ln10 Panel Data II Additional Topics (Wooldridge， Ch. 11).pdf

《ln10 Panel Data II Additional Topics (Wooldridge， Ch. 11).pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、ApEc8212EconometricAnalysis--Lecture#10PanelDataII:AdditionalTopics(Wooldridge,Ch.11)I.IntroductionThislectureexaminesfiveadditionaltopicsregardingpaneldatamodels:1.GeneralizedMethodofMoments(GMM)EstimationofPanelDataModels2.RandomandFixedEffectsEstimationUsingInstrumentalVariable

2、s3.Hausman-TaylorModels4.FirstDifferencingwithInstrumentalVariables5.PanelDataandMeasurementError6.EstimationunderSequentialExogeneityThisisallfromChapter11ofWooldridge.NotethatIdonotcoveronetopic,whichismodelswithindividual-specificslopes.Youcanreadthisonyourownonpp.374-387.1II.G

3、MMEstimationandPanelDataRecallthebasicpaneldata(unobservedeffects)model:yit=xit′β+ci+uitt=1,2,…Tyi=Xiβ+cijT+ui=Xiβ+vi(vectorform)wherejTisaT×1columnvectorofones.Asdiscussedinthepreviouslecture,randomeffects(RE),fixedeffects(FE)andfirstdifferencing(FD)areeachasymptoticallyefficient

4、underdifferentassumptionsaboutspecificassumptionsaboutthe(conditional)variance-covariancematrixofvi(REcase),ui(FE)orΔui(FD).Ingeneral,twothingsareneededregardingtherelevantvariance-covariancematrixtoobtainefficiency:1.Theunconditionalvariance-covariancematrixhasaspecificstructure;

5、and2.“System”homoscedasticityisassumed;thatistheelementsofthevariance-covariancematrixdonotvarywithrespecttoxiorci.Infact,wereallydonotneedthefirstrequirement.Wecanallowtheunconditionalvariance-covariance2matrixtohaveanystructureandthenuseFGLStoobtainanefficientresultaslongasthese

6、condrequirementholds.Ifthatrequirementdoesnothold,thenGMMestimationwithanoptimalweightingmatrixisgenerallymoreefficient.Toseehowthisworks,let’sstartwiththerandomeffectsmodel.SupposethatAssumptionRE.1holds:AssumptionsRE.1(a)E[uit

7、xi,ci]=0t,=1,2,…T(b)E[ci

8、xi]=E[ci]=0Together(a)and(b

9、)implythatE[vi

10、xi]=0.(Why?)oLetxidenotethe(column)vectorofall“non-redundant”elementsinxi(i.e.anyelementsthatarefixedovertimeappearonlyonce).AssumptionRE.1oimpliesthatE[xivit]=0forallt.ThissuggeststhefollowingmatrixofIVs:oZi≡ITxi′Thisamountstousingvaluesofxifromothertimeperiods(bo

11、thpastandfuture)asinstrumentsforx