STATAGMM广义矩估计.pdf

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1、GeneralizedmethodofmomentsestimationinStata11DavidM.DrukkerStataCorpStataConferenceWashington,DC20091/27Outline1AquickintroductiontoGMM2gmmexamplesOrdinaryleastsquaresTwo-stageleastsquaresCross-sectionalPoissonwithendogenouscovariatesFixed-effectsPoissonregression2/27AquickintroductiontoGMMMethodofM

2、oments(MM)Weestimatethemeanofadistributionbythesamplemean,thevariancebythesamplevariance,etcWewanttoestimateµ=E[y]PNWeuseµb=(1/N)i=1yiThisestimatorhasnicepropertiesbecauseitsolvesthesamplemomentconditionXN(1/N)(yi−µ)=0i=1whichisthesampleanalogofthepopulationmomentconditionE[y−µ]=0Estimatorsthatsolv

3、esamplemomentequationstoproduceestimatesarecalledmethod-of-moments(MM)estimatorsThismethoddatesbacktoPearson(1895)3/27AquickintroductiontoGMMGeneralizedmethod-of-moments(GMM)TheMMonlyworkswhenthenumberofmomentconditionsequalsthenumberofparameterstoestimateIftherearemoremomentconditionsthanparameter

4、s,thesystemofequationsisalgebraicallyoveridentifiedandcannotbesolvedGeneralizedmethod-of-moments(GMM)estimatorschoosetheestimatesthatminimizeaquadraticformofthesamplemomentconditionsGMMgetsasclosetosolvingtheover-identifiedsystemofsamplemomentequationsaspossibleGMMreducestoMMwhenthenumberofparameters

5、equalsthenumberofmomentconditionsHansen(1982)producedmanyofthekeyresults;Wooldridge(2002);CameronandTrivedi(2005)providegoodintroductions4/27AquickintroductiontoGMMDefinitionofGMMestimatorOurresearchquestionimpliesqpopulationmomentconditionsE[m(wi,θ)]=0misq×1vectoroffunctionswhoseexpectedvaluesareze

6、rointhepopulationwiisthedataonpersoniθisk×1vectorofparameters,k≤qThesamplemomentsthatcorrespondtothepopulationmomentsarePNm(θ)=(1/N)i=1m(wi,θ)Whenk

7、epropertiesoftheGMMestimatorθb≡argminm(θ)′Wm(θ)GMMθWhenk=q,theMMestimatorsolvesm(θ)exactlysom(θ)′Wm(θ)=0WonlyaffectstheefficiencyoftheGMMestimatorSettingW=Iyieldsconsistent,butinefficientestimatesSettingW=Cov[m(