在计量经济学的Endogeneity：有助易变的估计t 3.ppt

EndogeneityinEconometrics InstrumentalVariableEstimation MingLU Endogeneity OmittingvariablebiasSimultaneityMeasurementerror Canweignoretheomittedvariablesbias Itcanbesatisfactoryiftheestimatesarecoupledwiththedirectionofthebiasesforthekeyparameters Canweuseproxytoeliminateomittedvariablebias Sometimes CanFEestimationsolveomittingvariableproblem Firstdifferencingorfixedeffectsestimationeliminatestime constantvariables Inaddition thepaneldatamethodsdonotsolvetheproblemoftime varyingomittedvariables IdeaofIVEstimation Exogenousvariable IndirecteffectsofIV Example WhatcanserveasIVforedu Mother seducation Numberofsiblings Thereportofothers Adummyvariablethatisequalto1ifamanisborninthefirstquarteroftheyear AngristandKrueger 1991 Problematic InChina theyearsofprimaryedu IVforskippedclass Thedistancefromhometoschool OtherexamplesofIV IVforinstitution Language History Mauro 1995 使用人口的种族和语言构成作为腐败的工具变量 HallandJones 1999 用距离赤道的距离和以西欧语言为第一语言的程度作为制度质量的工具变量 LaPortaetal 1997 1998 1999 把法律的起源作为各种法律结构的工具变量 Acemoglu Johnson andRobinson 2001 2002 使用殖民地时代 1500年前后 的死亡率和人口密度作为制度的工具变量IVforschoolchoice Numberofsteams Identification Referto 15 9 and 15 10 The asymptotic standarderrorof SSTisthetotalsumofsquaresofthexi Self selection Angrist 1990 studiedtheeffectthatbeingaveteranintheVietnamwarhadonlifetimeearnings DraftlotterynumberisagoodIVcandidateforveteran SomeadditionalwordsaboutnaturalexperimentandDID PropertiesofIVwithaPoorInstrumentalVariable PoorIVcancauseseriousbias R2 MostregressionpackagescomputeanR squaredafterIVestimation usingthestandardformula R2 1 SSR SST whereSSRisthesumofsquaredIVresiduals andSSTisthetotalsumofsquaresofy R2canbenegativeinthiscase IVESTIMATIONOFTHEMULTIPLEREGRESSIONMODEL structuralequation Estimation EfficientIV Equation 15 26 isanexampleofareducedformequation whichmeansthatwehavewrittenanendogenousvariableintermsofexogenousvariables TWOSTAGELEASTSQUARES 2SLSinwords Thefirststageistoruntheregressionin 15 36 whereweobtainthefittedvaluesy 2 ThesecondstageistheOLSregression 15 38 Becauseweusey 2inplaceofy2 the2SLSestimatescandiffersubstantiallyfromtheOLSestimates Anotherinterpretation MultipleEndogenousExplanatoryVariables ORDERCONDITIONFORIDENTIFICATIONOFANEQUATION Weneedatleastasmanyexcludedexogenousvariablesasthereareincludedendogenousexplanatoryvariablesinthestructuralequation IVSOLUTIONSTOERRORS IN VARIABLESPROBLEMS OnepossibilityistoobtainasecondmeasurementonX 1 say z1 asIV AnalternativeistouseotherexogenousvariablesasIVsforapotentiallymismeasuredvariable TESTINGFORENDOGENEITYANDTESTINGOVERIDENTIFYINGRESTRICTIONS The2SLSestimatorislessefficientthanOLSwhentheexplanatoryvariablesareexogenous aswehaveseen the2SLSestimatescanhaveverylargestandarderrors Howtotestendogeneity 1 ComparingtheOLSand2SLSestimatesanddeterminingwhetherthedifferencesarestatisticallysignificant Hausman 1978 2 Aregressiontest Anotherinterpretationof2SLS Includingv 2intheOLSregression 15 51 clearsuptheendogeneityofy2 Wecanalsotestforendogeneityofmultipleexplanatoryvariables Foreachsuspectedendogenousvariable weobtainthereducedformresiduals Then wetestforjointsignificanceoftheseresidualsinthestructuralequation usinganFtest TestingOveridentificationRestrictions Ifwehavemorethanoneinstrumentalvariable wecaneffectivelytestwhethersomeofthemareuncorrelatedwiththestructuralerror UseoneIVandgetthepredictedresidual thentestthecorrelationbetweenotherIVsandtheresidual TESTINGOVERIDENTIFYINGRESTRICTIONS i Estimatethestructuralequationby2SLSandobtainthe2SLSresiduals u 1 ii Regressu 1onallexogenousvariables ObtaintheR squared sayR12 iii UnderthenullhypothesisthatallIVsareuncorrelatedwithu1 nR12 X2 q whereqisthenumberofinstrumentalvariablesfromoutsidethemodelminusthetotalnumberofendogenousexplanatoryvariables IfnR12exceeds say the5 criticalvalueintheX2 q distribution werejectH0andconcludethatatleastsomeoftheIVsarenotexogenous IsitbettertohavemoreIVs Addinginstrumentstothelistimprovestheasymptoticefficiencyofthe2SLS Butthisrequiresthatanynewinstrumentsareinfactexogenous Withthetypicalsamplesizesavailable addingtoomanyinstruments thatis increasingthenumberofoveridentifyingrestrictions cancauseseverebiasesin2SLS 2OmittedTopics 2SLSWITHHETEROSKEDASTICITYAPPLYING2SLSTOTIMESERIESEQUATIONS APPLYING2SLSTOPOOLEDCROSSSECTIONSANDPANELDATA Forpooledcrosssectionsdata addtimedummy Forpaneldata Inthefirststage usethedifferencedIVtogetanestimateoftheendogenousvariable Question IfthepanelmodelisaFEone howt