曼昆宏觀經(jīng)濟學課件mankiw7e chap14

ADynamicModelofAggregateDemandandAggregateSupply14ADynamicModelofAggregateDInthischapter,youwilllearn:howtoincorporatedynamicsintothe

AD-ASmodelwepreviouslystudiedhowtousethedynamicAD-ASmodeltoillustratelong-runeconomicgrowthhowtousethedynamicAD-ASmodeltotraceouttheeffectsovertimeofvariousshocksandpolicychangesonoutput,inflation,andotherendogenousvariablesInthischapter,youwilllearIntroductionThedynamicmodelofaggregatedemandandaggregatesupplygivesusmoreinsightintohowtheeconomyworksintheshortrun.ItisasimplifiedversionofaDSGEmodel,

usedincutting-edgemacroeconomicresearch. (DSGE=Dynamic,Stochastic,GeneralEquilibrium)IntroductionThedynamicmodelIntroductionThedynamicmodelofaggregatedemandandaggregatesupplyisbuiltfromfamiliarconcepts,suchas:theIScurve,whichnegativelyrelatestherealinterestrateanddemandforgoods&servicesthePhillipscurve,whichrelatesinflationtothegapbetweenoutputanditsnaturallevel,expectedinflation,andsupplyshocksadaptiveexpectations,asimplemodelofinflationexpectationsIntroductionThedynamicmodelHowthedynamicAD-ASmodelisdifferentfromthestandardmodelInsteadoffixingthemoneysupply,thecentralbankfollowsamonetarypolicyrulethatadjustsinterestrateswhenoutputorinflationchange.TheverticalaxisoftheDAD-DASdiagrammeasurestheinflationrate,notthepricelevel.Subsequenttimeperiodsarelinkedtogether:

Changesininflationinoneperiodalterexpectationsoffutureinflation,whichchangesaggregatesupplyinfutureperiods,whichfurtheraltersinflationandinflationexpectations.HowthedynamicAD-ASmodelisKeepingtrackoftimeThesubscript“t”denotesthetimeperiod,e.g.Yt

=realGDPinperiodt

Yt-1=realGDPinperiodt

–1Yt+1=realGDPinperiodt

+1Wecanthinkoftimeperiodsasyears.

E.g.,ift=2008,thenYt

=Y2008

=realGDPin2008Yt-1=Y2007

=realGDPin2007Yt+1=Y2009

=realGDPin2009KeepingtrackoftimeThesubscThemodel’selementsThemodelhasfiveequationsandfiveendogenousvariables:

output,inflation,therealinterestrate,thenominalinterestrate,andexpectedinflation.Theequationsmayusedifferentnotation,

buttheyareconceptuallysimilartothings

you’vealreadylearned.Thefirstequationisforoutput…Themodel’selementsThemodelOutput:

TheDemandforGoodsandServicesoutputnaturallevelofoutputrealinterestrateNegativerelationbetweenoutputandinterestrate,sameintuitionasIScurve.Output:

TheDemandforGoodsOutput:

TheDemandforGoodsandServicesdemandshock,randomandzeroonaveragemeasurestheinterest-ratesensitivityofdemand“naturalrateofinterest”–

inabsenceofdemandshocks,whenOutput:

TheDemandforGoodsTheRealInterestRate:

TheFisherEquationnominalinterestrateexpectedinflationrateexante

(i.e.expected)realinterestrateincreaseinpricelevelfromperiodttot+1,

notknowninperiodtexpectation,formedinperiodt,

ofinflationfromttot+1TheRealInterestRate:

TheInflation:

ThePhillipsCurvepreviouslyexpectedinflationcurrentinflationsupplyshock,randomandzeroonaverageindicateshowmuchinflationrespondswhenoutputfluctuatesarounditsnaturallevelInflation:

ThePhillipsCurvExpectedInflation:

AdaptiveExpectationsForsimplicity,weassumepeopleexpectpricestocontinuerisingatthecurrentinflationrate.ExpectedInflation:

AdaptiveTheNominalInterestRate:

TheMonetary-PolicyRulenominalinterestrate,seteachperiodbythecentralbanknaturalrateofinterestcentralbank’sinflationtargetTheNominalInterestRate:

TTheNominalInterestRate:

TheMonetary-PolicyRulemeasureshowmuchthecentralbankadjuststheinterestratewheninflationdeviatesfromitstargetmeasureshowmuchthecentralbankadjuststheinterestratewhenoutputdeviatesfrom

itsnaturalrateTheNominalInterestRate:

TCASESTUDY

TheTaylorRuleEconomistJohnTaylorproposedamonetarypolicyruleverysimilartoours:iff=

+2+0.5

(

–2)–0.5

(GDPgap)

whereiff=nominalfederalfundsratetargetGDPgap=100x =percentbywhichrealGDPisbelowits

naturalrateTheTaylorRulematchesFedpolicyfairlywell.…CASESTUDY

TheTaylorRuleEconCASESTUDY

TheTaylorRuleTaylor’sruleactualFederalFundsrateCASESTUDY

TheTaylorRuleTaylThemodel’svariablesandparametersEndogenousvariables:OutputInflationRealinterestrateNominalinterestrateExpectedinflationThemodel’svariablesandparaThemodel’svariablesandparametersExogenousvariables:Predeterminedvariable:NaturallevelofoutputCentralbank’stargetinflationrateDemandshockSupplyshockPreviousperiod’sinflationThemodel’svariablesandparaThemodel’svariablesandparametersParameters:Responsivenessofdemandto

therealinterestrateNaturalrateofinterestResponsivenessofinflationtooutputinthePhillipsCurveResponsivenessofitoinflation

inthemonetary-policyruleResponsivenessofitooutput

inthemonetary-policyruleThemodel’svariablesandparaThemodel’slong-runequilibriumThenormalstatearoundwhichtheeconomyfluctuates.Twoconditionsrequiredforlong-runequilibrium:Therearenoshocks:Inflationisconstant:Themodel’slong-runequilibriThemodel’slong-runequilibriumPluggingtheprecedingconditionsintothe

model’sfiveequationsandusingalgebra

yieldstheselong-runvalues:Themodel’slong-runequilibriTheDynamicAggregateSupplyCurveTheDAScurveshowsarelationbetweenoutputandinflationthatcomesfromthePhillipsCurveandAdaptiveExpectations:(DAS)TheDynamicAggregateSupplyCTheDynamicAggregateSupplyCurveDASslopesupward:highlevelsofoutputareassociatedwithhighinflation.Y

πDAStDASshiftsinresponsetochangesinthenaturallevelofoutput,previousinflation,

andsupplyshocks.TheDynamicAggregateSupplyCTheDynamicAggregateDemandCurveToderivetheDADcurve,wewillcombinefourequationsandtheneliminatealltheendogenousvariablesotherthanoutputandinflation. Startwiththedemandforgoodsandservices:usingtheFishereq’nTheDynamicAggregateDemandCTheDynamicAggregateDemandCurveresultfrompreviousslideusingtheexpectationseq’nusingmonetarypolicyruleTheDynamicAggregateDemandCTheDynamicAggregateDemandCurveresultfrompreviousslidecombineliketerms,solveforYwhere(DAD)TheDynamicAggregateDemandCTheDynamicAggregateDemandCurveDADslopesdownward:Wheninflationrises,thecentralbankraisestherealinterestrate,reducingthedemandforgoods&services.Y

πDADshiftsinresponsetochangesinthenaturallevelofoutput,theinflationtarget,anddemandshocks.DADtTheDynamicAggregateDemandCYtTheshort-runequilibriumIneachperiod,theintersectionofDADandDASdeterminestheshort-runeq’mvaluesofinflationandoutput.πtYtY

πDADtDAStAIntheeq’mshownhereatA,outputisbelowitsnaturallevel.YtTheshort-runequilibriumInLong-rungrowthPeriodt:

initialeq’matAY

πDAStYtDADtAYtπtPeriodt+1:

Long-rungrowthincreasesthenaturalrate

ofoutput.Yt+1DASt+1DADt+1Bπt+1πt=DASshiftsbecauseeconomycanproducemoreg&sDADshiftsbecausehigherincomeraisesdemand

forg&sNeweq’matB,incomegrowsbutinflationremainsstable.Yt+1Long-rungrowthPeriodt:

initiAshocktoaggregatesupplyPeriodt–1:

initialeq’matAπt–1Yt–1Periodt:

Supplyshock

(ν>0)shifts

DASupward;inflationrises,centralbankrespondsbyraisingrealinterestrate,outputfalls.Periodt+1:

Supplyshock

isover(ν=0)

butDASdoesnotreturntoitsinitialpositionduetohigherinflationexpectations.Periodt+2:

Asinflationfalls,inflationexpectationsfall,DASmovesdownward,

outputrises.Y

πDASt-1YDADADAStYtBπtDASt+1CDASt+2DYt+2πt+2Thisprocesscontinuesuntiloutputreturnstoitsnaturalrate.LReq’matA.AshocktoaggregatesupplyPerThus,wecaninterpret

asthepercentagedeviationofoutputfromitsnaturallevel.Yt

–

YtParametervaluesforsimulationsCentralbank’sinflationtargetis2percent.A1-percentage-pointincreaseintherealinterestratereducesoutputdemandby1percentofitsnaturallevel.Thenaturalrateofinterestis2percent.Whenoutputis1percentaboveitsnaturallevel,inflationrisesby0.25percentagepoint.ThesevaluesarefromtheTaylorRule,whichapproximatestheactualbehavioroftheFederalReserve.Thefollowinggraphsarecalledimpulseresponsefunctions.Theyshowthe“response”oftheendogenousvariablestothe“impulse,”i.e.theshock.Thus,wecaninterpret

astheThedynamicresponsetoasupplyshockAone-periodsupplyshockaffectsoutputformanyperiods.ThedynamicresponsetoasuppThedynamicresponsetoasupplyshockBecauseinflationexpect-ationsadjustslowly,actualinflationremainshighformanyperiods.ThedynamicresponsetoasuppThedynamicresponsetoasupplyshockTherealinterestratetakesmanyperiodstoreturntoitsnaturalrate.ThedynamicresponsetoasuppThedynamicresponsetoasupplyshockThebehavior

ofthenominalinterest

ratedepends

onthat

oftheinflationandrealinterestrates.ThedynamicresponsetoasuppAshocktoaggregatedemandPeriodt–1:

initialeq’matAπt–1Y

πDASt-1,tYDADt,t+1,…,t+4DADt-1,t+5DASt+5Yt–1ADASt+1CDASt+2DDASt+3EDASt+4FYtBπtYt+5Gπt+5Periodt:

Positivedemandshock(ε>0)shifts

ADtotheright;outputandinflationrise.Periodt+1:

Higherinflationintraisedinflationexpectations

fort+1,

shiftingDASup.Inflationrisesmore,outputfalls.Periodst+2

to

t+4

:

Higherinflationinpreviousperiodraisesinflationexpectations,shiftsDASup.Inflationrises,outputfalls.Periodt+5:

DASishigherduetohigherinflationinprecedingperiod,butdemandshockendsandDADreturnstoitsinitialposition.Eq’matG.Periodst+6

andhigher:

DASgraduallyshiftsdownasinflationandinflationexpectationsfall,

economygraduallyrecoversuntilreaching

LReq’matA.AshocktoaggregatedemandPerThedynamicresponsetoademandshockThedemandshockraisesoutputforfiveperiods.Whentheshockends,outputfallsbelowitsnaturallevel,andrecoversgradually.ThedynamicresponsetoademaThedynamicresponsetoademandshockThe

demandshockcausesinflation

torise.Whentheshockends,inflationgraduallyfallstowarditsinitiallevel.ThedynamicresponsetoademaThedynamicresponsetoademandshockThedemandshockraisestherealinterestrate.Aftertheshockends,therealinterest

ratefallsandapproachesitsinitiallevel.ThedynamicresponsetoademaThedynamicresponsetoademandshockThebehavior

ofthenominalinterestratedependsonthat

oftheinflationandrealinterestrates.ThedynamicresponsetoademaAshiftinmonetarypolicyPeriodt–1:

targetinflationrateπ*

=2%,

initialeq’matAπt–1

=2%Yt–1Periodt:

Centralbanklowerstarget

toπ*

=1%,raisesrealinterestrate,shiftsDADleftward.Outputandinflationfall.Periodt+1:

Thefallinπtreducedinflationexpectations

fort+1,shiftingDASdownward.Outputrises,inflationfalls.Y

πDASt-1,tYDADt

–1ADADt,t

+

1,…DASfinalYtπtBDASt+1CSubsequentperiods:

Thisprocesscontinuesuntiloutputreturnstoitsnaturalrateandinflationreachesitsnewtarget.Zπfinal

=1%

,

YfinalAshiftinmonetarypolicyPeriThedynamicresponsetoareductionin

targetinflationReducingthetargetinflationratecausesoutputtofallbelowitsnaturallevelforawhile.Outputrecoversgradually.ThedynamicresponsetoareduThedynamicresponsetoareductionin

targetinflationBecauseexpect-ationsadjustslowly,

ittakesmanyperiodsforinflationtoreachthenewtarget.ThedynamicresponsetoareduThedynamicresponsetoareductionin

targetinflationToreduceinflation,

thecentralbankraisestherealinterestratetoreduceaggregatedemand.Therealinterestrategraduallyreturnstoitsnaturalrate.ThedynamicresponsetoareduThedynamicresponsetoareductionin

targetinflationTheinitialincreaseintherealinterestrateraisesthenominalinterestrate.Astheinflationandrealinterestratesfall,thenominalratefalls.ThedynamicresponsetoareduAPPLICATION:

Outputvariabilityvs.inflationvariabilityAsupplyshockreducesoutput(bad)

andraisesinflation(alsobad).Thecentralbankfacesatradeoffbetweenthese“bads”–itcanreducetheeffectonoutput,

butonlybytoleratinganincreaseintheeffect

oninflation….APPLICATION:

OutputvariabilitAPPLICATION:

Outputvariabilityvs.inflationvariabilityCASE1:θπ

islarge,θY

issmallY

πDADt–1,tDAStDASt–1Yt–1πt–1YtπtAsupplyshockshiftsDASup.Inthiscase,asmallchangeininflationhasalargeeffectonoutput,soDAD

isrelativelyflat.Theshockhasalargeeffectonoutput,butasmalleffectoninflation.APPLICATION:

OutputvariabilitAPPLICATION:

Outputvariabilityvs.inflationvariabilityCASE2:θπ

issmall,θY

islargeY

πDADt–1,tDAStDASt–1Yt–1πt–1YtπtInthiscase,alargechangeininflationhasonlyasmalleffectonoutput,soDAD

isrelativelysteep.Now,theshockhasonlyasmalleffectonoutput,butabigeffectoninflation.APPLICATION:

OutputvariabilitAPPLICATION:

TheTaylorPrincipleTheTaylorPrinciple(namedafterJohnTaylor):

Thepropositionthatacentralbankshouldrespondtoanincreaseininflationwithanevengreaterincreaseinthenominalinterestrate

(sothattherealinterestraterises).

I.e.,centralbankshouldsetθπ

>0.Otherwise,DADwillslopeupward,economymaybeunstable,andinflationmayspiraloutofcontrol.APPLICATION:

TheTaylorPrinciAPPLICATION:

TheTaylorPrincipleIfθπ

>0:Wheninflationrises,thecentralbankincreasesthenominalinterestrateevenmore,whichincreasestherealinterestrateandreducesthedemandforgoods&services.DADhasanegativeslope.(DAD)(MPrule)APPLICATION:

TheTaylorPrinciAPPLICATION:

TheTaylorPrincipleIfθπ

<0:Wheninflationrises,thecentralbankincreases

thenominalinterestratebyasmalleramount.

Therealinterestratefalls,whichincreasesthedemandforgoods&services.DADhasapositiveslope.(DAD)(MPrule)APPLICATION:

TheTaylorPrinciAPPLICATION:

TheTaylorPrincipleIfDADisupward-slopingandsteeperthanDAS,thentheeconomyisunstable:outputwillnotreturntoitsnaturallevel,andinflationwillspiralupward

(forpositivedemandshocks)ordownward

(fornegativeones).Estimatesofθπfrompublishedresearch:θπ

=–0.14from1960-78,beforePaulVolckerbecameFedchairman.Inflationwashighduringthistime,especiallyduringthe1970s.θπ=0.72duringtheVolckerandGreenspanyears.Inflationwasmuchlowerduringtheseyears.APPLICATION:

TheTaylorPrinciChapterSummaryTheDAD-DASmodelcombinesfiverelationships:anIS-curve-likeequationofthegoodsmarket,theFisherequation,aPhillipscurveequation,anequationforexpectedinflation,andamonetarypolicyrule.Thelong-runequilibriumofthemodelisclassical.Outputandtherealinterestrateareattheirnaturallevels,independentofmonetarypolicy.Thecentralbank’sinflationtargetdeterminesinflation,expectedinflation,andthenominalinterestrate.ChapterSummaryTheDAD-DASmodChapterSummaryTheDAD-DASmodelcanbeusedtodeterminetheimmediateimpactofanyshockontheeconomy,andcanbeusedtotraceouttheeffectsoftheshockovertime.TheparametersofthemonetarypolicyruleinfluencetheslopeoftheDAScurve,sotheydeterminewhetherasupplyshockhasagreatereffectonoutputorinflation.Thus,thecentralbankfacesatradeoffbetweenoutputvariabilityandinflationvariability.ChapterSummaryTheDAD-DASmodChapterSummaryTheDAD-DASmodelassumesthattheTaylorPrincipleholds,i.e.thatthecentralbankrespondstoanincreaseininflationbyraisingtherealinterestrate.Otherwise,theeconomymaybecomeunstableandinflationmayspiraloutofcontrol.ChapterSummaryTheDAD-DASmodADynamicModelofAggregateDemandandAggregateSupply14ADynamicModelofAggregateDInthischapter,youwilllearn:howtoincorporatedynamicsintothe

AD-ASmodelwepreviouslystudiedhowtousethedynamicAD-ASmodeltoillustratelong-runeconomicgrowthhowtousethedynamicAD-ASmodeltotraceouttheeffectsovertimeofvariousshocksandpolicychangesonoutput,inflation,andotherendogenousvariablesInthischapter,youwilllearIntroductionThedynamicmodelofaggregatedemandandaggregatesupplygivesusmoreinsightintohowtheeconomyworksintheshortrun.ItisasimplifiedversionofaDSGEmodel,

usedincutting-edgemacroeconomicresearch. (DSGE=Dynamic,Stochastic,GeneralEquilibrium)IntroductionThedynamicmodelIntroductionThedynamicmodelofaggregatedemandandaggregatesupplyisbuiltfromfamiliarconcepts,suchas:theIScurve,whichnegativelyrelatestherealinterestrateanddemandforgoods&servicesthePhillipscurve,whichrelatesinflationtothegapbetweenoutputanditsnaturallevel,expectedinflation,andsupplyshocksadaptiveexpectations,asimplemodelofinflationexpectationsIntroductionThedynamicmodelHowthedynamicAD-ASmodelisdifferentfromthestandardmodelInsteadoffixingthemoneysupply,thecentralbankfollowsamonetarypolicyrulethatadjustsinterestrateswhenoutputorinflationchange.TheverticalaxisoftheDAD-DASdiagrammeasurestheinflationrate,notthepricelevel.Subsequenttimeperiodsarelinkedtogether:

Changesininflationinoneperiodalterexpectationsoffutureinflation,whichchangesaggregatesupplyinfutureperiods,whichfurtheraltersinflationandinflationexpectations.HowthedynamicAD-ASmodelisKeepingtrackoftimeThesubscript“t”denotesthetimeperiod,e.g.Yt

=realGDPinperiodt

Yt-1=realGDPinperiodt

–1Yt+1=realGDPinperiodt

+1Wecanthinkoftimeperiodsasyears.

E.g.,ift=2008,thenYt

=Y2008

=realGDPin2008Yt-1=Y2007

=realGDPin2007Yt+1=Y2009

=realGDPin2009KeepingtrackoftimeThesubscThemodel’selementsThemodelhasfiveequationsandfiveendogenousvariables:

output,inflation,therealinterestrate,thenominalinterestrate,andexpectedinflation.Theequationsmayusedifferentnotation,

buttheyareconceptuallysimilartothings

you’vealreadylearned.Thefirstequationisforoutput…Themodel’selementsThemodelOutput:

TheDemandforGoodsandServicesoutputnaturallevelofoutputrealinterestrateNegativerelationbetweenoutputandinterestrate,sameintuitionasIScurve.Output:

TheDemandforGoodsOutput:

TheDemandforGoodsandServicesdemandshock,randomandzeroonaveragemeasurestheinterest-ratesensitivityofdemand“naturalrateofinterest”–

inabsenceofdemandshocks,whenOutput:

TheDemandforGoodsTheRealInterestRate:

TheFisherEquationnominalinterestrateexpectedinflationrateexante

(i.e.expected)realinterestrateincreaseinpricelevelfromperiodttot+1,

notknowninperiodtexpectation,formedinperiodt,

ofinflationfromttot+1TheRealInterestRate:

TheInflation:

ThePhillipsCurvepreviouslyexpectedinflationcurrentinflationsupplyshock,randomandzeroonaverageindicateshowmuchinflationrespondswhenoutputfluctuatesarounditsnaturallevelInflation:

ThePhillipsCurvExpectedInflation:

AdaptiveExpectationsForsimplicity,weassumepeopleexpectpricestocontinuerisingatthecurrentinflationrate.ExpectedInflation:

AdaptiveTheNominalInterestRate:

TheMonetary-PolicyRulenominalinterestrate,seteachperiodbythecentralbanknaturalrateofinterestcentralbank’sinflationtargetTheNominalInterestRate:

TTheNominalInterestRate:

TheMonetary-PolicyRulemeasureshowmuchthecentralbankadjuststheinterestratewheninflationdeviatesfromitstargetmeasureshowmuchthecentralbankadjuststheinterestratewhenoutputdeviatesfrom

itsnaturalrateTheNominalInterestRate:

TCASESTUDY

TheTaylorRuleEconomistJohnTaylorproposedamonetarypolicyruleverysimilartoours:iff=

+2+0.5

(

–2)–0.5

(GDPgap)

whereiff=nominalfederalfundsratetargetGDPgap=100x =percentbywhichrealGDPisbelowits

naturalrateTheTaylorRulematchesFedpolicyfairlywell.…CASESTUDY

TheTaylorRuleEconCASESTUDY

TheTaylorRuleTaylor’sruleactualFederalFundsrateCASESTUDY

TheTaylorRuleTaylThemodel’svariablesandparametersEndogenousvariables:OutputInflationRealinterestrateNominalinterestrateExpectedinflationThemodel’svariablesandparaThemodel’svariablesandparametersExogenousvariables:Predeterminedvariable:NaturallevelofoutputCentralbank’stargetinflationrateDemandshockSupplyshockPreviousperiod’sinflationThemodel’svariablesandparaThemodel’svariablesandparametersParameters:Responsivenessofdemandto

therealinterestrateNaturalrateofinterestResponsivenessofinflationtooutputinthePhillipsCurveResponsivenessofitoinflation

inthemonetary-policyruleResponsivenessofitooutput

inthemonetary-policyruleThemodel’svariablesandparaThemodel’slong-runequilibriumThenormalstatearoundwhichtheeconomyfluctuates.Twoconditionsrequiredforlong-runequilibrium:Therearenoshocks:Inflationisconstant:Themodel’slong-runequilibriThemodel’slong-runequilibriumPluggingtheprecedingconditionsintothe

model’sfiveequationsandusingalgebra

yieldstheselong-runvalues:Themodel’slong-runequilibriTheDynamicAggregateSupplyCurveTheDAScurveshowsarelationbetweenoutputandinflationthatcomesfromthePhillipsCurveandAdaptiveExpectations:(DAS)TheDynamicAggregateSupplyCTheDynamicAggregateSupplyCurveDASslopesupward:highlevelsofoutputareassociatedwithhighinflation.Y

πDAStDASshiftsinresponsetochangesinthenaturallevelofoutput,previousinflation,

andsupplyshocks.TheDynamicAggregateSupplyCTheDynamicAggregateDemandCurveToderivetheDADcurve,wewillcombinefourequationsandtheneliminatealltheendogenousvariablesotherthanoutputandinflation. Startwiththedemandforgoodsandservices:usingtheFishereq’nTheDynamicAggregateDemandCTheDynamicAggregateDemandCurveresultfrompreviousslideusingtheexpectationseq’nusingmonetarypolicyruleTheDynamicAggregateDemandCTheDynamicAggregateDemandCurveresultfrompreviousslidecombineliketerms,solveforYwhere(DAD)TheDynamicAggregateDemandCTheDynamicAggregateDemandCurveDADslopesdownward:Wheninflationrises,thecentralbankraisestherealinterestrate,reducingthedemandforgoods&services.Y

πDADshiftsinresponsetochangesinthenaturallevelofoutput,theinflationtarget,anddemandshocks.DADtTheDynamicAggregateDemandCYtTheshort-runequilibriumIneachperiod,theintersectionofDADandDASdeterminestheshort-runeq’mvaluesofinflationandoutput.πtYtY

πDADtDAStAIntheeq’mshownhereatA,outputisbelowitsnaturallevel.YtTheshort-runequilibriumInLong-rungrowthPeriodt:

initialeq’matAY

πDAStYtDADtAYtπtPeriodt+1:

Long-rungrowthincreasesthenaturalrate

ofoutput.Yt+1DASt+1DADt+1Bπt+1πt=DASshiftsbecauseeconomycanproducemoreg&sDADshiftsbecausehigherincomeraisesdemand

forg&sNeweq’matB,incomegrowsbutinflationremainsstable.Yt+1Long-rungrowthPeriodt:

initiAshocktoaggregatesupplyPeriodt–1:

initialeq’matAπt–1Yt–1Periodt:

Supplyshock

(ν>0)shifts

DASupward;inflationrises,centralbankrespondsbyraisingrealinterestrate,outputfalls.Periodt+1:

Supplyshock

isover(ν=0)

butDASdoesnotreturntoitsinitialpositionduetohigherinflationexpectations.Periodt+2:

Asinflationfalls,inflationexpectationsfall,DASmovesdownward,

outputrises.Y

πDASt-1YDADADAStYtBπtDASt+1CDASt+2DYt+2πt+2Thisprocesscontinuesuntiloutputreturnstoitsnaturalrate.LReq’matA.AshocktoaggregatesupplyPerThus,wecaninterpret

asthepercentagedeviationofoutputfromitsnaturallevel.Yt

–

YtParametervaluesforsimulationsCentralbank’sinflationtargetis2percent.A1-percentage-pointincreaseintherealinterestratereducesoutputdemandby1percentofitsnaturallevel.Thenaturalrateofinterestis2percent.Whenoutputis1percentaboveitsnaturallevel,inflationrisesby0.25percentagepoint.ThesevaluesarefromtheTaylorRule,whichapproximatestheactualbehavioroftheFederalReserve.Thefollowinggraphsarecalledimpulseresponsefunctions.Theyshowthe“response”oftheendogenousvariablestothe“impulse,”i.e.theshock.Thus,wecaninterpret

astheThedynamicresponsetoasupplyshockAone-periodsupplyshockaffectsoutputformanyperiods.ThedynamicresponsetoasuppThedynamicresponsetoasupplyshockBecauseinflationexpect-ationsadjustslowly,actualinflationremainshighformanyperiods.ThedynamicresponsetoasuppThedynamicresponsetoasupplyshockTherealinterestratetakesmanyperiodstoreturntoitsnaturalrate.ThedynamicresponsetoasuppThedynamicresponsetoasupplyshockThebehavior

ofthenominalinterest

ratedepends

onthat

oftheinflationandrealinterestrates.ThedynamicresponsetoasuppAshocktoaggregatedemandPeriodt–1:

initialeq’matAπt–1Y

πDASt-1