carrillo jsslides

JobSearch: TheWorkersproblemSearchTheoryoftheLabourMarketJobSearchTheoryCarlosCarrillo-TudelaUniversityofEssexFebruary,2013CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemMotivatingevidence

Modernlabourmarketsarecharacterisedbylargeowsofworkersbetweenemployment,unemploymentandnon-participationstates.

Furtheremployedworkerscommonlychangejobswithoutandinterveningspellofnon-employment.

Typicallyworkersthatchangejobsobtainawageincrease.

However,animportantproportionofthemobtainawagedecrease.

Whenemployedthelikelihoodofmakingajob-to-jobtransitiondecreaseswithjobduration.

DurationofunemploymentdependsonthethelevelofUIbenets.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemMotivatingevidence






DurationofunemploymentdependsonthethelevelofUIbenets.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemMotivatingevidence






DurationofunemploymentdependsonthethelevelofUIbenets.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEvidencefromJolivetetal(EER,2006)CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEvidencefromJolivetetal(EER,2006)CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEvidencefromTatsiramos(JEEA,2009)CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEvidencefromTatsiramos(JEEA,2009)CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEvidencefromRubinsteinandWeiss(HBE,2011)CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEvidencefromRubinsteinandWeiss(HBE,2011)CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemWhatisSearchTheoryabout?

SearchTheorystartswiththepostulatethatthereareinformationalfrictionsinthelabourmarket.

Workersandrmsdonotknowthelocationofeachotherandmustinvestresourcesinordertoacquirethisinformation.

Onceameetingtakesplace:

Therearematch-specicrentstobeshared.

Thewaytheserentsareshareddependsontheinformationstructureandthewagedeterminationmechanism.

Ifbothpartiescometoanagreementonhowtosharetherents,productiontakesplace.

Overtime,workerscanchangeemployerorexperiencedisplacementduetojobdestruction.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemWhatisSearchTheoryabout?

SearchTheorystartswiththepostulatethatthereareinformationalfrictionsinthelabourmarket.

Workersandrmsdonotknowthelocationofeachotherandmustinvestresourcesinordertoacquirethisinformation.

Onceameetingtakesplace:

Therearematch-specicrentstobeshared.

Thewaytheserentsareshareddependsontheinformationstructureandthewagedeterminationmechanism.

Ifbothpartiescometoanagreementonhowtosharetherents,productiontakesplace.

Overtime,workerscanchangeemployerorexperiencedisplacementduetojobdestruction.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemWhySearchTheoryisrelevant?

Searchtheoryprovidesacoherent,dynamictheorythatcanbeusedtoanalyse:

Laboursupplyanddemandinamoresatisfactorywaythantheperfectcompetitiveapproach.

Thenatureofunemploymentandworkersandvacancyows.

Thedynamicofwagesoverworkerslabourmarkethistories.

Thedistributionofwagesacrossworkers.

Providesastrongtheoreticalbackgroundforempirical/quantitativeimplementation.

Usefultoolforpolicy.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemWhatarewegoingtostudy?

JobSearchtheory(McCallmodelofjobsearch).

Thebasicstools: Bellmanequations,Poissonprocesses,Optimalstoppingrules.

Unemploymentandemploymentduration.

Averagewage-experienceprole.

Equilibriumwagepostingmodels(BurdettandMortensenframework).

Wagedierentialsamongsimilarworkers.

Thewagedistributionandwagedynamics.

Humancapitalandon-the-jobsearch

Optimalwagecontracts.

Returnstoexperienceandtenure.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemWhatarewegoingtostudy?

SearchandMatchingmodels(Diamond-Mortensen-Pissaridesframework).

Thematchingfunction.

EquilibriumunemploymentandtheBeverigecurve.

Unemployment,vacanciesandtheBusinesscycle.

Othermodelsofsearchfrictions:

Stock-Flowmatchingmodels.

Islandsmodels

DirectedandCompetitiveSearch.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemWhatarewegoingtostudy?







Islandsmodels








Islandsmodels








Islandsmodels

DirectedandCompetitiveSearch.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemJobSearch: BasicFramework

Consideraninnitehorizoneconomyinwhichtimeisdiscrete;t= 0, 1, 2, ...

Thereisaunitmassofidenticalworkers.

TheobjectiveofanyworkeristomaximiseexpectedlifetimeutilityE0

t=0tu(yt),where (0, 1)isthediscountfactor,ytistheinstantaneousincomeatdatet,u(yt)istheinstantaneousutilityfunctionandE0istheexpectationconditionalontheinformationavailableatdatet= 0.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemJobSearch: BasicFramework

Consideraninnitehorizoneconomyinwhichtimeisdiscrete;t= 0, 1, 2, ...

Thereisaunitmassofidenticalworkers.

TheobjectiveofanyworkeristomaximiseexpectedlifetimeutilityE0

t=0tu(yt),where (0, 1)isthediscountfactor,ytistheinstantaneousincomeatdatet,u(yt)istheinstantaneousutilityfunctionandE0istheexpectationconditionalontheinformationavailableatdatet= 0.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemJobSearch: BasicFramework

Forsimplicityassumethatworkersareriskneutralsuchthatu(yt) = yt.

Instantaneousincomeisgivenby

Ifemployedatwagew,yt= w.

Ifunemployed,yt= z.

Fixthehoursofworktounitysothatwrepresentsthehourlywageorthetotal(perperiod)associatedwithajob.

Theopportunitycostofemploymentz,canbeinterpretedtoinclude

thevalueofleisureandhomeproductionactivities

plusunemploymentbenets

minusout-of-thepocketsearchcosts.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemJobSearch: BasicFramework




Ifunemployed,yt= z.









Ifunemployed,yt= z.









Ifunemployed,yt= z.





minusout-of-thepocketsearchcosts.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemBasicFramework

Anunemployedworkerisnotworkingbutactivelysearchingforajob.

Consistentwiththedenitionusedtomeasureunemployment.

Theworkersproblemistochoosewhentoacceptemployment(leaveunemployment)suchthathemaximisesexpectedlifetimeutility.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemBasicFramework

Anunemployedworkerisnotworkingbutactivelysearchingforajob.

Consistentwiththedenitionusedtomeasureunemployment.

Theworkersproblemistochoosewhentoacceptemployment(leaveunemployment)suchthathemaximisesexpectedlifetimeutility.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemAsequential(random)searchprocess

AnunemployedworkersamplesoneiidwageoereachperiodfromaknownwageoerdistributionF.

Letwandwdenotethe(nite)inmumandsupremumofthesupportofF.

Ifthewageoerisaccepted,theworkerisemployedatthatwageforever.

Ifthewageoerisrejected,theworkerremainsunemployedandcontinuesthesearch.

Thereisnorecallofpastoers.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemAsequential(random)searchprocess





Thereisnorecallofpastoers.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemAsequential(random)searchprocess





Thereisnorecallofpastoers.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemBellmanequations

LetV(w)denotethelifetimeutilityofemploymentatwagew.Sincejobsareretainedforever,V(w) =

t=0tw=w1 ,V(w) = w+V(w).

LetUdenotetheexpectedlifetimeutilityofunemployment.Sincethewageoersareiid,U= z +

wwmax[V(w), U]dF(w).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemBellmanequations

LetV(w)denotethelifetimeutilityofemploymentatwagew.Sincejobsareretainedforever,V(w) =

t=0tw=w1 ,V(w) = w+V(w).

LetUdenotetheexpectedlifetimeutilityofunemployment.Sincethewageoersareiid,U= z +

wwmax[V(w), U]dF(w).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemOptimalstoppingrule

AworkerwillacceptemploymentatwagewifandonlyifV(w) Uorequivalentlyw1 z +

wwmax[V(w), U]dF(w).

TheminimumacceptablewageRsuchthatforallw Riscalledthereservationwage.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemOptimalstoppingrule

AworkerwillacceptemploymentatwagewifandonlyifV(w) Uorequivalentlyw1 z +

wwmax[V(w), U]dF(w).

TheminimumacceptablewageRsuchthatforallw Riscalledthereservationwage.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemOptimalstoppingrule

RthensolvesV(R) = UandhenceR= z(1 ) +

wwmax[w, R]dF(w).

Theoptimalstoppingpolicythenimpliesareservationstrategy.

WeusethecontractionmappingtheoremtoprovethatthereexistsauniqueR.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemOptimalstoppingrule

RthensolvesV(R) = UandhenceR= z(1 ) +

wwmax[w, R]dF(w).

Theoptimalstoppingpolicythenimpliesareservationstrategy.

WeusethecontractionmappingtheoremtoprovethatthereexistsauniqueR.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContractionMappingTheorem

LetC[w,w]denotethesetofcontinuousandboundedfunctionson[w, w] [w, w].

DenethemappingT: C[w,w] C[w,w]asT max

w1 , z +

ww(w

)dF(w

)

.

ThusTtakesafunctionandmapsitintoanotherfunctionT.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContractionMappingTheorem

Usingthesup-normmetricd(, ) = supwww| (w) (w) |,guaranteesthemetricspaceis(C[w,w], d)iscomplete;

TisdeneonaBanachspace.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContractionMappingTheorem

TheBlackwellsucientconditionsthenguaranteesthatTisacontractionwithmodulus:

Tismonotone: Given(w) (w)forallw [w, w],itfollowsthatT T.

Tsatisesthediscountingproperty: Foranypositiveconstantm,T( + m) = T +m.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContractionMappingTheorem

TheContractionMappingTheorem(BanachFixedPointTheorem)guaranteesthatthereexistsauniquesolutionsuchthat= T.

Let = max[V(w), U]

NotethatVisincreasinginwandUisindependentofit

ThereexistsauniqueRsuchthatV(w) Uifandonlyifw R.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContractionMappingTheorem

TheContractionMappingTheorem(BanachFixedPointTheorem)guaranteesthatthereexistsauniquesolutionsuchthat= T.

Let = max[V(w), U]

NotethatVisincreasinginwandUisindependentofit

ThereexistsauniqueRsuchthatV(w) Uifandonlyifw R.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemUsefulrepresentationofR

NotethatthevaluefunctionsUandVcanbeexpressedasV(w) = w+V(w)U= z +U +

wR[V(w) U]dF(w).

SinceU= V(R),thereservationwageisgivenbyR= z +1

wR[w R]dF(w).

IntegrationbypartsthenimpliesR= z +1

wR[1 F(w)]dw.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemUsefulrepresentationofR


wR[V(w) U]dF(w).


wR[w R]dF(w).


wR[1 F(w)]dw.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemUsefulrepresentationofR


wR[V(w) U]dF(w).


wR[w R]dF(w).


wR[1 F(w)]dw.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemJoboersandlayos

Supposethatattheendofeachperiodthereisapositiveprobabilitythatajoboerarrives.

TheexpectedvalueofunemploymentisgivenbyU= z +[(1 )U +

wwmax[V(w), U]dF(w)],CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemJoboersandlayos

Supposethatattheendofeachperiodthereisapositiveprobabilitythatajoboerarrives.

TheexpectedvalueofunemploymentisgivenbyU= z +[(1 )U +

wwmax[V(w), U]dF(w)],CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemJoboersandlayos

Nextsupposethatonceemployed,theworkerfacesaprobabilityofbeingdisplacedattheendofeachperiod.

TheexpectedvalueofemploymentisV(w) = w+[(1 )V(w) +U],

Ex. 1: ShowthatRexists,isuniqueandsolvesR= z +1 +









wR[1 F(w)]dw.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemSurplusfunctionandcomparativestatics

DenethesurplusfunctionS(R) =

wR[1 F(w)]dw.

Dierentiation(LeibnizsRule)impliesS

(R) = [1 F(R)] < 0forR< wS

(R) = F

(R) > 0whenFisdierentiableandhasapositivedensity.

Ex. 2: Usingthesurplusfunctionre-doEx. 1.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemSurplusfunctionandcomparativestatics


wR[1 F(w)]dw.


(R) = [1 F(R)] < 0forR< wS

(R) = F




wR[1 F(w)]dw.


(R) = [1 F(R)] < 0forR< wS

(R) = F



DenetheimplicitfunctionG(R, z, , ) R z 1 +S(R) = 0.

Ex. 3: VerifythatthefollowinginequalitiesaretrueRz> 0,R> 0,R< 0.Discusstheeconomicintuitionoftheseresults.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemSurplusfunctionandcomparativestatics

DenetheimplicitfunctionG(R, z, , ) R z 1 +S(R) = 0.

Ex. 3: VerifythatthefollowinginequalitiesaretrueRz> 0,R> 0,R< 0.Discusstheeconomicintuitionoftheseresults.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContinuoustimeapproximationandthePoissonprocessPoissonprocess

Consideraninnitehorizoneconomywithtimeperiodsoflengthdt.

Supposethatineachperiodtheworkerreceivesn = 0, 1, 2, ...iidwageoerswithprobabilitya(n, dt).

Property1: LetN()denotethenumberofwageoersreceivedbytime 0,suchN(0) = 0.

Property2: Assumethata(n, dt)followsaPoissondistributionsuchthata(n, dt) =edt(dt)nn!.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContinuoustimeapproximationandthePoissonprocessPoissonprocess









Property3: Assumeindependentincrements: Thenumberofoersreceivedisindependentacrossperiods.

Thesepropertiesimplythatthecountingprocess{N(), 0}isaPoissonprocesswithrate > 0.

TheusefulnessofthePoissonprocessisthatprob[N(dt) = 1] = dt + O(dt)prob[N(dt) 2] = O(dt),whereafunctionf issaidtobeO(dt)iflimdt0f (dt)dt= 0.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContinuoustimeapproximationandthePoissonprocessPoissonprocess



TheusefulnessofthePoissonprocessisthatprob[N(dt) = 1] = dt + O(dt)prob[N(dt) 2] = O(dt),whereafunctionf issaidtobeO(dt)iflimdt0f (dt)dt= 0.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContinuoustimeapproximationandthePoissonprocessPoissonprocess



TheusefulnessofthePoissonprocessisthatprob[N(dt) = 1] = dt + O(dt)prob[N(dt) 2] = O(dt),whereafunctionf issaidtobeO(dt)iflimdt0f (dt)dt= 0.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContinuoustimeapproximationandthePoissonprocessBellmanequations

AssumethatlayosalsofollowaPoissonprocesswithrate> 0.

Letr denotethediscountrate.

TheexpectedvalueofunemploymentisthengivenbyU= zdt+11 + rdt

(1 dt)U +dt

wwmax[V(w), U]dF(w)

+O(dt).

TheexpectedvalueofemploymentatawagewisgivenbyV(w) = wdt +11 + rdt[(1 dt)V(w) +dtU] + O(dt)CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContinuoustimeapproximationandthePoissonprocessBellmanequations




(1 dt)U +dt

wwmax[V(w), U]dF(w)

+O(dt).





(1 dt)U +dt

wwmax[V(w), U]dF(w)

+O(dt).


Re-arranginganlettingdt 0,wehavethatrU= z +

wwmax[V(w) U, 0]dF(w)rV(w) = w+[U V(w)].

TheseBellmanequationscanbeinterpretedasassetpricingequationsinperfectcapitalmarkets.

Duetoarbitragetheexpectedreturnofanassetelsewhere(atrater )equalstheowpayooftheassetduringthenextperiod(e.g. dividends)plusanycapitalgainsduetopricechanges.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContinuoustimeapproximationandthePoissonprocessBellmanequations




Duetoarbitragetheexpectedreturnofanassetelsewhere(atrater )equalstheowpayooftheassetduringthenextperiod(e.g. dividends)plusanycapitalgainsduetopricechanges.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContinuoustimeapproximationandthePoissonprocessBellmanequations




Duetoarbitragetheexpectedreturnofanassetelsewhere(atrater )equalstheowpayooftheassetduringthenextperiod(e.g. dividends)plusanycapitalgainsduetopricechanges.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContinuoustimeapproximationandthePoissonprocessReservationwage

InthisnewenvironmentthereservationwageisgivenbyR= z +

wR[V(w) U]dF(w).

IntegrationbypartsthenimpliesR = z +r+

wR[1 F(w)]dw= z +r+S(R).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemContinuoustimeapproximationandthePoissonprocessReservationwage

InthisnewenvironmentthereservationwageisgivenbyR= z +

wR[V(w) U]dF(w).

IntegrationbypartsthenimpliesR = z +r+

wR[1 F(w)]dw= z +r+S(R).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheort

Uptonowwehaveassumethatworkerscannotcontroltherateatwhichjoboersarrive.

Supposethatthewageoerarrivalrateis = (s),wheres 0denotesthesearchintensityortheamountofeortdevotedintosearch. Assumethat(0) = u> 0and

> 0,

< 0.

Supposethereisapercostk(s)ofsearchsuchk(0) = 0andthatk

> 0,k

> 0.

Theopportunitycostofemploymentisthengivenbyz= b k(s).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheort



> 0,

< 0.


> 0,k

> 0.




> 0,

< 0.


> 0,k

> 0.


TheexpectedvalueofunemploymentisnowgivenbyrU= maxs0

b k(s) +(s)

wwmax[V(w) U, 0]dF(w)

.

Letsdenotetheoptimalsearchintensity. Sincethereservationwagecanbederivedgivenanysearchintensity,wehavethatR= b k(s) +(s)r+S(R).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheort

MaximisingthevalueofunemploymentthenimpliesthatssatisestheKhun-Tuckercondition(r+)k

(s)

(s)S(R) =ifs> 0.

Giventhepropertiesofandk,thereexistsauniques> 0thatmaximisesU.

Theworkeroptimalsearchstrategyisthengivenbythepair(R, s).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheort


(s)

(s)S(R) =ifs> 0.


Theworkeroptimalsearchstrategyisthengivenbythepair(R, s).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheort


(s)

(s)S(R) =ifs> 0.


Theworkeroptimalsearchstrategyisthengivenbythepair(R, s).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemOn-the-jobsearch

ThisextensionisbasedonBurdett,(AER1978).

Supposethattheoerarrivalratetounemployedworkersisu.

Supposethatemployedworkerscancontinuesearchingfromthesameoerdistribution.

Assumethatoersarrivetoemployedworkersatratee.

TheexpectedvalueofunemploymentisrU= z +u

wwmax[V(w) U, 0]dF(w).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemOn-the-jobsearch

ThisextensionisbasedonBurdett,(AER1978).

Supposethattheoerarrivalratetounemployedworkersisu.

Supposethatemployedworkerscancontinuesearchingfromthesameoerdistribution.

Assumethatoersarrivetoemployedworkersatratee.

TheexpectedvalueofunemploymentisrU= z +u

wwmax[V(w) U, 0]dF(w).CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemOn-the-jobsearch

TheexpectedvalueofemploymentatwagewisrV(w) = w+e

wwmax[V(w

)V(w), 0]dF(w

)+[UV(w)]

TheoptimalsearchstrategyforanunemployedworkerisstilldescribedbyareservationwageRsuchthattheworkeracceptsemploymentifandonlyifw R.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemOn-the-jobsearch

TheexpectedvalueofemploymentatwagewisrV(w) = w+e

wwmax[V(w

)V(w), 0]dF(w

)+[UV(w)]

TheoptimalsearchstrategyforanunemployedworkerisstilldescribedbyareservationwageRsuchthattheworkeracceptsemploymentifandonlyifw R.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemOn-the-jobsearch

Theoptimalsearchstrategyforanemployedworkeristomovetoadierentjobifandonlyifw

> w.

ThereservationwageinthiscaseisR= z + (ue)

wR[1 F(w)]r+ +e(1 F(w))dw.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheortwithOJS

Letsuandsedenotethesearcheortofanunemployedandemployedworker,respectively.

Theoerarrivalratesaregivenbyi= (si)with(0) = and

> 0,

< 0fori = u, e.

Thesearchcostki= k(si)suchthatki(0) = 0andk

i> 0,k

i> 0fori = u, e.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheortwithOJS



> 0,

< 0fori = u, e.


i> 0,k




> 0,

< 0fori = u, e.


i> 0,k


ThevaluefunctionsinthiscasearegivenbyrU= maxsu0

b ku(su) +(su)

wR[V(w) U]dF(w)

rV(w) = maxse0

w ke(se) +(se)

ww[V(w

) V(w)]dF(w

)

+[U V(w)]CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheortwithOJS

SolvingthemazimisationproblemyieldsthefollowingKuhn-Tuckerconditions

(su)

wR[V(w) U]dF(w) k

u(su) with =ifsu> 0,

(se)

ww[V(w

)V(w)]dF(w

) = k

e(se) with =ifse> 0.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheortwithOJS

Thepropertiesofandkimplythatsu> 0andse> 0.

Itiseasytoverifythatifk

e> k

uforallsthensu> se.

Further,workerswithhigherwageswillspendlesseortinsearch.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheortwithOJS



e> k

uforallsthensu> se.

Further,workerswithhigherwageswillspendlesseortinsearch.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemEndogenoussearcheortwithOJS



e> k

uforallsthensu> se.

Further,workerswithhigherwageswillspendlesseortinsearch.CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemDurationofUnemploymentandEmployment

ThePoissonprocessassumptionimpliesthatthedurationofunemploymentisexponentiallydistributedwithparameteru(su)[1 F(R)].

Theaveragedurationofunemploymentis1(su)[1 F(R)]

Similarly,thedurationofemploymentatwagewisexponentiallydistributedwithparameter +(se)[1 F(w)].

Theaveragedurationofemploymentatwagewis1 +(se)[1 F(w)].CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemDurationofUnemploymentandEmployment

ThePoissonprocessassumptionimpliesthatthedurationofunemploymentisexponentiallydistributedwithparameteru(su)[1 F(R)].

Theaveragedurationofunemploymentis1(su)[1 F(R)]

Similarly,thedurationofemploymentatwagewisexponentiallydistributedwithparameter +(se)[1 F(w)].

Theaveragedurationofemploymentatwagewis1 +(se)[1 F(w)].CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemDurationofUnemploymentandEmployment

Animportantimplicationofthistheoryisthatthereis:

Apositiverelationshipbetweenwagesandlabourmarketexperience

Tenureonthejobandwagesarepositivelyrelated.

Quitratesandwagesarenegativelyrelated.

Ex. 4:Whataretheeectsof,iandzonthedurationofemploymentandunemployment?CarlosCarrillo-Tudela SearchTheoryoftheLabourMarketJobSearch: TheWorkersproblemDurationofUnemploymentandEmployment















Ex. 4:Whataretheeectsof,iandzonthedurationofemploymentandunemployment?CarlosCarrillo-Tudela SearchTheoryoftheLabourMarket

carrillo jsslides

Documents

productiontak overtime