lect_5_late_fig

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1、Imbens/Wooldridge,LectureNotes5,Summer’071What’sNewinEconometricsNBER,Summer2007Lecture5,Monday,July30th,4.30-5.30pmInstrumentalVariableswithTreatmentEffectHeterogeneity:LocalAverageTreatmentEffects1.IntroductionHereweinvestigatetheinterpretationofinstrumentalvariablesestimatorsallowingfor

2、generalheterogeneityintheeffectoftheendogenousregressor.Weshallseethatinstrumentalvariablesestimatorsgenerallyestimateaveragetreatmenteffects,withthespecificaveragedependingonthechoiceofinstruments.Initiallywefocusonthecasewheretheendogenousregressorisbinary.Theexamplewewilluseisbasedonwork

3、byJoshuaAngristonestimatingtheeffectofveteranstatusonearnings(Angrist,1990).Wealsodiscussthecasewheretheendogenousvariabletakesonmultiplevalues.Thegeneralthemeofthislectureisthatwithheterogenoustreatmenteffects,endogeneitycreatessevereproblemsforidentificationofpopulationaverages.Population

4、averagecausaleffectsareonlyestimableunderverystrongassumptionsontheeffectoftheinstrumentontheendogenousregressor(“identificationatinfinity”,orundertheconstanttreatmenteffectassumptions).Withoutsuchassumptionswecanonlyidentifyaverageeffectsforsubpopulationsthatareinducedbytheinstrumenttochanget

5、hevalueoftheendogenousregressors.Werefertosuchsubpopulationsascompliers,andtotheaveragetreatmenteffectthatispointidentifedasthelocalaveragetreatmenteffect.Thisterminologystemsfromthecanonicalexampleofarandomizedexperimentwithnoncompliance.Inthisexamplearandomsubpopulationisassignedtothetre

6、atment,butsomeoftheindividualsdonotcomplywiththeirassignedtreatment.Thesecompliersubpopulationsarenotnecessarilythesubpopulationsthatareexantethemostinterestingsubpopulations,butthedataisingeneralnotinformativeaboutav-erageeffectsforothersubpopulationswithoutextrapolation,similartothewayi

7、nwhicharandomizedexperimentconductedonmenisnotinformativeaboutaverageeffectsforImbens/Wooldridge,LectureNotes5,Summer’072womenwithoutextrapolation.Thesetuphereallowstheresearchertosharplyseparatetheextrapolationtothe(sub-)populationofinterestfromexplorationoftheinformation