ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015
The Original Keynesian Models of Aggregate Fluctuations
Keynesian Models and the Phillips Curve
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 2
• Aswehavealreadymen=oned,followingtheGreatDepressionofthe1930s,theanalysisofaggregatefluctua=onsdevelopedintomacroeconomics,onthebasisoftheso-calledKeynesianmodels.
• Thesemodels,werederivedfromtheGeneralTheoryofKeynes(1936),whoarguedagainstthethenprevailing“classical”equilibriumtheoryofemploymentandaggregatefluctua=ons.
• Keynesproceededtoarguethatageneraltheory,asopposedtotheclassicaltheory,oughttobeabletoexplaininvoluntaryunemployment,whichheproceededtodulydefineasasitua=oninwhichtherealwageishigherthanthemarginaldisu=lityoflabor.
• TheKeynesianapproachwasdevelopedthroughasequenceofmodelsintheGeneralTheory.
TheKeynesianApproach
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 3
• TheKeynesiancrossfocusedonthecondi=onsforshortrunequilibriuminthemarketforgoodsandservices,whenpricesarefixed.
• Asecondmodel,againbasedontheassump=onoffixedprices,focusedonthecondi=onsforsimultaneousequilibriuminthemarketforgoodsandservicesandthemarketformoney.Thismodel,wascodifiedastheIS-LMmodelbyHicks(1937),andwasformanyyearsthedominantKeynesianparadigm,bothamongacademiceconomistsandpolicymakers.
• Athirdmodel,combinedtheIS-LMmodelwithtwoaddi=onalassump=ons.First,thatthenominalwageisfixedintheshortrun,and,second,thatemployersdetermineemploymentbyequa=ngtherealwagewiththemarginalproductoflabor.ThismodelwascodifiedastheAD-ASmodel,orneoclassicalsynthesis,andwasusedtodeterminebothunemploymentandthepricelevel.
TheThreeModelsoftheGeneralTheory
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 4
• IntheKeynesianmodels,theimmediateadjustmentofpricesandwagesasequilibra=ngmechanismswasreplacedbytheassump=onthat,intheshort-term,pricesand/ornominalwagesarefixedoradjustonlypar=ally.
• Thus,thelevelofincomeandemploymentbecomesanaddi=onaladjustmentmechanismforthemarketforgoodsandservicesandthemarketforlabor.
• InthislecturewepresentthestructureofthebasicKeynesianmodels,assumingini=allyaconstantlevelofpricesand/ornominalwages,andthengradualadjustmentofpricesandnominalwages,basedonthePhillipscurve,whichwasasubsequentaddi=ontothebasicKeynesianmodels.
TheDis=nguishingDifferenceoftheKeynesianApproach
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 5
• TheKeynesianmodelstartsbyconsideringthedetermina=onofaggregatedemand.Theassump=onisthattotalrealoutputandincomeY,isequaltothesumofrealconsump=onC,realgrossinvestmentΙandrealgovernmentexpenditureG.
• Inthesimplestversion,thatoftheKeynesiancross,investmentandgovernmentexpenditureareconsideredexogenous,andconsump=onisassumedtobeaposi=vefunc=onofcurrentrealdisposableincome.
TheKeynesianCross
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 6
TheModeloftheKeynesianCross
Yt = Ct + It +Gt
Ct = C Yt −Tt( )
0 <CY =∂C
∂(Y −T )<1
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 7
ShortRunEquilibriumintheModeloftheKeynesianCross
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 8
TheEquilibriumCondi=onintheProductMarketandtheMul=pliers
Yt = C Yt −Tt( )+ It +Gt
dYtdIt
= dYtdGt
= 11−CY
>1
dYtdGt dGt=dTt
= 1
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 9
• Realoutputisdeterminedbytheequalityofaggregatesupplyandaggregatedemand,whichisthesumofrealconsump=on,investmentandgovernmentexpenditure.Pricesareassumedfixedorsluggishtoadjust,soachangeinaggregatedemandbringsaboutachangeinaggregatesupplythroughcorrespondingchangesinemployment.
• Anexogenouschangeinaggregatedemand,eitherthroughinvestmentorthroughgovernmentexpenditure,resultsinachangeinrealoutputwhichisamul=pleoftheoriginalchangewhichishigherthanone,sincethemarginalpropensitytoconsumeislessthanone.
• Whenaggregatedemandincreases,realoutputandincomeincreasesinordertomaintainequilibriumbetweenrealoutputandexpenditure.
TheEquilibriumCondi=onintheProductMarketandtheMul=pliers
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 10
• Anincreaseininvestment,orgovernmentexpenditure,causesacorrespondingonetooneincreaseinaggregatedemand,andaggregaterealoutput.
• Theincreaseinrealoutputinducesanincreaseinprivateconsump=onthroughtheconsump=onfunc=on,whichbringsaboutafurtherincreaseinaggregatedemandandrealoutputandincome.
• Consequently,agivenexogenousriseinaggregatedemandhasamul=pleeffectonaggregaterealincome,duetothesecondroundeffectsthroughaggregateconsump=on,whichinturnproducefurtherincreasesinrealdemandandrealoutputandemployment.
WhyistheMul=plierHigherThanOne
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 11
• Anincreaseinpublicexpenditure,fundedbyanequalincreaseintaxes,increasestotalaggregateexpenditureandrealoutputandincomebythesameamount.
• ThisissomethingthatwasprovenbyHaavelmo(1945)whoderivedthebalancedbudgetmulAplier.
• Governmentexpenditureincreasesaggregatedemandonetoone,butthetaxincreasereducesprivateconsump=onbylessthanonetoone,becausethemarginalpropensitytoconsumeislessthanone.Consequently,theini=alimpactonoverallexpenditureisequalto1-CY=mesthechangeingovernmentexpenditure,andtheoveralleffectofachangeingovernmentexpenditurefinancedbyincreasedtaxesisequaltounity.
WhyistheBalancedBudgetMul=plierEqualtoUnity
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 12
• Inanimportantpaper,Samuelson(1939)combinedthemodeloftheKeynesiancrosswithaninvestmentfunc=onbasedontheprincipleofaccelera=on,toderiveendogenouscycles.
• IntheSamuelsonmodel,theinvestmentfunc=onisbasedonthesocalledacceleraAonprinciple,whichimpliesthatwhenthereisaposi=vechangeinconsump=on,firmswillinvestmore,inordertoproducethehigherquan=tyofconsumergoodsdemanded.Theacceleratormeasuresthesensi=vityofinvestmenttochangesinaggregateconsump=on.
• Theconsump=onfunc=onislinear,accordingtowhichconsump=onisafunc=onoflaggedandnotcurrentincome,andgovernmentexpenditureisassumedexogenousandconstant.
• TheSamuelsonmodelresultsinasecondorderlineardifferenceequa=on,which,dependingonthevalueoftheaccelerator,resultsineithermonotonicconvergenceorendogenouscycles.
TheSamuelsonModeloftheInterac=onoftheMul=plierwiththeAccelerator
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 13
• ThebasicmodeloftheKeynesiancross,assumesthatinvestmentisexogenous.
• AmoregeneralformoftheKeynesianmodelconsidersthataggregateinvestmentdependsontherealinterestrate,andintroducestheequilibriumcondi=oninthemarketformoney,inordertoanalyzethesimultaneousdetermina=onofrealoutputandtheinterestrate.ThisformofthemodelwaspresentedinChapters10-18oftheGeneralTheory,andwascodifiedastheIS-LMmodel,intheimportantcontribu=onofHicks(1937).ThiswasthemostwidelyusedversionoftheKeynesianmodel.
• ThemaindifferencefromthepreviousmodeloftheKeynesiancrossisthatinvestmentceasestobetreatedasexogenous,andisconsideredtodependnega=velyontherealinterestrate.Assumingthatinfla=onaryexpecta=onsaregiven,investmentwilldependnega=velyonthecurrentnominalinterestrate.
TheIS-LMModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 14
• Thiscondi=ondescribesthecombina=onsofrealoutputandthenominalinterestratethatensureequilibriuminthemarketforgoodsandservices.Itisdepicteddiagramma=callyasadownwardslopingIS(Investment-Savings)curve.
EquilibriumCondi=onintheMarketforGoodsandServices
Yt = C Yt −Tt( )+ It (it )+Gt
∂I∂i
< 0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 15
• Thiscondi=ondescribesthecombina=onsofrealoutputandthenominalinterestratethatensureequilibriuminthemoneymarket,inthesensethatmoneydemandisequaltotheexogenousmoneysupply.Itisdepicteddiagramma=callyasanupwardslopingLM(Liquidity-Money)curve.
EquilibriumCondi=onintheMoneyMarket
Mt
Pt= m Yt ,it( )
∂m∂Y
> 0, ∂m∂i
< 0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 16
TheIS-LMModelofSimultaneousEquilibriumintheOutputandMoneyMarkets
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 17
• Realoutputandthenominalinterestratearedeterminedatthepointwhereboththemarketforgoodsandservicesandthemarketformoneyareinequilibrium.
• Atthepointofintersec=onoftheIScurve,whichdescribesequilibriuminthemarketforgoodsandservices,andtheLMcurve,whichdescribesequilibriuminthemoneymarket,theeconomyisthusinshortrunequilibrium.
• Sincethepricelevelisassumedtobefixed,thisequilibriumcouldbeatlessthanfullemployment.Infact,thisisassump=onusuallymadeinKeynesianmodels.
ShortRunEquilibriumintheIS-LMModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 18
• Anincreaseingovernmentexpenditure,orataxcut,shifstheIScurvetotheright,andcausesanincreaseinrealoutputandthenominalinterestrate.
• AnincreaseinthemoneysupplyshifstheLMcurvetotheright,andcausesanincreaseinrealincomeandareduc=oninthenominalinterestrate.
• Bothfiscalandmonetarypoliciescanthusleadtoanincreaseinaggregatedemand,andanincreaseinrealoutputandemployment.
• Thisisthera=onaleforaggregatedemandpoliciesintheKeynesianmodel.
TheEffectsofMonetaryandFiscalPolicyintheIS-LMModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 19
• Thelastandmoresophis=catedformofthebasicKeynesianmodelisanalyzedaferChapter19oftheGeneralTheory.
• Inthisformofthemodel,thepricelevelceasestobeexogenous,andisallowedtochangeinordertoequilibrateaggregatedemandforgoodsandserviceswithalessthanperfectlyelas=caggregatesupply.However,nominalwagesares=llconsideredtobefixedintheshortrun.
• TheaggregatedemandfuncAon(AD)isderivedfromthesimultaneoussa=sfac=onoftheequilibriumcondi=oninthemarketforgoodsandservices(IS)andtheequilibriumcondi=oninthemoneymarket(LM).
• TheaggregatesupplyfuncAon(AS),isderivedfromthemaximizingbehaviorofarepresenta=vecompe==vefirm,selec=ngthelevelofemploymentandoutput,takingnominalwagesandpricesasgiven.
TheAD-ASModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 20
Ahigherpricelevel,giventhemoneysupply,meanslowerrealmoneybalances,highernominalinterestratesandlowerinvestmentdemand.Thus,giventhemoneysupply,anincreaseinthepricelevelreducesaggregatedemand,andafallinthepricelevel,increasesaggregatedemand.TheADscheduleisthusdownwardsloping.
TheAggregateDemandSchedule(AD)
Yt = DMt
Pt,Gt ,Tt
⎛⎝⎜
⎞⎠⎟
∂D∂Pt
< 0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 21
Sincemaximizingbehaviorbytherepresenta=vefirmimpliesadownwardslopinglabordemandcurvewithrespecttotherealwage,employmentandoutputareanega=vefunc=onoftherealwage.Ifthenominalwageisexogenouslyfixed,asassumedinthisversionoftheKeynesianmodel,thenaggregatesupplyisaposi=vefunc=onofthepricelevel,asahigherpricelevelisassociatedwithalowerrealwage.
TheAggregateSupplySchedule,AS
Yt = SWt
Pt
⎛⎝⎜
⎞⎠⎟
∂S∂Pt
> 0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 22
TheAD-ASModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 23
ShortRunEquilibriumwithLowEmploymentintheAD-ASModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 24
• Assumeanoriginalequilibriumisat“high”employmentoutput.Anega=vedisturbanceinaggregatedemand,shifstheaggregatedemandcurveADtothelef.Inthenewshort-runequilibrium,incomeandemploymentdeclines,andthepricelevelfalls.Becauseoftherigidityofnominalwages,theeconomymovestoanequilibriumwithlowerrealoutputandemploymentandhigherunemployment.
• Ifnominalwageswerenotfixedintheshortrun,andadjustedtoachievehighemployment,theaggregatesupplyfunc=onwouldbeperpendiculartothelevelofhighemployment,andchangesinaggregatedemandwouldonlyresultinchangesinthepricelevel.Consequently,withfullflexibilityofwagesandpricesandwages,thismodelhasthesameproper=esasa“classical”model.
• Incontrasttothe“classical”modeloffulladjustmentofwagesandprices,intheKeynesianmodelwithnominalwagerigidity,evenmonetarydisturbancescanshifaggregatedemandandcausefluctua=onsinrealoutput,employmentandotherrealvariablessuchasrealwagesandinterestrates.
AggregateDemandDisturbancesandAggregateFluctua=onsintheAD-ASModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 25
• Howcantheimpactofshockstoaggregatedemandandsupplybeaddressed?AccordingtotheKeynesianapproach,anappropriatesolu=oncancomefrommacroeconomicpolicy.Anincreaseofgovernmentexpenditure,areduc=onintaxesoranincreaseinthemoneysupplycanmovetheaggregatedemandcurvetotheright,andcounteracttheconsequencesofanini=aldemandorsupplyshockonrealoutputandunemployment.Inthecaseofdemandshocks,thepricelevelreturnstoitsoriginalequilibrium.Inthecaseofanega=vesupplyshocktherearefurthereffectsonthepricelevel.
• Thisisthejus=fica=onandtheeffectsofaggregatedemandpoliciesintheKeynesianmodel.Inprinciple,aggregatedemandpolicies,suchasmonetarypolicy,couldbeusedtocounteracttheeffectsofbothdemandandsupplyshocksonaggregateoutputandunemployment.Thiswouldimplythataggregatedemandpoliciescouldinprinciplebeusedtostabilizeeconomiesaroundlevelsofhighemploymentandhelpavoidtherepe==onofphenomenasuchastheGreatDepression.
TheJus=fica=onforAggregateDemandPoliciesintheKeynesianModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 26
RecessionsandRealOutputintheUSA,1854-2014
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ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 27
RecessionsandUnemploymentintheUSA,1889-2014
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ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 28
RecessionsandInfla=onintheUSA,1854-2014
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Recession% Infla8on%(based%on%CPI)%
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 29
• Theassump=onofabsolutenominalrigidityineitherpricesorwagesisobviouslynotrealis=c.Economiesarecharacterizedbythesimultaneousexistenceofinfla=onandunemployment,aphenomenonwhichimpliesthatbothpricesandwagesadjustgradually.
• Sincethelate1950s,acentralpointofreferencefortheKeynesianmodelwasthePhillipscurve.Thiswasanega=verela=onshipbetweenunemploymentandwageinfla=on,documentedbyPhillips(1958).
• ThePhillipscurve,wascombinedwiththeIS-LMmodelofaggregatedemand,tosimultaneouslydeterminebothinfla=onandunemployment.
TheKeynesianApproachandthePhillipsCurve
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 30
• ThePhillipscurvewasanempiricalrela=onship,es=matedeconometricallybyA.W.Phillipsinthelate1950s:
ThePhillipsCurve
• whereπdenotesinfla=on,utheunemploymentrateandu0theequilibriumunemploymentrate,i.etheonecorrespondingtozeroinfla=on.Thefunc=onalrela=onshipφbetweeninfla=onandunemploymentes=matedbyPhillipswasnonlinear.
π =ϕ(u), ϕ(u0 ) = 0, ′ϕ (u) < 0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 31
• ΗκαμπύλητηνοποίαεκτίμησεοικονομετρικάοPhillipsείχετηνεξήςμορφή:
TheOriginalPhillipsCurve,1861-1913
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 32
AGeneralRepresenta=onofthePhillipsCurve
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 33
• InthecontextofthebasicKeynesianmodel,combiningtheIS-LMmodelofaggregateddemandwiththePhillipscurve,onecoulddeducethatanincreaseinaggregatedemandwouldleadtohigherrealincomeandemployment,lowerunemployment,andariseininfla=onalongthePhillipscurve.
• Conversely,adeclineinaggregatedemandwouldleadtoalowerlevelofrealincomeandemployment,higherunemploymentandareduc=onininfla=onalongthePhillipscurve.
• Usingthiscombinedapproach,SamuelsonandSolow(1960),arguedthattheshort-termproblemofmacroeconomicpolicycouldbeseenasthedetermina=onofthelevelofaggregatedemand,inordertoselectthesociallydesiredcombina=onofinfla=onandunemployment.
• In=mesofrecession,anincreaseinaggregatedemandwillleadtoareduc=oninunemployment,butatthecostofhigherinfla=on.In=mesofeconomicboomandhighinfla=on,infla=oncouldbereducedthroughareduc=oninaggregatedemand,butthiswouldalsoresultinhigherunemployment.
MacroeconomicPolicyintheKeynesianModelCombinedwiththePhillipsCurve
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 34
• Sincethemid-1960s,thenega=verela=onshipbetweeninfla=onandunemploymentbegantoshif.Higherinfla=onledtoareduc=onofunemploymentonlytemporarily,asunemploymentroseaferawhiletoreturntoitsoriginallevelwithoutareduc=onininfla=on.
• Thiswasa�ributedtotheimpactofinfla=onaryexpecta=ons.AsarguedbyPhelps(1967)andFriedman(1968),asustainedincreaseininfla=onwouldleadtoexpecta=onsofhigherfutureinfla=ononpartofhouseholdsandfirms.Theresultofthiswouldbethatinfla=onwouldhavetoincreaseevenfurtherinordertoachieveareduc=oninunemployment.
TheInstabilityofthePhillipsCurveandInfla=onaryExpecta=ons
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 35
• Essen=ally,PhelpsandFriedmanarguedthatthePhillipscurvetakestheform,
AnExpecta=onsAugmentedPhillipsCurve
• whereπisinfla=on,πeexpectedinfla=on,utheunemploymentrate,andu0theequilibriumunemploymentrate,correspondingtotheequalitybetweenactualandexpectedinfla=on.
π = π e +ϕ(u), ϕ(u0 ) = 0, ′ϕ (u) < 0
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 36
Infla=onaryExpecta=onsandtheShifingPhillipsCurve
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 37
• AccordingtoFriedman(1968),eacheconomytendstowardsanequilibriumunemploymentrateu0,whichcanbelabelledthe“natural”rateofunemployment.
• The“natural”rateofunemploymentdependsonlyonrealfactors,includinglabormarketfric=ons,distor=onsandinefficiencies.
• Tryingtoreducetheunemploymentratebelowthis“natural”rate,byincreasingaggregatedemandandinfla=on,wouldonlymeetwithtemporarysuccess.
• Asinfla=onaryexpecta=onsadjusttohigherinfla=on,unemploymenttendstoreturntothe“natural”rate.Onewouldneedcon=nuousincreasesininfla=oninordertokeepunemploymentbelowits“natural”rate.
The“Natural”RateofUnemployment
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 38
InordertoanalyzetheFriedman-Phelpsargument,assumethatthePhillipscurveislinearandgivenby,
The“Natural”RateHypothesisandthePhillipsCurve
π t = π te + a − but
whereaandbareposi=veparameters.Theeconomyisatits“natural”ratewheninfla=onaryexpecta=onsareequaltoactualinfla=on.Consequently,the“natural”rateofunemploymentinthismodelisgivenby,
u0 =ab
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 39
Formanyyears,thedominantapproachtotheforma=onofexpecta=onsinmacroeconomicswastheadap=veexpecta=onshypothesisofCagan(1956).
Accordingtothishypothesis,expecta=onsineachperiodareadjustedbyapercentageofthedevia=onoftheactualfromtheexpectedvalueofavariableinthepreviousperiod.Consequently,theadjustmentofinfla=onaryexpecta=onsinlinewiththishypothesiswouldtaketheform,
Infla=onaryExpecta=onsandtheAdap=veExpecta=onsHypothesis
π te −π t−1
e = (1− λ)(π t−1 −π t−1e )
Infla=onaryexpecta=onsareadjustedbyapercentage1-λofthedivergencebetweenactualandexpectedinfla=oninthepreviousperiod.1-λisthespeedofadjustmentofexpecta=ons.λ=0impliesfulladjustmentwithinaperiod,andλ=1impliesnoadjustment(staAcexpectaAons).
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 40
Whatwouldhappeninthismodelifthegovernmenthadafixedtargetforunemployment,whichwaslowerthanthe“natural”rateofunemployment?Inthiscase,thegovernmentandthemonetaryauthori=eswouldseekapathforinfla=oninordertomaintainunemploymentbelowits“natural”rateu0atuA,whereuA<u0.
Infla=onineachperiodwouldbedeterminedby,
ThePathofInfla=onandUnemploymentunderAdap=veExpecta=ons
π t = π te + a − buA = π t
e + b(u0 − uA )
Infla=onaryexpecta=onsineachperiodwouldbedeterminedby,
π te = (1− λ)π t−1 + λπ t−1
e = 1− λ1− λL
π t−1 = (1− λ) λ iπ t−1−ii=0
∞∑
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 41
Solvingforinfla=on,subs=tu=ngouttheadap=veexpecta=onshypothesis,infla=onineachperiodwouldbedeterminedby,
ThePathofInfla=onandUnemploymentunderAdap=veExpecta=ons
π t = π t−1 + b(1− λ)(u0 − uA )
Infla=onhasaunitroot,andthusnotonlydoesitnotconverge,butitincreasesineachperiodbyapercentagewhichdependsonthedifferencebetweenthe“natural”rateofunemploymentrateu0fromthegovernment'stargetunemploymentrateuA.Asthegovernmenta�emptstokeepunemploymentbelowits“natural”rate,itmustberelyingonconstantlyincreasinginfla=on,sothatinfla=onisalwayshigherthaninfla=onaryexpecta=ons.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 42
TheShifingPhillipsCurveandthe“Natural”RateofUnemployment
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 43
TheinstabilityofthePhillipscurvederivesdirectlyfromthea�emptbythegovernmenttokeepunemploymentbelowits“natural”rate.Otherwise,infla=onwouldconverge.
Assumethatthegovernmenthadafixedinfla=ontargetπ0,andkeptinfla=onconstantatthistarget.
Theninfla=onaryexpecta=onswouldfollow,
TheInstabilityofthePhillipsCurveandGovernmentPolicy
π te = (1− λ)π 0 + λπ t−1
e
which,forλ<1,convergestoπ0.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 44
• TheinstabilityoftheoriginalPhillipscurveobservedinthelate1960s,andtheinterpreta=ongiventoitbyPhelpsandFriedman,sparkedarevolu=onintheanalysisofaggregatefluctua=onsandmacroeconomicpolicy.
• Theliteraturehassincemovedintwodirec=ons.
• First,greatemphasiswasplacedonthemicroeconomicfounda=onsofthedetermina=onofwages,prices,thesupplyanddemandforgoodsandservicesandthedetermina=onoftheequilibriumunemploymentrate.Theresultisthattodayboth“newclassical”andthe“newKeynesian”modelsofaggregatefluctua=onsarebasedondynamicstochas=cgeneralequilibriummodelswithdetailedandconsistentmicroeconomicfounda=ons.
• Secondly,thisdevelopmentledtotheadop=onofthehypothesisofra=onalexpecta=onsinsteadofadap=veexpecta=ons.
TheInstabilityofthePhillipsCurveandMacroeconomicTheoryandPolicy
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 45
InthislecturewehaveintroducedthebasicKeynesianmodels,whichwereassociatedwiththedevelopmentofmacroeconomicsfromthemid-1930stotheendofthe1960s.
WehaveshownthatwhatseparatesclassicalfromKeynesianmodelsistheassump=onofnominalrigidityand/orgradualadjustmentinnominalwagesandthepricelevel.ThisiswhatallowsKeynesianmodelstoexplaintherealeffectsofmonetaryandaggregatedemandshocks,andprovideara=onaleaggregatedemandpolicies.
Muchofthetheore=calresearchofthelastfivedecadeshasfocusedonthemicroeconomicfounda=onsofKeynesianmodels,andinpar=cularthePhillipscurve.Thisisanimportantpartoftheso-callednewKeynesianapproach.
Inthenextlectureweanalyzeasimpledynamicmodelthatbelongstothiscategoryandlookatthepredic=onsofthe“new”Keynesianapproachforaggregatefluctua=onsandtherela=onshipbetweeninfla=onandunemployment.
Evalua=ngtheTradi=onalKeynesianModels
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 46
Inanimportantpaper,Samuelson(1939)combinedthemodeloftheKeynesiancrosswithaninvestmentfunc=onbasedontheprincipleofaccelera=on,toderiveendogenouscycles.SamuelsonconsideredthefollowingversionoftheKeynesianmodel.
AnnexontheSamuelsonMul=plierAcceleratorModel
Yt = Ct + It +Gt
It = a(Ct −Ct−1)+ b
Ct = cYt−1 + d
Gt = e
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 47
• a,b,c,dandeareconstantparameters.aistheaccelerator,whichdetermineshowachangeinconsump=onaffectscurrentinvestment,andbisautonomousinvestment.c<1isthemarginalpropensitytoconsume,anddisautonomousconsump=on.Finallyeisgovernmentexpenditure,assumedconstant.
• Theinvestmentfunc=onisbasedonthesocalledacceleraAonprinciple,whichimpliesthatwhenthereisaposi=vechangeinconsump=on,firmswillinvestmore,inordertoproducethehigherquan=tyofconsumergoodsdemanded.Whenthereisanega=vechangeinconsump=on,firmswillreduceinvestment,astheyneedlesscapitaltomeetthelowerdemandforconsumergoods.Theacceleratorameasuresthesensi=vityofinvestmenttochangesinaggregateconsump=on.
• Theconsump=onfunc=onislinear,accordingtowhichconsump=onisafunc=onoflaggedandnotcurrentincome.
• Governmentexpenditureisassumedexogenousandconstantate.
TheParametersoftheSamuelsonModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 48
Subs=tu=ngtheconsump=onfunc=onintotheinvestmentfunc=on,
TheDynamicsoftheSamuelsonModel
It = ac(Yt−1 −Yt−2 )+ b
Subs=tu=ngthisinvestmentfunc=onandtheconsump=onfunc=onintotheequilibriumcondi=onintheoutputmarket,
Yt = c(1+ a)Yt−1 − acYt−2 + b + d + e
Ifthisdifferenceequa=onconverges,equilibriumisgivenby,
Y*= b + d + e1− c
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 49
Equilibriumoutputdependsonlyonautonomousexpenditureandthemul=plier1/(1-c),assuggestedbythemodeloftheKeynesiancross.However,thepathofoutputisdeterminedbyasecondorderdifferenceequa=on,whichdependsonboththemul=plierandtheaccelerator.
Forthedifferenceequa=ontobestable,andfortheeconomytoconvergetoequilibriumoutput,acmustbelessthanone,ortheacceleratormustsa=sfya<1/c.Ifthiscondi=onisnotsa=sfied,outputwilldiverge.
Thus,forstabilitytheacceleratormustbesmallerthantheinverseofthemarginalpropensitytoconsume.
Proper=esoftheSamuelsonModel
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 50
Fortherootstoberealandforincometoconvergemonotonicallytoitsequilibriumvalue,thecondi=onis,
ConvergenceintheSamuelsonModel
4a(1+ a)2
≤ c < 1a
Ifthecondi=ononthelefhandsideisnotsa=sfied,butthecondi=onontherighthandsideis,convergencetakesplacenon-monotonicallyanddisplaysoscilla=onsastherootsarenotreal.
ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 51
ConvergenceintheSamuelsonModelforc=0.75andDifferentValuesofa
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
a=0.10 a=0.333 a=1.10
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