在计量经济学的Endogeneity ： 有助易变的估计 (1).pptx

在计量经济学的Endogeneity ： 有助易变的估计 (1).pptx

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EndogeneityinEconometrics:

InstrumentalVariableEstimationMingLUEndogeneityOmittingvariablebiasSimultaneityMeasurementerrorCanweignoretheomittedvariablesbias?

Itcanbesatisfactoryiftheestimatesarecoupledwiththedirectionofthebiasesforthekeyparameters.Canweuseproxytoeliminateomittedvariablebias?

Sometimes.CanFEestimationsolveomittingvariableproblem?

Firstdifferencingorfixedeffectsestimationeliminatestime-constantvariables.Inaddition,thepaneldatamethodsdonotsolvetheproblemoftime-varyingomittedvariablesIdeaofIVEstimationExogenousvariable.IndirecteffectsofIV.ExampleWhatcanserveasIVforedu?

Motherseducation?

Numberofsiblings?

Thereportofothers?

Adummyvariablethatisequalto1ifamanisborninthefirstquarteroftheyear.AngristandKrueger（1991）.（Problematic.）InChina,theyearsofprimaryedu?

IVforskippedclass?

Thedistancefromhometoschool.OtherexamplesofIVIVforinstitution:

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?

IdentificationReferto（15.9）and（15.10）The（asymptotic）standarderrorofSSTisthetotalsumofsquaresofthexiSelf-selectionAngrist（1990）studiedtheeffectthatbeingaveteranintheVietnamwarhadonlifetimeearnings.DraftlotterynumberisagoodIVcandidateforveteran.SomeadditionalwordsaboutnaturalexperimentandDIDPropertiesofIVwithaPoorInstrumentalVariablePoorIVcancauseseriousbias.R2MostregressionpackagescomputeanR-squaredafterIVestimation,usingthestandardformula:

R2=1-SSR/SST,whereSSRisthesumofsquaredIVresiduals,andSSTisthetotalsumofsquaresofy.R2canbenegativeinthiscase.IVESTIMATIONOFTHEMULTIPLEREGRESSIONMODELstructuralequationEstimationEfficientIVEquation（15.26）isanexampleofareducedformequation,whichmeansthatwehavewrittenanendogenousvariableintermsofexogenousvariables.TWOSTAGELEASTSQUARES2SLSinwordsThefirststageistoruntheregressionin（15.36）,whereweobtainthefittedvaluesy2.ThesecondstageistheOLSregression（15.38）.Becauseweusey2inplaceofy2,the2SLSestimatescandiffersubstantiallyfromtheOLSestimates.Anotherinterpretation:

MultipleEndogenousExplanatoryVariablesORDERCONDITIONFORIDENTIFICATIONOFANEQUATION:

Weneedatleastasmanyexcludedexogenousvariablesasthereareincludedendogenousexplanatoryvariablesinthestructuralequation.IVSOLUTIONSTOERRORS-IN-VARIABLESPROBLEMSOnepossibilityistoobtainasecondmeasurementonX*1,say,z1,asIV.AnalternativeistouseotherexogenousvariablesasIVsforapotentiallymismeasuredvariable.TESTINGFORENDOGENEITYANDTESTINGOVERIDENTIFYINGRESTRICTIONSThe2SLSestimatorislessefficientthanOLSwhentheexplanatoryvariablesareexogenous;aswehaveseen,the2SLSestimatescanhaveverylargestandarderrors.Howtotestendogeneity?

1.ComparingtheOLSand2SLSestimatesanddeterminingwhetherthedifferencesarestatisticallysignificant.（Hausman,1978）2.Aregressiontest:

Anotherinterpretationof2SLSIncludingv2intheOLSregression（15.51）clearsuptheendogeneityofy2.Wecanalsotestforendogeneityofmultipleexplanatoryvariables.Foreachsuspectedendogenousvariable,weobtainthereducedformresiduals.Then,wetestforjointsignificanceoftheseresidualsinthestructuralequation,usinganFtest.TestingOveridentificationRestrictionsIfwehavemorethanoneinstrumentalvariable,wecaneffectivelytestwhethersomeofthemareuncorrelatedwiththestructuralerror.UseoneIVandgetthepredictedresidual,thentestthecorrelationbetweenotherIVsandtheresidual.TESTINGOVERIDENTIFYINGRESTRICTIONS:

（i）Estimatethestructuralequationby2SLSandobtainthe2SLSresiduals,u1.（ii）Regressu1onallexogenousvariables.ObtaintheR-squared,sayR12.（iii）UnderthenullhypothesisthatallIVsareuncorrelatedwithu1,nR12X2（q）,whereqisthenumberofinstrumentalvariablesfromoutsidethemodelminusthetotalnumberofendogenousexplanatoryvariables.IfnR12exceeds（say）the5%criticalvalueintheX2（q）distribution,werejectH0andconcludethatatleastsomeoftheIVsarenotexogenous.IsitbettertohavemoreIVs?

Addinginstrumentstothelistimprovestheasymptoticefficiencyofthe2SLS.Butthisrequiresthatanynewinstrumentsareinfactexogenous.Withthetypicalsamplesizesavailable,addingtoomanyinstrumentsthatis,increasingthenumberofoveridentifyingrestrictionscancauseseverebiasesin2SLS.2OmittedTopics2SLSWITHHETEROSKEDASTICITYAPPLYING2SLSTOTIMESERIESEQUATIONSAPPLYING2SLSTOPOOLEDCROSSSECTIONSANDPANELDATAForpooledcrosssectionsdata:

addtimedummy.Forpaneldata:

Inthefirststage,usethedifferencedIVtogetanestimateoftheendogenousvariable.Question:

IfthepanelmodelisaFEone,howtochecktheefficiencyofIViftheIVistimeinvariant?

STATAcommandsTocompareOLSand2SLSivregy（x=iv）x2eststoref2regyxx2hausmanf2Thesequenceisimportant.STATAcommandsTocompareFEandIV-FExtivregy（x=iv）x2,feeststoref2xtregyxx2,fehausmanf2Theend.