DID双重差分回归ppt课件.ppt

1 DifferenceinDifferenceModels 2 WhatisDID HowcanweestimatetheeffectsofhighereducationreforminChina YangandChen 2009 3 Problemsetup Cross sectionalandtimeseriesdataOnegroupis treated withinterventionHavepre postdataforgroupreceivinginterventionCanexaminetime serieschangesbut unsurehowmuchofthechangeisduetosecularchanges 4 time Y t1 t2 Ya Yb Yt1 Yt2 Trueeffect Yb Ya Estimatedeffect Yt2 Yt1 ti 5 Interventionoccursattimeperiodt1TrueeffectoflawYa YbOnlyhavedataatt1andt2Ifusingtimeseries estimateYt1 Yt2Solution 6 Differenceindifferencemodels Basictwo wayfixedeffectsmodelCrosssectionandtimefixedeffectsUsetimeseriesofuntreatedgrouptoestablishwhatwouldhaveoccurredintheabsenceoftheinterventionKeyconcept cancontrolforthefactthattheinterventionismorelikelyinsometypesofstates 7 time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Treatmenteffect Yt2 Yt1 Yc2 Yc1 8 DifferenceinDifference 9 KeyAssumption ControlgroupidentifiesthetimepathofoutcomesthatwouldhavehappenedintheabsenceofthetreatmentInthisexample YfallsbyYc2 Yc1evenwithouttheinterventionNotethatunderlying levels ofoutcomesarenotimportant returntothisintheregressionequation 10 time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Treatmenteffect Yt2 Yt1 Yc2 Yc1 TreatmentEffect 11 Incontrast whatiskeyisthatthetimetrendsintheabsenceoftheinterventionarethesameinbothgroupsIftheinterventionoccursinanareawithadifferenttrend willunder overstatethetreatmenteffectInthisexample supposeinterventionoccursinareawithfasterfallingY 12 time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Truetreatmenteffect Estimatedtreatment TrueTreatmentEffect 13 BasicEconometricModel Datavariesbystate i time t OutcomeisYitOnlytwoperiodsInterventionwilloccurinagroupofobservations e g states firms etc 14 ThreekeyvariablesTit 1ifobsibelongsinthestatethatwilleventuallybetreatedAit 1intheperiodswhentreatmentoccursTitAit interactionterm treatmentstatesaftertheinterventionYit 0 1Tit 2Ait 3TitAit it 15 Yit 0 1Tit 2Ait 3TitAit it 16 Moregeneralmodel Datavariesbystate i time t OutcomeisYitManyperiodsInterventionwilloccurinagroupofstatesbutatavarietyoftimes 17 uiisastateeffectvtisacompletesetofyear time effectsAnalysisofcovariancemodelYit 0 3TitAit ui t it 18 Whatisniceaboutthemodel SupposeinterventionsarenotrandombutsystematicOccurinstateswithhigherorloweraverageYOccurintimeperiodswithdifferentY sThisiscapturedbytheinclusionofthestate timeeffects allowscovariancebetweenuiandTitAit tandTitAit 19 GroupeffectsCapturedifferencesacrossgroupsthatareconstantovertimeYeareffectsCapturedifferencesovertimethatarecommontoallgroups 20 Questionstoask Whatparameterisidentifiedbythequasi experiment Isthisaneconomicallymeaningfulparameter Whatassumptionsmustbetru