Consumption Commitments, Unemployment Durations, a

NBERWORKINGPAPERSERIESCONSUMPTIONCOMMITMENTS,UNEMPLOYMENTDURATIONS,ANDLOCALRISKAVERSIONRajChettyWorkingPaper10211©2003byRajChetty.Allrightsreserved.Shortsectionsoftext,nottoexceedtwoparagraphs,maybequotedwithoutexplicitpermissionprovidedthatfullcredit,including©notice,isgiventothesource.ConsumptionCommitments,UnemploymentDurations,andLocalRiskAversionRajChettyNBERWorkingPaperNo.10211January2004JELNo.D8,E21,G1,J6,R21ABSTRACTStudiesofriskpreferencehaveempiricallyestablishedtworegularitiesthatareinconsistentwiththecanonicalexpectedutilitymodel:(1)riskaversionoversmallgamblesgreatlyexceedsriskaversionoverlargerstakesand(2)insurancebuyersplaythelottery.Thispapercharacterizesriskpreferencesboththeoreticallyandempiricallyinaworldwithtwoconsumptiongoods,oneofwhichinvolvesacommitmentinthatanadjustmentcostmustbepaidwhenthegoodissold.Inthismodel,utilityoverwealthismorecurvedlocallythanglobally:individualsaremoreriskaversewithrespecttomoderate-scaleincomefluctuationsthantheyaretolargeincomefluctuations.Commitmentsalsocreateagamblingmotive.Theempiricalimportanceofcommitmentsistestedusingthelabor-supplymethodofestimatingriskaversionofChetty(2003a).Globalcurvatureisimputedusingexistinglaborsupplyelasticities,andvariationsinunemploymentinsurancelawsareusedtoestimatelocalcurvatureinadynamicjobsearchmodel.Commitmentssignificantlychangepreferencesoverwealth:Thelocalcoefficientofrelativeriskaversionisanorderofmagnitudelargerthantheglobalone.Implicationsforabroadsetofquestionssuchasoptimalsocialinsurancepoliciesandportfoliochoicearediscussed.RajChettyDepartmentofEconomicsUC-Berkeley521EvansHall#3880Berkeley,[e-mail]pproximately$200billiononsocialinsurancein2000.1ThelargesizeandcontinuedgrowthofsocialsafetynetsintheUSandothercountriesposeaninterestingpuzzleinpublicfinance.WorkbyBaily(1978)andGruber(1997)suggeststhattheoptimalbenefitlevelforunemploymentinsuranceislowerthan20%ofanindividual’spre-unemploymentwage,andperhapseven0.2Thereasonisthatempiricalestimatesofthedistortionarycostsofunemploymentinsurancetendtooutweighitsconsumption-smoothingbenefitsforreasonablelevelsofriskaversion.Thedifferencebetweenthesetheoreticalpredictionsandactualbenefitlevels,whicharearound50%ofpre-unemploymentwages,isstriking.This“socialinsurancepuzzle”canbeviewedasonemanifestationofthegeneralproblemofexplainingmoderate-stakeriskaversionusingcanonicalexpectedutilitytheory.3Rabin(2000)givesapowerfulcalibrationtheoremwhichshowsthatexpectedutilitywithstrictlyconcaveutilityoverwealthcannotexplainobservedriskpreferencesoversmallandlargegamblessimultaneously.Totakeonenotableexample,anexpectedutilitymaximizerwhorejectsa50-50betoflosing$1000andwinning$1010willrejecta50-50betoflosing$100,000orwinninganyamount.4Inotherwords,thelevelofriskaversionimpliedbytypicalpreferencesovergamblesinvolvingmoderatestakes—suchasthedemandforasubstantialamountofunemployment,automobile,andnon-catastrophichealthinsurance—translates1Here,Idefinesocialinsuranceasprogramsthatinsureincomefluctuations.UnemploymentInsurancecostswere$25billionin2000(Source:WaysandMeansGreenBook2000);WorkersCompensation,$56billion(NationalAcademyofSocialInsurance);andSurvivorsBenefitsandDisabilityInsurance,$113billion(OfficeofManagementandBudget).2Thisisbecausetheconsumption-smoothingbenefitsofUIareoutweighedbyitsdistortionarycosts.Thezeroreplacementrateresultassumesacoefficientofrelativeriskaversionlessthan2,asestimatede.g.inChetty(2003a).Higherlevelsofriskaversionobviouslyincreasetheoptimalreplacementrate.3Analternativeviewisthatsocialinsurancereflectsgovernmentinefficiency.Thosewhotakethisviewmayprefertoresolvethispuzzleusingapoliticaleconomymodelthatshowswhyextensivesocialsafetynetsemergeevenwhentheydonotimprovesocialwelfare.Thisapproachisnotconsideredhere.4Thisclaimrequiresthatagentsrejectthe$1000/$1010betatallwealthlevels,butsimilarresultsareobtainedwhentherangeofwealthlevelsoverwhichriskpreferencesareobservedisrestricted.1intounrealisticlevelsofriskaversionoverlargerstakes.AnimportantassumptioninRabin’scalibrationargumentandinmostexistingmodelsofriskpreferenceisthatagentsconsumeonegood,i.e.,consumptionisacompositecommodity.Thisassumptionisinnocuousifagentscan