Endogeneity in Econometrics Instrumental Variable Estimation(截面和面板數(shù)據(jù)分析)課件

EndogeneityinEconometrics:

InstrumentalVariableEstimationMingLUEndogeneityOmittingvariablebiasSimultaneityMeasurementerrorCanweignoretheomittedvariablesbias?Itcanbesatisfactoryiftheestimatesarecoupledwiththedirectionofthebiasesforthekeyparameters.Canweuseproxytoeliminateomittedvariablebias?–Sometimes.CanFEestimationsolveomittingvariableproblem?Firstdifferencingorfixedeffectsestimationeliminatestime-constantvariables.Inaddition,thepaneldatamethodsdonotsolvetheproblemoftime-varyingomittedvariablesIdeaofIVEstimationExogenousvariable.IndirecteffectsofIV.ExampleWhatcanserveasIVforedu?Mother’seducation?Numberofsiblings?Thereportofothers?Adummyvariablethatisequalto1ifamanisborninthefirstquarteroftheyear.AngristandKrueger(1991).(Problematic.)InChina,theyearsofprimaryedu?IVforskippedclass?Thedistancefromhometoschool.OtherexamplesofIVIVforinstitution:Language?History?Mauro(1995)使用人口的種族和語言構(gòu)成作為腐敗的工具變量，HallandJones(1999)用距離赤道的距離和以西歐語言為第一語言的程度作為制度質(zhì)量的工具變量，LaPortaetal.(1997,1998,1999)把法律的起源作為各種法律結(jié)構(gòu)的工具變量。Acemoglu,Johnson,andRobinson(2001,2002)使用殖民地時代(1500年前后)的死亡率和人口密度作為制度的工具變量IVforschoolchoice:Numberofsteams?IdentificationReferto(15.9)and(15.10)The(asymptotic)standarderrorof

SSTisthetotalsumofsquaresofthexiSelf-selectionAngrist(1990)studiedtheeffectthatbeingaveteranintheVietnamwarhadonlifetimeearnings.DraftlotterynumberisagoodIVcandidateforveteran.SomeadditionalwordsaboutnaturalexperimentandDIDPropertiesofIVwithaPoorInstrumentalVariable

PoorIVcancauseseriousbias.R2MostregressionpackagescomputeanR-squaredafterIVestimation,usingthestandardformula:R2=1-SSR/SST,whereSSRisthesumofsquaredIVresiduals,andSSTisthetotalsumofsquaresofy.R2canbenegativeinthiscase.IVESTIMATIONOFTHEMULTIPLEREGRESSION

MODELstructuralequationEstimationEfficientIVEquation(15.26)isanexampleofareducedformequation,whichmeansthatwehavewrittenanendogenousvariableintermsofexogenousvariables.TWOSTAGELEASTSQUARES2SLSinwordsThefirststageistoruntheregressionin(15.36),whereweobtainthefittedvaluesy?2.ThesecondstageistheOLSregression(15.38).Becauseweusey?2inplaceofy2,the2SLSestimatescandiffersubstantiallyfromtheOLSestimates.Anotherinterpretation:MultipleEndogenousExplanatoryVariablesORDERCONDITIONFORIDENTIFICATIONOFANEQUATION:Weneedatleastasmanyexcludedexogenousvariablesasthereareincludedendogenousexplanatoryvariablesinthestructuralequation.IVSOLUTIONSTOERRORS-IN-VARIABLESPROBLEMSOnepossibilityistoobtainasecondmeasurementonX*1,say,z1,asIV.AnalternativeistouseotherexogenousvariablesasIVsforapotentiallymismeasuredvariable.TESTINGFORENDOGENEITYANDTESTINGOVERIDENTIFYINGRESTRICTIONSThe2SLSestimatorislessefficientthanOLSwhentheexplanatoryvariablesareexogenous;aswehaveseen,the2SLSestimatescanhaveverylargestandarderrors.Howtotestendogeneity?1.ComparingtheOLSand2SLSestimatesanddeterminingwhetherthedifferencesarestatisticallysignificant.(Hausman,1978)2.Aregressiontest:Anotherinterpretationof2SLSIncludingv?2intheOLSregression(15.51)clearsuptheendogeneityofy2.Wecanalsotestforendogeneityofmultipleexplanatoryvariables.Foreachsuspectedendogenousvariable,weobtainthereducedformresiduals.Then,wetestforjointsignificanceoftheseresidualsinthestructuralequation,usinganFtest.TestingOveridentificationRestrictionsIfwehavemorethanoneinstrumentalvariable,wecaneffectivelytestwhethersomeofthemareuncorrelatedwiththestructuralerror.UseoneIVandgetthepredictedresidual,thentestthecorrelationbetweenotherIVsandtheresidual.TESTINGOVERIDENTIFYINGRESTRICTIONS:(i)Estimatethestructuralequationby2SLSandobtainthe2SLSresiduals,u?1.(ii)Regressu?1onallexogenousvariables.ObtaintheR-squared,sayR12.(iii)UnderthenullhypothesisthatallIVsareuncorrelatedwithu1,nR12~aX2(q),whereqisthenumberofinstrumentalvariablesfromoutsidethemodelminusthetotalnumberofendogenousexplanatoryvariables.IfnR12exceeds(say)the5%criticalvalueintheX2(q)distribution,werejectH0andconcludethatatleastsomeoftheIVsarenotexogenous.IsitbettertohavemoreIVs?Addinginstrumentstothelistimprovestheasymptoticefficiencyofthe2SLS.Butthisrequiresthatanynewinstrumentsareinfactexogenous.Withthetypicalsamplesizesavailable,addingtoomanyinstruments—thatis,increasingthenumberofoveridentifyingrestrictions—cancauseseverebiasesin2SLS.2OmittedTopics2SLSWITHHETEROSKEDASTICITYAPPLYING2SLSTOTIMESERIESEQUATIONSAPPLYING2SLSTOPOOLEDCROSSSECTIONS

ANDPANELDATAForpooledcrosssectionsdata:addtimedummy.Forpaneldata:Inthefirststage,usethedifferencedIVtogetanestimateoftheendogenousvariable.Question:IfthepanelmodelisaFEone,howtocheckt