College degree Country France USA France USA France USA France USA 31-35 11.6 (1.1) 36-40 7.3 (0.8) 41-45 5.9 (0.7) 46-50 6.2 (0.7) 51-55 6.3 (0.7) 56-60 3.4 (0.6) Table 2 – Unemployment rates, men, France and USA France USA 16-30 -0.041 (0.015) 31-40 -0.128 (0.021) 41-50 -0.199 (0.026) 51-65 -0.201 (0.039) ers, men and women, France and USA.