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《计量经济学导论》ch(13).ppt

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Chapter12PropertiesofOLSwithseriallycorrelatederrorsOLSstillunbiasedandconsistentiferrorsareseriallycorrelatedCorrectnessofR-squaredalsodoesnotdependonserialcorrelationOLSstandarderrorsandtestswillbeinvalidifthereisserialcorrelationOLSwillnotbeefficientanymoreifthereisserialcorrelationSerialcorrelationandthepresenceoflaggeddependentvariablesIsOLSinconsistentifthereareser.corr.andlaggeddep.variables?No:IncludingenoughlagssothatTS.3‘holdsguaranteesconsistencyIncludingtoofewlagswillcauseanomittedvariableproblemandserialcorrelationbecausesomelaggeddep.var.endupintheerrortermTestingforserialcorrelationTestingforAR(1)serialcorrelationwithstrictlyexog.regressorsExample:StaticPhillipscurve(seeabove)Durbin-WatsontestunderclassicalassumptionsUnderassumptionsTS.1–TS.6,theDurbin-Watsontestisanexacttest(whereastheprevioust-testisonlyvalidasymptotically).Example:StaticPhillipscurve(seeabove)TestingforAR(1)serialcorrelationwithgeneralregressorsThet-testforautocorrelationcanbeeasilygeneralizedtoallowforthepossibilitythattheexplanatoryvariablesarenotstrictlyexogenous:ThetestmaybecarriedoutinaheteroscedasticityrobustwayGeneralBreusch-GodfreytestforAR(q)serialcorrelationCorrectingforserialcorrelationwithstrictlyexog.regressorsUndertheassumptionofAR(1)errors,onecantransformthemodelsothatitsatisfiesallGM-assumptions.Forthismodel,OLSisBLUE.Problem:TheAR(1)-coefficientisnotknownandhastobeestimatedCorrectingforserialcorrelation(cont.)ReplacingtheunknownbyleadstoaFGLS-estimatorTherearetwovariants:Cochrane-OrcuttestimationomitsthefirstobservationPrais-WinstenestimationaddsatransformedfirstobservationInsmallersamples,Prais-WinstenestimationshouldbemoreefficientComparingOLSandFGLSwithautocorrelationForconsistencyofFGLSmorethanTS.3‘isneeded(e.g.TS.3)becausethetransformedregressorsincludevariablesfromdifferentperiodsIfOLSandFGLSdifferdramaticallythismightindicateviolationofTS.3Serialcorrelation-robustinferenceafterOLSInthepresenceofserialcorrelation,OLSstandarderrorsoverstatestatisticalsignifica