曼昆第10版讲义mankiw10e-irm-ch15

|CHAPTER15 ADynamicModelofEconomicFluctuations

LectureNotes|

CHAPTER15

ADynamicModelofEconomicFluctuations

NotestotheInstructor

ChapterSummary

PartVofthetextpresentssomeadvancesinmacroeconomictheorythatclarifyourunderstandingoftheeconomy.ThispartofthetextbeginswithChapter15,whichextendstheanalysisofshort-runfluctuationstoconsidertheresponseovertimeofkeymacroeconomicvariables.Thechapterdoesthisbyconstructingadynamicmodelofaggregatedemandandaggregatesupplyinwhichthetimedimensionisexplicitlyconsidered.Afeatureofthemodelisthatitincorporatestheresponseofmonetarypolicytoeconomicconditions,therebyprovidingamorerealisticsettingforunderstandingtheinteractionofpolicyandeconomicoutcomes.

Comments

ThematerialpresentedinthischapterismoredifficultthantheAD–ASandIS–LMmodelsanalyzedinearlierchapters.Butbecausemanyofthebuildingblockshavealreadybeendiscussed,instructorsshouldhavearelativelyeasytimemotivatingtheapproach,andstudentsshouldreadilyseetheconnectionstowhattheyhavealreadylearned.Themodelconsistsoffiveequations—arelativelylargenumberforundergraduatestoworkwith—butthediscussionsurroundingthemodelrequiresonlybasicalgebra.Dynamicsolutionofthemodelisdonethroughsimulationexercises,withfiguresillustratingthetimepathsofdifferentvariables.Facultywhodon’tfeelcomfortablewithgoingthroughthealgebraofthemodel’sdetailscanstillusethechaptereffectivelybyrelyingonthesimulationfigurestodiscusshowvariousshocksandchangesinpolicyaffecttheeconomyovertime.

UseoftheEWebsite

GototheEwebsiteanddownloadannualdataonthefederalfundsrate,realGDP,andtheGDPpriceindexoverthepast30years.ComputethetrendlevelofrealGDPovertimebygraphingitandchoosingasendpoints1979and2006(cyclicalpeaks).NowconstructaGDPgapseriesbysubtractingyourtrendGDPfromactualGDP.ComputetheinflationrateusingtheGDPpriceindex.UsingthespecificationoftheTaylorrulediscussedinChapter15,computepredictionsforthefederalfundsrateoverthistimeperiod.Nowcompareyourpredictionswiththeactualfederalfundsrate.Whenaretheysimilarandwhenaretheydifferent?Doestherulefitbetteraftertheshiftin1984tointerest-ratetargetingandawayfrommonetary-aggregatetargetingbytheFederalReserve?Assesswhetheryourfindingssuggestthatmonetarypolicymayhavebeentooexpansionaryintheearlytomid-2000s,duringthetimewhenrealestatepricesbegantorisesharply.

ChapterSupplements

Thischapterincludesthefollowingsupplements:

15-1 HowaRealBusinessCycleModelIsConstructed

15-2 TheMicroeconomicsofLaborSupply

15-3 QuitsandLayoffs

15-4 InvoluntaryUnemploymentandOverqualification

15-5 WhyTechnologyShocksAreSoImportantinRealBusinessCycleModels

15-6 RealBusinessCyclesandRandomWalks

15-7 InflationInertia

15-8 VolatilityandGrowth

15-9 HowLongIstheLongRun?PartIV

15-10 AdditionalReadings

LectureNotes

Introduction

ThechapterbuildsontheearlierdevelopmentoftheAD–ASandIS–LMmodelsbydevelopingadynamicmodelofaggregatedemandandaggregatesupply.Usingthismodelisanotherwaytostudyshort-runbusiness-cyclefluctuationsandtheeffectsoffiscalandmonetarypolicies.Themodelisasimplifiedversionofthesortsofmodelspolicymakersusetoformulatemacroeconomicpolicy.

15-1 ElementsoftheModel

Manyofthevariablesinthemodelarefamiliarfrompreviouschapters,butnowwewilluseatsubscripttodenotethetimeperiod.Thus,totaloutputandnationalincomeinperiodtwillbegivenasYtand,similarly,inperiodt–1itisgivenasYt–1.Themodeliscomposedoffiveequations,whichwedescribebelow.

Output:TheDemandforGoodsandServices

Thedemandforgoodsandservicesintheeconomyisdeterminedby:

whereYtisthetotaloutputofgoodsandservices,istheeconomy’snaturallevelofoutput,rtistherealinterestrate,tisarandomdemandshock,andandareparametersgreaterthanzero.ThisequationissimilartotheISequationfromChapter11.Anincreaseintherealinterestratelowersdemandthroughareductioninbothinvestmentspendingbybusinessfirmsandconsumptionspendingbyhouseholds,withtheresponsedependingonthesizeoftheparameter(ahigherinterestratemightalsoappreciatetherealexchangerate,dampeningnetexports).Thedemandforgoodsandservicesgrowswiththenaturallevelofoutput.Thisfeatureallowsustoconsiderlong-runeconomicgrowthinthismodel.Finally,thedemandshockrepresentsexogenousshiftsinspendingthatincludeshiftsinfiscalpolicy.Theparameteristhenaturalrateofinterest,whichisthevalueoftherealinterestratewhenthedemandforgoodsandservicesequalsthenaturallevelofoutput.

TheRealInterestRate:TheFisherEquation

Wedefinetherealinterestasequaltothenominalrateminusexpectedinflation:

rt=it–Ett+1,

whichissimilartotheFisherequation.ThevariableEtt+1representstheperiodtexpectationofinflationforperiodt+1.Notationandtimingreflecttheconventionofdatingvariablesbywhentheyareknown.Accordingly,theexanterealinterestratertandthenominalinterestrateitareknownattimetandrepresentreturnsbetweenperiodtandt+1,andtheinflationratet+1,whichisafunctionofpricesinperiodtandt+1,isknownatt+1.Theexpectationofinflationinperiodtis,therefore,knowninperiodt.

Inflation:ThePhillipsCurve

ThemodelusesastandardPhillipscurve,similartotheonederivedinChapter14:

AsinChapter14,inflationdependsonexpectedinflation,thegapbetweenoutputanditsnaturallevel,andasupplyshockt.Theparameterdetermineshowresponsiveinflationistochangesintheoutputgap.

ExpectedInflation:AdaptiveExpectations

Expectationsofinflationareformedadaptively,sothatlastperiod’sinflationrateisusedastheexpectationforinflationinthecurrentperiod:

AsdiscussedinChapter14,thisassumptionaboutexpectationsignoresthepossibilitythatpeopleareforward-lookinganduseallavailableinformationtoformtheirexpectations.Analternativeapproach,knownasrationalexpectations,assumesforward-lookingbehaviorbutismorecomplicatedmathematically(anditsempiricalvalidityisopentoquestion).Usingadaptiveexpectationssimplifiestheanalysisofthemodelwhilemaintainingitskeyimplications.

TheNominalInterestRate:TheMonetary-PolicyRule

Thelastequationofthemodelisaruleformonetarypolicyinwhichthecentralbanksetsatargetforthenominalinterestratebasedoninflationandoutput:

Thepolicyruleassumesthatthecentralbankrespondstodeviationininflationfromitstargetinflationratet*andtodeviationsinoutputrelativetoitsnaturallevel.Policyparameters,andY,determinehowmuchthecentralbankrespondstothesedeviations.Intheabsenceofdeviationsfromtargetinflation(t=t*)andfromthenaturallevelofoutput(Yt=),thecentralbanksetstherealinterestrate,it–t,equaltothenaturalrateofinterest.(Recallthatrt=it–Ett+1=it–tunderadaptiveexpectations.)Thus,wheninflationexceedsitstarget(t>t*)oroutputisaboveitsnaturallevel(Yt>),therealinterestraterises.Andwheninflationisbelowitstargetoroutputisbelowitnaturallevel,therealinterestratefalls.

Unlikeearlierchaptersthatfocusedonchangesinthemoneysupplyasthepolicyinstrumentforthecentralbank,herethepolicyinstrumentistheinterestrate.Theimplicitassumptionhereisthatthecentralbankadjuststhemoneysupplyasnecessarytoachieveitstargetfortheinterestrate.Choosingtheinterestrateasthepolicyinstrumentismorerealisticasitcloselymatchesthepracticeofcentralbanksaroundtheworld.

CaseStudy:TheTaylorRule

TheFedchoosesatargetforfederalfundsrateusingtwogeneralguidelines:wheninflationrises,thefederalfundsrateshouldrise,andwheneconomicactivityslowsdown,thefederalfundsrateshouldfall.EconomistJohnTaylorhasproposedasimpleruleforthefederalfundsratefollowingtheseguidelines:

NominalFederalFundsRate=

Inflation+2.0+0.5(Inflation–2.0)+0.5(GDPgap)

wheretheGDPgapisthepercentagebywhichrealGDPexceedsitsnaturallevel.ThefederalfundsraterespondstobothinflationandtheGDPgapwhenusingthisrule.Foreachpercentagepointbywhichinflationrisesabove2percent,therealfederalfundsraterisesby0.5percent;andforeachpercentagepointbywhichrealGDPrisesaboveitsnaturalrate,therealfederalfundsraterisesbythesameamount—0.5percent.Ifinsteadinflationfallsbelow2percentorGDPfallsbelowitsnaturalrate,thefederalfundsratefallsaccordingly.JohnTaylor’smonetaryrulemaybetherulethattheFedimplicitlyfollowsinsettingpolicy.

Figure15-1

AccordingtotheTaylorrule,ifinflationandoutputarelowenough,thenthenominalinterestrateshouldbenegative.Thissituationoccurredduringthefinancialcrisisof2008–2009.Butthecentralbankcannotsetanegativeinterestratebecausepeoplewouldsimplyholdmoney(whichpayszero)ratherthanlendatanegativeinterestrate.Thebestthatthecentralbankcandoiskeeptheinterestratenearzero,astheFeddidduringtherecoveryfromthecrisis.

By2011,theTaylorrulebeganrecommendinganincreaseinthefederalfundsrate.ButtheFedkepttherateclosetozero.SomeeconomistsbelievethiswasneededtomakeupfortheperiodoftimewhenanegativeinterestratewassuggestedbytheTaylorrule.OthereconomistshavearguedthatthenaturalrateofinteresthadfallenandsotheconstanttermintheTaylorrulewaslower.Stillothereconomists,however,believethattheFedhaswaitedtoolongtoraiseinterestratesaseconomicexpansiongainedspeed.Theseeconomistsareconcernedthatlowinterestratesmightfuelfutureinflation.

15-2 SolvingtheModel

Table15-1

Thefiveequationspresentedabovedeterminethepathsofthemodel’sfiveendogenousvariables(Table1):outputYt,therealinterestratert,inflationt,expectedinflationEt–1t,andthenominalinterestrateit.Beforeusingthemodeltoanalyzetheeconomy’sresponsetoeconomicshocks,wefirstdescribethemodel’slong-runequilibrium.

Table1 TheVariablesandParametersintheDynamicAD–ASModel

EndogenousVariables

t

Inflation

rt

Realinterestrate

it

Nominalinterestrate

Ett+1

Realinterestrate

ExogenousVariables

Yt

Naturallevelofoutput

t*

Centralbank’stargetforinflation

t

Shocktothedemandforgoodsandservices

t

ShocktothePhillipscurve(supplyshock)

PredeterminedVariable

t-1

Previousperiod’sinflation

Parameters

Theresponsivenessofthedemandforgoodsandservicestotherealinterestrate

Thenaturalrateofinterest

TheresponsivenessofinflationtooutputinthePhillipscurve

Theresponsivenessofthenominalinterestratetoinflationinthemonetary-policyrule

Y

Theresponsivenessofthenominalinterestratetooutputinthemonetary-policyrule

TheLong-RunEquilibrium

Long-runequilibriumforthemodelisthesituationinwhichtherearenoshocksandinflationisconstantovertime.Applyingthistothefiveequationsofthemodelgivesoutputandtherealinterestrateequaltotheirnaturalvalues,inflationandexpectedinflationequaltothetargetrateofinflation,andthenominalinterestrateequaltothenaturalrateofinterestplustargetinflation(Yt=,rt=,t=t*,Ett+1=t*,it=+t*).Thelong-runequilibriumreflectstheclassicaldichotomywherebyrealvariablesaredeterminedseparatelyfromnominalones,anditexhibitsmonetaryneutralitysothatmonetarypolicydoesnotinfluencerealvariables.

TheDynamicAggregateSupplyCurve

Toanalyzetheeconomyintheshortrun,weneedtoderivetwoequationsthataretheanaloguesoftheADandASequationsofChapter14.ThedynamicaggregatesupplyequationisthePhillipscurve,withlaggedinflationsubstitutedforexpectedinflation:

(DAS)

Figure15-2

Thisequationgivesrisetoanupward-slopingschedulecalledthedynamicaggregatesupplycurvewhenplottedwithinflationontheverticalaxisandoutputplottedonthehorizontalaxis(Figure1).ItsslopereflectsthePhillipscurvewherebyhighlevelsofeconomicactivitygiverisetohighinflation.Thecurveisdrawnforgivenvaluesoflaggedinflation,thenaturallevelofoutput,andthesupplyshock.Ifthesevariableschange,DASwillshift.

Figure1

TheDynamicAggregateDemandCurve

Toderivethedynamicaggregatedemandcurve,startwiththedemandforgoodsandservicesequationandsubstitutefortherealinterestrateusingtheFisherequation.Next,eliminatethenominalinterestratebyusingthemonetarypolicyequationandsubstituteforexpectedinflationusingtheequationforinflationexpectations.Finally,canceltermsandrearrangetheequationtoyield:

(DAD)

Figure15-3

Thisequationisrepresentedasadownward-slopingschedulecalledthedynamicaggregatedemandcurvewhenplottedwithinflationontheverticalaxisandoutputplottedonthehorizontalaxis(Figure2).Itsslopereflectstheresponseofthecentralbanktoinflation,wherebyanincreaseininflationleadstoanincreaseinthenominalinterestratebymorethantheriseininflation.Thismeansthattherealinterestratealsoincreases,therebyreducingthequantityofgoodsandservicesdemanded.Thecurveisdrawnforgivenvaluesofthenaturallevelofoutput,theinflationtarget,andthedemandshock.Ifthesevariableschange,DADwillshift.

Figure2

TheShort-RunEquilibrium

Theintersectionofthedynamicaggregatedemandcurveandthedynamicaggregatesupplycurvedeterminestheeconomy’sshort-runequilibrium.Thesetworelationshipsdeterminetwoendogenousvariables(inflationandoutputinperiodt),giventhefiveotherexogenous(orpredetermined)variables(Figure3).Thesearethenaturallevelofoutput,thetargetinflationrate,thedemandshock,thesupplyshock,andthepreviousperiod’sinflationrate.Theshort-runequilibriumlevelofoutputcanbelessthan,equalto,orgreaterthanitsnaturallevel.Inthelongrun,itwillequalitsnaturallevel.

Figure15-4

Notethattheshort-runequilibriumrateofinflationbecomesnextperiod’slaggedinflationrateandsowillinfluencethepositionofthedynamicaggregatesupplycurveinperiodt+1.Thislinkbetweenperiodsisresponsibleforthedynamicpatternsofadjustmentoftheeconomyinresponsetoshocksorchangesinpolicy.Inotherwords,expectationsofinflationinperiodt+1,whichdeterminethepositionofthedynamicaggregatesupplycurveinperiodt+1,dependontheoutcomeofinflationinperiodt,providingalinkbetweentimeperiods.Thiscontinuesintothefuture,withinflationinperiodt+1inturndeterminingexpectedinflationinperiodt+2,etc.

Figure3

15-3 UsingtheModel

Wecanusethemodeltoassesstheeffectsofchangeintheexogenousvariables.Tosimplifytheanalysis,weassumetheeconomyisinitiallyatitslong-runequilibrium.

Long-RunGrowth

Figure15-5

Supplement15-1,“HowaRealBusinessCycleModelIsConstructed”

Supplement15-2,“TheMicroeconomicsofLaborSupply”

Supplement15-3,“QuitsandLayoffs”

Supplement15-4,“InvoluntaryUnemploymentandOverqualification”

Supplement15-5,“WhyTechnologyShocksAreSoImportantinRealBusinessCycleModels”

Supplement15-6,“RealBusinessCyclesandRandomWalks”

AsdiscussedinChapters8and9,increasesovertimeinthenaturallevelofoutput,,mayoccurduetopopulationgrowth,capitalaccumulation,andtechnologicalprogress.BoththeDADandDAScurvesshifttotherightbyanamountequaltotheincreaseinthenaturallevelofoutput.Outputincreasesbythesameamountandinflationisunchanged(Figure4).

Figure4

AShocktoAggregateSupply

Figure15-6

Figure15-7

Supposethattheaggregatesupplyshockvariableυtincreasesto1percentforoneperiodoftimeandthenreturnstozero.TheDAScurvewillshiftupinperiodtbyexactlytheamountoftheshock.TheDADcurvewillremainunchanged.Inflationrisesandoutputfallsinperiodt.Theseeffectsreflectinparttheresponseofthecentralbankthroughitspolicyrulethatleadstohighernominalandrealinterestrates,whichinturnreducesdemandforgoodsandservicesandpushesoutputbelowitsnaturallevel.Loweroutputdampensinflationarypressure,soinflationdoesnotrisebythefullextentofthesupplyshock(Figure5).Inperiodsfollowingtheshock,expectedinflationishigher(sinceitdependsonthepreviousperiod’sinflation),sotheDAScurvedoesnotreturnimmediatelytoitsinitialposition.Instead,adjustmentoccursgraduallywithinflationdecliningandoutputrising,astheDAScurvegraduallyshiftstotheright.

Simulationanalysisthatusesrealisticparametervalues(seetheFYIbox“TheNumericalCalibrationandSimulation”)helpstoillustratetheadjustmentpath(Figure6)fortheeconomyovertimeinresponsetoasupplyshock,includingpathsforthenominalandrealinterestrates.Thesimulationanalysisshowsthephenomenonknownasstagflation.

Figure5

Figure6

FYI:TheNumericalCalibrationandSimulation

Thetextbookusessimulationanalysistoexploretheadjustmentoftheeconomytovariousshocksandchangesinpolicies.Eachperiodisbestthoughtofasoneyearinlength.Themodeliscalibratedusingnumericalvaluesfortheparametersofthemodelandsomeoftheexogenousvariables.ThesearetakentoapproximatetheactualU.S.economyandthepolicyruleJohnTaylorproposed,whichbroadlycapturesthebehavioroftheFed.Graphsofthetimepathsoftheendogenousvariablesafterashockareknownasimpulseresponsefunctions.

AShocktoAggregateDemand

Figure15-

Figure15-9

Supposethattheaggregatedemandshockvariableεtequalsoneforfiveperiodsandthenreturnstoitsnormalvalueofzero.Thispositiveshockmightreflectawarthatincreasesgovernmentpurchasesorastock-marketboomthatraiseswealthandconsumption.Moregenerally,ademandshockcouldrepresentanyeventthatchangesthedemandforgoodsandservicesatgivenvaluesofthenaturallevelofoutputandtherealinterestrate.Inperiodt,theDADcurvewillshifttotheright.TheDAScurveremainsunchangedinperiodt.Outputandinflationbothincrease.Asintheanalysisofthesupplyshock,theeffectsworkpartlythroughthecentralbank’spolicyrule.Inresponsetohigheroutputandinflation,thecentralbankraisesnominalandrealinterestrates,therebypartlydampeningtheexpansionaryeffectofthedemandshock(Figure7).

Figure7

Insubsequentperiods,expectedinflationishigher,andsotheDAScurveshiftsupwardcontinually,reducingoutputandincreasinginflation.Whenthedemandshockdisappearsinperiodt+5,theDAScurvereturnstoitsoriginalposition.ButtheDAScurveremainshigherthanitsoriginallevelsinceexpectedinflationremainsaboveitsoriginalvalue.Asaresult,thedeclineindemandpushesoutputbelowitsnaturallevel.Theeconomythengraduallyadjuststoitsoriginalpositionasinflationisslowlyreducedandoutputexpands.

Simulationanalysisthatusesrealisticparametervalueshelpstoillustratetheadjustmentpath(Figure8)fortheeconomyovertimeinresponsetoademandshock,includingpathsforthenominalandrealinterestrates.

Figure8

AShiftinMonetaryPolicy

Figure15-10Figure15-11

Supposethatthecentralbanklowersitstargetforinflationfrom2percentto1percentandkeepsitatthelowervaluefromthenon.ThiswillcausetheDADcurvetoshifttotheleft(and,tobeexact,downwardbyonepercentagepoint)(Figure9).Sincethetargetforinflationdoesnotenterthedynamicaggregatesupplyequation,theDAScurvedoesnotshiftinitially.Outputandinflationinitiallyfall.Onceagain,theresponseofmonetarypolicyisbehindthisoutcome:alowerinflationtargetimpliesthatactualinflationisnowabovetarget,sothecentralbankraisesrealandnominalinterestrates.Thehigherrealinterestratereducesthedemandforgoodsandservices,therebyloweringoutputbelowitsnaturallevelandloweringinflationalongtheinitialDAScurve.Withinflationlower,expectedinflationfallsaswell,causingtheDAScurvetoshiftdownward.Overtime,theprocesscontinues,withoutputrisingandinflationfallinguntiltheeconomyreacheslong-runequilibrium,withoutputatitsnaturallevelandinflationatthenewtargetrateof1percent.

Figure9

Simulationanalysisthatusesrealisticparametervalueshelpstoillustratetheadjustmentpath(Figure10)fortheeconomyovertimeinresponsetoareductionintargetinflation.

Figure10

Supplement15-7,“InflationInertia”

Theeconomy’sadjustmenttothischangeinmonetarypolicyassumesthatexpectationsareformedadaptively.Butifthecentralbank’sannouncementofthechangeinitstargetinflationrateiscredible,thenpeoplemaylowertheirexpectationaboutinflationimmediately.Inthiscase,whereexpectationsareformedrationallybasedonallavailableinformation,theDAScurvewillshiftdownwardbythesameamountandatthesametimethatthepolicychangeshiftstheDADcurve,andtheeconomywillinstantlyreachitsnewlong-runequilibrium.

15-4 TwoApplications:LessonsforMonetaryPolicy

Themodeldevelopedintheprevioussectionscanbeusedtomotivateadiscussionaboutthedesignofmonetarypolicy.Inparticular,wecanconsiderhowthevaluesoftheparametersofthemonetarypolicyruleinfluencetheeffectivenessofmonetarypolicy.

TheTradeoffBetweenOutputVariabilityandInflationVariability

Figure15-12

Considertheeffectofasupplyshockontheeconomy.Asshownearlier,theinitialresponseisforoutputtofallbelowitsnaturallevelandinflationtoriseabovethecentralbank’starget.ButtheextenttowhichoutputdeclinesorinflationrisesdependsontheslopeoftheDADcurve.Whentheslopeissteep,inflationrisesrelativelymoreandoutputdeclinesrelativelyless,whereaswhentheslopeisflat,inflationrisesrelativelylessandoutputdeclinesrelativelymore(Figure11).

Figure11

BecausetheslopeoftheDADcurvedependsontheparametersofthemonetarypolicyrule,thecentralbankcanaffecttheslopebychoosingwhethertorespondmoreorlessstronglytodeviationsfromtargetinflationorthenaturallevelofoutput.Inparticular,whenislargecomparedto,theDADcurveisrelativelyflat,andthecentralbankrespondsstronglytodeviationsfromitsinflationtargetbyraisinginterestratesalottokeepinflationcontained;anditrespondsonlyweaklytodeviationsofoutputfromthenaturallevel.Inthiscase,asupplyshockhasarelativelysmalleffectoninflationandarelativelylargeeffectonoutput.Alternatively,whenthecentralbankrespondsweaklytodeviationsfromitsinflationtargetandstronglytodeviationsofoutputfromitsnaturallevel,theDADcurveisrelativelysteep,andasupplyshockhasarelativelylargeeffectoninflationandarelativelysmalleffectonoutput.Thecentralbankthusfacesatradeoffbetweenthevariabilityofoutputandthevariabilityofinflation.

Supplement15-8,“VolatilityandGrowth”

Asdiscussedearlier,thecentralbankdoesnotfaceatradeoffbetweenthelevelofoutputandtherateofinflationinthelongrun—sincetheclassicaldichotomyholds.Butitdoesfaceatradeoffbetweenthevariabilityofoutputandthevariabilityofinflation.

CaseStudy:DifferentMandates,DifferentRealities:

TheFedVersustheECB

ThelegislationthatcreatedtheFederalReservegaveitthedualmandateofstabilizingbothemploymentandprices,whereastheEuropeanCentralBank(ECB)ischargedwiththeprimaryobjectiveofmaintainingpricestability,definedasinflationcloseto2percentoverthemediumterm.Thesedifferencesinmandatescanbeinterpretedinourmodelasbeingreflectedindifferentparametersinthemonetarypolicyrule.FortheECBcomparedtotheFed,moreweightisgiventoinflationstabilityandlesstooutputstability.Theeventsof2008,whenoilpricesrosesharplyandtheworldeconomyheadedintorecession,supportthisinterpretation:theFedloweredinterestratesfrom5percenttoarangeof0to0.25percent,whiletheECBcutinterestratesbymuchless.In2011,astheglobaleconomyrecovered,theECBbegantoraiseinterestrateswhiletheFedkeptthemclosetozero.Apparently,theECBwaslessconcernedaboutrecessionandmoreconcernedaboutkeepinginflationcontained,whereastheFedwasmoreconcernedaboutlimitingtherecession.Overtime,onemightexpecttheECB’smonetarypolicytoresultinmorevariableoutputandmorestableinflationinEuropecomparedtotheUnitedStates.Assessingthispredictionisdifficult,however,becausetheECBhasonlybeeninexistencesince1998—notlongenoughtohavesufficientdatatodeterminethelong-termresultsofitspolicy.Also,EuropeandtheUnitedStatesdifferinotherwaysbesidesthepolicymandatesoftheircentralbanks,andthesemayinfluenceoutputandinflationindependentlyfrommonetarypolicy.Oneexampleisthatin2010severalEuropeannations,mostprominentlyGreece,almostdefaultedontheirgovernmentdebt.Thiscrisisintheeurozoneloweredconfidenceandaggregatedemandaroundtheworld,buttheeffectsweremoresevereinEuropethanintheUnitedStates.

TheTaylorPrinciple

Figure15-13

Supposethatthecentralbankrespondedtoariseininflationaboveitstargetbycuttingtherealinterestrate.Fromthemonetarypolicyequation,thiswouldimplythattheparameterislessthanzero:

Inotherwords,thecentralbankwouldincreasethenominalinterestratebylessthantheriseininflation.ThispolicyresponsewillproduceapositivelyslopedDADcurve.Nowconsideraone-perioddemandshock.ThiswillshifttheDADcurvetotherightandinitiallyleadtoariseininflationandanincreaseinoutput.Higherinflationwillleadtoanincreaseinexpectedinflationfornextperiod,whichwillshifttheDAScurveupward.ButwithapositivelyslopedDADcurve,outputrisesfurtherandremainsaboveitsnaturallevelbecausethecentralbanklowerstherealin