Panel Data Models .pdf

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1、PanelDataModels(I)PhDEconometricsWeiTanHanqingAdvancedInstituteofEconomicsandFinanceRenminUniversityofChinaWeiTan(RUC)PanelDataModels(I)1/64IntroductionIntroductionRandomE¤ectFixedE¤ectExampleWeiTan(RUC)PanelDataModels(I)2/64IntroductionLetyandxfx1;


;xKgbeobse

2、rvablerandomvariables,andletcbeanunobservablerandomvariable;thevector(y;x1;x2;


;xK;c)representsthepopulationinterest.Weareinterestedinthepartiale¤ectsoftheobservableexplanatoryvariablesxjinthepopulationregressionfunctionE(yjx1;x2;


;xK;c)Inwords,wewouldliketoh

3、oldcconstantwhenobtainingpartiale¤ectsoftheobservableexplanatoryvariables.Weusectodenotetheunobservablevariable,sinceweemphasizethattheunobservableisarandomvariable,butnotaparametertobeestimated.WeiTan(RUC)PanelDataModels(I)3/64IntroductionAssumingalinearmodelE(y

4、jx;c)=0+x+c(1)IfCov(xj;c)6=0forsomej,withoutadditionalinformationwe(1)cannotconsistentlyestimate;(2)arenotabletodeterminewhetherthereisaproblem.UnderadditionalassumptionstherearewaystoaddresstheproblemCov(x;c)6=0inthecrosssectionsetting.Proxyvariableforc,estimate

5、theequationbyOLS.IVfortheelementsofxthatarecorrelatedwithc.Findindicatorsofcthatcanbeusedinmultipleindicatorinstrumentalvariablesprocedure.WeiTan(RUC)PanelDataModels(I)4/64IntroductionInthepaneldatasetting,supposethatt=1;2,andcistimeconstant.Thenweareinterestedin

6、thepopulationregression:E(ytjxt;c)=0+xt+c;t=1;2Weassumethatcisconstantovertime,andhasaconstantpartiale¤ectovertime.Theunobserved,time-constantvariableiscalledanunobservede¤ectinpaneldataanalysis.Writethemodelinerrorformyt=0+xt+c+ut(2)where,byde…nitionE(utjxt;c)=0

7、;t=1;2(3)whichimpliesthatE(x0u)=0;t=1;2(4)ttWeiTan(RUC)PanelDataModels(I)5/64IntroductionIfweweretoassumeE(x0tc)=0,wecouldapplypooledOLS.Ifciscorrelatedwithanyelementofxt,thenpooledOLSisbiasedandinconsistent.Withtwoyearsofdatawecandi¤erenceequation(2)acrossthetwo

8、timeperiodstoeliminatethetime-constantunobservablec.De…ne
y=y2y1,
x=x2x1,and
u=u2u1.Thendi¤erencingequation(2)gives
y=
x+
u(5)ThekeyconditionsforOLStoconsis