macro lect 15 new keynesian model wage contracts · prof george alogoskoufis, dynamic macroeconomic...
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ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015
Labor Market “Insiders”, Nominal Wage Contracts and
Unemployment
A New Keynesian Model with Periodic Wage Contracts
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 2
• Sincethe1970s,themacroeconomicsofaggregatefluctua?onshasbeenemphasizingthemicroeconomicfounda?onsofallbehavioralrela?ons,andinpar?culartheconsump?onandinvestmentfunc?onsandtheshort-termdetermina?onofwages,pricesandtheequilibriumunemploymentrate.
• Inaddi?on,the“ra?onalexpecta?ons”hypothesis,whichrequiresthathouseholdsandfirmsformtheirexpecta?onsaboutfuturevariables,takingintoaccounttheactualprocessdeterminingtheevolu?onofthesevariables,hasbecomethedominantexpecta?onshypothesis.Thehypothesisofadap?veexpecta?ons,wasgraduallyabandoned.
• Thus,macroeconomicmodelsofaggregatefluctua?onsgraduallyevolvedintodynamicstochas3cgeneralequilibriummodelsbasedonra?onalexpecta?ons.
DynamicStochas?cGeneralEquilibriumModels
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 3
• The“newclassical”modelisadynamicstochas?cgeneralequilibriummodel,inwhichwagesandpricesareperfectlyflexibleandequilibrateboththeproductandlabormarkets.
• In“newclassical”models,onlyrealshocks,suchasshockstoproduc?vity,canaffectthefluctua?onsofoutput,employmentandotherrealvariables.
• Monetaryshocksonlyaffectnominalvariables,suchasthepricelevelandinfla?onbutnorealvariables.
• Inaddi?on,employmentfluctua?onsarebasedonlabormarketequilibriumandintertemporalsubs?tu?oninlaborsupply,and,thus,thereisnoinvoluntaryunemploymentinthe“newclassical”model.
Weaknessesofthe“New”ClassicalModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 4
• Theshortrunneutralityofmoneyimpliedby“newclassical”modelswasini?allytroublesomefortheirproponents,asthesemodelswerenotcompa?blewiththeexistenceofaposi?veshortrunrela?onbetweeninfla?onandemployment,assuggestedbytheexpecta?onsaugmentedPhillipscurve.
• Lucas(1972,1973),developeda“newclassicalmodel”whichwasconsistentwithaposi?veshortrunrela?onbetweeninfla?onandemployment.Thismodelwasbasedontheassump?onthatfirmsdidnothavefullinforma?onaboutthepricelevelatthe?metheymadetheirproduc?ondecisions,andtheya[ributedpartofanychangeinthepriceleveltoachangeintherela?vepriceoftheirproduct.Thus,wheninfla?onwasunexpectedlyhigh,allproducersthoughttherela?vepriceoftheiroutputhadgoneup,andthusincreasedproduc?onandemployment.Theoppositehappenedwheninfla?onwasunexpectedlylow.
• However,this“newclassical”explana?onoftheshortrunrela?onbetweeninfla?onandoutputandemploymentwass?llincompa?blewithinvoluntaryunemployment,andcouldonlyaccountfortemporarydevia?onsofoutputandemploymentfromtheir“naturallevels”duetointer-temporalsubs?tu?oninlaborsupplyandunan?cipatedinfla?on.
RealEffectsofMoneyinthe“New”ClassicalModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 5
• Analterna?veapproach,duetoGray(1976),Fischer(1977)andTaylor(1979),emphasizedperiodicnominalwagecontracts.
• ThisapproachdescendeddirectlyfromtheGeneralTheory,trea?ngnominalwagesastemporarilyfixed.
• IntheGray-Fischermodel,nominalwagecontractsareassumedtobenego?atedatthebeginningofeveryperiod,oratthebeginningofalternateperiods.Inaddi?on,nominalwagesareassumedtoremainfixedforthedura?onofthecontract.Thus,nominalwagesdependonpriorexpecta?onsabouttheevolu?onofthepricelevel,produc?vityandallothershocks.
• Ifinfla?onturnsouttobehigherthanexpected,thenrealwagesfall,firmsdemandmorelabor,andemploymentrises.Theoppositehappenswheninfla?onturnsouttobelowerthanexpected.Thus,thesemodelshavekeynesianfeatures,andhaveformedthebasisofthesocallednewkeynesianapproachtoaggregatefluctua?ons.
The“New”KeynesianApproach:PeriodicNominalWageContracts
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 6
• The“new”keynesianapproachalsoemphasizedlabormarketdistor?onsthatmadethe“natural”rateofunemploymentinefficientlyhigh.
• Onesuchdistor?onthatweshallemphasizeisthedis?nc?onbetween“insiders”and“outsiders”inthelabormarket.
• “Outsiders”aredisenfranchisedfromthelabormarket,and,asaresult,wagecontractsdonotaimtomaintainfullemployment.Evenwithoutshocks,thereisan“inefficiently”high“natural”rateofunemployment.
• Sincefirmsdetermineemployment,giventhewagecontracts,forthosewhoturnoutunemployed,the“outsiders”,unemploymentisinvoluntary.
The“New”KeynesianApproach:AnInefficientlyHigh“Natural”Rate
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 7
• Inthislectureweanalyzea“newKeynesian”modelbasedonsuchperiodicnominalwagecontracts,whichiscomparabletothe“newclassical”modelwithoutcapital.
• Itnotonlyallowsfornominalshocksandmonetarypolicytoaffectthefluctua?onsofrealvariables,butitalsoallowsfortheexistenceof“involuntary”unemployment.
• ThemodelbuildsononeofthekeyinsightsoftheGeneralTheory,namelytheshortrunrigidityofnominalwages,asenvisagedbyGrayandFischercontracts.
• Inallotherrespectsitisbasedoninter-temporalop?miza?ononthepartofbothhouseholdsandfirms.
• Themodelisinessenceadynamicstochas?cgeneralequilibriummodelthatincorporatesmanyofthefeaturesoftheAS-ADversionoftheKeynesianmodel.
A“New”KeynesianModelwithaPosi?veNaturalRateofUnemploymentandPeriodicNominal
WageContracts
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 8
Weconsideraneconomyconsis?ngofcompe??vefirms,indexedbyi,wherei∈[0,1].Laboristheonlyvariablefactorofproduc?on,andfirmsdetermineemploymentbyequa?ngthemarginalproductoflabortotherealwage.Theproduc?onfunc?onoffirmiisgivenby,
Output,EmploymentandLaborDemand
Y (i)t = AtL(i)t1−α
Firmsdetermineemploymentbyequa?ngthemarginalproductoflabortotherealwage.Labordemandbyfirmiisgivenby,
(1−α )AtL(i)t−α = W (i)t
Pt
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 9
Inlog-linearform,theproduc?onfunc?onandlabordemandcanbewri[enas,
Output,EmploymentandLaborDemandinLog-linearForm
y(i)t = at + (1−α )l(i)t l(i)t = l_− 1α(w(i)t − pt − at )
Aggrega?ngacrossfirms,aggregateoutputandemploymentaredeterminedby,
yt = at + (1−α )lt lt = l_− 1α(wt − pt − at )
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 10
Nominalwagesaresetby“insiders”ineachfirm,atthebeginningofeachperiod,beforevariables,suchascurrentproduc?vityandthecurrentpricelevelareknown.Thus,nominalwagesaresetonthebasisofthera?onalexpecta?onsof“insiders”abouttheseshocks.Nominalwagesremainconstantforoneperiod,andtheyareresetatthebeginningofthefollowingperiod.
Objec?veofNominalWageContracts
minEt−1 β ss=0
∞∑ 12l(i)t+s − n
_(i)t+s
⎛⎝
⎞⎠
2⎡
⎣⎢
⎤
⎦⎥
Et−1l(i)t = n_(i)t
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 11
Weassumethatthetotalnumberof“insiders”intheeconomyisalwaysstrictlysmallerthanthelaborforce.Wethusassumethat,
“Insiders”andthe“NaturalRate”ofUnemployment
n_(i)t dii=0
1
∫ = n_t < nt
Sincewagecontractsmakeexpectedemploymentequaltothenumberof“insiders”,itfollowsthat,
Et−1lt = n_t < nt
The“natural”rateofunemployment,whichisinvoluntary,becauseoutsiderswouldbepreparedtoworkattheprevailingrealwage,isdefinedas,
u_t ! nt − n
_t > 0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 12
Thewageissetsoastomakeexpectedemploymentequaltothenumberofinsiders,andisbasedononeperiodaheadexpecta?onsaboutthepricelevelandproduc?vity.Itthussa?sfies,
NominalWageContractsandtheDetermina?onofEmployment
wt = Et−1pt + Et−1at −α (n_t− l
_)
Oncethewagecontracthasbeensigned,firmsdetermineemployment,afertheyhaveobservedthecurrentpricelevelandcurrentproduc?vity.Thus,employmentisdeterminedby,
lt = n_t+1α
pt − Et−1pt + at − Et−1at( ) = n_t+1α
π t − Et−1π t + at − Et−1at( )
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 13
Employmentdeviatesfromits“natural”leveltotheextentthatthereareunan?cipatedshockstoinfla?onandproduc?vity.
Unan?cipatedincreasesininfla?oncauseareduc?oninrealwagesandincreaselabourdemandandemployment.
Unan?cipatedincreasesinproduc?vityincreaseproduc?vityrela?vetorealwages,andthusalsoincreaselabourdemandandemployment.
Thisemploymentfunc?onisthebasisforan“expecta?onsaugmentedPhillipscurve”inthismodel.
Themodelis“Keynesian”,butitalsoincorporatesthe“naturalrate”hypothesisofFriedman.
Infla?onandEmploymentwithNominalWageContracts
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 14
Thecurrentunemploymentrateisdefinedby,
NominalWageContractsandtheExpecta?onsAugmented“PhillipsCurve”
ut ! nt − lt
Usingtheemploymentfunc?ontosubs?tuteforcurrentemployment,
ut = u_t−1α
π t − Et−1π t + at − Et−1at( )
Theunemploymentratedeviatesfromits“natural”rateasaresultofunexpectedshockstoinfla?onandproduc?vity,becausebothreducerealwagesrela?vetoproduc?vity,comparedwiththepriorexpecta?onsofwagese[ers.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 15
Unexpectedshockstoinfla?onandproduc?vitycauseoutputtobehigherthanits“natural”level,astheycauseemploymenttobehigherthanitsown“natural”level.Thisequa?oncanbeseenastheoutputversionofthe“expecta?onsaugmentedPhillipscurve”,orasashortrun“outputsupplyfunc?on”.
NominalWageContractsandFluctua?onsofOutput
Usingtheemploymentfunc?ontosubs?tuteforcurrentemploymentintheproduc?onfunc?on,
yt = y_
t+1−αα
π t − Et−1π t + at − Et−1at( )
where,y_
t = (1−α )n_t+ at
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 16
Itisworthdis?nguishingbetweenthe“natural”levelofoutputandthe“fullemployment”leveloutput.Fullemploymentoutputisgivenby,
The“NaturalRate”ofUnemploymentandthe“NaturalLevel”ofOutput
ytf = (1−α )nt + at
Fullemploymentoutputisalwayshigherthanthe“natural”levelofoutputinthismodel.Thereasonisthatequilibriumemploymentislowerthanfullemployment,sincethepoolof“insiders”,whoaretheoneswhodetermineequilibriumemploymentthroughtheirwagesegngbehavior,issmallerthanthelaborforce.Thus,becauseofthisrealdistor?oninthelabormarket,the“natural”levelofoutputisinefficientlylow,andthe“naturalrate”ofunemploymentisinefficientlyhigh.Theirrela?onisgivenby,
ytf − y
_
t = (1−α )(nt − n_t ) = (1−α )u
_t
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 17
• Weassumethattheeconomyconsistsofalargenumberofiden?calhouseholdsj,wherej∈[0,1].
• Eachhouseholdmembersuppliesoneunitoflabor,andunemploymentimpactsallhouseholdsinthesamemanner.
• Thus,ifHisthenumberofhouseholdsandNistheaggregatelaborforce,eachhouseholdhasN/Hmembers.Ofthose,someare“insiders”inthelabormarket,andtherestare“outsiders”.
• Thepropor?onofinsidersisthesameforallhouseholds.Inaddi?on,thepropor?onoftheunemployedisalsoassumedtobethesameforallhouseholds.
Households,EmploymentandUnemployment
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 18
Therepresenta?vehouseholdchooses(aggregate)consump?onandrealmoneybalancestomaximize,
Households,Consump?onandMoneyDemand
Et1
1+ ρ⎛⎝⎜
⎞⎠⎟s=0
∞∑s
11−θ
Vt+sC Ct+s
1−θ +Vt+sM M
P⎛⎝⎜
⎞⎠⎟ t+s
1−θ⎛
⎝⎜⎞
⎠⎟⎛
⎝⎜
⎞
⎠⎟
subjecttothesequenceofexpectedbudgetconstraints,
Et Ft+s+1 − (1+ it+s ) Ft+s −it+s1+ it+s
Mt+s + Pt+s Yt+s −Ct+s −Tt+s( )⎛⎝⎜
⎞⎠⎟
⎛
⎝⎜⎞
⎠⎟= 0
Ft = Bt +Mt
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 19
Fromthefirstordercondi?onsfortherepresenta?vehousehold,
FirstOrderCondi?onsoftheRepresenta?veHousehold
VtCCt
−θ = λt (1+ it )Pt VtM M
P⎛⎝⎜
⎞⎠⎟ t
−θ
= λtitPt Etλt+1 = Et1+ ρ1+ it+1
⎛⎝⎜
⎞⎠⎟λt
Attheop?mumthehouseholdequatesthemarginalu?lityofconsump?ontothevalueofsavings.Italsoequatesthemarginalu?lityofrealmoneybalancestotheopportunitycostofholdingmoney.Finally,therealinterestrate,adjustedfortheexpectedincreaseinthemarginalu?lityofconsump?on,isequaltothepurerateof?mepreference.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 20
Elimina?ngλfromthethreefirstordercondi?ons,wederivethemoneydemandfunc?onandtheEulerequa?onforconsump?on.
FromtheFirstOrderCondi?onstotheEulerEqua?onforConsump?onandtheMoney
DemandFunc?on
MP
⎛⎝⎜
⎞⎠⎟ t
= CtVt
C
VtM
it1+ it
⎛⎝⎜
⎞⎠⎟
−1θ
EtVt+1
C Ct+1( )−θPt+1
⎛
⎝⎜
⎞
⎠⎟ =
1+ ρ1+ it
⎛⎝⎜
⎞⎠⎟Vt
C Ct( )−θPt
⎛
⎝⎜
⎞
⎠⎟
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 21
Log-linearizingtheEulerEqua?onforConsump?onandtheMoneyDemandFunc?on,andimposingtheproductmarketequilibriumcondi?onCt=Yt,
ALog-linearVersionoftheEulerEqua?onforConsump?onandMoneyDemand,andProduct
MarketEquilibrium
mt − pt = yt −1θln it1+ it
⎛⎝⎜
⎞⎠⎟+ 1θvtM − vt
C( )
yt = Etyt+1 −1θit − Etπ t+1 − ρ( )+ 1
θ(vt
C − Etvt+1C )
Thosetwoequa?onsareofenreferredtoasthe“newkeynesian”IScurve,andthe“newkeynesian”LMcurve,describingaggregatedemandforoutputandequilibriuminthemoneymarket.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 22
• Sinceoutputdemanddependsondevia?onsoftherealinterestfromthepurerateof?mepreference,therealinterestrateistherela?vepricethatadjuststoequilibrateoutputdemandwithoutputsupply.
• Nootherrela?vepricecanplaythisrole,astherealwageisdeterminedinordertomakeexpectedlabordemandequaltothenumberof“insiders”inthelabormarket.
AdjustmentoftheRealInterestRatetoEquilibratetheProductMarket
TherealinterestrateisdefinedbytheFisherequa?on,
rt = it − Etπ t+1
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 23
The“natural”realinterestrateisdeterminedbytheproductmarketequilibriumcondi?on,whenoutputisatits“natural”level.Fromthe“newkeynesian”IScurveandthedefini?onofthe“natural”levelofoutput,
The“Natural”RealInterestRate
r_t = ρ −θ (1−α ) n
_t− Et n
_t+1
⎛⎝
⎞⎠ + at − Etat+1( )⎛
⎝⎜⎞⎠⎟ + vt
C − Etvt+1C( )
The“natural”realinterestrateisequaltothepurerateof?mepreference,butalsodependsondevia?onsofcurrentrealshocksfroman?cipatedfutureshocks.Realshocksthatcauseatemporaryincreaseinthe“natural”levelofoutputreducethe“natural”realrateofinterest,inordertobringaboutancorrespondingreduc?oninconsump?onandmaintainproductmarketequilibrium.Ontheotherhand,realshocksthatcauseatemporaryincreaseinconsump?on,requireanincreaseinthe“natural”realrateofinterest,inordertoinducelowerconsump?on,andmaintainproductmarketequilibrium.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 24
Becauseofthenominalrigidityofwagesforoneperiod,thecurrentequilibriumrealinterestdeviatesfromits“natural”rate.Thecurrentrealinterestrateisdeterminedbytheequa?onofthe“newkeynesian”IScurvewiththeshortrunoutputsupplyfunc?on.Itisthusdeterminedas,
TheCurrentRealInterestRate
rt = r_t−
θ 1−α( )α
π t − Et−1π t + at − Et−1at( )
Unan?cipatedshockstoinfla?onorproduc?vity,whichcauseatemporaryriseincurrentoutputrela?vetoits“natural”level,alsoreducethecurrentrealinterestraterela?vetoits“natural”rate.Thisisthe“Wicksellian”mechanisminthismodel.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 25
Inwhatfollows,weshallassumethatthelogarithmsoftheexogenousshockstopreferencesandproduc?vityfollowsta?onaryAR(1)processes.
Assump?onsaboutExogenousShocks
vtC =ηCvt−1
C + ε tC vt
M =ηMvt−1M + ε t
M at =ηAat−1 + ε tA
Weshallfurtherassumethatthe(logofthe)laborforceisfixedatn,andthattheexogenousnumberof“insiders”alsofollowsasta?onaryAR(1)process,oftheform,
n_t = (1−ηN )n
_+ηN n
_t−1+ ε t
N
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 26
Sincethenumberof“insiders”fluctuates,the“natural”rateofunemploymentalsofluctuates,accordingto,
Fluctua?onsinthe“Natural”RatesofUnemploymentandOutput
u_t = (1−ηN )u
_+ηN u
_t−1− ε t
N
Sincethenumberof“insiders”andtotalfactorproduc?vityfluctuate,the“natural”levelofoutputalsofluctuates,accordingto,
y_
t = (1−α )n_t+ at
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 27
Fluctua?onsinEmployment,UnemploymentandOutput
lt = n_t+1α
π t − Et−1π t + ε tA( )
ut = u_t−1α
π t − Et−1π t + ε tA( )
yt = y_
t+1−αα
π t − Et−1π t + ε tA( )
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 28
Fluctua?onsintheRealWageandtheRealInterestRate
wt − pt = (w − p_)t − π t − Et−1π t( )
rt = r_t−
θ 1−α( )α
π t − Et−1π t + ε tA( )
where,
(w − p_)t =ηAat−1 −α (n
_t− l
_)
r_t = ρ −θ (1−α )(1−ηN )(n
_t− n
_)+ (1−ηA )at
⎛⎝
⎞⎠ + (1−ηC )vt
C
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 29
• The“natural”rates(orlevels)ofrealvariablesevolveasfunc?onsoftheexogenousrealshocks.
• Intheabsenceofthenominalrigidityduetotheassump?onthatnominalwagesaresetinadvanceandremainfixedforoneperiod,theevolu?onofrealvariableswouldbeequaltotheir“natural”levels.Themodelwouldinallrespectsbesimilartoa“newclassical”model.
• However,unan?cipatedinfla?on,andinnova?onsinproduc?vity,byreducingrealwagesrela?vetoproduc?vity,causeatemporaryincreaseinemploymentandoutputabovetheir“natural”level,andatemporaryreduc?oninunemploymentandtherealinterestratebelowtheir“natural”rates.
• Sinceinfla?onisalsoaffectedbynominalshocks,unan?cipatednominalshockshaverealeffectsinthismodel.
Proper?esoftheModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 30
Weshallini?allyassumethatthemoneysupplyfollowsarandomwalkwithdrif,oftheform,
AnExogenousMoneySupplyRule
mt = µ +mt−1 + ε tS
Withthisassump?on,thesteadystaterateofgrowthofthemoneysupplyisequaltoμ,andsincegrowthisequaltozerointhismodel,steadystateinfla?onisalsoequaltoμ,andthesteadystatenominalinterestrateisequaltoρ+μ.
Τhemoneydemandfunc?oninlogsisgivenby,
mt − pt = yt −1θln it1+ it
⎛⎝⎜
⎞⎠⎟+ 1θ(vt
M − vtC )
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 31
TheMoneyDemandFunc?oninLog-linearForm
Τhemoneydemandfunc?oncanbeapproximatedaroundthesteadystatenominalinterestrateρ+μas,
mt − pt ! m0 + yt −ζ (rt + Etπ t+1)+1θ(vt
M − vtC )
where,
m0 = − 1θln ρ + µ1+ ρ + µ
⎛⎝⎜
⎞⎠⎟− 11+ ρ + µ
⎛⎝⎜
⎞⎠⎟
ζ = 1θ(ρ + µ)(1+ ρ + µ)
> 0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 32
Subs?tu?ngforrealoutputandtherealinterestrateinthemoneydemandfunc?on,andsolvingforthepricelevel,wegetthat,
TheDetermina?onofthePriceLevelunderaMoneySupplyRule
pt 1+ζ + (1+ζθ )(1−α )α
⎛⎝⎜
⎞⎠⎟ − Et−1pt
(1+ζθ )(1−α )α
⎛⎝⎜
⎞⎠⎟ −ζEt pt+1 = zt
where,
zt = mt − y_
t+ζ r_t−
(1+ζθ )(1−α )α
⎛⎝⎜
⎞⎠⎟ ε t
A − 1θ(vt
M − vtC )−m0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 33
where,
TheSolu?onforthePriceLevelunderaMoneySupplyRule
pt = p_+mt−1 + χAat−1 + χCvt−1
C + χMvt−1M + χN (n
_t− n
_)+ψ Aε t
A +ψ Cε tC +ψ Sε t
S +ψ Mε tM
p_= µ −m0 − (1−α )n
_+ζρ
χA = −1+ζθ(1−ηA )1+ζ (1−ηA )
ηA χC = 1+ζθ(1−ηC )1+ζ (1−ηC )
ηC
θχM = − 1
1+ζ (1−ηM )ηM
θ χN = −1+ζθ(1−ηN )1+ζ (1−ηN )
(1−α )
ψ A = − (1+ζθ )(1−α )α
+α 1+ζθ(1−ηA )( )
α (1+ζ (1−ηA ))+ (1+ζθ )(1−α )⎛⎝⎜
⎞⎠⎟
ψ C =α 1+ζθ(1−ηC )( )
α (1+ζ (1−ηC ))+ (1+ζθ )(1−α )1θ
ψ S =α
α + (1−α )(1+ζθ )ψ M = − α
θ α 1+ζ (1−ηM )( )+ (1−α )(1+ζθ )( )
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 34
Alltherelevantshocks,realandnominal,affectunan?cipatedinfla?on.Thus,alltherelevantshocksaffectoutputandunemploymentfluctua?onsaswell.Fluctua?onsofoutputandunemploymentaroundtheir“natural”ratesaregivenby,
Unan?cipatedInfla?onandFluctua?onsinOutputandUnemploymentunderaMoney
SupplyRule
π t − Et−1π t =ψ Aε tA +ψ Cε t
C +ψ Sε tS +ψ Mε t
M
yt = y_
t+1−αα
(1+ψ A )ε tA +ψ Cε t
C +ψ Sε tS +ψ Mε t
M( )
ut = u_t−1α(1+ψ A )ε t
A +ψ Cε tC +ψ Sε t
S +ψ Mε tM( )
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 35
Inreality,moderncentralbanksdonotallowthemoneysupplytofollowanexogenousprocess.Monetarypolicyusuallyreactstodevia?onsofinfla?onfromtargetanddevia?onsofoutputandunemploymentfromtarget.
Inaddi?on,centralbanksusuallyconductmonetarypolicybycontrollingthenominalinterestrateratherthanthemoneysupply.Thisisbecauseofthedifficul?esincontrollingthemoneysupply,andbecausethemoneydemandfunc?onissubjecttoshocksduetofinancialinnova?ons.
Inwhatfollowsweshallthusexaminethebehaviorofthemodelundertheassump?onthatthecentralbankfollowsafeedbackruleforthenominalinterestrate.Inpar?cular,weshallassumethatthecentralbankfollowsafeedbackruleoftheTaylor(1979)form,
AFeedbackNominalInterestRateRule
it = r_t+ µ +φ1(π t − µ)+φ2 (yt − y
_
t )+ ε ti
φ1,φ2 > 0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 36
• TheTaylor(1993)ruleisageneraliza?onoftheWicksellrulethatweexaminedinthecaseofthe“newclassical”model.
• Accordingtothisrule,thecentralbankaimsforanominalinterestratewhichisequaltothe“natural”realrateofinterest,plusatargetinfla?onrateequaltoμ.
• Ifactualinfla?onishigherthanthetargetμ,thenthecentralbankraisesinterestratesinordertoreduceinfla?on.
• Inaddi?on,ifoutputishigherthanits“natural”levelandunemploymentlowerthanits“naturalrate”,thenthecentralbankalsoraisesinterestrates,inordertobringoutputbacktoits“natural”levelandunemploymentbacktoits“naturalrate”.
Proper?esoftheTaylorRule
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 37
Subs?tu?ngtheTaylorRuleintheFisherequa?on,andusingtherealinterestrateequa?onandtheoutputsupplyfunc?onofthemodel,wegetthefollowingprocessforinfla?on.
TheInfla?onProcessunderaTaylorRule
π t = γ 1Et−1π t + γ 2Etπ t+1 + (φ1 −1)γ 2µ − γ 1ε tA − γ 2ε t
i
γ 1 =(φ2 +θ )(1−α )
φ1α + (φ2 +θ )(1−α )γ 2 =
αφ1α + (φ2 +θ )(1−α )
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 38
• Theinfla?onaryprocessdependsonthepolicyparametersoftheTaylorruleandtheotherstructuralparametersofthemodel,suchasαandθ.
• Itisdrivenbytwoshocks.Shockstoproduc?vity,astheseshockscausedevia?onsofoutputfromits“natural”level,duetothefactthatnominalwagesweredeterminedbeforetherealiza?onoftheseshocks,andalsoshockstothepolicyrule(monetaryshocks).
• Noothershocksaffecttheinfla?onaryprocessunderthisrule,asthenominalinterestrateadjuststoreflectchangesinthe“natural”rateofinterest,whichisaffectedbytheothernominalandrealshocks.
• Theinfla?onprocessinstableifγ1+γ2<1.
TheInfla?onProcessunderaTaylorRule
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 39
Theinfla?onprocessunderaTaylorruleisstableifγ1+γ2<1.Anecessaryasufficientcondi?onforthisisthatφ>1.
TheCondi?onforStabilityoftheInfla?onProcessunderaTaylorRule
γ 1 + γ 2 =α + (φ2 +θ )(1−α )φ1α + (φ2 +θ )(1−α )
<1⇒φ1α >α ⇒φ1 >1
Thiscondi?onisusuallyreferredtoastheTaylorprinciple,andrequiresthatthenominalinterestratereactsmorethanonetoonetodevia?onsofcurrentinfla?onfromitstargetμ.Weshallassumethatitisalwayssa?sfiedbythecentralbank.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 40
AssumingthattheTaylorprincipleissa?sfied,thenthera?onalexpecta?onssolu?onoftheinfla?onprocesstakestheform,
SolvingfortheInfla?onProcessundertheTaylorRule
π t = µ − γ 1ε tA − γ 2ε t
i
Infla?ondeviatesfromthecentralbanktargetμ,onlyinresponsetocurrentshockstoproduc?vityandshockstothenominalinterestrate(monetaryshocks).Thus,unan?cipatedinfla?onisgivenby,
π t − Et−1π t = −γ 1ε tA − γ 2ε t
i
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 41
Subs?tu?ngforunan?cipatedinfla?oninthe“Phillipscurve”andtheoutputsupplyfunc?on,
Fluctua?onsofOutputandUnemploymentunderaTaylorRule
ut − u_t =
1α
−(1− γ 1)ε tA + γ 2ε t
i( ) yt − y_
t =1−αα
(1− γ 1)ε tA − γ 2ε t
i( )
UnderaTaylorrule,onlyproduc?vityandmonetarypolicyshocksaffectfluctua?onsinrealvariables,suchasoutputandunemployment,aroundtheir“natural”level.Thisisincontrasttotheexogenousruleformonetarygrowth,whichresultsinallshocksaffec?ngdevia?onsofoutputfromits“natural”rate,andthusahigherpoten?alvarianceofunemploymentandoutput.Furthermore,theimpactoftheseshocksdependsontheparametersoftheTaylorrule.Thus,inthismodelthereisscopeformonetarypolicytoaffecttheshortrunfluctua?onsofrealvariablesbyappropriatechoiceofthepolicyparameters.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 42
• ThemodelwehavepresentedbuildsononeofthekeyinsightsoftheGeneralTheory,theshortrunrigidityofnominalwages,butinallotherrespectsitisbasedoninter-temporalop?miza?ononthepartofbothhouseholdsandfirms.
• Themodelischaracterizedbyanexpecta?onsaugmented“Phillipscurve”,inwhichdevia?onsofoutputandunemploymentfromtheir“natural”leveldependonunan?cipatedcurrentinfla?on,whichreducesrealwagesrela?vetoproduc?vity,andunan?cipatedproduc?vityshocks,whichalsoaffecttherela?onbetweenrealwagesandproduc?vity.
• Nominalshocksand,byextension,monetarypolicyareabletoaffectfluctua?onsinbothinfla?onandrealvariablessuchasoutput,employment,unemployment,realwagesandtherealinterestrate.
NominalandRealShocksandAggregateFluctua?ons
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 43
• Weanalyzedaggregatefluctua?onsinthismodelundertwoalterna?vemonetaryrules.Thefirstisanexogenousprocessfortherateofgrowthofthemoneysupplyandthesecondisafeedbackinterestraterule,accordingtowhichthenominalinterestraterespondstodevia?onsofinfla?onfromthetargetofthecentralbank,anddevia?onsofoutputfromits“natural”level.
• Thevarianceofsuchdevia?onsdependsonthemonetaryrule.Underanexogenousprocessfortherateofgrowthofthemoneysupply,allshocksaffectaggregatefluctua?ons.UnderaTaylorfeedbackinterestraterule,onlyproduc?vityshocksandshockstomonetarypolicyaffectaggregatefluctua?ons,andtheireffectdependsontheparametersoftheTaylorrule.
• Wehavethusdemonstratedthedependenceofaggregatefluctua?onsnotonlyonexogenousshocks,butalsoontheformofthemonetarypolicyrulefollowedbythecentralbank.
MonetaryPolicyandAggregateFluctua?ons
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 44
• Oneweaknessofthemodelaswehaveanalyzeditsofaristhatincannotaccountforpersistentdevia?onsofinfla?onfromtarget,andoutputandunemploymentfromtheir“natural”rates.
• Fluctua?onsofinfla?onfromtarget,andoutputandunemploymentaroundtheir“natural”levelsandarethesumoftwowhitenoiseprocesses,i.ewhitenoiseprocessesthemselves.Alldevia?onslastforoneperiodandthereisnopersistence.
• Thislackofpersistenceisaseriousweaknessofthemodel,aspersistenceofaggregatefluctua?onsisoneofthemaincharacteris?csofbusinesscycles.
• However,themodelcanbeextendedtoaccountforpersistence.
ExplainingPersistenceinInfla?onandAggregateFluctua?ons
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 45
• FollowingBlanchardandSummers(1986),weassumethattheemploymentobjec?vewhichdeterminesthenominalwageinthecontractdependsonboththeexogenousnumberof“coreinsiders”ineachfirm,butalsothosewhowereemployedinperiodt-1.Theexpecta?onsonthebasisofwhichwagesaresetdependoninforma?onavailableun?ltheendofperiodt-1,butnotoninforma?onaboutpricesandproduc?vityinperiodt.
• Onthebasisoftheabove,weassumethattheobjec?veof“insiders”istomakeexpectedemploymentsa?sfyapaththatminimizesthefollowingquadra?cinter-temporallossfunc?on,subjecttothesequenceofexpectedlabordemandcurvesoffirms.ωistherela?veweightofrecentemployeesinthewagesegngprocess.
AGeneralizedBlanchardandSummersModelofUnemploymentPersistence
minEt−1 β ss=0
∞∑ 12l(i)t+s − n
_(i)⎛
⎝⎞⎠
2
+ ω2l(i)t+s − l(i)t+s−1( )2⎡
⎣⎢
⎤
⎦⎥
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 46
Fromthefirstordercondi?onsforaminimum,wagesaresetsothatexpectedemploymentforeachfirmsa?sfies,
FirstOrderCondi?onsforaMinimumandtheDetermina?onofExpectedEmployment
1+ω (1+ β )( )Et−1l(i)t − βωEt−1l(i)t+1 −ωl(i)t−1 = n_(i)
Integra?ngoverthenumberoffirmsi,expectedaggregateemploymentmustthensa?sfy,
1+ω (1+ β )( )Et−1lt − βωEt−1lt+1 −ωlt−1 = n_
Weshallassumethatthetotalnumberofcore“insiders”intheeconomyisalwaysstrictlysmallerthanthelaborforce.Weshallthusassumethat,
n_(i)di
i=0
1
∫ = n_< n
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 47
Expectedemploymentandexpectedunemploymentarethusdeterminedby,
ExpectedEmploymentandExpectedUnemployment
Et−1lt =1
1+ω (1+ β )n_+ ω1+ω (1+ β )
lt−1 +βω
1+ω (1+ β )Et−1lt+1
Et−1ut =1
1+ω (1+ β )u_+ ω1+ω (1+ β )
ut−1 +βω
1+ω (1+ β )Et−1ut+1
wherewehaveusedthedefini?onsthat, ut ! n − lt u_! n − n
_
Wecanusethose2ndorderdifferenceequa?onstosolveforexpectedemploymentandunemployment.Thesehavetworootsthatlieoneithersideofunity.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 48
Solvingforexpectedemploymentandexpectedunemployment,weget,
SolvingforExpectedEmploymentandExpectedUnemployment
Et−1lt = λ1lt−1 +λ1
ω (1− βλ1)n_= λ1lt−1 + (1− λ1)n
_
Et−1ut = λ1ut−1 +λ1
ω (1− βλ1)u_= λ1ut−1 + (1− λ1)u
_
λ1isthesmallerroot,andthetworootssa?sfythecondi?ons,
λ1 + λ2 =1+ω (1+ β )
βωλ1λ2 =
1β
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 49
Itisstraighnorwardtoshowthatanincreaseinω,therela?veweightofrecentemployeesinthewagesegngprocess,resultsinanincreaseinλ1,thecoefficientthatdeterminesthepersistenceofexpectedunemployment.Fromthecondi?onswhichdefinethetworoots,itfollowsthat,
ThePersistenceofEmploymentandtheRela?veWeightofRecentEmployeesintheWageSegng
Process
∂λ1∂ω
= λ1ω
⎛⎝⎜
⎞⎠⎟2
> 0
Thus,thehighertheweightofrecentemployeesrela?vetocore“insiders”inthewagesegngprocess,thehigherthepersistenceofunemployment.
Forexample,assumingβ=0.99,withω=1,λ1=0.38.Withω=2,λ1=0.50,withω=10,λ1=0.73andwithω=100,λ1=0.91.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 50
Weshallagainassumethatwagese[ersdeterminethenominalwageisordertomaketheexpectedrealwageconsistentwithexpectedemployment.Employmentisdeterminedonthelabordemandcurve.
WageSegngandEmployment
lt = l_− 1α(wt − pt − at )
Thus,thewageissetat,
wt = Et−1pt + Et−1at −α Et−1lt − l_⎛
⎝⎞⎠
Subs?tu?ngforthewageintheemploymentequa?on,employmentfollows,
lt = λ1lt−1 + (1− λ1)n_+ 1α(pt − Et−1pt + at − Et−1at )
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 51
Subtrac?ngthelogofemploymentfromthelogofthelaborforcen,andrearranging,theunemploymentrateevolvesaccordingto,
ADynamicModelofthePhillipsCurve
ut − u_= λ1(ut−1 − u
_)− 1
α(π t − Et−1π t + at − Et−1at )
Devia?onsofunemploymentfromits“natural”leveldependnega?velyonunan?cipatedshockstoinfla?onandproduc?vity,asthesecauseadiscrepancybetweenrealwagesandproduc?vity,duetothefactthatnominalwagesarepredeterminedfortheperiod.
Followinganunan?cipatedshocktoinfla?onorproduc?vity,unemploymentwillconvergegraduallybacktoits“natural”rate,withthespeedofadjustmentbeingequalto1-λ1perperiod.Thus,followingshockstoinfla?onorproduc?vity,devia?onsofunemploymentfromits“natural”ratewilldisplaypersistence.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 52
Thepersistenceofemploymentandunemployment,willalsobetranslatedintopersistentoutputfluctua?ons.Subs?tu?ngforemploymentintheproduc?onfunc?on,devia?onsofoutputfromits“natural”levelwillevolveaccordingto,
TheRela?onbetweenthePersistenceofUnemploymentandOutput
yt − y_
t = λ1(yt−1 − y_
t−1)+1−αα
(π t − Et−1π t + at − Et−1at )
Thisisadynamicoutputsupplyfunc3on.Devia?onsofoutputfromits“natural”leveldependposi?velyonunan?cipatedshockstoinfla?onandproduc?vity,asthesecauseadiscrepancybetweenrealwagesandproduc?vity,duetothefactthatnominalwagesarepredetermined.Thisdiscrepancyaffectsemploymentandtranslatesintooutput,throughtheproduc?onfunc?on.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 53
Fluctua?onsinEmployment,UnemploymentandOutput,whenthereisEmploymentPersistence
lt = (1− λ1)n_+ λ1lt−1 +
1α
π t − Et−1π t + ε tA( )
ut = (1− λ1)u_+ λ1ut−1 −
1α
π t − Et−1π t + ε tA( )
yt = y_
t+ λ1(yt−1 − y_
t−1)+1−αα
π t − Et−1π t + ε tA( )
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 54
Fluctua?onsintheRealWageandtheRealInterestRate
wt − pt = (w − p_)t +αλ1(ut−1 − u
_)− π t − Et−1π t( )
rt = r_t+θ 1−α( )(1− λ1)(ut − u
_)
where,
(w − p_)t = at −α (n
_− l_)
r_t = ρ −θ(1−ηA )at + (1−ηC )vt
C
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 55
WeshallassumethatthecentralbankfollowsaTaylorruleoftheform,
TheTaylorRulefortheNominalInterestRate
it = r_t+ µ +φ1 π t −π *( )−φ2 (ut − u
_t )+ ε t
i
WehavenowexpressedtheTaylorruleintermsofdevia?onsofunemploymentandnotoutputfromits“natural”rate.Thisdoesnotaffectthenatureoftheresults,asinthismodeldevia?onsofunemploymentfromits“naturalrate”arealinearfunc?onofdevia?onsofoutputfromits“naturallevel”.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 56
AssumingthatthecentralbankfollowsaTaylorrule,subs?tu?ngforthenominalinterestrateintheFisherequa?on,andusingthedynamicPhillipscurvewehavederived,theinfla?onaryprocessisdeterminedby,
TheInfla?onaryProcessunderaTaylorRule
π t = γ 1Etπ t+1 + γ 2Et−1π t + γ 3π t−1 + γ 4µ + γ 5ε tA + γ 6ε t
i + γ 7ε t−1i
where,
γ 1 =α
φ1α +φ2 +θ(1− λ1)(1−α )+ λ1αγ 2 =
φ2 +θ(1− λ1)(1−α )φ1α +φ2 +θ(1− λ1)(1−α )+ λ1α
γ 3 =λ1φ1α
φ1α +φ2 +θ(1− λ1)(1−α )+ λ1αγ 4 =
(φ1 −1)(1− λ1)αφ1α +φ2 +θ(1− λ1)(1−α )+ λ1α
γ 5 = −γ 2 γ 6 = −γ 1 γ 7 = λ1γ 1
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 57
• Becauseofthepersistenceofunemployment,theinfla?onaryprocessalsodisplayspersistence.
• Italsodependsoncurrentexpecta?onsaboutfutureinfla?on,throughthedefini?onoftherealinterestrate.
• ItalsodependsonbothparametersoftheTaylorrule,asunan?cipatedinfla?oncausestheunemploymentrateandtherealinterestratetodeviatefromtheir“naturalrates”.
• Finally,becauseofthepersistenceinunemploymentbothcurrentandpastnominalinterestrateshocksaffecttheinfla?onaryprocess.
• Theeffectsofproduc?vityandnominalinterestrateshocksoninfla?onalsodependontheparametersoftheTaylorrule.
TheInfla?onaryProcessunderaTaylorRule
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 58
Solvingforinfla?onunderra?onalexpecta?ons,onecanshowthat,iftheTaylorprincipleφ1>1issa?sfied,infla?onfollowsastableprocessoftheform,
SolvingforInfla?onunderRa?onalExpecta?ons
π t = (1− λ1)µ + λ1π t−1 −ψ 1ε tA −ψ 2ε t
i +ψ 3ε t−1i
where,ψ 1 =
φ2 +θ(1− λ1)(1−α )φ1α +φ2 +θ(1− λ1)(1−α )
<1
ψ 2 =φ1 − λ1φ1
αφ1α +φ2 +θ(1− λ1)(1−α )
> 0
ψ 3 =λ1φ1
> 0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 59
• Fluctua?onsofinfla?onaroundthetargetofthemonetaryauthori?esμarepersistent,anddependonthecurrentinnova?oninproduc?vityandcurrentandpastnominalinterestrateshocks.
• Furthermore,thepersistenceofinfla?onisequaltothepersistenceofdevia?onsofunemploymentandotherrealvariables,suchasoutput,fromtheir“natural”level.
• Thereasonisthatboththeequilibriumrealinterestrateanddevia?onsofunemploymentfromits“natural”ratedisplaypersistence.Thus,underaTaylorrule,thenominalinterestrateandinfla?onwillalsodisplaypersistence.
ThePersistenceofInfla?onunderaTaylorRule
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 60
Unan?cipatedinfla?onunderaTaylorrulewillbegivenby,
Unan?cipatedInfla?onandFluctua?onsofDevia?onsofUnemploymentandOutputfrom
their“Natural”Rates
π t − Et−1π t = −ψ 1ε tA −ψ 2ε t
i
Fluctua?onsofdevia?onsofunemploymentandoutputfromtheir“natural”rateswillbegivenby,
(ut − u_) = λ1(ut−1 − u
_)− 1
α(1−ψ 1)ε t
A −ψ 2ε ti( )
(yt − y_
t ) = λ1(yt−1 − y_
t−1)+1−αα
(1−ψ 1)ε tA −ψ 2ε t
i( )
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 61
• UndertheTaylorrule,onlyinnova?onsinproduc?vityandnominalinterestrateshocksinducefluctua?onsofdevia?onsofunemploymentandoutputfromtheir“natural”rates.
• Otherdemandshocks,suchasshockstoconsump?onpreferences,arefullyneutralizedbymonetarypolicy,sincethenominalinterestrateisassumedtofullyaccommodatechangesinthe“natural”rateofinterest.
• However,becauseofthepersistenceindevia?onsofunemploymentandoutputfromtheir“natural”levels,theeffectsoftheseshocksarenolongershortlived,buttheydisplaypersistence.Thehigherthepersistenceofdevia?onsofunemploymentfromits“natural”rate,thehigherthepersistenceoftheeffectsoftemporarynominalandrealshocks.
AggregateFluctua?onsunderaTaylorRule
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 62
• Inordertodemonstratetheimpulseresponsefunc?onsofthemodeltonominalandrealshocks,wepresenttheresultsofadynamicsimula?onofthemodel,followinganunan?cipatedtemporary1%shocktothenominalinterestrate,andanunan?cipated1%shocktoproduc?vityrespec?vely.
• Inthesimula?onswehaveassumedthefollowingvaluesoftheparameters:α=0.333,ρ=0.02,θ=1,ω=2,implyingavalueofλ1=0.5,φ1=1.5,φ2=0.5andηΑ=0.75.Wehavealsoassumeda“naturalrate”ofunemploymentequalto5%andatargetinfla?onrateof2%.
ImpulseResponseFunc?onsoftheModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 63
A1%Unan?cipatedTemporaryShocktotheNominalInterestRate
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 64
A1%Unan?cipatedShocktoProduc?vity
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 65
• Inthislecturewehaveintroducedadynamicstochas?c“newKeynesian”model,whichnotonlyallowsfortheexistenceofinvoluntaryunemployment,butalsofornominalshocksandmonetarypolicytoaffectthefluctua?onsofallrealvariables.
• ThemodelbuildsononeofthekeyinsightsoftheGeneralTheory,theshortrunrigidityofnominalwages,butinallotherrespectsitisbasedoninter-temporalop?miza?ononthepartofbothhouseholdsandfirms.
• Themodelischaracterizedbyanexpecta?onsaugmented“Phillipscurve”,inwhichdevia?onsofoutputandemploymentfromtheir“natural”leveldependonunan?cipatedcurrentinfla?on,whichreducesrealwagesrela?vetoproduc?vity,andunan?cipatedproduc?vityshocks,whichalsoaffecttherela?onbetweenrealwagesandproduc?vity.
• Nominalshocksand,byextension,monetarypolicyareabletoaffectfluctua?onsinbothinfla?onandrealvariablessuchasoutput,employment,unemployment,realwagesandtherealinterestrate.
Characteris?csof“NewKeynesian”ModelsofAggregateFluctua?ons
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 66
• Weanalyzedaggregatefluctua?onsinthismodelundertwoalterna?vemonetaryrules.
• Thefirstisanexogenousprocessfortherateofgrowthofthemoneysupplyandthesecondisafeedbackinterestraterule,accordingtowhichthenominalinterestraterespondstodevia?onsofinfla?onfromthetargetofthecentralbank,anddevia?onsofoutputfromits“natural”level.
• Contrarytothe“newclassical”model,monetaryshocksaffectrealvariablesinthismodel,causingtemporarydevia?onsofoutput,employment,unemployment,realwagesandtherealinterestratefromtheir“natural”levels.
• Theexactvarianceofsuchdevia?onsdependsonthemonetaryrule.Underanexogenousprocessfortherateofgrowthofthemoneysupply,allshocksaffectaggregatefluctua?ons.UnderaTaylorfeedbackinterestraterule,onlyproduc?vityshocksandshockstomonetarypolicyaffectaggregatefluctua?ons.
• Wehavethusdemonstratedthedependenceofaggregatefluctua?onsnotonlyonexogenousshocks,butontheformofthemonetarypolicyrulefollowedbythecentralbank.
AggregateFluctua?onsunderAlterna?veMonetaryPolicyRules
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 67
• Wehavealsoextendedthemodeltoaccountforpersistenceindevia?onsofunemploymentandoutputfromtheir“natural”levels.
• Theextensionisbasedonadynamicmodelofthe“PhillipsCurve”,inwhichunan?cipatedshockstoinfla?onandproduc?vityhavepersistenteffectsonunemployment,andthesepersistenteffectsarecompa?blewithfullinter-temporalop?miza?ononthepartoflabormarket“insiders”.
• Thepropaga?onmechanismthatcausesunan?cipatednominalandrealshockstoproducepersistentdevia?onsofunemploymentandoutputfromtheir“natural”rateisthepar?aladjustmentoflabormarketinsiderstoemploymentshocks.
• WedemonstratedthatunderaTaylorrule,theonlyshocksthatcannotbecompletelyneutralizedbymonetarypolicyareproduc?vityshocksand,ofcourse,monetarypolicyshocks.Fluctua?onsofdevia?onsofunemploymentandoutputfromtheir“natural”ratesdisplaypersistenceandaredrivenbythesetwotypesofshocks.Becauseoftheendogenouspersistenceofdevia?onsofunemploymentfromits“natural”rate,theequilibriuminfla?onratealsodisplayspersistencearoundtheinfla?ontargetofthecentralbank.
ThePersistenceofAggregateFluctua?ons