optimal unemployment insurance

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1、Chapter22OptimalUnemploymentInsurance22.1.History-dependentunemploymentinsuranceThischapterappliestherecursivecontractmachinerystudiedinchapters20,21,and23incontextsthataresimpleenoughthatwecangoalongwaytowardcomputingoptimalcontractsbyhand.Thecontractsencodehistorydepe

2、ndencebymappinganinitialpromisedvalueandarandomtimetobservationintoatimetconsumptionallocationandacontinuationvaluetobringintonextperiod.Weuserecursivecontractstostudygoodwaysofprovidingconsumptioninsurancewhenincentiveproblemscomefromtheinsuranceauthority’sinabilitytoo

3、bservetheeffortthatanunemployedpersonexertssearchingforajob.WebeginbystudyingasetupofShavellandWeiss(1979)andHopenhaynandNicolini(1997)thatfocusesonasingleisolatedspellofunemploymentfollowedbypermanentemployment.LaterwetakeupsettingsofWangandWilliamson(1996)andZhao(2001)

4、withalternatingspellsofemploymentandunemploymentinwhichtheplannerhaslimitedinformationaboutaworker’seffortwhileheisonthejob,inadditiontonotobservinghissearcheffortwhileheisunemployed.Herehistorydependencemanifestsitselfinanoptimalcontractwithintertemporaltie-insacrossthes

5、espells.Zhaouseshermodeltorationalizeunemploymentcompensationthatreplacesafractionofaworker’searningsonhisorherpreviousjob.–913–914OptimalUnemploymentInsurance22.2.Aone-spellmodelThissectiondescribesamodelofoptimalunemploymentcompensationalongthelinesofShavellandWeiss(1

6、979)andHopenhaynandNicolini(1997).WeshallusethetechniquesofHopenhaynandNicolinitoanalyzeamodelclosertoShavellandWeiss’s.Anunemployedworkerordersstochasticprocessesofconsumptionandsearcheffort{c,a}∞accordingtottt=0∞Eβt[u(c)−a](22.2.1)ttt=0whereβ∈(0,1)andu(c)isstrictlyinc

7、reasing,twicedifferentiable,andstrictlyconcave.Weassumethatu(0)iswelldefined.Werequirethatct≥0andat≥0.Alljobsarealikeandpaywagew>0unitsoftheconsumptiongoodeachperiodforever.Anunemployedworkersearcheswitheffortaandwithprobabilityp(a)receivesapermanentjobatthebeginningofthen

8、extperiod.Onceaworkerhasfoundajob,heisbeyondthegraspoftheunemploymentinsuranceagency.1Furthermore,a=0whenthewo