Estimation of Parameters in the Presence of Model misspecification 在模型误设下的参数估计.ppt

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1、EstimationofParametersinthePresenceofModelmisspecificationandMeasurementErrorP.A.V.B.Swamy,GeorgeS.Tavlas,StephenG.HallAndGeorgeHondroyiannisIntroductionMosteconometricrelationshipsaresubjecttoatleastthefollowingthreeproblemsMeasurementErrorThetruefunctionalformisunknownOmittedvariablesWhiletherear

2、especifictechniquesorproceduresthatdealwiththeseproblemsoneatatimethereisnosingleapproachwhichworksforthemall.Thispaperproposesanewestimationstrategywhichpotentiallydealswithallformsofmodelmisspecificationsimultaneously.Unlikesomenon-parametrictechniquestheproposedmethodisfeasiblewithrelativelysmal

3、ldatasetsItalsooffersanewinterpretationofregressioncoefficientsinthepresenceofmisspecificationandaformalrepresentationofthebiaseswhichresult2.TheInterpretationofModelCoefficientsConsidertherelationshipbetweenanendogenousvariableandK-1ofitsdeterminants….WhereinparticularK-1maybeonlyasubsetofthefulls

4、etofdeterminantssothatwehaveomittedvariables.Inadditionwehavemeasurementerror=+,=+AndwemaybeestimatingthewrongfunctionalformWhatistheeconometriciantryingtoachieve?Ouranswertothisistoderiveanestimateofthepartialderivativeofwithrespectto,andtotesthypothesisaboutthis.Ifyouwanttoestimatethetruemodelthe

5、ntherereallyisnoalternativetospecifyingitcorrectly.Howeverifyouareonlyinterestedinpartialeffectsthenweofferanotherwayforward.Considerthefollowingtimevaryingparametermodel=++…+AllpotentialmisspecificationiscapturedinthetimevaryingcoefficientswhichofferacompleteExplanationofy.Nowthekeyquestioniswhata

6、rethestochasticassumptionsabouttheTVCsThecorrectstochasticassumptionsabouttheTVCcomesfromanunderstandingofthemisspecificationwhichdrivesthetimevariation.NotationandassumptionsLetdenotethetotalnumberofdeterminantsofy,thiscannotgenerallybeknown,butingeneralm>k-1.Nowletandj=1…K-1andg=k…mbethetruecoeff

7、icientsontheunderlyingmodel,wheretheparametersvarybecauseofeitheranon-linearfunctionalformortrulychangingparametersNowforg=k…letdenotetheinterceptandj=1…K-1denotetheothercoefficientsoftheregressionofon…Then