Econometric analysis of dynamic panel-data models using Stata

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1、Econometricanalysisofdynamicpanel-datamodelsusingStataDavidM.DrukkerStataCorpSummerNorthAmericanStataUsersGroupmeetingJuly24-25,20081/321Dynamicpanel-datamodels2TheArellano-Bondestimator3TheArellano-Bover/Blundell-Bondestimator2/32Dynamicpanel-datamodelsWhydynamicpanel-datamodelsreq

2、uirespecialestimatorsIntroductionWeareinterestedinestimatingtheparametersofmodelsoftheformyit=yit−1γ+xitβ+ui+ǫitfori={1,...,N}andt={1,...,T}usingdatasetswithlargeNandfixedTByconstruction,yit−1iscorrelatedwiththeunobservedindividual-leveleffectuiRemovinguibythewithintransform(removingt

3、hepanel-levelmeans)producesaninconsistentestimatorwithTfixedFirstdifferencebothsidesandlookforinstrumental-variables(IV)andgeneralizedmethod-of-moments(GMM)estimators3/32TheArellano-BondestimatorTheArellano-BondestimatorIFirstdifferencingthemodelequationyields∆yit=∆yit−1γ+∆xitβ+∆ǫitThe

4、uiaregone,buttheyit−1in∆yit−1isafunctionoftheǫit−1whichisalsoin∆ǫitSo∆yit−1iscorrelatedwith∆ǫitbyconstruction[AndersonandHsiao(1981)]suggesteda2SLSestimatorbasedonfurtherlagsof∆yitasinstrumentsfor∆yit−1Forinstance,ifǫitisIIDoveriandt,∆yit−2wouldbeavalidinstrumentfor∆yit−1[Andersonan

5、dHsiao(1981)]alsosuggestedsuggesteda2SLSestimatorbasedonlaggedlevelsof∆yitasinstrumentsfor∆yit−1Forinstance,ifǫitisIIDoveriandt,yit−2wouldbeavalidinstrumentfor∆yit−14/32TheArellano-BondestimatorTheArellano-BondestimatorII[Holtz-Eakinetal.(1988)Holtz-Eakin,Newey,andRosen]and[Arellano

6、andBond(1991)]showedhowtoconstructestimatorsbasedonmomentequationsconstructedfromfurtherlaggedlevelsofyitandthefirst-differencederrorsWearecreatingmomentconditionsusinglaggedlevelsofthedependentvariablewithfirstdifferencesoftheerrorsǫitFirst-differencesofstrictlyexogenouscovariatesareals

7、ousedtocreatemomentconditionsAssumethatǫitareIIDoveriandt,i.e.noserialcorrelationintheerrorsWewilldropthisassumptionlaterWehavemoreinstrumentsthanparameters,souseGMMframework5/32TheArellano-BondestimatorStrictExogeneityIftheregressorsarestrictlyexogenous,ǫitcannotaffectxisforanysortI

8、ftheregressorsarepr