Chapter6

MicroeconomicFoundationsofIncompleteNominalAdjustment周泳宏tzhouyhjnu@Chapter6

MicroeconomicFoundintroductionThesluggishadjustmentofnominalwagesandpricesiscentraltoKeynesianmodels.InvestigatingthemicroeconomicfoundationsofthatsluggishadjustmentisnecessaryformakingthemodelsfullyspecifiedButsimplyintroducingsomedeparturefromperfectmarketsisnotenoughtoimplythatnominaldisturbancesmatterintroductionThesluggishadjusAnymicroeconomicbasisforfailureoftheclassicaldichotomyrequiressomekindofnominalimperfectionClassicalDichotomyMonetarydisturbancescauseallnominalpricesandwagestochange,leavingtherealequilibriumunchangedAnymicroeconomicbasisforfaWeexaminethreenominalimperfectionsPartALucas(1972)andPhelps(1970)ThenominalimperfectionisthatproducersdonotobservetheaggregatepricelevelPartBMonetaryshockshaverealeffectsbecausenotallpricesorwagesareadjustedsimultaneouslyPartCSmallcostsofchangingnominalpricesorwagesOthersmallfrictioninnominaladjustmentWeexaminethreenominalimperPartATheLucasImperfect-InformationModelPartATheLucasImperfect-InfoIntroductionWhenaproducerobservesachangeinthepriceofhisorherproduct,heorshedoesnotknowwhetheritreflectsachangeinthegood’srelativepriceorachangeintheaggregatepricelevelAchangeintherelativepricealterstheoptimalamounttoproduceAchangeintheaggregatepricelevelleavesoptimalproductionunchangedIntroductionWhenaproducerob6.1thecaseofperfectinformation（1）ProducerBehaviorRepresentativeofatypicalgoodiQi:theamountheorsheproducesLi:theamountthattheindividualworksCi:theindividual’sconsumptionP:thepriceofthemarketbasketofgoods——anindexofthepricesofallgoodsTheindividual’sconsumptionequalshisorherrealincome6.1thecaseofperfectinformUtilitydependspositivelyonconsumptionandnegativelyontheamountworkedPisgivenTheindividual’slaborsupplyandproductionareincreasingintherelativepriceofhisorherproductUtilitydependspositivelyon（2）DemandThedemandforagivengoodisassumedtodependonthreefactors:realincome,thegood’srelativeprice,andarandomdisturbancetopreferencesThedemandforgoodiis:y:thelogaggregaterealincomez:theshocktothedemand.Thezi’shaveameanofzeroacrossgoods.η:theelasticityofdemandyisassumedtoequaltheaverageacrossgoodsoftheqi’sandPistheaverageofthepi’s（2）Demandy:thelogaggregateTheaggregatedemandsideofthemodelTherearevariousinterpretationsofthisequationThereisaninverserelationshipbetweenthepricelevelandoutputmshouldbethoughtofasagenericvariableaffectingaggregatedemandratherthanasmoneyTheaggregatedemandsideoft（3）EquilibriumDemandperproducerequalsupplyInacaseofperfectinformation,moneyisneutral:anincreaseinmleadstoanincreaseinp.Norealvariablesareaffected（3）EquilibriumInacaseofper6.2thecaseofimperfectinformationDefiningtherelativepriceofgoodibyriTheindividualdoesnotobserveri,butmustestimateitgiventheobservationofpiRationalexpectations——theproducerfindstheexpectationofrigivenpirationally6.2thecaseofimperfectinfoIndividual’sproblemProveitThefractionofthedepartureofthepifromitsmeanthatisestimatedtobeduetothedepartureofrifromitsmeanisWhentwovariablesarejointlynormallydistributed,theexpectationofoneisalinearfunctionoftheobservationoftheotherIndividual’sproblemWhentwovLucassupplycurveLucassupplycurve——thedepartureofoutputfromitsnormallevel(whichiszero)isanincreasingfunctionofthesurpriseinthepricelevelLucassupplycurveLucassupplyEquilibriumThecomponentofaggregatedemandthatisobserved,E(m),affectsonlyprices,butthecomponentthatisnotobserved,m-E(m),hasrealeffectsTakingtheexpectationsofbothsidesEquilibriumThecomponentofagTheexpressionofbTheexpressionofbTheexpressionofbbisincreasinginVzanddecreasinginVmThespecialcase:Theexpressionofbbisincrea6.3ImplicationsandLimitationsThePhillipsCurveandtheLucasCritiqueLucas’smodelimpliesthatunexpectedlyhighrealizationsofaggregatedemandleadtobothhigheroutputandhigher-than-expectedpricesThemodelimpliesapositiveassociationbetweenoutputandinflation6.3ImplicationsandLimitatioAnexampleWhitenoisearandomwalkwithdriftAnexampleWhitenoisearandomPhillipscurveHowever,thestatisticalrelationshipbetweenoutputandinflationmaychangeifpolicymakersattempttotakeadvantageofitPhillipscurve——apositiverelationshipbetweenoutputandinflationPhillipscurveHowever,thestaLucascritiqueExpectationsarelikelytobeimportanttomanyrelationshipsamongaggregatevariables,andchangesinpolicyarelikelytoaffectthoseexpectationsIfpolicymakersattempttotakeadvantageofstatisticalrelationships,effectsoperatingthroughexpectationsmaycausetherelationshipstobreakdownLucascritiqueExpectationsareAnticipatedandUnanticipatedmoneyOnlyunobservedaggregatedemandshockshaverealeffectsMonetarypolicycanstabilizeoutputonlyifpolicymakershaveinformationthatisnotavailabletoprivateagentsAnyportionofpolicythatisaresponsetopubliclyavailableinformation——suchasinterestrates,theunemploymentrate,ortheindexofleadingindicators——isirrelevanttotherealeconomyAnticipatedandUnanticipatedOnlyunobservedaggregatedemandshockshaverealeffectsletOnlyunobservedaggregatedemaEmpiricalapplication:internationalEvidenceonOutput-InflationTradeoffsLucas’implicationIfaggregateshocksarelarge,suppliersattributemostofthechangesinthepricesoftheirgoodstochangesinthepricelevel,andsotheyaltertheirproductionrelativelylittleinresponsetovariationsinpricesEmpiricalapplication:internaTheestimatesoftheresponsivenessofoutputtoaggregatedemandmovementsTheaveragesizeofcountries’aggregatedemandshocks:ThestandarddeviationofthechangeinlognominalGDPAmeasureofaggregatedemandshock:thechangeinlognominalGDPthereallogGDPNominalshockshavesmallerrealeffectsinsettingswhereaggregatedemandismorevolatileTheestimatesoftheresponsivPartB

StaggeredPriceAdjustmentPartB

StaggeredPriceAdjustIntroductionThenextsourceofnominalimperfectionsweconsiderisstaggeredadjustmentofpricesandwagesTherearethreereasonsfortheimportanceofthemicroeconomicfoundationsIfnotallpricesorwagesarefreetochange,aggregatedemandpolicycanbestabilizingevenunderrationalexpectationLaythegroundworkforthemodelwherenominalrigidityisderivedfromoptimizingbehavioratthemicroeconomiclevelItshowsthattheinteractionsamongprice-setterscaneithermagnifyordampentheeffectsofbarrierstopriceadjustmentIntroductionThenextsourceofWeconsiderthreemodelsofstaggeredadjustmentTime-dependentmodels——WagesorpricesaresetbymultiperiodcontractsorcommitmentsFischermodelassumesthatpricesorwagesarepredeterminedbutnotfixed——acontractcanspecifyadifferentpriceforeachperiodTaylormodelassumesthatthepricesarefixed——acontractmustspecifythesamepriceeachperiodCaplin-Spulber’sState-dependentpricingmodelPriceschangesaretriggeredbydevelopmentswithintheeconomyAsaresult,thefractionofpricesthatchangeinagiventimeintervalisendogenousWeconsiderthreemodelsofstBeforeturningtostaggeredadjustment,wefirstinvestigateamodelofaneconomyofimperfectlycompetitiveprice-setterswithcompletepriceflexibilityWecanunderstandthebarriersofpriceadjustmentwellItshowsthatwhatpricesfirmswouldchooseintheabsenceofbarrierstoadjustmentandwhathappenswhenpricesdepartfromthoselevelsBeforeturningtostaggeredad6.4AmodelofImperfectCompetitiveandPrice-SettingAssumptionsLargenumberofindividualsEachonesetsthepriceofsomegoodandisthesoleproducerofthatgoodLaboristheonlyinputintoproductionIndividualsdonotproducetheirowngoodsdirectlyAcompetitivelabormarketwheretheycanbothselltheirlaborandhireworkers6.4AmodelofImperfectCompeTheshockstothedemandsfortheindividualgoods(z)areabsentTheutilityofatypicalindividualisSellerswithmarketpowersetpriceabovemarginalcost.Individuali’sprofitincomeisTheshockstothedemandsforIndividuali’sincomeisthesumofprofitincomeandlaborincomeCiistheindividual’sincomedividedbythepriceindexTheaggregatedemandsideofthemodelIndividuali’sincomeisthesIndividualBehaviorAproducerwithmarketpowersetspriceasamarkupovermarginalcost,withthesizeofthemarkupdeterminedbytheelasticityofdemandLaborsupplyisanincreasingfunctionoftherealwagetheelasticityIndividualBehaviorAproducerEquilibriumlevelofoutputEachproducerschargesthesamepriceEquilibriumlevelofoutputEacImplicationSymmetricallocationEquilibriumlevelofoutputWhenproducershavemarketpower,theyproducelessthanthesociallyoptimalamountThegapbetweentheequilibriumandoptimallevelsofoutputisgreaterwhenproducershavemoremarketpower(ηislower)andwhenlaborsupplyismoreresponsivetotherealwage(γislower)ImplicationSymmetricallocatioEquilibriumlevelofpriceEquilibriumlevelofpriceChapter6

MicroeconomicFoundationsofIncompleteNominalAdjustment周泳宏tzhouyhjnu@Chapter6

MicroeconomicFoundintroductionThesluggishadjustmentofnominalwagesandpricesiscentraltoKeynesianmodels.InvestigatingthemicroeconomicfoundationsofthatsluggishadjustmentisnecessaryformakingthemodelsfullyspecifiedButsimplyintroducingsomedeparturefromperfectmarketsisnotenoughtoimplythatnominaldisturbancesmatterintroductionThesluggishadjusAnymicroeconomicbasisforfailureoftheclassicaldichotomyrequiressomekindofnominalimperfectionClassicalDichotomyMonetarydisturbancescauseallnominalpricesandwagestochange,leavingtherealequilibriumunchangedAnymicroeconomicbasisforfaWeexaminethreenominalimperfectionsPartALucas(1972)andPhelps(1970)ThenominalimperfectionisthatproducersdonotobservetheaggregatepricelevelPartBMonetaryshockshaverealeffectsbecausenotallpricesorwagesareadjustedsimultaneouslyPartCSmallcostsofchangingnominalpricesorwagesOthersmallfrictioninnominaladjustmentWeexaminethreenominalimperPartATheLucasImperfect-InformationModelPartATheLucasImperfect-InfoIntroductionWhenaproducerobservesachangeinthepriceofhisorherproduct,heorshedoesnotknowwhetheritreflectsachangeinthegood’srelativepriceorachangeintheaggregatepricelevelAchangeintherelativepricealterstheoptimalamounttoproduceAchangeintheaggregatepricelevelleavesoptimalproductionunchangedIntroductionWhenaproducerob6.1thecaseofperfectinformation（1）ProducerBehaviorRepresentativeofatypicalgoodiQi:theamountheorsheproducesLi:theamountthattheindividualworksCi:theindividual’sconsumptionP:thepriceofthemarketbasketofgoods——anindexofthepricesofallgoodsTheindividual’sconsumptionequalshisorherrealincome6.1thecaseofperfectinformUtilitydependspositivelyonconsumptionandnegativelyontheamountworkedPisgivenTheindividual’slaborsupplyandproductionareincreasingintherelativepriceofhisorherproductUtilitydependspositivelyon（2）DemandThedemandforagivengoodisassumedtodependonthreefactors:realincome,thegood’srelativeprice,andarandomdisturbancetopreferencesThedemandforgoodiis:y:thelogaggregaterealincomez:theshocktothedemand.Thezi’shaveameanofzeroacrossgoods.η:theelasticityofdemandyisassumedtoequaltheaverageacrossgoodsoftheqi’sandPistheaverageofthepi’s（2）Demandy:thelogaggregateTheaggregatedemandsideofthemodelTherearevariousinterpretationsofthisequationThereisaninverserelationshipbetweenthepricelevelandoutputmshouldbethoughtofasagenericvariableaffectingaggregatedemandratherthanasmoneyTheaggregatedemandsideoft（3）EquilibriumDemandperproducerequalsupplyInacaseofperfectinformation,moneyisneutral:anincreaseinmleadstoanincreaseinp.Norealvariablesareaffected（3）EquilibriumInacaseofper6.2thecaseofimperfectinformationDefiningtherelativepriceofgoodibyriTheindividualdoesnotobserveri,butmustestimateitgiventheobservationofpiRationalexpectations——theproducerfindstheexpectationofrigivenpirationally6.2thecaseofimperfectinfoIndividual’sproblemProveitThefractionofthedepartureofthepifromitsmeanthatisestimatedtobeduetothedepartureofrifromitsmeanisWhentwovariablesarejointlynormallydistributed,theexpectationofoneisalinearfunctionoftheobservationoftheotherIndividual’sproblemWhentwovLucassupplycurveLucassupplycurve——thedepartureofoutputfromitsnormallevel(whichiszero)isanincreasingfunctionofthesurpriseinthepricelevelLucassupplycurveLucassupplyEquilibriumThecomponentofaggregatedemandthatisobserved,E(m),affectsonlyprices,butthecomponentthatisnotobserved,m-E(m),hasrealeffectsTakingtheexpectationsofbothsidesEquilibriumThecomponentofagTheexpressionofbTheexpressionofbTheexpressionofbbisincreasinginVzanddecreasinginVmThespecialcase:Theexpressionofbbisincrea6.3ImplicationsandLimitationsThePhillipsCurveandtheLucasCritiqueLucas’smodelimpliesthatunexpectedlyhighrealizationsofaggregatedemandleadtobothhigheroutputandhigher-than-expectedpricesThemodelimpliesapositiveassociationbetweenoutputandinflation6.3ImplicationsandLimitatioAnexampleWhitenoisearandomwalkwithdriftAnexampleWhitenoisearandomPhillipscurveHowever,thestatisticalrelationshipbetweenoutputandinflationmaychangeifpolicymakersattempttotakeadvantageofitPhillipscurve——apositiverelationshipbetweenoutputandinflationPhillipscurveHowever,thestaLucascritiqueExpectationsarelikelytobeimportanttomanyrelationshipsamongaggregatevariables,andchangesinpolicyarelikelytoaffectthoseexpectationsIfpolicymakersattempttotakeadvantageofstatisticalrelationships,effectsoperatingthroughexpectationsmaycausetherelationshipstobreakdownLucascritiqueExpectationsareAnticipatedandUnanticipatedmoneyOnlyunobservedaggregatedemandshockshaverealeffectsMonetarypolicycanstabilizeoutputonlyifpolicymakershaveinformationthatisnotavailabletoprivateagentsAnyportionofpolicythatisaresponsetopubliclyavailableinformation——suchasinterestrates,theunemploymentrate,ortheindexofleadingindicators——isirrelevanttotherealeconomyAnticipatedandUnanticipatedOnlyunobservedaggregatedemandshockshaverealeffectsletOnlyunobservedaggregatedemaEmpiricalapplication:internationalEvidenceonOutput-InflationTradeoffsLucas’implicationIfaggregateshocksarelarge,suppliersattributemostofthechangesinthepricesoftheirgoodstochangesinthepricelevel,andsotheyaltertheirproductionrelativelylittleinresponsetovariationsinpricesEmpiricalapplication:internaTheestimatesoftheresponsivenessofoutputtoaggregatedemandmovementsTheaveragesizeofcountries’aggregatedemandshocks:ThestandarddeviationofthechangeinlognominalGDPAmeasureofaggregatedemandshock:thechangeinlognominalGDPthereallogGDPNominalshockshavesmallerrealeffectsinsettingswhereaggregatedemandismorevolatileTheestimatesoftheresponsivPartB

StaggeredPriceAdjustmentPartB

StaggeredPriceAdjustIntroductionThenextsourceofnominalimperfectionsweconsiderisstaggeredadjustmentofpricesandwagesTherearethreereasonsfortheimportanceofthemicroeconomicfoundationsIfnotallpricesorwagesarefreetochange,aggregatedemandpolicycanbestabilizingevenunderrationalexpectationLaythegroundworkforthemodelwherenominalrigidityisderivedfromoptimizingbehavioratthemicroeconomiclevelItshowsthattheinteractionsamongprice-setterscaneithermagnifyordampentheeffectsofbarrierstopriceadjustmentIntroductionThenextsourceofWeconsiderthreemodelsofstaggeredadjustmentTime-dependentmodels——WagesorpricesaresetbymultiperiodcontractsorcommitmentsFischermodelassumesthatpricesorwagesarepredeterminedbutnotfixed——acontractcanspecifyadifferentpriceforeachperiodTaylormodelassumesthatthepricesarefixed——acontractmustspecifythesamepriceeachperiodCaplin-Spulber’sState-dependentpricingmodelPriceschangesaretriggeredbydevelopmentswithintheeconomyAsaresult,thefractionofpricesthatchangeinagiventimeintervalisendogenousWeconsiderthreemodelsofstB