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1、Chapter10RicardianEquivalence10.1.BorrowinglimitsandRicardianequivalenceThischapterstudieswhetherthetimingoftaxesmatters.Undersomeassump-tionsitdoesandunderothersitdoesnot.TheRicardiandoctrinedescribesassumptionsunderwhichthetimingoflumptaxesdoesnotmatter.Inthischapter,wewillstudyhowthetimi
2、ngoftaxesinteractswithrestrictionsontheabilityofhouseholdstoborrow.Westudytheissueintwoequivalentsettings:(1)anin?nitehorizoneconomywithanin?nitelylivedrepresentativeagent;and(2)anin?nitehorizoneconomywithasequenceofone-period-livedagents,eachofwhomcaresaboutitsimmediatedescendant.Weassumet
3、hattheinterestrateisexogenouslygiven.Forexample,theeconomymightbeasmallopeneconomythatfacesagiveninterestratedeterminedintheinternationalcapitalmarket.Chapters11amd13willdescribegeneralequilibriumanalysesoftheRicardiandoctrinewheretheinterestrateisdeterminedwithinthemodel.Thekey?ndingsofthe
4、chapterarethatinthein?nitehorizonmodel,Ricar-dianequivalenceholdsunderwhatweearliercalledthenaturalborrowinglimit,butnotundermorestringentones.Thenaturalborrowinglimitletshouseholdsborrowuptothecapitalizedvalueoftheirendowmentsequences.Theseresultshavelimitedcounterpartsintheoverlappinggene
5、rationsmodel,sincethatmodelisequivalenttoanin?nitehorizonmodelwithano-borrowingconstraint.1Intheoverlappinggenerationsmodel,ano-borrowingconstrainttranslatesintoarequirementthatbequestsbenonnegative.Thus,intheoverlappinggenerationsmodel,thedomainoftheRicardianpropositionisrestricted,atleast
6、relativetothein?nitehorizonmodelunderthenaturalborrowinglimit.1Thisisoneoftheinsightsinthein?uentialpaperofBarro(1974)thatreignitedmoderninterestinRicardianequivalence.–363–364RicardianEquivalence10.2.In?nitelylivedagenteconomyEachofNidenticalhouseholdsordersaconsumptionstreamby∞βtu(c),(10
7、.2.1)tt=0whereβ∈(0,1)andu(·)isastrictlyincreasing,strictlyconcave,twice-di?erentiableone-periodutilityfunction.WeimposetheInadaconditionlimu(c)=c↓0+∞.Thisconditionisimportantbecausewewillbestressingthefeaturethatc≥0.Thereisnouncertainty.Thehouseholdcani
