New Classical Models of Aggregate Fluctua5ons · New Classical Models of Aggregate Fluctua5ons The Stochas5c Growth Model and a New Classical Model without Capital. Prof George Alogoskouﬁs,

Prof George Alogoskoufis, Dynamic Macroeconomic Theory, 2015

NewClassicalModelsofAggregateFluctua5ons

TheStochas5cGrowthModelandaNewClassicalModelwithoutCapital


AggregateFluctua5ons• Economiesarecharacterizedbyfluctua5onsinrela5ontotheirlong-termtrends.In

someperiodsoutput,consump5onandemploymentgrowathighrates,whileatother5mestheygrowatloworevennega5verates.Insomeperiodsunemploymentislowandinothersquitehigh.Infla5ondisplayssignificantfluctua5onsaswell.

• Understandingthedeterminantsofaggregatefluctua5onsisthesecondmainobjec5veofmacroeconomics.Inthis,andthelecturesthatfollow,wepresentthemaintheoriesregardingthenatureofaggregatefluctua5ons.

• Inthislecturewestartbyintroducingclassicalmodelsofaggregatefluctua5ons.“New”classicalmodelsareessen5allydynamicstochas3cgeneralequilibriummodels(DSGE),basedonop5mizinghouseholdsandfirms,flexiblewagesandpricesandfullycompe55vemarkets.Fluctua5onsinthesemodelsarecausedbyrealshockstoproduc5vity,householdpreferencesandgovernmentexpenditure,andtheeffectsoftheseshocksarepropagatedthroughendogenousdynamicprocesses,suchasconsump5onandinvestment.

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ΑΕΠ"κατά"κεφαλήν"ΗΠΑ"(σταθερές"τιμές)"

PerCapitaGDPintheUSA(logscale)

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GrowthRateofPerCapitaGDPintheUSA

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Infla5onRateintheUSA

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TheNatureandKeyCharacteris5csofAggregateFluctua5ons

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• Aggregatefluctua5onsarenotcharacterizedbysomesimplerepe55veregularityandseemtobecharacterizedbyrandomness.

• Theprevailingviewtoday,whichdatesbacktoFrisch(1930)andSlutsky(1937),isthateconomiesaresubjecttovariouskindsofrandomdisturbances,which,throughtheopera5onofeconomictransmissionmechanismssuchastheopera5onofmarkets,affectoutput,employment,realwages,realinterestrates,thepricelevelandinfla5on,andsetinmo5ondynamicstochas5cadjustmentprocesses.

• Thedynamicstochas5capproachtoaggregatefluctua5onsowesalottothecontribu5onsofLucas(1977)andKydlandandPresco[(1982).


Lucas(1977)ontheNatureofAggregateFluctua5ons

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“Technically,movementsabouttrendingrossna5onalproductinanycountrycanbewelldescribedbyastochas5callydisturbeddifferenceequa5onofveryloworder.Thesemovementsdonotexhibituniformityofeitherperiodoramplitude,whichistosay,theydonotresemblethedeterminis5cwavemo5onswhichsome5mesariseinthenaturalsciences.Thoseregulari5eswhichareobservedareintheco-movementsamongdifferentaggrega5ve5meseries…Oneisledbythefactstoconcludethat,withrespecttothequalita5vebehaviorofco-movementsamongseries,businesscyclesareallalike.Totheore5callyinclinedeconomists,thisconclusionshouldbea[rac5veandchallenging,foritsuggeststhepossibilityofaunifiedexplana5onofbusinesscycles,groundedinthegenerallawsgoverningmarketeconomies,ratherthaninpoli5calorins5tu5onalcharacteris5csspecifictopar5cularcountriesorperiods.”(p.9-10).


TheStochas5cGrowthModel:AnExtensionoftheRamseyModel

• Westartwiththesocalledstochas3cgrowthmodel,whichisanextendedstochas5cversionoftheRamseymodel.

• Thisisacompe55vedynamicstochas5cgeneralequilibriummodel,withoutexternali5es,asymmetricinforma5on,fric5onsandotherimperfec5onsofmarkets.Thereforeitisanaturalstar5ngpointfortheinves5ga5onofaggregatefluctua5ons.

• Thismodelisnothingbutageneraliza5onoftheRamseymodel.Itnotonlyexcludesanymarketimperfec5ons,butalsoallissuesrelatedtoheterogeneityofeconomicagents.TheRamseymodelisthereforethenaturalstar5ngpointforthestudyofaggregatefluctua5ons,likeitisthe“natural”star5ngpointforthestudyofthelongrungrowth.

• However,inordertostudyaggregatefluctua5ons,oneneedstoextendtheRamseymodel.

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ExtensionsoftheRamseyModel

• First,oneshouldallowforrandomdisturbances,whichcancausefluctua5ons.Withoutrandomdisturbances,theRamseymodelconvergestoauniquesteadystate.ThedisturbancesusuallyintroducedintheRamseymodelaredisturbancesintotalfactorproduc5vity(technologyshocks),aswellasrealdemandshocks,suchasshockstothepreferencesofconsumersorrealgovernmentexpenditure.Sincebothkindsofshocksarereal-unlikemonetaryornominalshocks-thismodelturnsouttobearealbusinesscyclemodel.

• Second,inordertoallowthemodeltoexplainfluctua5onsnotonlyintotaloutput,butalsoemployment,employmentmustbecomeendogenous.Thisisachievedthroughtheintroduc5onofemploymentintheu5lityfunc5onofarepresenta5vehousehold,inordertoestablishanendogenouslaborsupplyfunc3on.

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HouseholdsandFirmsintheStochas5cGrowthModel

• Thereareanumberofiden5calhouseholdsandfirms,sothisisacompe55verepresenta5vehouseholdmodel.

• Firmsuselaborandcapitalinorderproduceahomogeneousproduct.Theychooseinvestmentandemploymentinordertomaximizetheirprofits.

• Householdschooseconsump5onandlaborsupplyinordertomaximizetheirinter-temporalu5lity.

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Firms,Produc5onandInvestment

Yt = Ktα (AtLt )

1−α

Yt = Ct +Gt + Kt+1 − Kt +δKt

Kt+1 = Kt +Yt −Ct −Gt −δKt

Produc5onFunc5on

Consump5on,InvestmentandGovernmentExpenditure

CapitalAccumula5onEqua5on

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Maximiza5onofProfitsofFirms

wt = (1−α )Kt

AtLt

⎛⎝⎜

⎞⎠⎟

α

At

rt =αAtLtKt

⎛⎝⎜

⎞⎠⎟

1−α

−δ

TheDetermina5onofRealWages

TheDetermina5onoftheRealInterestRate

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TheRepresenta5veHousehold

U = E01

1+ ρ⎛⎝⎜

⎞⎠⎟

t

u(ct ,1− lt )Nt

Ht=0

∞∑

ut = lnct + b ln(1− lt )

Therepresenta5vehouseholdmaximizesitsexpectedinter-temporalu5lityfunc5on,whichdependsonthepathofrealconsump5onofgoodsandservicesandleisure.Theu5lityfunc5onisdefinedby,

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Popula5on,EfficiencyofLaborandGovernmentExpenditure

lnNt = N_+ nt

Popula5onincreasesexogenouslyataratenperperiod

lnAt = A_+ gt + vt

A vtA =ηAvt−1

A + ε tA

TheEfficiencyofLaborGrowsananexogenousrategandissubjectedtoAR(1)stochas5cdisturbances

GovernmentExpenditureGrowsatanexogenousrateg+nandissubjectedtoAR(1)stochas5cdisturbances

lnGt = G_+ (n + g)t + vt

G vtG =ηGvt−1

G + ε tG

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LaborSupplyoftheRepresenta5veHousehold:TheOnePeriodCase

u = lnc + b ln(1− l)

ThefirstdifferenceofthismodelfromtheRamseymodelarisesfromtheintroduc5onofleisure5meintheu5lityfunc5onofthehousehold,whichmakeslaborsupplyendogenous.Toanalyzetheimportanceofthisaddi5on,letusfirstconsiderthesta5onaryproblemofahouseholdlivingforasingle5meperiodandhasnoassets.Theproblemofthathouseholdisdefinedasthemaximiza5onof,

undertheconstraint

c = wl

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Fromthefirstordercondi5onsforanop5mum,

Itfollowsthat,

1c− λ = 0 − b

1− l+ λw = 0 c = wl

− b1− l

+ 1l= 0

Laborsupplyisindependentoftherealwage.Thisisbecauseoftheassump5onoflogarithmicpreferences,implyingthattheelas5cityofsubs5tu5onbetweenconsump5onandleisureisequaltounity.Thus,thesubs5tu5oneffectfromachangeintherealwageiscounteractedbytheincomeeffect.However,thisdoesnotmeanthattemporarychangesinrealwagesdonotaffectlaborsupply.Thiscanbeseenifwelookatthebehaviorofahouseholdlivingfortwoperiods.

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LaborSupplyoftheRepresenta5veHousehold:TheOnePeriodCase

Prof George Alogoskoufis, Dynamic Macroeconomic Theory, 2015 18

lnc1 + b ln(1− l)1 +1

1+ ρlnc2 + b ln(1− l)2( )

c1 +11+ r

c2 = w1l1 +11+ r

w2l2

Weshallnowanalyzethebehaviorofahouseholdlivingfortwoperiods,hasnoini5alwealth,andnouncertaintyabouttherealinterestrateortherealwageofthesecondperiod.

LaborSupplyoftheRepresenta5veHousehold:TheTwoPeriodCase


b1− l1

= λw1

Fromthefirstordercondi5onsforlaborsupply:

b1− l2

= 1+ ρ1+ r

λw2

Rela5velaborsupplyinthetwoperiodsdependsposi5velyontherela5verealwageinthetwoperiods,aswellastherealinterestrate.

1− l11− l2

= 1+ ρ1+ r

w2w1

Inter-temporalSubs5tu5oninLaborSupply

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Implica5onsofInter-temporalSubs5tu5onforLaborSupply

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• Thehighertherealwageofthefirstperiodinrela5ontotherealwageofthesecondperiod,thehigherthelaborsupplyofthefirstperiod,inrela5ontothatofthesecond.Thehouseholdsubs5tuteslaborbetweenperiods,dependingonrela5verealwagesbetweenperiods.Becauseoflogarithmicpreferences,theinter-temporalsubs5tu5onelas5cityisequaltoone.

• Moreover,thehighertherealinterestraterthegreaterthelaborsupplyofthefirstperiodcomparedtothesecondperiod.Theincreaseintheinterestrateincreasesthea[rac5venesstoworktodayandsave,comparedtoworkinginthefuture.Ithastheoppositeeffectofthepurerateof5mepreferencerateρ.

• Theseeffectsofrela5vewagesover5meandtherealinterestrateonlaborsupplyareknownasinter-temporalsubs3tu3oninlaborsupply.

• Consequently,fluctua5onsinrealwagesandtherealinterestratecancausefluctua5onsinemployment,althoughpermanentchangesinrealwagescannot.


UncertaintyandtheEulerEqua5onforConsump5on

1ct

= 11+ ρ

Et1ct+1

1+ rt+1( )⎡

⎣⎢

⎤

⎦⎥

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• Thesecondelementthatdifferen5atesthestochas5cgrowthmodelfromtheRamseymodelisuncertaintyarisingfromthestochas5cdisturbances.Therefore,theexpecta3onsoftherepresenta5vehouseholdforfuturedevelopmentsplayasignificantrole.

• Itcanbeshownthat,forthegeneralcasewhenthehouseholdmaximizestheexpectedinter-temporalu5lityfunc5on,theEulerequa5onforconsump5ontakestheform,


UncertaintyandtheBehavioroftheRepresenta5veHousehold

1ct

= 11+ ρ

Et1ct+1

⎡

⎣⎢

⎤

⎦⎥

⎧⎨⎩⎪

Et 1+ rt+1( )+Cov 1ct+1, 1+ rt+1( )⎛

⎝⎜⎞⎠⎟⎫⎬⎭⎪

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Themathema5calexpecta5onoftheproductoftworandomvariablesisnotequaltotheproductofmathema5calexpecta5ons.Itisequaltotheproductofmathema5calexpecta5onsplusthecovarianceoftworandomvariables.


ct1− lt

= wt

b

Thisconditionlinkslaborsupply(leisure)andconsumptionwiththerealwage.Itincludesonlycurrentvariables,asthereisnouncertaintyinthecurrentperiod.

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Fromthefirst-ordercondi5onsforconsump5onandlaborsupply,thera5oofconsump5ontoleisureisposi5vefunc5onoftherealwageoftheform,

TheFirstOrderCondi5onsforConsump5onandLaborSupply


Kt+1 = Yt −Ct 1+ rt =αAtLtKt

⎛⎝⎜

⎞⎠⎟

1−α

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• Thismodelisnoteasytosolveanaly5cally,asitcontainsfactorsthatarelinear,andfactorsthatarelog-linearinitsvariables.Theproper5esofthemodelcanbedescribedifwesimplifyitfurther,orifweusealog-linearapproxima5onaroundthebalancedgrowthpath,andsolveitnumericallyforspecificvaluesoftheparameters.

• InaspecialAnnex,wepresenttheCampbell(1994)log-linearapproxima5onofthefullmodel,arounditsbalancedgrowthpath.Thisallowsustodescribethefullproper5esofthemodel.

• Intheremainderweshallconcentrateontheproper5esofasimplifiedversionofthemodel,withoutgovernmentexpenditureandadeprecia5onrateof100%..

ASpecialCaseoftheModel


ct = (1− st )Yt / Nt 1+ rt+1 = aYt+1 /Kt+1

Kt+1 = stYt

s^= α (1+ n)1+ ρ

l^= 1−α

(1−α )+ b(1− s^)

Itfollowsthatthesavingsrateandlaborsupplyareconstantinthisspecialcase,becauseoflogarithmicpreferencesandtheCobbDouglasproductionfunction.

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TheSpecialCaseoftheStochas5cGrowthModel


Laborsupplyisconstantbecausetheimpactoftheshocksintechnology(laborefficiency)ontherealwageandtherealinterestratecanceleachotherout,sothereisnointer-temporalsubs5tu5on.Thisisduetothespecificassump5onthatwemadeinordertosimplifythemodel,andasonecanseefromtheanalysisofthefullmodelintheAnnexisnotageneralfeatureofthemodel.

TheConstancyofLaborSupply


Fluctua5onsinRealOutput

lnYt =α lnKt + (1−α )(lnAt + lnLt )

Kt = s^Yt−1

Fromtheproductionfunction,

Giventhat, Lt = l^Nt

lnYt =α ln s^+α lnYt−1 + (1−α )(lnAt + ln l

^+ lnNt )


lnYt =α ln s^+α lnYt−1 + (1−α ) (A

_+ gt)+ vt

A + (ln l^+ N

_+ nt)⎡

⎣⎢⎤⎦⎥

SubstitutingforAandN,

Expressingrealoutputaslogarithmicdeviationsfromitslongruntrend,

Y~t = (α +ηA )Y

~t−1−αηAY

~t−2+ (1−α )ε t

A

Y~t =αY

~t−1+ (1−α )vt

A

whichcanbesolvedas,

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Fluctua5onsinRealOutput


Y~t =αY

~t−1+ (1−α )ε t

A

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• Thepercentage(logarithmic)devia5onsoftotalrealoutputfromtrendfollowasecondorderautoregressiveprocess(AR(2)).

• Becauseαislow(about1/3),thedynamicbehavioroftotalrealoutputdependsprimarilyonthedegreeofpersistenceofproduc5vityshocks.Ifthepersistenceofproduc5vityshocksηAishigh,thenwehaveconsiderablepersistenceinthefluctua5onsofoutput.Otherwise,thepersistenceofoutputfluctua5onsaroundtrendislow.

• Ifrealshocksdisplaynopersistence(i.eifηA=0),then,

ConclusionsfromtheSpecialCaseoftheModel


EconometricEs5matesforthelogofUSGDP1890-2014

lnYt=0,270+1,211lnYt-1-0,319lnYt-2+0,0036t(0,083)(0,086)(0,087)(0,0012)

R2=0,999,DW=2.020,T=125

Fromthesees5matesitfollowsthatα=0,386(s.e.0.132)andηΑ=0,824(s.e.0.082).Italsofollowsthatg+n=0,033(s.e.0.001).


• Thesimplifiedformofthemodel,containsmanyofitsessen5alelements,andprovidesthebasic“newclassical”accountoffluctua5onsintotaloutput(GDP)aroundtrend,mainlyonthebasisofpersistentproduc5vityshocksandcapitalaccumula5on.

• However,manyotherfeaturesofaggregatefluctua5onsarenotadequatelydescribedbythissimplifiedversionofthestochas5cgrowthmodel.

• Theconstantsavingsra3o.Thismeansthatconsump5onwilldisplaythesamedegreeofvariabilityasoutputandinvestment,whichdoesnottendtohappeninreality.

• Theconstantemploymentrate.Inreality,theemploymentrateisnotconstantoverthebusinesscycle.Employmentispro-cyclical,movinginthesamedirec5onasoutput.

• RealWagesovertheBusinessCycle.Inthesimplifiedstochas5cgrowthmodelrealwagesarepro-cyclicalandequallyvola5leasGDPpercapita,whichisnotalwaysthecase.

WeaknessesoftheSimplifiedDynamicGrowthModel


• Whenoneexaminesthemoregeneralformofthemodel,assumingalowdeprecia5onrate,aswedointheAnnextothislecture,manyoftheseweaknessesarecorrected,assavings,investmentandemploymentalsodisplayfluctua5onsinresponsetoproduc5vityshocks.

• Forexample,inthefullstochas5cgrowthmodel,analyzedintheAnnex,thesavingsrateisnotconstant,andconsump5ontendstobelessvariablethaninvestmentandoutput.Inaddi5on,inthefullstochas5cgrowthmodel,theemploymentrateispro-cyclical,andmovesinthesamewayasoutput.Moreover,theintroduc5onofpublicexpenditureshocksorpreferenceshockscouldrelaxthestrictdependenceoffluctua5onsinrealwagesonfluctua5onsinaggregateproduc5vity.

TheMoreGeneralVersionoftheStochas5cGrowthModel


TheImpactofaProduc5vityShockintheFullStochas5cGrowthModel


• Weshallnextfocusonananaly5callysimplerversionofthe“newclassical”modelofaggregatefluctua5ons,inwhichtheonlyvariablefactorofproduc5onislabor.Weshallthusabstractfromcapitalaccumula5on.

• Inthisanaly5callysimplermodelweallowforamoregeneralapproachtothepreferencesoftherepresenta5vehousehold,andalsodis5nguishbetweennominalandrealvariables.

• Thisallowsustoconsiderthedetermina5onofthelevelofpricesandwages,infla5onandnominalinterestrates,andtheroleofmonetaryfactorsinclassicalmodels.

ANewClassicalModelwithoutCapital


Therepresenta5vehouseholdisassumedtomaximize,

TheRepresenta5veHousehold

Et1

1+ ρ⎛⎝⎜

⎞⎠⎟

s

u(Ct+s ,Lt+s )s=0

∞∑

Subjectto,

PtCt +11+ it

Bt ≤ Bt−1 +WtLt −Tt limT→∞

EtBT ≥ 0


Weassumethattheperperiodu5lityfunc5onisgivenby,

FirstOrderCondi5onsfortheRepresenta5veHousehold

U(Ct ,Lt ) =C

t

1−θ

1−θ− Lt

1+λ

1+ λ

Thefirstordercondi5onsinthiscasetaketheform,

Wt

Pt= Ct

θLtλ 1

1+ it= 11+ ρ

EtCt+1

Ct

⎛⎝⎜

⎞⎠⎟

−θPtPt+1

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪


Therepresenta5vefirmiscompe55ve,andchoosesemploymentinordertomaximizeprofits,forgivennominalwagesandprices.Profitsaremaximizedsubjecttoaproduc5onfunc5onwithlaborastheonlyvariablefactorofproduc5on.

TheRepresenta5veFirm

PtYt −WtLt = Pt (AtLt1−α )−WtLt

Profitmaximiza5onimpliesthatemploymentwillbedeterminedsoastoequatethemarginalproductoflabortotherealwage.Thus,

Wt

Pt= (1−α )AtLt

−α


TheModelinLogLinearForm

wt − pt = θct + λlt ct = Et (ct+1)−1θit − Et (π t+1)− ρ( )

wt − pt = at −αlt + ln(1−α )

yt = at + (1−α )lt

FirstOrderCondi5onsfortheHousehold

FirstOrderCondi5onfortheFirm

Produc5onFunc5onandProductMarketEquilibrium

ct = yt


ImposingEquilibriumintheLaborandProductMarkets,itfollowsthatalltherealvariablesdependonthestochas5cprocessdrivingtotalfactorproduc5vity.

Solu5onoftheModel

lt =ηLAat + l_

yt = ct =ηYAat + y_

wt − pt =ηWAat +ω_

rt = it − Et (π t+1) = ρ +θηYAEt (Δat+1)


Theparametersdefiningtheeffectsoftotalfactorproduc5vityare,

ParametersoftheSolu5on

ηLA =1−θ

θ(1−α )+α + λ

ηYA = 1+ (1−α )ηLA =1+ λ

θ(1−α )+α + λ

ηWA = 1−αηLA =θ + λ

θ(1−α )+α + λ


• Output,consump5onandrealwagesareposi5vefunc5onsofproduc5vity,whileemploymentisaposi5vefunc5onofproduc5vityonlyifθ<1,i.e.iftheinter-temporalelas5cityofsubs5tu5onofconsump5onisgreaterthanone.

• Ifθ>1,employmentisanega5vefunc5onofproduc5vity,whileifθ=1,employmentisindependentofproduc5vity.Thisisbecauseifθ<1thesubs5tu5oneffectdominatesovertheincomeeffect,aperachangeinproduc5vityandrealwages,andemploymentrises.Ifθ>1theincomeeffectdominatesoverthesubs5tu5oneffect,whileinthecaseθ=1thetwoeffectscanceleachotherout,andemploymentisnotaffected.

• Onlyrealfactors,suchasrealproduc5vity,affectfluctua5onsinrealvariables.Asinthestochas5cgrowthmodel,monetaryfactorssuchasmoneysupplyandnominalinterestrateshavenoimpactontheevolu5onofrealvariables.

Proper5esoftheSolu5on


Inordertoexaminetheimpactofmonetaryfactorsinthe“new”classicalmodel,weshallassumetheexistenceofamoneydemandfunc5onbyhouseholdsandfirms,which,inlogarithms,takestheform,

MonetaryFactorsintheNewClassicalModel

mt − pt = yt −ηit

whereηisthesemi-elas5cityofmoneydemandwithrespecttothenominalinterestrate,whichisdefined,bytheFisherequa5on,as,

it = rt + Et (π t+1)

Realvariables,suchasyandraredeterminedwithoutreferencetomonetaryfactors,asfunc5onsofshockstototalfactorproduc5vity.


Ifthecentralbankdeterminesanexogenouspathforthemoneysupply,then,fromthemoneymarketequilibriumcondi5onandtheFisherequa5on,itfollowsthat,

AnExogenousPathfortheMoneySupply

pt =η1+η

Et (pt+1)+1

1+ηmt −

11+η

yt −ηrt( )

Undertheassump5onthatη>0,thesolu5onofthispriceequa5onis,

pt =1

1+ηη1+η

⎛⎝⎜

⎞⎠⎟j=0

∞∑j

Et mt+ j − yt+ j +ηrt+ j( )


Ifweassumethatthecentralbankfollowsanexogenouspathforthenominalinterestrate,fromtheFisherequa5on,iffollowsthat,

AnExogenousPathfortheNominalInterestRate

Et (π t+1) = it − rtWithanexogenouspathforthenominalandtherealinterestrate,thisdoesnotdetermineinfla5on,butexpectedinfla5on,andisconsistentwithanypricelevelthatsa5sfies,

pt+1 = pt + it − rt + ξt+1 Et ξt+1( ) = 0foranyξforwhich

Thissuggeststhattherearemul5pleequilibriaforthepricelevelandinfla5on,dependingonξ.Thus,inthiscasewehavepricelevelandinfla5onindeterminacy.


• Centralbankspredominantlyusethenominalinterestrateastheirpreferredmonetaryinstrument.

• Ifsuchpoliciescausedindeterminacyofthepricelevelandinfla5on,i.epricebubbles,thiswouldhavebeenextremelyworrying.

• However,CentralBanksdonotfollowexogenousnominalinterestratepath,butpoliciesaccordingtowhichthepathofnominalinterestratesdependsonpast,currentandexpectedeconomicdevelopments,mainlyinfla5on.Forexample,ifinfla5onrises,centralbanksusuallyraisenominalinterestratesinordertoreduceit,andviceversa.ThiswasaperalltheessenceoftheWicksellrule.Whataretheimplica5onsofsuchpoliciesinthe“newclassical”model?

CentralBanksandInterestRateRules


Letusassumethefollowingrulefordeterminingnominalinterestrates:

AnInfla5onBasedInterestRateRule

it = ρ +φπ t

whereφ>0isthereac5onofthecentralbanknominalinterestratetoinfla5on.FromthispolicyruleandtheFisherequa5onitfollowsthat,

π t =1φEt π t+1( )+ 1

φrt − ρ( )

Undertheassump5onthatφ>1(Taylorprinciple),thiscanbesolvedas,

π t =1φ

⎛⎝⎜

⎞⎠⎟s=0

∞∑s+1

Et rt+s − ρ( )


• Ifthecentralbankdeterminesanexogenouspathforthemoneysupply,thepricelevelandinfla5onaredeterminedasfunc5onsoftheexogenouspathofthemoneysupply,andthepathsofrealoutputandtherealinterestrate,whichareindependentofmonetaryfactorsinthe“new”classicalmodel.

• Ifthecentralbankfollowsanexogenouspathforthenominalinterestrate,theresultisindeterminacyofthepricelevelandinfla5on.

• Ifthecentralbanknominalinterestratesreacttoinfla5on,andthereac5onissufficientlypronounced(φ>1),thenthereisnoindeterminacyproblemforinfla5on.Ifthereac5onofthenominalinterestratestoinfla5onisnotsufficientlypronounced(φ≦1),thentheproblemofindeterminacyofinfla5onremains.

• Inanycase,inthe“new”classicalmodelofaggregatefluctua5onsonlyrealfactorsaffectfluctua5onsinrealvariables.Monetaryfactorsandmonetarypolicyonlyaffecttherealmoneybalances,andnominalvariablessuchasthepricelevelandinfla5on,nominalinterestratesandthemoneystock.

MonetaryFactorsandMonetaryPolicyintheNewClassicalModel

Documents

New Classical Models of Aggregate Fluctua5ons · New Classical Models of Aggregate Fluctua5ons The Stochas5c Growth Model and a New Classical Model without Capital. Prof George Alogoskouﬁs,