How Should Unemployment Benefits Respond to the Business Cycle?

How Should Unemployment Benefits Respond to the Business Cycle? Michael T.Kiley* September2002 Version1.3 *Address:WhileonLeave(September2001-August2003)—OECDEconomicsDepartmentCS1,2rue AndrePascal,75016ParisFRANCE.Email:Michael.Kiley@oecd.org.PermanentAddress:MailStop67, FederalReserveBoard,Washington,DC20551.Email:mkiley@frb.gov. Acknowledgements:IwouldlikeseminarparticipantsatINSEADandcolleaguesattheFederalReserve BoardandtheOECDfordiscussionsinvolvingthisresearchandLauraVeldkamp,AlanKrueger,andtwo anonymousrefereesforcommentingonpreviousversionsofthispaper. Theviewsexpressedhereinare thoseoftheauthor,anddonotrepresentthoseoftheOECD,theFederalReserveBoard,ortheirrespective staffs. i

How Should UnemploymentBenefits Respond totheBusiness Cycle? Abstract Unemployment insuranceprograms balancethebenefits ofconsumptionsmoothingfor unemployed workers against thedisincentive effects ofunemployment benefits.Sucha balancingofbenefits andcosts is likelysensitivetothecyclical stateofthe economy,and hencethe generosityofbenefits shouldalsorespondtothe cyclical stateoftheeconomy. Thenatureofsuchresponses inanoptimal unemployment insurance(UI)program is analyzedin asimplemodel.Theresults suggest that anoptimal UIprogram would increasetheinitial level ofbenefits andprobablyextendhigherbenefits overtimein responsetoarecessionaryshock.Asimple extensionofbenefits,suchas exists automaticallyinthesystem intheUnitedStates,provides bothpoorerinsuranceand poorerincentives thantheoptimal program, anddoes soat ahighercost.Moreover,the current UIsystem intheU.S.provides asubstantiallyhigherlevel ofwelfaretoworkers who losejobs duringtight labormarkets. JELCodes: E24,J65,J64 Keywords: Unemployment Insurance,Time-VaryingBenefits ii

1.Introduction Unemployment insuranceprograms havebeendesigned, at least tosomeextent,to balancethebenefits regardingconsumptionsmoothingforunemployedworkers who cannot self-insureagainst thedisincentive effects ofunemployment benefits on labor market searchandthewillingness oftheunemployedtoaccept joboffers.Such a balancingofbenefits andcosts is likelysensitivetothecyclical stateofthe economy,and hencethe generosityofbenefits shouldalsorespondtothe cyclical stateoftheeconomy. Thenatureofsuchresponses inanoptimal unemployment insuranceprogram is analyzed inasimplemodel that balances the consumptionsmoothingbenefits ofunemployment insurance against thecosts interms ofdiminishedlabormarket searchandhencehigher unemployment.The results suggest that anoptimal UIprogram wouldincreasetheinitial level ofbenefits andprobablyextendhigherbenefits overtimeinresponsetoa recessionaryshock.Asimpleextensionofbenefits provides bothpoorerinsuranceand poorerincentives thantheoptimal program, anddoes soat ahighercost. Theimportanceoftheanalysis is several-fold.First,thebalancingofthe consumptionsmoothingaspect ofunemployment insurance against thedisincentives such insuranceprovides forlabormarket searchandwillingness toaccept joboffers lies at the centerofmost workonoptimal unemployment insurance (UI).1 Hence,sucha balancing is thenatural placetobegin ananalysis ofthedependenceofoptimal UIbenefits onthe cyclical stateoftheeconomy. IntheUnitedStates,thecurrent structureoftheUIsystem contains triggers fortheextensionofemergencybenefits. Inpractice,suchtriggers make thegenerosityoftheUIsystem greaterduringperiods ofhighunemployment,andthis automaticfeatureoftheU.S.system has tendedtobeamplifiedbydiscretionary implementationofemergencybenefits duringrecessions.Theoptimalityofsuchchanges ingenerosityoverthebusiness cyclehas not beenmodeled formally,andthe analysis hereinbothfills thegapinqualitativeresults andpresents a roughquantitativeexercise 1ForworkontheconsumptionsmoothingbenefitofUI,seeGruber(1997).Importantworkonthe disincentiveeffectsofUIbenefitsintheUnitedStatesincludesFeldstein(1974),Meyer(1990),andCard andLevine(2000).WorkillustratinghowanoptimalUIsystembalancesthesebenefitsandcostsincludes Baily(1978),ShavellandWeiss(1979),andHopenhaynandNicolini(1997).AcemogluandShimer (1999)provideonenotablealternativemotivationforUI.Intheiranalysis,aUIprogramencouragesrisktaking,whichraisestheefficiencyoftheeconomy. 1

that gauges thedegreetowhichUIbenefits shouldvaryoverthecycle.Thequantitative results suggest that thedegreeofvariation in benefits overthebusiness cycle would need to belargein orderto equatethewelfareofjob losers at different points ofthebusiness cycle. Theanalysis is important fortwoother reasons.In theUnitedStates, congressional debateover “emergency”extensionof(UI) benefits inresponsetothe recentlydeclaredrecession(National BureauofEconomicResearch(2001)) focused almost exclusivelyontwofactors: stimulus (aggregatedemandmanagement) and disincentiveeffects ofhigherbenefits onlabormarket search,andhencenegativeeffect onaggregatemeasures ofunemployment (Goldreich (2001)).Theinsuranceaspect ofthe UIprogram receivedfarless attention.The analysis hereinshows that higherbenefits in recessions exacerbatetheincentiveproblems createdbya UIprogram,as fearedinthe popularcommentary; however,theinsuranceaspect oftheprogram is morevaluable whenjobsearchis less productive–i.e., duringrecessions –andhenceincreased generosityis optimal. In addition,theUnitedStates is relativelyunusual inallowingthe generosityof UIbenefits tovarywiththecyclical stateofthe economy: Canada’s program contains similarelements,but most otherOECDcountries –whileprovidingsubstantiallymore generous UIbenefits thanintheU.S.–donot varythe generosityofbenefits with aggregatelabormarket conditions.Theresults hereinsuggest that aprogram withsuch cyclical variationachieves ahigherlevel ofwelfareduringperiods oflabormarket stress andsmoothes thelevel ofwelfareofthenewlyunemployedovertime,byconcentrating benefits duringperiods whensearchactivityis less fruitful andloweringbenefits when search activityis morelikelyto yieldajob. Theeconomic forces generatingtheresults areintuitive.Followingashockthat lowers theproductivityofsearch effort (e.g.,someshockloweringthesupplyofjobs), an insuranceprogram designedtomaintain thepresent discountedvalueoftheutilityofthe newlyunemployedequal tothevaluefornewlyunemployed absent theshock(i.e.,in steadystate)wouldincreasetheinitial level ofbenefits andprobablylowerbenefits over timebyasmalleramount.Theincreaseintheinitial level ofbenefits relativetothe steadystatereflects thelowerprobabilityoffindingajob given anylevel ofsearcheffort 2

afterthenegativeshock; sincetheprobabilityoffindingajobis nowlower,benefits are higher. Thelowerrateofdecreaseofbenefits overtimereflects thetradeoffbetween providingconsumptioninsuranceandinducingsearcheffort bytheunemployed: Since searchis less productiveaftertheshockbut will becomemoreproductiveas the recession wanes,andbecauseoptimal benefits fall withthedurationoftheunemployment spell solelyinordertospurproductivesearch,thepaceat whichbenefits fall afteranegative shockis smallerunderanoptimal insuranceprogram. Section2presents backgroundinformationofthe changes inUIbenefits overthe business cycleintheUnitedStates tomotivatethediscussion.Section3discusses the responseofbenefits tocyclical conditions inasimpletwo-periodmodel,illustratingthat benefits shouldbemoregenerous whenthelabormarket deteriorates.Section4provides adynamicmodel and asimplequantitativeanalysis ofthedegreetowhichbenefits shouldvaryoverthebusiness cyclewithinthecontext ofarepeatedprincipal-agent problem.Section5considers the effect ofdifferent assumptions regardinghow recessions affect theproductivityofsearch andwages uponreemployment.Section6concludes. 2.Background2 Inthe UnitedStates,unemployment insurancewas bornduringtheGreat Depression,and its form reflects,inpart,theconcerns ofthat era (Baicker,Goldin,andKatz (1998)).The Social SecurityAct of1935(Public Law74-271) createdthe Federal-State Unemployment CompensationProgram.Twomainobjectives were given: (1)an insurancegoal –toprovidetemporaryincometoinvoluntarilyunemployedworkers; and (2)astimulus goal –tostabilizetheeconomyduringrecessions.Theanalysis herein focuses ontheinsuranceaspect of UI. TheUIsystem consists ofindividual state-administeredprograms,whichuse diversemethods todetermine UIeligibility.Forthemost part,threemajorfactors are used: (1)recent employment and earnings history; (2)the abilitytoseekandaccept suitableemployment; and(3)certaindisqualifications relatedtoa claimant's most recent jobseparationorjob-offer refusal. In general,weeklybenefit amounts areset as a 2ThissectionreliesheavilyonCommitteeonWaysandMeans(2000)andO’LearyandWandner(1997). 3

fractionoftheindividual's averageweeklywage.Theweeklybenefit amounts typically replacebetween50and70percent oftheaverageweeklypretax wageuptosome maximumlevel.Becauseofthemaximum benefit level,thereplacement ratetends to varyinverselywiththeclaimant's average weeklypretax wage.As aresult,theaverage replacement rate was only35percent in thefourthquarterof1999. Inthequantitative exercises below,thereplacement rateis set at 60percent,inthemiddleoftherange across states forlow-wageworkers; this was doneas theexercises wereviewed as most relevant fortheinsuranceprovidedtothelow-wage group,but thenatureofthe results is littlechangedifareplacement ratenear35percent is chosen. Themaximum durationofbenefit receipt is 39weeks.The “regular”programs usuallyprovideupto 26weeks.TheFederal-StateExtendedBenefits Program, enactedin 1970,provides upto13additional weeks instates whereunemployment rates are relativelyhigh at benefit levels that areidentical tothoseundertheregularprogram.3 The natureofthe extendedbenefits program makes the generosityofthe UIsystem greater duringrecessions orperiods oflabor-market weakness. Inpractice,thecyclical sensitivity oftheUIprogram has beeneven greaterbecauseofenactment of emergencyextensions sixtimes since1958. In1958 and1961,emergencyprograms extendingbenefits for13 weeks,as underthe current automaticprogram,wereimplemented.Duringthe recession ofthemid-1970s (aftertheenactment ofthepermanent extendedbenefit program), extendedbenefits wereavailableineverystate,reflectingtheseverityoftherecession. Twomoreemergencyprograms were enactedinJanuaryandMarchof1975, addinga total of26moreweeks ofextendedbenefits (toatotal potential durationofbenefits of65 weeks betweenMarch1975 andMarch1977).Aless generous emergencyextension followedinApril 1977.By1980 and1981,theshiftingpolitical climate and dissatisfactionwiththeresults ofextendedbenefits ledtoasubstantial curtailingofthe program.However,therecessionof1982led againtoanemergencyexpansionofbenefit duration.Anotheremergencyextensionofbenefits occurredbetweenNovember1991 and February1994, followingtherecessionoftheearly1990s.TheCongress approved 3ThetriggersforautomaticextensionofbenefitsarecomplicatedandarediscussedinCommitteeonWays andMeans(2000). 4

andthePresident signedlegislationtemporarilyextendingbenefits oncemoreinMarch 2002. TheU.S.system of extendedbenefits in cyclical downturns is relativelyunusual: Canada’s UIsystem contains similarelements,but most otherOECDcountries donot. Theextensionofbenefits inrecessions maybejustifiedoninsurance grounds (O’Leary andWandner(1997)),but aformal analysis has not beenundertaken.Moreover, popular debateand eveninput from economists havefocusedlittleonincreasedbenefit levels, ratherthan extendedduration,inresponseto adeterioratinglabormarket intheUnited States (withsomesmall exceptions; seeKrueger(2001)). In fact, acommonreactiontothis researchhas beenthat otherfactors,suchas low wages forworkers uponreemployment (e.g.,Hipple1999),discouragesearchin recessions andhenceUIbenefits shouldbeless generous at suchtimes toencourage search. Otherobjections havefocussedwhetherassumptions about themarginal productivityofsearchinrecessions drivetheresults becauseofempiricallyunjustified assumptions regardingthesemagnitudes.Theformal analysis insection4will consider theform ofanoptimal benefit schedule followinga negativeshockinthelabormarket andexaminethesensitivityoftheresults toeachoftheseconcerns.Thelackofacentral focus inthedebateandtheseobjections highlight howtheresults,whilevery straightforwardoncedevelopedbelow,have goneunder-appreciated.First, asimple model will bedevelopedinpreparationforthenumerical analysis insection4. 3.SimpleAnalytics Tobegin, atwo-periodmodel illustratingtheforces affectingtheoptimal responseofUI benefits toarecessionis examined.Considerthefollowingenvironment.Thepreferences ofanunemployedworkeroverconsumption(c(t))andsearcheffort (a(t)) are givenby Equation1 u(c(1)) − a(1) + βEu(c(2)), whereEis the expectations operator,0<β<1,andu(c(t))is strictlyincreasing,twice differentiable,andstrictlyconcave. Bothconsumptionandsearch effort must benonnegative.Employedworkers receivewagew.Theconsumptiongoodis non-storable,and 5

theunemployedcannot borroworlend, andhavenoassets.Hence,theconsumptionof theunemployedequals theunemployment benefit theyreceivefrom theUIagency. Theprobabilityanunemployedworker finds employment (inthefirst periodto beginthenext period)is givenbyp(a(1),r),wherer is astatevariable governingthe tightness inthelabormarket.Theprobabilityof findingajobis increasinginsearch effort,andsearcheffort is subject todiminishingreturns (i.e.,p >0,p <0,where a aa subscript denotes partial derivative).Lowervalues ofrimplythat it is moredifficult to find ajobat anygivenlevel ofeffort (i.e.,p>0). r Giventheseconditions,theunemployedworker chooses search effort to maximizethefollowingobjective(whereb(t)is theUIbenefit inperiodt) Equation2 u(b(1)) − a(1) + β[p(a(1),r)u(w) + (1− p(a(1),r))u(b(2))]. Theoptimal choiceofsearcheffort is therefore governedby Equation3 βp a (a(1),r)[u(w) −u(b(2))] ≤1, withequalityifa>0. As asimplethought experiment,considertheeffects ontheunemployedworker ofanadverselabormarket shock.At unchangedbenefit levels,theworseninginlabor market prospects lowers utility.4 Therefore, aUIagencyconcernedwithtargetingsome constant level ofwelfarefor anunemployedworker wouldneedtoraisebenefit levels in eitherperiod1orperiod2.Raisingbenefits inperiod1has theadvantageofnot affecting thesearchefforts oftheworker (equation3),i.e.,does not producedisincentives inthe labormarket.However,raisingbenefits inperiod1has animportant disadvantage. A givenlevel ofutilityis achievedat lowercost byprovidingbenefits inbothperiod1and 2,becauseofbothdiminishingreturns toconsumptionandthe fact that a certain fraction oftheunemployedwill findajobbeforeperiod2,andhencenot receiveperiod2 benefits.Therefore,a cost-minimizingUIagencywouldrespondtoan adverselabor market shockbyincreasingbenefits inbothperiods 1and2.Withthis intuitioninhand,a slightlymorecomplicatedmodel is developed. 4Thisresultcomesfromapplyingtheenvelopetheoremtoequation2. 6

4.Dynamic Model and QuantitativeAnalysis Amodel moresuitabletoquantitativeimplementationandcapableof considering alternativeassumptions regardingtheproductivityofsearchin recessions andthe responseofwages uponreemployment tolabormarket weakness is considered.The model follows thosepresentedinShavell andWeiss (1979), Hopenhayn andNicolini (1997),and Ljungqvist andSargent (2001).The analysis follows Ljungqvist andSargent (2001)most closely; theimportant modificationis theintroductionofapossiblytimevaryingstatevariablethat governs thedegreeoftightness inthelabormarket,andhence canbevariedtoproxyfor recessions (orbooms).As discussedmore fullybelow, alternativeassumptions regardingtheeffect ofthis shockontheproductivityofsearch andwages are alsoexamined. Thepreferences ofanunemployed workeroversequences ofconsumption(c(t)) andsearcheffort (a(t)) from thecurrent period(period1)overtheindefinitehorizonare givenby ∞ Equation4 E (cid:1) βt−1 [u(c(t)) − a(t)], t=1 whereEis the expectations operator,0<β<1,andu(c(t))is strictlyincreasing,twice differentiable,andstrictlyconcave. Bothconsumptionandsearch effort must benonnegative.Employedworkers receivewagew,whichdoes not varyovertime.Moreover, it will beassumedthat theunemployment insurance agencyhas nointeractionwith employed workers,andhencecannot implement anypolicythat involves taxationofthe previouslyunemployedaftersuchindividuals findemployment.5 Theconsumptiongood is non-storable,andtheunemployedcannot borroworlend, andhavenoassets. Hence, theconsumptionoftheunemployedequals theunemployment benefit theyreceivefrom theUIagency. Theprobabilityanunemployedworker finds employment (inthecurrent periodto beginnext period)is givenbyp(a(t),r(t)).R(t)is astatevariable governingthetightness 5AsinHopenhaynandNicolini(1997).Suchanassumptionhasthevirtueofadministrativesimplicityand willimplythatoptimalbenefitsarelessradicallydifferentfromcurrentUIprograms,whichinvolvesimple benefitschedules,thanthebenefitandtaxpolicydevelopedunderthealternativeassumption. 7

inthelabormarket that follows a first-orderdeterministicprocess. Lowervalues ofr(t) makeit moredifficult tofindajobat anygivenlevel of effort (i.e.,p>0,wheresubscript r denotes partial derivative)–i.e., correspondtorecession-likeperiods.Theprobabilityof findingajobis increasinginsearcheffort,andsearcheffort is subject todiminishing returns (i.e.,p >0,p <0). a aa Underthese assumptions,thevalueofcurrent employment Veequals thepresent discountedvalueof consumingthewage (andhencedoes not varyovertime), u(w) Equation5 V e = . 1−β Thevalueofunemployment Vu(t,r(t))depends ontheentiresequenceofbenefits (b(t)) receivedbytheworker,andthis dependenceis reflectedinthedependenceof Vu on the timeperioddirectly(t); for example,ifthebenefit sequenceconsists ofaninitiallyhigh benefit inperiod1and alowornobenefit infutureperiods,thenVu will,all elseequal, behigherinperiod1 theninlaterperiods. Inaddition,thevalueofunemployment depends onthetightness ofthelabormarket (r(t)).The Bellmanequationforthevalue of unemployment is Equation6 ( ) V u (t,r(t)) = max u(b(t)) − a(t) + β[p(a(t),r(t))V e + (1− p(a(t),r(t)))V u (t +1,r(t +1))] a(t) Theoptimal choiceofsearcheffort is therefore governedby Equation7 βp a (a(t),r(t))[V e −V u (t +1,r(t +1))] ≤1, withequalityifa>0. Ifthe UIagencycannot choose searcheffort fortheworkers,its decisionregardingtheoptimal benefit sequencemust respect theindividual rationality constraint givenbyequation7. TheUIagencychooses asequenceofbenefits fortheunemployedworkerto achieve atarget level ofutilityVu(1)forthenewly(i.e.,period1)unemployed; this target level is exogenouslydetermined elsewhere (perhaps bythepolitical process).The agency wishes toachievethis target level ofbenefits at minimum cost,andsuchaminimum cost sequenceis termedtheoptimal UIprogram.Two cases canbeimagined: afull informationcaseinwhichtheagencycanchoosethesequenceofbenefits andsearch 8

effort levels (i.e.,noenforceabilityproblems),andan asymmetricinformationcasein whichthesequenceofbenefits and effort levels are consistent withtheunemployed workers’desiredsearchlevels (i.e., consistent withequation7).The full informationcase solves thecost minimizationproblem Equation8 ( ) C[V u (t,r(t)), r(t)] = min b(t) + β(1− p(a(t),r(t)))C[V u (t+1,r(t+1)),r(t+1)] b(t),a(t),Vu(t+1,r(t+1)) subject totheconstraint V u (t, r(t)) ≤ u(b(t)) − a(t) + β[p(a(t),r(t))V e + (1− p(a(t),r(t)))V u (t+1,r(t +1))] where Vu(1)is exogenouslydetermined,andthe cost functionC[.] depends uponthe continuationvalueofunemployment providedbythe UIagencytotheunemployed workerVu(t,r(t))andonthestateofthelabormarket,r(t).Noticethat thecost function depends uponthediscountedpresent valueofcosts intothefuture, andthat discounting takes intoaccount thediscount factorofconsumers andtheprobabilityofunemployment continuingintofutureperiods.Theasymmetricinformationcasesolves thecost minimizationproblem Equation9 ( ) C[V u (t,r(t)), r(t)] = min b(t) + β(1− p(a(t),r(t)))C[V u (t+1,r(t+1)),r(t+1)] b(t),a(t),Vu(t+1,r(t+1)) subject totheconstraints equation7and V u (t, r(t)) ≤ u(b(t)) − a(t) + β[p(a(t),r(t))V e + (1− p(a(t),r(t)))V u (t+1,r(t +1))] wherethe additional constraint (equation7)reflects theincentives oftheunemployed giventhebenefit stream.Assumingthat the cost functionis strictlyconvex inthe 9

promisedcontinuationlevel ofutility6,thesolutions totheseproblems yieldtheresults of Shavell andWeiss (1979)orHopenhaynandNicolini (1997)forsteady-statepolicies: Previous Result: In asteadystate withconstant labormarket conditions (r(t) =r), A. theoptimal UIschemeinthefull informationcasedelivers a constant benefit level (b(t)=b ∀t)andproscribes a constant level ofsearcheffort (a(t)= a∀t); B.This effort level is not incentive compatible,andhencetheoptimal UIprogram underasymmetric informationdelivers aweaklydecliningbenefit sequence (b(t+1)≤ b(t)∀t).Thesequenceis strictlydecliningifsearcheffort is productive(p >0). a Proof: SeeShavell andWeiss (1979),HopenhaynandNicolini (1997), Ljungqvist andSargent (2000),orthe appendix. Theresults under asymmetricinformationareintuitive.Becausehigherfuture benefit levels raisethevalueofbeingunemployedinthe future,theylowersearch effort (equation7).Hence, a givenlevel ofutilitycanbeachievedat lowercost byhavingan initiallyhighlevel ofbenefits whichdeclines overtime–therebyraisingsearcheffort andloweringtheexpected expenses onbenefits (becausethehighersearcheffort raises theprobabilitythat theunemployedworkerfinds ajob). Notethat benefits declineover timeintheasymmetricinformationcaseonlywhensearch effort is productive(p >0); a absent productivesearch,efficient insurancewouldsmoothconsumptionovertime througha constant benefit level. In addition,ournumerical analysis establishes thefollowingresult,alongthelines oftheintuitionfrom section3,regardingthe responseofinitial benefit levels tolabormarket weakness: New Result: In responsetoadeteriorationinthelabormarket,theoptimal program increases initial benefit levels andproscribes asequence 6AsdiscussedinHopenhaynandNicolini(1997)orLjungqvistandSargent(2000),theconstraintsonthe minimizationproblemsarenonlinearandneednotdefineaconvexset,andhencetheconditionsunder whichthecostfunctionisconvexarenoteasytoprove.Thiscomplicationcouldbeovercomebyusing lotteriestoconvexifytheconstraintset(followingPhelanandTownsend(1991)).Insimilarproblems, numericalanalysisoftenshowsthatsuchlotteriesareunnecessary,andhencethiscomplicationisignored. 10

ofbenefits that declines moreslowlyovertime, assumingless productivesearchina recession. Theintuitionremains similartosection3.At unchangedbenefit levels,theworseningin labormarket prospects lowers utility. Therefore,aUIagencyconcernedwithtargeting someconstant level ofwelfarefor anunemployedworkerneeds toraisebenefit levels.To examineingreaterdetail theeffects of adverselabormarket shocks (e.g.,recessions)on optimal policyandtocomparesuchpolicies withthestandardpracticeofextended benefits intheUnitedStates,aquantitativeversionofthemodel is calibratedand simulated. Theutilityfunctionis isoelastic(u(c)= c1-s/(1-s)).Thelengthofamodel periodis oneweek, andconsequentlythediscount factorβ equals 0.999.Thelevel ofthewage earnedbyemployedworkers (w)is set at 100; withisoelasticutility,this level is unimportant fortheresults (andthechosenvaluesimplyprovides aconvenient scale). Theintertemporal elasticityofsubstitutionis set at 2(s=0.5).This highvalueis justified bytheweeklyfrequencyofthemodel periodandmatches thebaselinevalueof Hopenhaynand Nicolini (1997). Lowervalues ofthis parameterdonot change the qualitativeresults.7 Regardingtheproductivityofsearch,thespecific functional form p(a(t),r(t)) equal to1-e-a(t)r(t)is assumedforthebaselineresults; this is thesameform as usedin Hopenhaynand Nicolini (1997)orSargent and Ljungqvist (2000),except inthosecases r(t)is heldconstant.Figure1 graphs theprobabilityofremainingunemployed(1p(a(t),r(t))) fortwoillustrativevalues ofr(t)– atight labormarket valueand aweaklabor market value. Intheweakmarket,theprobabilityofremainingunemployedis higherat anylevel ofsearch effort (panel a). Inthepanel b(whichis plottedonalogscale),it is shownthat thesemi-elasticityoftheprobabilityofremainingunemployedwithrespect to search effort –theslopeofthelineinthelowerpanel –is morenegativein atight labor market undertheassumedfunctional form; this seems likethenatural assumption,as it implies anincreasein effort has a greater(inabsolutevalue,i.e.morenegative) 7HopenhaynandNicolini(1997)providesomeillustrativesimulations.Notethatinthemodel,withno avenueforsavingsbyworkers,theintertemporalelasticityofsubstitutionmustbegreaterthanoneor periodutilityisnotdefined 11

percentageeffect ontheprobabilityofremainingunemployedinatight labormarket – i.e.,searchis moreproductiveina boom.Withregardtoplausibility,it is important to notethat this assumptiondoes not implythat additional searchhas alargereffect onthe probabilityoffindingajobinaboom thanin arecession.Forexample,it is plausible additional searchhas onlya small effect ontheprobabilityof findingajobinaverytight labormarket where, forexample,theprobabilityoffindingajob at a givenlevel of searchis closetoone. Ina weakerlabormarket,extrasearchmayhavealargermarginal impact ontheprobabilityof findingajob.These effects areconsistent withtheassumed probabilityfunction,whichimplies that thepercent changeintheprobabilityof remainingunemployedfrom anadditional unit ofsearchis largerinaboom.Becausethe probabilityofremainingunemployedinatight labormarket is smallerat anygivenlevel ofeffort,thepercent changeinthis probabilitycanbelargerthaninarecessionevenif thelevel changeis smaller.However,the functional form andassignedparametervalues will implythat,intheregionofequilibrium searcheffort,additional searchis more productive(inlevel terms,not onlypercentageterms)in astronglabormarket.8 Section5 discusses this morethoroughly. Finally,theprocess forthestate ofthelabormarket is givenbyr(t)=0.97t-1r(1) + (1-0.97t-1)r*.Thesteady-statevalueoflabormarket conditions (r*)is chosensuchthat thesteady-statemediandurationofunemployment (i.e.,thevalue whenr(1)=r*)equals 7 weeks,themedianvalueofmediandurationover1967-2001intheU.S.(andhencer* equals 0.00175).Forthis calculation,mediandurationis foundbysolvingequation7 giventhe current U.S.UIsystem,whichis characterizedby26weeks ofbenefits equal to 60percent oftheweeklywage–avalueappropriatefor lowwageworkers as discussed insection2.Fortherecessionscenario,theinitial stateofthelabormarket is chosensuch that themediandurationofunemployment rises to9weeks underthecurrent U.S.system without extendedbenefits (yieldingr(1) equal to0.0015); suchavaluerepresents the edgeoftheupper20percent bandinthehistogram ofmedianunemployment duration since1967,andhencecouldbeviewed as amodest recession. 8Thequalificationstothisstatement,notablythatitistrueintheregionofequilibriumsearcheffortforthe assignedparametervalues,arenecessarybecauseadditionalsearchcannotbemoreproductiveinlevel 12

Table1andthe accompanyingfigures present theinformationonthecosts and benefits ofdifferent UIprograms,bothinthesteadystateandinthe recessionscenario. Theupperportionoftable1presents informationonthecurrent U.S.UIsystem (with26 weeks ofbenefits at a replacement rateof60percent)andtheoptimal system that delivers thesamelevel ofutility,bothinsteadystate.Thefirst rowpresents thebenefit from eachsystem,inunits ofconsumption,relativetothecurrent system insteadystate; notethat thebenefit is equal byconstruction.Thesecondrowpresents the expected annuitycost of eachsystem as apercent oftheweeklywage(i.e.,100*(1-β)* C[Vu(1),r*] / w).Theoptimal program,whichinitiallyhas ahigherreplacement ratethan thecurrent program (figure2),delivers modest cost savings (around6to7percent, as foundforsomewhat different parametervalues inHopenhaynandNicolini (1997)).The thirdcolumnreports themediandurationofunemployment under eachprogram; forthe current system andtheoptimal program,thesemediandurations arequitesimilarin steady-statelabormarket conditions.Thefinal columnreports theaveragedurationof unemployment.Theoptimal program shaves oneweekofftheaveragedurationof unemployment,reflectingtheincentives tofindajobprovidedbythe fallingscheduleof benefits showninfigure2.9 Overall,theseresults are inlinewiththeprevious literature. Thedeparturefrom previous worklies inthe recessionscenarios,providedinthe bottom rows oftable1.Row3shows theeffects ofthecurrent system absent extended benefits.Byconstruction,medianand averageunemployment durationaremuchhigher inthis scenario(columns C andD).Moreover,thecost ofUI(column B)is muchhigher intherecession(about 0.60percent ofthebasewageinannuityterms,ratherthan0.49 percent insteadystate) andlifetimeutility(columnA) falls by0.8percent of consumption(inperpetuity).A13-weekextensionofbenefits is showninrow4: Suchan extensionraises utilitymodestly,raises costs perunemployed workerbymorethan16 percent, andincreases the averagedurationofunemployment by1.45weeks.Notethat termsforallpossiblevaluesofeffortineitheraweakorstronglabormarketiftheprobabilityvaluesareto remainboundedbetweenzeroandoneandeffortlevelsarenotboundedfromabove. 9Thecalibrationmatchesthemediandurationofunemploymentinthedata,butsubstantiallyunderpredicts themeanduration.Thiscouldbebecausethedatacountasunemployedsomeworkerswithverylittle searchactivityor whoareonlyverymarginallyattachedtothelaborforce.Alternatively,thedatamay understatethemedianfortheconverseoftheabovereasons.Alternativeparameterizationsdonotchange theinterestingresults. 13

this last figure– anincreaseof0.1 weekin averagedurationperextraweekofbenefits – lies withintherangeofavailableestimates ofthedisincentiveeffects oftheU.S.UI program,suggestingthecalibrationis reasonable.10 Rows 5to7oftable1provideinformationonoptimallydesignedUIprograms that meet different criteria.Row5presents aprogram that has thesame expectedcost per unemployed workeras theextendedbenefit program (EB)–70cents per$100inwages (columnB).Such aprogram yields asmall gaininutilityrelativetotheEBprogram (in fact,sosmall that it is not apparent inthetable). However,theincentives providedbythe fallingbenefit schedule(showninfigure3withtheextendedbenefit schedule) yielda substantiallylower averagedurationofunemployment (columnD); the averageduration ofunemployment is evenlowerthanunderthecurrent system without EB(row3,column D).Similarly,row6presents a UIprogram that delivers thesamelevel ofutilityas the EBprogram,but does soat minimum cost.As shownincolumnB,thecost of anoptimal program that delivers thesameexpectedutilityas theEBprogram is essentiallythesame as thecurrent program without extendedbenefits (about 60cents inarecession).This suggests policydebates regardingthe expenditureconsequences ofmore generous UI benefits inarecessionareunnecessary,ifsuch generosityis appropriatelydesigned. In particular,thesamelevel ofutilityas anEBprogram canbedeliveredbyabenefit schedulewithhigherinitial benefits that thendeclineovertime(as showninfigure4), without raisingcosts appreciablyabovethoseofthe current system absent extended benefits. Insum,thecurrent designoftheU.S.UIprogram provides poorerinsurance and poorerincentives thananoptimally-designedprogram,andthis weakness is particularly acutefortheextendedbenefits portionoftheU.S.system. Figure5presents benefit schedules indifferent UIprograms toillustratehowan optimallydesignedUIprogram responds toarecession; alog-scaleis usedtohighlight boththelevel ofbenefits andtheslopeofthe curves.Thefirst schedulereportedis the current 26-weekbenefit schedulewitha replacement rateof60percent (thesolidline). Thesecondis theoptimal program that delivers thesamelevel ofutilityinsteadystate 10O’LearyandWandner(1997)reportarangeof0.1to0.5forestimatesfortheincreaseinaverage unemploymentdurationassociatedwithoneextraweekofbenefitsintheU.S.,withmostoftheestimates lyingclosertothebottomofthatinterval(seetheirtable7.1). 14

(thedottedline).As notedpreviously,theoptimal schedulehas higherinitial benefits that fall overtime,as showninShavell andWeiss (1979) andHopenhaynandNicolini (1997).Thethirdscheduleis theoptimal UIprogram that delivers thesteady-statelevel ofutilityina recession(thesolidlinewith*’s).Notethat this schedulehas amuchhigher level ofbenefits initially, andthebenefits declinesomewhat moreslowlyovertimethan thebenefits intheoptimal steady-stateprogram.Theseresults areintuitiveinlight ofthe model andtheanalytical results ofsection3andthe propositionofthis section.The higherlevel ofbenefits is necessarybecausetherecession(lowerr(t))implies that workers will remainunemployedlonger, andhence achievingthesamelevel ofutility requires higherbenefits.Theflatterslope ofthebenefit scheduleoccurs becausethe recessionlowers theproductivityofcurrent searchrelativetothat offuturesearch (becausetherecessionis transitory).Rememberthat fallingbenefits areonlyoptimal to encouragesearch, andloweringthe returntocurrent search relativetofuturesearch lessens theimportanceofthis roleofdecliningbenefits.Hence,the consumptionsmoothingroleofUIassumes relativelymoreimportance,andbenefits declinemore slowlyinanoptimal UIprogram duringa recession. Finally,thefourth(dottedwithx’s)lineinfigure5is theoptimal benefit schedule that delivers thesameutilityas aEBprogram (i.e.,row6oftable1).Whileutilityis muchlowerthaninthesteady-stateprograms,this scheduleshares thehigher benefit level andflatterslopeoftheoptimal program that delivers steady-stateutilityina recession.This lineis shownbecauseprovidingthesteady-statelevel ofutilityina recessionis verycostly– about $1.85per$100inwages,versus the$0.61requiredto providetheutilityofextendedbenefits (optimally)in arecession(row6).This high cost occurs because recessions makesearchdifficult; hence,thehighlevel ofbenefits required tokeeputilityequal tosteady-stateutilityis accompaniedbyasteepdeclineinsearch. Maintainingsteady-stateutilityfornewlyunemployedworkers in arecession yields a drasticincreaseinmedian andaverageunemployment durationto17weeks. Twolessons areprovidedbythese exercises.First,anoptimal UIprogram has moregenerous benefits duringrecessions andaslowerdeclineinbenefits overtimefor anygiventarget forunemployedworkers’utility. Inaddition,recessions are periods of severelabormarket stress.Hence, anoptimally-designedUIprogram withsimilarcost to 15

thecurrent UIprogram intheU.S.wouldrequiresharplylowerbenefits during expansions andhigherbenefits duringrecessions,iftheprogram wishes todeliversimilar expectedutilitystreams tonewlyunemployed workers.This occurs becausejobs areeasy tofindduringexpansions andhardtofindduringrecessions for anylevel ofeffort,and hencesmoothingutilityacross booms and recessions requires low(high)benefits during booms (recessions).Thecurrent UIprogram delivers ahighlevel ofwelfaretoworkers wholosejobs outsiderecessions –sohighthat thecost ofdeliveringsuchalevel of welfareduringrecessions is verylarge. 5.SensitivityAnalysis Twosets ofassumptions canbe criticizedas lackingsupport from previous empirical work.Thefirst is theassumptionthat,intheregionof equilibrium choices,search effort is moreproductiveonthemargininastronglabormarket,i.e.that inastronglabor market additional searchhas largerimpact ontheprobabilityoffindingajob. Introspectioncansuggest that this is areasonableassumption,as it is possiblethat extra searchin arecession yields littlebenefit (because,forexample,anunemployedperson’s networkofformer employers andfriends possess fewpotential openings andhence can providelittlehelpifcontacted).But,as mentionedearlier,theoppositeis alsopossible, i.e.that inaverytight labormarket,additional searchis equallyormoreproductive (because,for example,anunemployedperson’s networkofformeremployers andfriends areinfrequentlycontactedbyotherpotential applicants insuchlabormarket conditions, andhencecanprovidesignificant helpif contacted).The author’s priors arethat this possibilityis less likely,but empirical evidenceis unavailable,as the effect oflabor market conditions onthemarginal impact ofsearchhas not beena researchpriority(as withmost cross-partial derivatives). Sensitivityanalysis demonstrates that theassumedimpact ofarecessiononthe marginal productivityofsearchis important. Inparticular,specifications inwhichthe marginal productivityofsearch(p )is independent oflabormarket conditions revealed a that theoptimal program ofunemployment benefits wouldinvolvehighercurrent and futurebenefits inarecession,but theslopeofthis benefit schedulewas independent of 16

labormarket conditions.11 This result isintuitive.12As discussedinsection4,optimal benefits declineovertimesolelytoinducedesiredsearch effort,andareconstant when searchis unproductiveonthemargin. Inthecasewherethemarginal productivityof searchis not affectedbylabormarket conditions,benefits must behigherinarecession tomeet thedesiredlevel ofwelfare(sinceunemployment spells,as elseequal, would tendtolast longer),but theslopeofthebenefit scheduleis unchangedas themarginal effects ofsearch effort havenot changedandthesemarginal effects determinetheslope ofthebenefit schedule. Anotherconcernthat has beenofferedas areasonwhyunemployment benefits shouldfall offmorerapidlyin arecession,ratherthanmoreslowlyas inthebaseline results,focuses onthe effect ofreemployment wages onsearcheffort. It is well known that reemployment wages tendtobelowerthanwages from previous employment and evidencesuggests this effect has beenlargerduringrecessions thanduringotherperiods (e.g.,Hipple(1999)). Becauseunemployment benefits arebasedonpast wages,thelower wages from reemployment discouragesearcheffort (relativetoacasewhere reemployment wages arenot lower, as inthebaselinemodel) (e.g., FeldsteinandPoterba (1984)). If reemployment wages werelowerduring recessions thanotherperiods,this effect wouldbemagnified. Therefore,ifonewantedtoencouragejobsearchduringa recession,UIbenefits shouldbelowerthanotherwise. Theapproachtakenhereindelivers theoppositeresult –namely,lower reemployment wages shouldleadtomore generous UIbenefits.This occurs becausethe model assumes theprogram provides insuranceandhenceattempts todeliveraspecified level ofwelfaretonewlyunemployedworkers. If reemployment wages arelower,the 11Theformofp(a,r)usedwas1-exa-r,wherexisaconstant.Highervaluesofrlowertheprobabilityof findingajobandhencecorrespondtoweaklabormarketconditions,butdonotaffectthemarginal productivityofsearch. 12Whileintuitive,theresultswerefoundusingnumericalexamples;analyticresultswerenotobtained.The resultsalsosuggestedthatthisspecificationwasqualitativelylesscapableofcapturingbasicintuition regardingtheeffectsofchanginglabormarketconditions.Inparticular,aworseninginlabormarket conditionsunderthisspecificationtendedtolowerutilitynoticeably,andhencespurasignificantadditional amountofsearch.Becausetheproductivityofsearchwasnotdiminishedbytheshockandsearchrose,the expecteddurationofunemploymenttendedtoactuallyfall,ratherthanrise,inresponsetothelabormarket deterioration.Analternativespecification(p=1–[r/(r+a)])thatcouldintheoryimplythatthemarginal impactofsearchontheprobabilityoffindingemploymentwaslowerinaboomwasalsoconsidered,but– 17

(present discountedvalueof)welfareoftheunemployedis lower,andhence aninsurance policyoffers higherbenefits tothosewhoenterunemployment duringrecessions.This will tendtolengthentheunemployment spell ofthenewlyunemployed,but suchleisure is simplypart ofthebundleofbenefits providedbyUItoensurea giventarget level of welfare.Thesuggestionthat UIbenefits shouldbeless generous andshortenedto encourageextrasearchlowers welfareandwouldexacerbatethelarge gapinthelevel of welfaredeliveredbyUIbetweenrecessions andotherperiods discussedinsection4. 6.Conclusion Theresults suggest that anoptimal UIprogram wouldincreasetheinitial level ofbenefits andprobablyextendhigherbenefits overtimeinresponsetoarecessionaryshock.A simpleextensionofbenefits provides bothpoorerinsurance andpoorerincentives than theoptimal program,anddoes so at ahigher cost.Moreover,thequantitativeexercise suggests that thecurrent UIprogram intheUnitedStates provides substantiallyhigher welfaretoworkers wholosejobs duringtight labor markets,inthesensethat delivering suchalevel of welfaretoworkers whobecomeunemployedduringrecessions would requireverygenerous benefit levels.Totheextent that simplemodels likethat hereincan beusedto guidepolicy(andinthe author’s viewthat extent is important but not overwhelming),theresults ofthis investigationsuggests that reform oftheUIprogram shouldlowerbenefits substantiallyduringtight labormarkets andraisebenefits during weaklabormarkets,andshould considerascheduleinwhichbenefits fall withduration as suggestedinprevious work.Moresimply,increasedearlygenerosityofbenefits in recessions is superiortoextendedbenefits inprovidinginsuranceandincentives. Several important aspects oftheanalysis deservefurtherscrutiny.The first is the informationrequirements oftime-varyingbenefit schemes. Inthis analysis,theUIagency hadaccess toinformationonthestateofthelabormarket (i.e., acurrent recession). In application,longunemployment spells couldreflect eitherthestateofthelabormarket or weaksearch activity.Thefeasibilityoftime-varyingbenefit schemes inan environment whereit is difficult todiscernthestateofthelabormarket from endogenous variables likethebaselinecase–thisspecificationimpliedthatthemarginalimpactofsearchontheprobabilityof 18

likeunemployment durationdeserves furtherresearcheffort. Inaddition,some simplifyingassumptions couldberelaxed,suchas the assumptionthat unemployed workers havenosavings or access tocredit markets.Whilesuchsimplifyingassumptions maybereasonable as afirst step,especiallyfor describingthebehaviorofverylowincomehouseholds,themorecomplex analysis requiredbyaddingasset accumulation couldprovefruitful.13 Moreover,theanalysis was decidedlypartial equilibrium innature, andabstractedfrom the financingofthe UIprogram.Giventhat aprogram couldbe designed withcyclical variationinbenefits that hadsimilarcost tothecurrent program (overabusiness cycle)andthat had a(relatively)smoothpathoftaxes (whichmaybe optimal fortraditional reasons), financingissues mayhavelittleeffect ontheresults herein. findingemploymentwashigherinaboomforreasonableparametervaluesandatequilibriumsearchlevels. 13Inthisregard,recentworkbyAbdulkadiroglu,KuruscuandSahin(2001)andWerner(2001)showthe complicationssuchanadditioncangenerateandprovidesometoolstohelpfutureanalyses. 19

References Abdulkadiroglu,Atila,BurhanettinKuruscu andAysegul Sahin(2001) Unemployment InsuranceandtheRoleofSelf-Insurance.ForthcomingintheReview of Economic Dynamics. Acemoglu,DaronandRobert Shimer(1999)Efficient Unemployment Insurance. Journal-of-Political-Economy107(5),October,pages 893-928. Baicker,Katherine,Claudia Goldinand LawrenceF. Katz (1998)ADistinctiveSystem: Origins and Impact of U.S.Unemployment Compensation. InBordo,Michael D., ClaudiaGoldinandEugeneWhite,eds. Thedefiningmoment:TheGreat DepressionandtheAmericaneconomyinthetwentiethcentury. Universityof ChicagoPress,NBER Project Report series,Chicagoand London,pages 227-63. Baily,MartinNeil (1978) SomeAspects of Optimal Unemployment Insurance.Journalof-Public-Economics 10(3),December,pages 379-402. Card,DavidandPhillipB. Levine (2000)ExtendedBenefits andthe Durationof UI Spells: Evidencefrom theNewJerseyExtendedBenefit Program.Journal-of- Public-Economics 78(1-2),October,pages 107-38. CommitteeonWayandMeans (2000)The2000GreenBookBackgroundMaterial and DataonPrograms withintheJurisdictionof theCommitteeon Ways andMeans. U.S.HouseofRepresentatives,October6,17thedition http://aspe.hhs.gov/search/2000gb/2000gb/index.htm#toc. Feldstein,MartinS.(1974)Unemployment Compensation: Adverse Incentives and Distributional Anomalies.National-Tax-Journal 27(2),June,pages 231-44. Feldstein,MartinS.andJames Poterba(1984)Unemployment Insurance andReservation Wages.Journal-of-Public-Economics 23(1-2),February-March,pages 141-67. Goldreich,Samuel (2001)Social Issues ResurfaceinJobless Debate. CQ Weekly59(41), October27,pages 2524-2525. Gruber,Jonathan(1997)TheConsumptionSmoothingBenefits ofUnemployment Insurance.American-Economic-Review 87(1),March,pages 192-205. Hipple,Steven(1999)Worker Displacement intheMid-1990s. Monthly-Labor-Review 122(7),July,pages 15-32. 20

Hopenhayn,HugoA. andJuan-PabloNicolini (1997)Optimal Unemployment Insurance. Journal-of-Political-Economy105(2),April,pages 412-38. Krueger,Alan B.(2001)EconomicScene; Thestimulus packageshouldfix the unemployment insuranceprogram first. TheNew YorkTimes, October18. Ljungqvist, Lars and Thomas J.Sargent (2000)RecursiveMacroeconomicTheory.MIT Press,Cambridge,MA. Meyer, BruceD.(1990)Unemployment InsuranceandUnemployment Spells. Econometrica 58(4),July,pages 757-82. National Bureauof EconomicResearch (2001)The Business-CyclePeakofMarch2001. November26. OrganisationforEconomicCo-operationandDevelopment (OECD) (1997) ImplementingtheOECDjobs strategy :lessons frommember countries' experience. OECD,Paris. O'Leary,ChristopherJ.andStephenA.Wandner,eds.(1997)Unemployment Insurance intheUnitedStates: Analysis of PolicyIssues.W.E.Upjohn Institutefor Employment Research,Kalamazoo,MI. Phelan,ChristopherandRobert M.Townsend(1991)ComputingMulti-period, Information-ConstrainedOptima. Review-of-Economic-Studies 58(5),October, pages 853-81. Shavell,Stevenand LaurenceWeiss (1979)TheOptimal Payment ofUnemployment InsuranceBenefits overTime.Journal-of-Political-Economy87(6),December, pages 1347-62. Werning, Ivan(2001)Optimal Unemployment InsurancewithUnobservableWealth. Mimeo,UniversityofChicago. 21

Appendix:Proof previous results Theproofofproposition1follows that inSargent and Ljungqvist (2000)forthe sameproblem.The first-orderconditions forthefull informationproblem are 1 A1 θ= , u (b(t)) c 1 A2 C[V u (t +1,r(t +1)),r(t +1)] =θ[ −(V e −V u (t +1,r(t +1)))] , βp (a(t),r(t)) a A3 C [V u (t +1,r(t +1)),r(t +1)] =θ, V whereθis themultiplierontheconstraint.Theenvelopetheorem implies A4 C [V u (t,r(t)),r(t)] =θ, V whichimplies that Vu is constant overtimeforaconstant valueofr (usingA3).Hence, consumptionandeffort oftheunemployedare constant overtimeinasteadystate,as in part Aoftheproposition. Thefirst-orderconditions forthe asymmetricinformationproblem are (assuming a(t)>0,so equation7binds) 1 A5 θ= , u (b(t)) c p (a(t),r(t)) A6 C[V u (t +1,r(t +1)),r(t +1)] = −η[ aa (V e −V u (t +1,r(t +1)))] , p (a(t),r(t)) a p (a(t),r(t)) A7 C [V u (t +1,r(t +1)),r(t +1)] =θ−η[ a ], V 1− p(a(t),r(t)) whereθis themultiplieronthesecondconstraint.The envelopetheorem implies A8 C [V u (t,r(t)),r(t)] =θ. V A6andtheassumptions regardingp(.) ensurethat η(themultiplieronequation7)is positive.Therefore,A8and A7ensurethat Vu falls overtimefor aconstant valueofr (becauseC[.] is convex).A5andA8thenimplythat thebenefit sequencemust fall over time.Also,ifp =0,A7andA8implyconstant benefits overtime,concludingpart bofthe a proposition. 22

Table1:Costs and Benefits of AlternativeUI programs A B C D Relative benefitof Annuitycost Median Average programin ofprogramas durationof durationof consumption percentof unemployment unemployment units(percent) weeklywage (weeks) (weeks) Steady-State(SS)LaborMarketConditions 1.CurrentProgram 100.0 0.49 7.0 8.29 2.OptimalProgram 100.0 0.46 7.0 7.28 RecessionConditionsinLaborMarket 3.CurrentProgram 99.2 0.60 9.0 10.35 4.CurrentProgramwith 99.3 0.70 10.0 11.80 ExtendedBenefits(EB) 5.OptimalProgramwhencost 99.3 0.70 9.0 10.12 equalsEBcost 6.OptimalProgramwhenutility 99.3 0.61 9.0 9.48 equalsEButility 7.OptimalProgramwhenutility 100.0 1.85 17.0 17.94 equalsSSutility 23

Figure1 PanelA:Probabilityofremainingunemployedindifferentlabormarkets 1 0 search effort PanelB:Semi-elasticity(slopeoflines)ofprobabilityofremainingunemployedindifferent labormarkets 24 ytilibaborp Weak labormarket tight labor market 1 0.1 0.01 0.001 search effort )elacsgol(ytilibaborp Weak labormarket tight labor market

Figure2:Benefits in CurrentProgramand Optimal Program(steady-statelabor market) 100 80 60 40 20 0 1 26 51 Duration ofunemployment(weeks) Notes: Expectedutilities foranewlyunemployedworkeris equal under eachprogram 25 )tnecrep( etar tnemecalpeR Currentprogram Optimalprograminsteadystate

Figure3:Benefits in Extended Benefits Program and Optimal Programwith identical cost(recessionarylabor market) 120 100 80 60 40 20 0 1 26 51 Duration ofunemployment(weeks) 26 )tnecrep( etar tnemecalpeR Extended benefits Optimalprogram

Figure4:Benefits in Extended Benefits Program and Optimal Programwith identical utility(recessionarylabormarket) 100 80 60 40 20 0 1 26 51 Duration ofunemployment(weeks) 27 )tnecrep( etar tnemecalpeR Extended benefits Optimalprogram

Figure5:AComparison of Alternative Programs 1000 100 10 1 1 26 51 Duration ofunemployment(weeks) 28 )tnecrep( etar tnemecalpeR Currentprogram OptimalSS program OptimalRecessionprogram(SS welfare) OptimalRecessionprogram(EB welfare)