Public Expenditures and Risk Reduction

PublicExpendituresandRiskReductionShantayananDevarajanandJeffreyS.HammerAbstractGovernmentsindevelopingcountriesspendmoneyongoodsandservicesthathaveanimpactonpeople’sexposuretorisk.Thispaperpresentsasimpleapproachtovaluingsuchexpendituresfromtheperspectiveofriskreduction.Therearetwotypesofexpenditures:publicprovisionofinsurance,suchasforhealthcareorcropyields;andpoliciesaimedatotherobjectivesthatchangepeoples’riskprofile,suchastransferprograms,taxandsubsidypolicies,andinfrastructureinvestments.Severalexamplesofeachtypeshowthatincorpo-223ShantayananDevarajan([e-mail])isChiefEconomistfortheHumanDevelopmentNetworkoftheWorldBank.JeffreyHammer([e-mail])isaLeadEconomistintheDevelopmentEconomicsResearchGroupoftheWorldBank.EarlierversionsofthispaperwerepresentedattheWorldCongressoftheInternationalInstituteofPublicFinance,Kyoto,andtheWorldBank’sEconomists’Forum.WearegratefultoTrinaHaque,KathyLindert,VitoTanzi,andKarlaHoff,forhelpfulcomments.Thefindings,interpretation,andconclusionsaretheauthors’ownandshouldnotbeattributedtotheWorldBank,itsExecutiveBoardofDirectors,oranyofitsmembercountries.WorldBankEconomists’ForumVol.2(2002),pp.223–246.224ShantayananDevarajanandJeffreyS.Hammerratingtherisk-reducingperspectivesignificantlyaltersthevalueofpublicexpenditures,whichindicatesthattheseconsiderationsshouldbeincludedinstandardpublicexpenditureanalysis.Thatpublicspendingriseswithacountry’spercapitaincomeiswellknown.IntheUnitedStates,forexample,publicspendingwas7.5per-centofgrossdomesticproduct(GDP)in1913andis33percenttoday.Governmentsinpresent-daydevelopedcountriesspendabouttwiceasmuchasdevelopingcountries.Lesswellknownisthatgovernmentspendingongoodsandservicesisthesameindevelopedanddevel-opingcountries;thedifferenceisalmostentirelytheresultoftransferpayments,whichareabout22percentofGDPintheindustrialworld(TanziandSchuknecht1997).Manyofthesetransferpayments—unemploymentinsurance,pensions,healthinsurance,andguaranteedloans—havethecharacteristicthattheyareaimedatmitigatingriskintheprivateeconomy.Inthispaper,weexplorehowtheexistingframeworkforevaluat-inggovernmentspendingongoodsandservices,welfareeconomics(Samuelson1954;Musgrave1959),canbeextendedtoincorporatethegovernment’svariousrisk-reducingactivities.Becausegovernmentsdonottypicallyclassifytheirexpendituresbytheirrisk-alteringchar-acteristics,ourapproachwillbemoreconceptualthanempirical.Weillustrateourpointswithsomesimpleexamplesandmodelsdesignedtocapturetherisk-reducingpropertiesofvariouspublicexpendi-tures.Weshowthatadoptingarisk-reducingperspectivehasimpli-cationsforthecostsandbenefitsofcertainpublicexpendituresandtaxesthataredifferentfromthestandardanalysis,whichindicatesdirectionsofchangeinthecompositionofpublicspendingthatarewelfare-enhancing.Inthefirstsectionofthepaper,AnalyticalFramework,wepresentanapproachtoevaluatingthewelfareconsequencesofpoliciesthatinfluencethesizeanddistributionofrisksthatpeopleface.Wealsoshowhowtheapproachcanprovideinsightintothepositivequestionofwhygovernmentsofdevelopedcountriesspendmoreonrisk-relatedexpendituresthangovernmentsofdevelopingcountries.Inthenextsection,ApplyingtheFramework,weapplytheframeworktothenormativequestionofevaluatingthebenefitsandcostsofcom-monprogramsassociated,directlyorindirectly,withthereductionofrisk,includingcropinsurance,medicalcare,incomesupport,floodcontrol,education,andloans.Thelastsectionofferssomeconcludingremarks.PUBLICEXPENDITURESANDRISKREDUCTION225AnalyticalFrameworkTheframeworkforevaluatingpublicexpendituresaimedatreducingriskbeginswiththemetricforvaluingthereductionofrisktotheindi-vidual,whichisthefamiliarvonNeumann-Morgensternframework.Riskaversionismodeledinthisframeworkbyautilityofincomefunc-tionthatrisesatadecreasingrate.Asaresult,peoplewillgenerallypreferacertainoutcometoariskyonewiththesameexpectedvalue.Ajobat$20,000peryearisbetterthantakinga50percentchanceongettingoneat$40,000witha50percentchanceofnoincomeatall.Howmuchthatisworthdependsonhowmuchgreaterthedifferenceinutilityisbetween$20,000andzerothanthedifferencebetween$20,000and$40,000.Thereisanamountofmoneythatoneiswillingtopaytoassureanincomeof$20,000(minusthatpayment)asopposedtotakingtherisk.Thisiscalledtheriskpremiumandtheamountofincomeleftoverafterpayingthepremiumiscalledthecer-taintyequivalentincometotheriskysituation.Formally,thiscanbeexpressedasU(W–V)=EU(W+∑ei)whereU(⋅)istheutilityfunctionofincome(strictlyspeaking,wealth)denotedW,andVisthemaximumamountonewouldpaytohaveacertainincomerelativetothevariableone.TheexpectationsoperatorEtakestheaverageofutilitywhenwealthisrisky,and∑eiisthesumofallriskycomponentsofwealth,eachnormalizedtohavezeromean.ThisexpressionsaysthatthereisavalueVthatmakestheindividualindifferentbetweenthesituationwithacertainincome,W–V,andthesituationinwhichthatpersonfacesallrisks.Theriskycomponentiswrittenasasumofpotentiallymanydifferent“shocks”toincomeinwhichonlytheirsum—theirnetimpactonincome—isofultimatecon-cerntotheindividual.Evenifwecan“explain”thehighergovernmentexpenditureindevelopedco