and studying difference equations(高级宏观经济学.pdf

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1、IntroductiontoAdvancedMacroeconomicAnalysis(IAMA)Lecture#4SolvingandstudyingdifferenceequationsintheoryIAMA/Lecture#41Summary•Reviewoflasttime•ThereducedformoftheAS-ADasasecondorder,scalar-valuedstochasticdifferenceequation•Solvingsecondorderdeterministicdifferenceequati

2、onsintheory•StudyingthecharacteristicrootsofthetransferfunctionIAMA/Lecture#421ReviewofLastTime•Extensionsofstaticmodelsnotcoveredincourse•Macroeconomicsasthestudyofaggregatedynamics•Thefoundationsofmacrodynamics•AS-ADmodelas“blackbox”forSlutsky´svisionIAMA/Lecture#43AS-

3、ADModelasasystemofstochasticdifferenceequationsAggregateDemand:Y=aY+a(m-p)+dt1t-12tttAggregateSupply/PhillipsCurve:p=`p+b(Y-`Y)+stt1tttCoreInflation/InflationaryExpectations:`p=lp+(1-l)pttt-1IAMA/Lecture#442where:Yt=realGDP(constantprices)int`Yt=potentialrealGDPintpt=inf

4、lationrateint`pt=coreinflationintdt=realdemandshockintst=supplyshockintmt=moneysupplygrowthintIAMA/Lecture#45AS-ADModelasasystemofstochasticdifferenceequationsThereduced(autoregressive)formofthemodelisfoundbyrewritingitinmatrixformandsolvingfor[Yt,pt]:Y1a1-a2Ytt-1

5、=ab
p1+ab(1-l)111p
t21
t-11-l-aabmt221
a1121-l1-l
dt
+abb1-b

1+a2b1(1-l)2111
st1-l1-l1-l1-lY
tIAMA/Lecture#463Slutsky´sVisionAssumedRandomShockspropagationCycles(input)mechanism(output)(input)IAMA/Lecture#47Randomshocks(whitenoise):43210-1

6、-2-3IAMA/Lecture#484Randomshocks(whitenoise):43210-1-2-3a1=0.7a2=0.5…asinputsforAS-ADmodelb1=0.2l=0.586420-2-4-6-8IAMA/Lecture#49Wold´svisionUniqueTimeSeriesDataInferredshocksstatistical(output)process(Input)plussomeassumptions(output)IAMA/Lecture#4105Wold´sRepresentatio

7、nTheoremThistimeinwords:Consideratimeseries{x}whichiscovariance-tstationaryinthesensethatithasatime-invariantexpectedvalueandautocovariancestructure.Thenthereexistsauniquerepresentationofthisseriesasarealizationofastationary,stochastictimeseriesprocessIAMA/Lecture#4113.S

8、olvingsecondorderdeterministicdifferenceequationsintheory•AS-ADmodelasasetofdifferenceequations(review)