Unemployment and Matching in the Labor Market · PDF fileProf George Alogoskoufis, Dynamic...

ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2016

Unemployment and Matching in the Labor Market

A Model of Search and Matching in the Labor Market

ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2016 2

AFullyCompe99veLaborMarketCannotAccountforUnemployment• Inafullycompe99velabormarket,withoutuncertaintyandfric9ons,

employerswouldbeindifferentaboutwhetheranemployeeleavesherjob,sincetheycanreplaceherimmediatelyandatnocost,andatthesamecompe99vewage,withanotheremployee.

• Accordingly,anemployeewouldbeindifferentaboutlosingherjob,sinceshecanreadilyfindanotheroneatthesamecompe99verealwage.

• Moreover,insuchamarket“involuntary”unemploymentcannotexist,becausetheexcesssupplyofworkerswouldcauseanimmediatedeclineinrealwages,whichwouldleadtotheelimina9onofunemployment.


UnemploymentandVacancies• Inalmostalleconomiesthereisaposi9veandnon-trivialunemploymentrateeven

inboomperiods.Therearemanyunemployedpeopleseekingjobssimilartothoseheldbyworkerswithsimilarcharacteris9cs,atwagesequivalenttothosegenerallyprevailinginthelabormarket.

• Atthesame9me,therearemanyfirmswithvacancies,seekingtofillthemwithemployees,possessingcharacteris9cssimilartothoseoftheunemployed,andatprevailingrealwages.Howcanthenoneexplaintheexistenceandthefluctua9onsofbothunemploymentandvacancies?

• Theexplana9onofunemploymentisoneofthecentraltasksofmacroeconomics.Therearetwotypesofques9onsthatarebeingasked.First,whatdeterminestheequilibriumrateofunemploymentinaneconomy,whatareitsimplica9ons,andtowhatextenttheequilibriumunemploymentratereflectslabormarketdistor9ons.Thesecondkeyques9onconcernsthecyclicalfluctua9onsofunemploymentduringtheeconomiccycle.


TheUnemploymentRateintheUSA

0

0.05

0.1

0.15

0.2

0.25

0.3

1890

1893

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Recession UnemploymentRate


EuropeanUnemployment:GermanyandtheUK

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

195019521954195619581960196219641966196819701972197419761978198019821984198619881990199219941996199820002002200420062008201020122014

Germany UK


TheUnemploymentRateinGreece

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

195619581960196219641966196819701972197419761978198019821984198619881990199219941996199820002002200420062008201020122014

Greece EuroArea


Alterna9veViewsoftheLaborMarketandEquilibriumUnemployment

Therearemanyalterna9veapproachestothemodelingofthelabormarketthatdifferfromthecompe99vemodelorthemodelofmonopolis9ccompe99on.Alltheseapproachesofferanalterna9veexplana9onastowhy,despiteunemploymentandvacancies,realwagesdonotadjustinordertoabsorbtheunemployedandeliminateunemployment.

• EfficiencyWagetheories.• TheoriesofLongTermLaborContracts.• SearchandMatchingtheories.


EfficiencyWageTheories• Inthesetheoriesthereisasymmetricinforma3on.Firmscannot

observeeithertheproduc9vityortheeffortofworkersdirectly.Thus,firmsofferwagesabovetheaverageproduc9vityofjobseekers,orexis9ngemployees,inorder,eithertoabractworkerswithaboveaverageproduc9vity,ortoprovideincen9vestotheiremployeestoworkmoreintensively.

• Theyarethereforenotpreparedtoreducerealwages,ortoreplaceworkersalreadyinjobswiththeunemployed,eveniftheunemployedofferedtoworkatlowerwages.

• Weiss(1980)andShapiroandS9glitz(1984)arethetwomostimportantearlymodelsbasedonthisapproach.


TheoriesofLongTermContracts

• Thesecontractspreventfirmsfromundertakingunilateralchangestowagesinresponsetoshocks,ifthisisnotprovidedforinthelong-termcontract.Thecontractscanbeexplicit,suchascollec9ve,industryandindividualemploymentcontractsorinformalandimplicit.

• FortheoriginalimplicitcontracttheoriesseeAzariadis(1975),Baily(1974)andGordon(1974).Thesetheoriesviewedemploymentcontractsasinsurancecontractsbetweenriskneutralemployersandriskaverseemployees,againstadverseshockstoemployment.Fortheoriesthatarebasedonexplicitnego9a9onsseeMcDonaldandSolow(1981).Fortheoriesthatdis9nguishbetweeninsidersandoutsidersinthelabormarketseeLindbeckandSnower(1986),BlanchardandSummers(1986),Gregory(1986)andGoiries(1992).


SearchandMatchingTheories• Thesetheorieshighlightthesearchcostsoflookingforan

appropriatejob,byunemployedjobseekers,andthesearchcostsoflookingforanappropriateemployee,byfirmswithvacancies.

• Inthesetheories,acostlysearchprocessisrequiredforthematchingofjobseekerswithappropriatevacanciesinordertocreateanewjob.Consequently,jobsentailrents,somethingthatdoesnotapplyinfullycompe99velabormarketmodels.

• Theearlysearchtheoriesdatebackto1970.SeePissarides(2000)foranextensiveanalysisofsuchmodels.Otherrela9velyrecentpapersinclude,Mortensen(1986),Pissarides(1985)andMortensenandPissarides(1994).


UnemploymentandMatchingintheLaborMarket:TheMortensen-PissaridesModel

• Inthismodel,employersareinves9nginordertocreatejobvacanciesandtheprocessoffillingavacancyinvolvesmatchingofafirm,whichhascreatedavacancywithanunemployedjobseeker.

• Ateachinstant,therearetwoflowsintoandoutofunemployment.Someworkerslosetheirjobsandmovefromjobsintounemployment,andsomeoftheunemployedfindjobs,throughthematchingprocess,withfirmswhichhavecreatedvacancies.

• Inthesimplerversionsofthemodeltheprobabilityofjobtermina3onsisexogenous.Thisparameterdescribesthestructuralorcyclicalshocksaffec9ngtheeconomy,andleadingtothedestruc9onofjobs.

• Theprobabilityoffillingavacancy,aswellastheprobabilityofanunemployedjobseekertofindajob,areendogenousvariablesinthismodel,anddependonthedegreeoflabormarket3ghtness,whichisdefinedbythera9oofvacanciestotheunemployed.Thehigherthe9ghtnessofthelabormarket,thegreatertheprobabilityofanunemployedjobseekertofindajob,andthelowertheprobabilityofafirmtofillavacancy.


EquilibriumUnemploymentintheMortensen-PissaridesModel• Inthesteadystate,theflowstoandfrom

unemploymentareequalized,andtheequilibriumunemploymentratedependsposi9velyontheexogenousprobabilityofjobtermina9ons,andnega9velyontheendogenousprobabilityofanunemployedjobseekertofindajob.

• Theequilibriumunemploymentratethereforedependsnega9velyonlabormarket9ghtness,andis,ofcourse,determinedendogenously.

• Thenega9verela9onshipbetweentheunemploymentrateandthevacancyratewhichisimpliedbythisdependenceisknownastheBeveridgecurve.


TheBehaviorofFirmsandtheCrea9onofVacanciesandJobs

• Firmsandtheunemployedmaketheirdecisionsra9onally,maximizingtheexpectedpresentvalueoftheirprofitsandincome.

• Firmscreatenewvacanciesaslongastheexpectedprofitsfromtheinvestmentrequiredtocreateavacancyareposi9ve.Thecondi9onforavacancytobefilled,andforanewjobtobecreatedisthattherealwageshouldbeequaltolaborproduc9vityminusthecostofcrea9ngandmaintainingavacancy.Byfillingavacancy,afirmmustinequilibriumcoverboththewagecostsandthecostsofitsinvestmentinthecrea9onofthevacancy.

• Thejobcrea9oncondi9onimpliesanega9verela9onshipbetweenthewagethatthefirmiswillingtopayandlabormarket9ghtness.Thehigherislabormarket9ghtness,theloweristheprobabilityoffillingavacancyandthegreaterthetotalcostofmaintainingavacancy,sincevacanciesremainunfilledforlonger.


TheBehaviorofUnemployedJobSeekersandtheDetermina9onofRealWages

• Anunemployedjobseekerwillagreetogetajobiftheexpectedpresentvalueofincomeofanemployedworkerisgreaterthantheexpectedpresentvalueofincomeofanunemployedjobseeker.Thiscondi9onissa9sfiedinthismodel,aslongastherealwageishigherthanunemploymentbenefits.

• Realwagesaredeterminedinequilibriumbydecentralizedbargainingbetweenfirmsthathavevacanciesandunemployedjobseekers.Theequilibriumrealwageistheresultofthisnego9a9on,anddependsposi9velyontherela9vebargainingpoweroftheunemployed,thelevelofunemploymentbenefits,laborproduc9vity,thecostofmaintainingavacancyandlabormarket9ghtness.

• Theequilibriumrealwagedependsposi9velyonlabormarket9ghtness,asthisincreasestheaveragerecruitmentcostperunemployedperson,therebyincreasingthe“threat”pointofprospec9veemployeesversusprospec9veemployers,andweakeningtheeffec9vebargainingposi9onofprospec9veemployers.


EquilibriumRealWagesandUnemployment

• Theposi9verela9onshipbetweenrealwagesandlabormarket9ghtness,resul9ngfromthenego9a9onbetweenfirmswithvacanciesandtheunemployed,andthenega9verela9onshipbetweenrealwagesandandlabormarket9ghtnessimpliedbythejobcrea9oncondi9onforfirms,jointlydeterminetheequilibriumrealwageandequilibriumlabormarket9ghtness.

• Forgivenequilibriumlabormarket9ghtness,theequilibriumunemploymentrateisthendeterminedthroughtheBeveridgecurve,whichimpliesanega9verela9onshipbetweentheunemploymentandvacancyrates.

• Intheequilibriumofthismodel,theunemployedareworseoffthantheemployed.Consequentlyunemploymentisanundesirableandinvoluntarycondi9on,andnottheresultofchoicebytheunemployed,asincompe99vemodelsofthelabormarketwithoutfric9ons.


TheMatchingFunc9onAkeyassump9onofthisclassofmodelsisthatthenumberofjobscreatedateachmomentisaposi9vefunc9onofthenumberoffirmslookingforemployeesandthenumberofunemployedjobseekers.Theoutcomeofthisprocessisdescribedbytheso-calledmatchingfunc3on,determiningthenumberofjobscreatedateachmomentin9me.Thematchingfunc9onisassumedtobeincreasingineveryoneofitsarguments,concaveandlinearlyhomogeneous.Thus,itischaracterizedbyconstantreturnstoscale.

mL = m(uL,vL)

L sizeofthelaborforceu unemploymentrate(unemployedasapropor9onofthelaborforce)v vacancyrate(vacanciesasapropor9onofthelaborforce)m thejobcrea9onrate(newjobsasashareofthelaborforce)


TheProbabilityofFillingaVacancy

Assumingthatallvacancieshavethesameprobabilityofbeingfilled,andthatalltheunemployedhavethesameprobabilityofbeingemployed,theprobabilityoffillingavacancyshallbeequaltothera9oofthenumberofnewjobscreatedoverallexis9ngvacancies.

Theprobabilityoffillingavacancyisafunc9ononlyofthera9ooftheunemployedtojobvacancies.Thisisduetotheassump9onthatthematchingfunc9onislinearlyhomogeneous.Themoretheunemployedpervacancy,thegreaterwillbethelikelihoodoffillinganypar9cularvacancy.

q = m(uL,vL)vL

= m uv,1⎛

⎝⎜⎞⎠⎟


LaborMarketTightnessandtheProbabilityofFillingaVacancy

Wedefineasθ,thera9oofvacanciestotheunemployed.θmeasuresthedegreeof9ghtnessinthelabormarket.Thehigherthenumberofvacanciesrela9vetotheunemployed,thegreaterthe9ghtnessofthelabormarket.

θ = vu

Theprobabilityoffillingavacancydependsnega9velyonθ.

q = q(θ )

′q (θ ) ≤ 0 −1<η(θ ) = θ ′q (θ )q(θ )

< 0

η(θ)istheelas9cityofqwithrespecttoθ.


TheExpectedDura9onofaVacancy

BecauseofthePoissonassump9onthatallvacancieshavethesameprobabilityofbeingfilled,theexpecteddura9onofavacancyisequalto1/qanddependsposi9velyonθ.Thus,thehigherislabormarket9ghtness,thehighertheexpecteddura9onofavacancy.

1q= 1q(θ )


TheProbabilityofFindingaJobforanUnemployedJobSeekerandtheExpected

Dura9onofUnemployment

Theprobabilityoffindingajob,foranunemployedjobseekerdependsposi9velyonlabormarket9ghtnessθ.Theelas9citywithrespecttoθisequalto1-η(θ)>0.

m(uL,vL)uL

= vum(uL,vL)

vL= θq(θ )

1θq(θ )Theexpecteddura9onofunemploymentisgivenby,


ThePriceMechanismandAdjustmentintheLaborMarket

• Itisworthno9ngthat,inmodelsofthistype,thepricemechanismcannotleadtheprobabilityoffillingavacancyortheprobabilityoffindingajobtounity,asthelabormarketdoesnotfunc9ononlyviathepricemechanism,butalsoviathedegreeof9ghtnessofthelabormarket,whichdeterminestheprobabili9esoffirmstofilltheirvacanciesoroftheunemployedtofindjobsinanypar9cularinstance.

• Thedependenceoftheprobabilityoffillingavacancyandtheprobabilityoffindingajobontherela9venumberofvacanciestotheunemployed(9ghtness)isanexampleofatradingexternality.Thesesearchexternali9esareimportantfortheproper9esofequilibriumunemploymentinthesemodels.


FlowsIntoandOutofUnemployment

• Themodelassumesthatapropor9onofexis9ngjobsareterminatedineveryinstant.Thedestruc9onofjobsandtheflowfromemploymenttounemployment,isduetoeithercyclicalorstructuralrealdisturbancesthatmakethemunprofitable.Itisassumedthatatanyinstanttheprobabilityofdestruc9onofanyjobisequaltoλ,whereλisanexogenousparameter.

• Ontheotherhand,jobcrea9onoccurswhenafirmandanemployeeagreetosignacontractwithawagewhichistheresultofabilateralnego9a9on.Thisleadstoaflowoutofunemployment.

• Therefore,atanygivenmomenttherearetwoflowsinthelabormarket.Oneflowisfromexis9ngjobsintounemployment,becauseofjobdestruc9on,andtheotherfromunemploymenttonewlycreatedjobs.


ChangesintheUnemploymentRate

Thechangeintheunemploymentrateateachpointin9medependsonthedifferencebetweenflowsintounemploymentandflowsoutofunemployment.Inotherwords,itdependsonthedifferenceinthepropor9onofjobsdestroyedfromthepropor9onofnewjobscreated,thepropor9onsbeingdefinedrela9vetothelaborforce.

u•= λ(1− u)−θq(θ )u


TheDetermina9onofEquilibriumUnemployment

Inthesteadystate,theunemploymentratewillbeconstant.Consequently,theequilibriumunemploymentrateisdeterminedbythecondi9on,

λ(1− u) = θq(θ )u

Thiscondi9onimplies,

u = λλ +θq(θ )


TheBeveridgeCurve• Theequilibriumunemploymentratedependsposi9velyonλ,

theexogenousrateofjobdestruc9onandnega9velyonlabormarket9ghtnessθ.Labormarket9ghtnessisanendogenousvariableinthismodel,andisdeterminedinthelabormarket.

• Thenega9verela9onshipbetweentheunemploymentrateandlabormarket9ghtnessθ,or,equivalently,betweentheunemploymentrateandthevacancyrate,isusuallycalledtheBeveridgecurve.

• TheBeveridgecurvedefinesjustanega9verela9onbetweenvacanciesandunemployment.Inorderforunemploymenttobedetermined,oneneedstoknowlabormarket9ghtness,whichisoneoftheendogenousvariablesinthismodel.


TheBeveridgeCurve


TheBeveridgeCurveandEquilibriumUnemployment

• TheBeveridgecurvecandetermineequilibriumunemploymentifweknowhow9ghtisthelabormarket.

• Inordertoexaminehow9ghtnessinthelabormarketisdeterminedwehavetoexaminethebehaviororprospec9veemployers(firms)whocreatevacancies,andunemployedjobseekers.

• Themodelassumesthatbothfirmsandunemployedjobseekersbehavera9onally,maximizingthepresentvalueoftheirexpectedincome.


JobCrea9onandVacancies• Wehavethecrea9onofanewjobwhenaprospec9veemployerand

aprospec9veemployeegettogetherandagreetoanemploymentcontract.

• Ofcourse,beforethishappens,thepoten9alemployerhastocreateavacancyandsearchforanemployeeandtheprospec9veemployeehastobeunemployedandlookingforanewjob.

• Allthisinvolves9meandcostsandisdescribedbythematchingfunc9on.

• Weassumethattheinstantaneousvalueoftheproductofajobisconstantandequaltop>0.Theinstantaneouscostofavacantposttoaprospec9veemployerisequaltopcwhere0<c<1.Duringtheperiodofsearch,theemployerfacesaprobabilityq(θ)offindingaasuitableemployee,whichisindependentofherac9ons.

• Thenumberofvacanciesisendogenousandisdeterminedbyprofitmaximiza9on.Anyfirmcancreateavacancyandsearchforemployees.


ThePresentValueofNetExpectedProfitsfromanExis9ngJob

WedenotebyJthepresentvalueofafirm’snetexpectedprofitsfromanexis9ngjob,bywtherealwageandbyrtherealinterestrate.

Theinstantaneousexpectednetprofitfromanexis9ngjobisequalto,

p −w − λJ

Assumingaperfectcapitalmarketandaninfinitehorizon,thepresentvalueofthisexpectednetprofitisequalto,

J = e−rt p −w − λJ( )t=0

∞

∫ dt = p −w − λJr


Implica9onsofaPosi9veNetPresentValueofExpectedProfitsfromanExis9ngJob

ThepresentvalueJofajobfortheemployeristhusdefinedas,

J = p −wr + λ

Thiswillonlybeposi9ve,ifproduc9vityexceedstherealwage,p>w.

Rearrangingthedefini9onofJ,weget,

w = p − (r + λ)J

Thiswillonlybeposi9ve,ifproduc9vityexceedstherealwage,p>w.Thewedgebetweenproduc9vityandtherealwagemustreflectthecapitalandinsurancecostsofmaintainingthejob.


Prospec9veEmployersandthePresentValueofNetExpectedProfitsfromaVacancy

WedenotebyVthepresentvalueofexpectednetprofitsfromajobvacancy.Theinstantaneousnetexpectedprofitfromavacancyisequaltotheprobabilityoffillingthevacancy,andearningthedifferencebetweenthepresentvalueofajobandthepresentvalueofthevacancy,minusthemaintenancecostofthevacancypc.Itisdefinedby,

q(θ )(J −V )− pc

Assumingaperfectcapitalmarketandaninfinite9mehorizon,thepresentvalueofexpectednetprofitsfromavacancyVisdefinedby,

V = e−rt q(θ )(J −V )− pc( )t=0

∞

∫ dt = q(θ )(J −V )− pcr


TheCondi9onfortheCrea9onofVacancies

Inequilibriumwithfreecrea9onofvacancies(freeentry),allprofitopportuni9esfromcrea9ngnewvacancieswillbeexploited,andtheexpectedprofitsfromthecrea9onofanaddi9onalvacancywillbeequaltozero.Soinequilibriumwithfreeentry,V=0.This,impliesthat,

J = pcq(θ )

Thisisanimportantpredic9onofthismodel.Inequilibriumwithfreeentry,theexpectednetpresentvalueofajobwillbeequaltotheexpectedcostofhiringanemployee.Thisisequaltotheinstantaneouscostpcofmaintainingavacancy,9mestheexpecteddura9onofthevacancy1/q(θ).Thus,compe99onforthecrea9onofvacanciesandfreeentryreducestheexpectednetpresentvalueofprofitsfromajobtotheleveloftheexpectedcostofhiringaworker.


TheJobCrea9onCondi9on

w = p − (r + λ)pcq(θ )

= 1− (r + λ)cq(θ )

⎛⎝⎜

⎞⎠⎟p

Combiningtheimplica9onsoffreeentry,thattheexpectednetpresentvalueofajobisequaltoexpectedcostofhiring,andthedefini9onoftheexpectednetpresentvalueofajob,weget,

Thisisthesecondkeyequa9onofthismodel,andcanbecalledthejobcrea3oncondi3on.Thefirmwillonlyhireanewworkerandcreateajobiftherealwageissmallerthanorequaltotheproduc9vityoftheworker,minusthemarginalhiringcost,whichisdefinedontheRHS.


RealWages,Produc9vity,theMarginalHiringCostandtheCrea9onofJobs

• Firmscreatevacanciesaslongastheexpectedpresentvalueofnetprofitsfromthecrea9onofavacancyareposi9ve.

• Thecondi9onforthecrea9onofajobisthattherealwagemustbeequaltoproduc9vityminustheopportunitycostofmaintainingajob.Becauseoffreeentrythisisequaltothemarginalhiringcost.

• Thejobcrea9oncondi9onimpliesanega9verela9onbetweenlabormarket9ghtnessandtherealwage.Thehigherislabormarket9ghtness,thehighertheexpecteddura9onofavacancy,andthehigherthemarginalhiringcost.Thus,therealwagethatthefirmwouldbepreparedtopay,rela9vetoproduc9vity,willbelower.


TheJobCrea9onCondi9on


TheBehaviorofUnemployedJobSeekers

• Anunemployedjobseekerwillacceptajobofferiftheexpectedpresentvalueofincomewhenemployedishigherthantheexpectedpresentvalueofincomewhenunemployed.

• Thetypicalworkerearnsarealwagewwhenemployed,andislookingforajobwhenunemployed.

• Forthedura9onofunemployment,shehasaninstantaneousrealincomez,whichdependsonunemploymentbenefitsandanyotherincomeorbenefitfromtheuseoffree9me.Forsimplicityweshallcallztheunemploymentbenefit.


TheExpectedPresentValueofIncomeofanUnemployedJobSeekerAnunemployedjobseekerhasaninstantaneousrealincomeequaltozandaninstantaneousprobabilityoffindingajobequaltoθq(θ).Asaresult,U,theexpectedpresentvalueofherincome,isdefinedby,

U = e−rtt=0

∞

∫ z +θq(θ )(W −U )( )dt = z +θq(θ )(W −U )r

whereUandWarethecorrespondingnetpresentvaluesofexpectedincomeofanunemployedjobseekerandanemployedworket.ThepermanentincomeofanunemployedjobseekerisequaltorU.


TheExpectedPresentValueofIncomeofanEmployedWorker

Anemployedworkerhasaninstantaneousrealincomew,therealwage,butateachinstantalsofacestheriskoflosingherjob,withprobabilityλ.Therefore,thepresentvalueofherexpectedincomeWisequalto,

W = e−rt w + λ(U −W )( )t=0

∞

∫ dt = w + λ(U −W )r

whereUandWarethecorrespondingnetpresentvaluesofexpectedincomeofanunemployedjobseekerandanemployedworket.ThepermanentincomeofanemployedworkerisequaltorU.


ThePermanentIncomeoftheEmployedandtheUnemployed

Fromthetwoequa9onsdefiningthepresentvalueofexpectedincomeoftheunemployedandtheemployed,wecansolveforthepermanentincomeoftheunemployedandtheemployedasfunc9onsoftheparametersofthemodel.Thesearedefinedby,

rU = (r + λ)z +θq(θ )wr + λ +θq(θ )

rW = λz + [r +θq(θ )]wr + λ +θq(θ )

Ifw≥z,thenW≥U,andthepermanentincomeofanemployedworkercannotbelowerthanthepermanentincomeofanunemployedjobseeker.Inwhatfollows,weshallassumethatwexceedsz,whichindeedturnsouttobethecaseinequilibrium.Asaresult,noworkerwishestoleaveherjobandallunemployedjobseekerswishtofindajob.Unemploymentisinvoluntary.


Ra9onalBehaviorofFirmswithVacanciesandUnemployedJobSeekersandJobCrea9on

• Anunfilledvacancyimpliesalowerexpectednetpresentvalueofprofitsthanajob,despitethefactthat,withsomeprobability,ajobmaydisappear.

• Unemploymentimpliesalowerpermanentincomeforthosewhoexperienceit,thanforemployedworkers,despitethefactthateventheworkerswhoareemployedmay,withsomeprobability,losetheirjobsandbecomeunemployedinthefuture.

• Afirmwithavacancywillacceptajobofferifthejobcrea9oncondi9onissa9sfied,i.eiftherealwageislowerthanorequaltoproduc9vityminusthemarginalhiringcost.

• Anunemployedjobseekerwillacceptajobofferiftherealwageishigherthantheunemploymentbenefit.


RealWageDetermina9on• Therealwageforapar9cularjobisdeterminedbyanego9a9on

betweenaprospec9veemployer,afirmwithavacancy,andaprospec9veemployee,anunemployedjobseeker.

• Becausealljobsareequallyproduc9veandalltheunemployedreceivethesameunemploymentbenefit,therealwagethatisdeterminedbyanindividualnego9a9onwillbethesameastherealwagethatprevailsintherestoftheeconomy.

• Fromtheassump9onsthatwehavemadeaboutproduc9vityandaggregatedisturbances,anyoneemployerandanyoneworker,whentheygettogetherthroughthematchingprocess,willcertainlyagreetoanemploymentcontractandcreateajob.Otherwisetheymustcon9nuesearching,withaddi9onalcostsforbothsides.

• Anemploymentcontractbetweenanemployerandanemployeeisdefinedbyarealwageandtheprovisionthatemploymentwillbeterminatedifthereisadisturbancethatmakesthejobuntenable.


TheImpactofRealWagesontheOpportunityCostofaJobandthePermanentIncomeofa

Worker

Forarealwagewi,theexpectedreturnforaprospec9veemployerandaprospec9veemployeearegivenby

rJi = p −wi − λ(Ji −V )

rWi = wi + λ(U −Wi )

Wehavenotmadeuseoftheassump9onthatcompe99onhasreducedtheexpectedpresentvalueofavacancyVtozero.Wehaveassumedthough,asitappropriate,thattheexpectedpresentvalueofavacancy,andoftheincomeoftheunemployedUdependsonrealwagesintherestoftheeconomy,andisthusindependentofi.


BargainingOvertheRealWage

Therealwageisdeterminedbya(generalized)Nashbargain,thatmaximizestheweightedproductofthesurplusoftheprospec9veemployerandtheprospec9veemployeefromtheagreementtocreateajob.Anagreementmeansthatthesurplusoftheprospec9veemployerisequaltoJi-V,andthatsurplusoftheprospec9veemployeeisWi-U.Thus,therealwagewillsa9sfy,

wi = argmax(Wi −U )β (Ji −V )

1−β

βisameasureoftherela9vebargainingpoweroftheprospec9veemployee,overandabovewhatresultsfromthe“threat”pointsUandV.Insymmetricbargaining,liketheoneweanalyze,areasonablevalueofβis½.


FirstOrderCondi9on

Thefirstordercondi9onforamaximumimpliesthattheworkergetsashareβofthetotalsurplus.

Wi −U = β(Ji +Wi −V −U )

Subs9tu9ngforJiandWi,itfollowsthattheemployeegetsarealwagewhichexceedsthepermanentincomeofanunemployedworkerbyamul9pleβofthedifferenceofproduc9vityfromthepermanentincomeofanunemployedworker.

wi = rU + β(p − rU ) = w


RealWageDetermina9on

Fromthefirstordercondi9onforthedetermina9onoftherealwage,andasduetofreeentryV=0,itfollowsthat.

W −U = β1− β

J = β1− β

pcq(θ )

Asaresult,

rU = z +θq(θ )(W −U ) = z + β1− β

pcθ


TheWageFunc9onSubs9tu9ngforrUinthewagedetermina9onequa9on,

w = (1− β )z + β p(1+ cθ ) = z + β(p − z)+ β pcθ

Therealwageexceedstheunemploymentbenefitz.Itexceedsitbyapropor9onβofthedifferencebetweenproduc9vityandtheunemploymentbenefit,plusapropor9onβoftheaveragerecruitmentcostperunemployedworker.

Higherlabormarket9ghtnessθresultsinahigherrealwage,asthisincreasestheaveragerecruitmentcostperunemployedperson,therebyincreasingthe“threat”pointofprospec9veemployeesversusprospec9veemployers,andweakeningtheeffec9vebargainingposi9onofprospec9veemployers.

Thewagefunc9onplaysaroleanalogoustoalaborsupplyfunc9oninacompe99velabormarketmodel.


Determina9onofRealWages,LaborMarketTightnessandUnemployment• Inthismodel,thelevelofrealwageswandlabor

market9ghtnessθ,isdeterminedindependentlyoftheunemploymentrateu.Thejobcrea9oncondi9onandthewageequa9onsufficeforthedetermina9onofrealwagesandlabormarket9ghtness.

• Oncelabormarket9ghtnessθisdetermined,wecansubs9tuteforitintheBeveridgecurve,anddetermineequilibriumunemployment.

• Thus,themodelhasarecursivestructure.Thedetermina9onofrealwagesandlabormarket9ghtnessisindependentoftheunemploymentrate,andtheunemploymentrateisdeterminedthroughtheBeveridgecurve.


Determina9onofRealWages,LaborMarketTightnessandEquilibriumUnemployment

Insteadystatethismodeldeterminesthethreeendogenousvariables,(u,θ,w)whichsa9sfytheBeveridgecurve,i.e.thecondi9onofequalityofflowsinandoutofunemployment,thejobcrea3oncondi3on,andthewageequa3on.

u = λλ +θq(θ )

w = 1− (r + λ)cq(θ )

⎛⎝⎜

⎞⎠⎟p w = z + β(p − z)+ β pcθ


TheModelundertheAssump9onz=ρw

Ifweassumethattheunemploymentbenefitzisaconstantshareoftherealwageρ<1,thenthewageequa9onismodifiedandthemodeltakestheform,

u = λλ +θq(θ )

w = β(1+ cθ )1− (1− β )ρ

pw = 1− (r + λ)cq(θ )

⎛⎝⎜

⎞⎠⎟p


TheDetermina9onofRealWagesandLaborMarketTightness


TheDetermina9onoftheUnemploymentRate


Implica9onsofanIncreaseinLaborProduc9vity


Implica9onsofanIncreaseinUnemploymentBenefitsortheReplacementRate


AnIncreaseinUnemploymentBenefitsortheReplacementRateandEquilibriumUnemployment


Implica9onsofanIncreaseintheRealInterestRate


AnIncreaseintheRealInterestRateandEquilibriumUnemployment


Implica9onsofanIncreaseintheProbabilityofJobDestruc9on


AnIncreaseintheProbabilityofJobDestruc9onandEquilibriumUnemployment


TheDeterminantsofEquilibriumUnemployment

• Ifunemploymentbenefitsarepropor9onaltotherealwage,laborproduc9vitydoesnotaffecttheequilibriumunemploymentrateinthismodel.

• Thehigherthepercentageofrealwagespaidoutasunemploymentbenefits,thehighertheequilibriumrealwage,thelowerislabormarket9ghtness,andthehighertheequilibriumunemploymentrate.

• Higherrealinterestratesalsohaveaposi9veimpactonunemploymentinthismodel,becausetheyincreasethecostofmaintainingavacancy,resul9nginthecrea9onoffewerjobvacancies.

• Ahigherexogenousprobabilityofjobtermina9onshasaposi9veimpactonunemploymentfortworeasons.Firstbecauseitdirectlyincreasestheflowsfromexis9ngjobstounemployment,and,second,becauseit,indirectly,reducestheflowsfromunemploymenttojobs.Thesecondeffecttakesplacebecausetheexpectedprofitfromthecrea9onandfillingofavacancyfalls,resul9nginfewervacanciesandreducedflowsfromunemploymenttojobs.


DynamicAdjustmenttotheSteadyState

Ouranalysissofarwasonlyconcernedwithsteadystateunemployment,andalmostnothingwassaidaboutthedynamicadjustmentofthelabormarketintheshortrun.

Vacanciesandrealwagesarenonpredeterminedvariablesintheshortrun,sincetheydependonforwardlookingexpecta9onsoffirmsandjobseekers.Unemploymentisapredeterminedvariable,andintheshortrunevolvesaccordingto,

u•(t) = λ − (λ +θEq(θE ))u(t)

whereθEisthesteadystatelabormarket9ghtnessdeterminedthroughthewagenego9a9onsoffirmswithvacanciesandunemployedjobseekers


ConvergenceoftheUnemploymentRatetotheSteadyState

Sincevacanciesareajumpvariable,andθisdeterminedindependentlyoftheunemploymentrate,θandrealwageswjumpimmediatelytotheirsteadystatevalues.Thevacancyratejumpstomaintainθatitssteadystatevalue,andtheunemploymentrateconvergestoitssteadystatevalueaccordingto,

whereu0istheunemploymentrateat9me0,anduEisthesteadystateunemploymentrate,definedby,

u(t) = uE + (u0 − uE )e−(λ+θEq(θE ))t

uE =λ

λ +θEq(θE )


TheDynamicAdjustmentofUnemploymentandVacancies


ANumericalExample

Weassumethefollowingini3alparametervalues:

λ=2.5%,p=1,c=1/2,r=3%,ρ=1/2,β=1/2,M=1/2,μ=1/2

Undertheseassump9ons,itfollowsthat,

w=0.95,θ=0.85,u=5.1%,v=4.4%

Weassumethefollowingformforthematchingfunc9on:

mL = M (uL)µ (vL)1−µ

whichimplies,

q(θ ) = mLvL

= M uv

⎛⎝⎜

⎞⎠⎟µ

= Mθ −µ


AnIncreaseintheProbabilityofTermina9onofaJob

Ifλweretodoublefrom2.5%to5%,itfollowsthat,

w=0.93,θ=0.79,u=10.1%,v=7.9%

Rela9vetotheoriginalequilibrium,therealwagefallsby2.1%,to93%ofproduc9vity,andthesteadystateunemploymentratealmostdoubles,to10.1%.


DynamicAdjustmentofUnemploymentandVacanciesFollowinganIncreaseintheProbabilityofTermina9on

ofaJobfrom2.5%to5%


AnIncreaseintheReplacementRateofUnemploymentBenefits

Ifρweretorisefrom50%oftherealwageto70%,itfollowsthat,

w=0.96,θ=0.50,u=6.6%,v=3.3%

Rela9vetotheoriginalequilibrium,therealwagerisesbyroughly1%,andtheunemploymentraterisesby1.5percentagepoints,to6.6%.Withaconstantlaborforce,thisisequivalenttoa29.4%riseinthenumberoftheunemployed.


DynamicAdjustmentofUnemploymentandVacanciesFollowinganIncreaseintheReplacementRatefrom

50%to70%


AnIncreaseoftheRealInterestRate

Ifrweretodoublefrom3%to6%,itfollowsthat,

w=0.925,θ=0.78,u=5.4%,v=4.2%

Rela9vetotheini9alequilibrium,therealwagefallsbyabout2.5%,andtheunemploymentraterisesby0.3percentagepoints,to5.4%.Withaconstantlaborforce,thisisequivalenttoa5.9%riseinthenumberoftheunemployed.


DynamicAdjustmentofUnemploymentandVacanciesFollowinganIncreaseintheRealInterestRatefrom

3%to6%


TheNatureoftheMatchingProcessandFlowsintoandoutofUnemployment

• Inthismodel,employersareinves9nginordertocreatejobvacanciesandtheprocessoffillingavacancyinvolvesmatchingofafirmwithavacancywithanunemployedjobseeker.

• Ateachinstant,therearetwoflowsintoandoutofunemployment.Someworkerslosetheirjobsandmovefromjobsintounemployment,andsomeoftheunemployedfindjobs,throughthematchingprocess,withfirmswhichhavecreatedvacancies.

• Theprobabilityoffillingavacancy,aswellastheprobabilityofanunemployedjobseekertofindajob,areendogenousvariablesinthismodel.Theydependonthedegreeoflabormarket9ghtness,whichisdefinedbythera9oofvacanciestotheunemployed.Thehigherthe9ghtnessofthelabormarket,thegreatertheprobabilityofanunemployedjobseekertofindajob,andthelowertheprobabilityofafirmtofillavacancy.


EquilibriumUnemployment• Inthesteadystate,theflowstoandfromunemploymentare

equalized,andtheequilibriumunemploymentratedependsposi9velyontheexogenousprobabilityoftermina9onofajob,andnega9velyontheendogenousprobabilityofanunemployedjobseekertofindajob.

• Theequilibriumunemploymentratethereforedependsnega9velyonlabormarket9ghtness,andis,ofcourse,determinedendogenously.Thenega9verela9onshipbetweentheequilibriumunemploymentrateandthevacancyratewhichisimpliedbythisdependenceisknownastheBeveridgecurve.


FirmsandUnemployedJobSeekers

• Firmsandtheunemployedmaketheirdecisionsra9onally,maximizingtheexpectedpresentvalueoftheirprofitsandincome.

• Firmscreatenewvacanciesaslongastheexpectedprofitsfromtheinvestmentrequiredtocreateavacancyareposi9ve.

• Thecondi9onforavacancytobefilled,andforanewjobtobecreatedisthattherealwageshouldbeequaltolaborproduc9vityminusthecostofcrea9ngandmaintainingavacancy.Thejobcrea9oncondi9onimpliesanega9verela9onshipbetweenthewagethatthefirmiswillingtopayandlabormarket9ghtness.Thehigherislabormarket9ghtness,theloweristheprobabilityoffillingavacancyandthegreaterthetotalcostofmaintainingavacancy,sincevacanciesremainunfilledforlonger.

• Ontheotherhand,anunemployedjobseekerwillagreetogetajobiftheexpectedpresentvalueofincomeofanemployedworkerisgreaterthantheexpectedpresentvalueofincomeofanunemployedjobseeker.Thiscondi9onissa9sfiedinthismodel,aslongastherealwageishigherthanunemploymentbenefits.


TheDetermina9onofRealWagesandLaborMarketTightness

• Realwagesaredeterminedinequilibriumbydecentralizedbargainingbetweenfirmsthathavevacanciesandunemployedjobseekers.

• Theequilibriumrealwageistheresultofthisnego9a9on,anddependsposi9velyontherela9vebargainingpoweroftheunemployed,thelevelofunemploymentbenefits,laborproduc9vity,thecostofmaintainingavacancyandlabormarket9ghtness.

• Theequilibriumrealwagedependsposi9velyonlabormarket9ghtness,asthisincreasestheaveragerecruitmentcostperunemployedperson,therebyincreasingthe“threat”pointofprospec9veemployeesversusprospec9veemployers,andweakeningtheeffec9vebargainingposi9onofprospec9veemployers.


SimultaneousDetermina9onofRealWagesandLaborMarketTightnessandtheDetermina9on

ofEquilibriumUnemployment

• Theposi9verela9onshipbetweenrealwagesandlabormarket9ghtness,resul9ngfromthenego9a9onbetweenfirmswithvacanciesandtheunemployed,andthenega9verela9onshipbetweenrealwagesandandlabormarket9ghtnessimpliedbythejobcrea9oncondi9onforfirms,jointlydeterminetheequilibriumrealwageandequilibriumlabormarket9ghtness.

• Onceequilibriumlabormarket9ghtnesshasbeendetermined,theequilibriumunemploymentrateisthendeterminedthroughtheBeveridgecurve,whichimpliesanega9verela9onshipbetweentheunemploymentandvacancyrates.


TheDependenceofEquilibriumUnemploymentonProduc9vity,UnemploymentBenefits,RealInterest

RatesandtheFrequencyofJobTermina9ons• Ifunemploymentbenefitsarepropor9onaltotherealwage,laborproduc9vitydoesnot

affecttheequilibriumunemploymentrateinthismodel.

• However,thehigherthepercentageofrealwagespaidoutasunemploymentbenefits,thehighertheequilibriumrealwageandthehighertheequilibriumunemploymentrate.Thereasonisthathigherrealwagesreduceincen9vesforcrea9ngnewjobs,thusreducingthenumberofvacancies,reducinglabormarket9ghtnessandincreasingunemployment.

• Higherrealinterestratesalsohaveaposi9veimpactonunemploymentinthismodel,becausetheyincreasethecostofmaintainingavacancy,resul9nginthecrea9onoffewerjobvacancies,lowerlabormarket9ghtnessandhigherunemployment.

• Ahigherexogenousprobabilityoftermina9onofajobhasaposi9veimpactonunemploymentfortworeasons.Firstbecauseitdirectlyincreasestheflowsfromexis9ngjobstounemployment,and,second,becauseit,indirectly,reducestheflowsfromunemploymenttojobs.Thesecondeffecttakesplacebecausetheexpectedprofitfromthecrea9onandfillingofavacancyfalls,resul9nginfewervacanciesandreducedflowsfromunemploymenttojobs.

Unemployment and Matching in the Labor Market · PDF fileProf George Alogoskoufis, Dynamic...

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