DID雙重差分回歸課件

1DifferenceinDifferenceModelsWhatisDIDHowcanweestimatetheeffectsofhighereducationreforminChina?YangandChen(2009)23ProblemsetupCross-sectionalandtimeseriesdataOnegroupis‘treated’withinterventionHavepre-postdataforgroupreceivinginterventionCanexaminetime-serieschangesbut,unsurehowmuchofthechangeisduetosecularchanges4timeYt1t2YaYbYt1Yt2Trueeffect=Yb-YaEstimatedeffect=Yt2-Yt1ti5Interventionoccursattimeperiodt1TrueeffectoflawYa–YbOnlyhavedataatt1andt2Ifusingtimeseries,estimateYt1–Yt2Solution?6DifferenceindifferencemodelsBasictwo-wayfixedeffectsmodelCrosssectionandtimefixedeffectsUsetimeseriesofuntreatedgrouptoestablishwhatwouldhaveoccurredintheabsenceoftheinterventionKeyconcept:cancontrolforthefactthattheinterventionismorelikelyinsometypesofstates7timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)8DifferenceinDifferenceBeforeChangeAfterChangeDifferenceGroup1(Treat)Yt1Yt2ΔYt=Yt2-Yt1Group2(Control)Yc1Yc2ΔYc=Yc2-Yc1DifferenceΔΔYΔYt–ΔYc9KeyAssumptionControlgroupidentifiesthetimepathofoutcomesthatwouldhavehappenedintheabsenceofthetreatmentInthisexample,YfallsbyYc2-Yc1evenwithouttheinterventionNotethatunderlying‘levels’ofoutcomesarenotimportant(returntothisintheregressionequation)10timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)TreatmentEffect2024/1/251112Incontrast,whatiskeyisthatthetimetrendsintheabsenceoftheinterventionarethesameinbothgroupsIftheinterventionoccursinanareawithadifferenttrend,willunder/overstatethetreatmenteffectInthisexample,supposeinterventionoccursinareawithfasterfallingY13timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2TruetreatmenteffectEstimatedtreatmentTrueTreatmentEffect14BasicEconometricModelDatavariesbystate(i)time(t)OutcomeisYitOnlytwoperiodsInterventionwilloccurinagroupofobservations(e.g.states,firms,etc.)15ThreekeyvariablesTit=1ifobsibelongsinthestatethatwilleventuallybetreatedAit=1intheperiodswhentreatmentoccursTitAit--interactionterm,treatmentstatesaftertheinterventionYit=β0+β1Tit+β2Ait+β3TitAit+εit16Yit=β0+β1Tit+β2Ait+β3TitAit+εitBeforeChangeAfterChangeDifferenceGroup1(Treat)β0+β1β0+β1+β2+β3ΔYt

=β2+β3Group2(Control)β0β0+β2ΔYc=β2DifferenceΔΔY=β317MoregeneralmodelDatavariesbystate(i)time(t)OutcomeisYitManyperiodsInterventionwilloccurinagroupofstatesbutatavarietyoftimes18uiisastateeffectvtisacompletesetofyear(time)effectsAnalysisofcovariancemodelYit=β0+β3TitAit+ui+λt+εit19WhatisniceaboutthemodelSupposeinterventionsarenotrandombutsystematicOccurinstateswithhigherorloweraverageYOccurintimeperiodswithdifferentY’sThisiscapturedbytheinclusionofthestate/timeeffects–allowscovariancebetweenuiandTitAitλtandTitAit20GroupeffectsCapturedifferencesacrossgroupsthatareconstantovertimeYeareffectsCapturedifferencesovertimethatarecommontoallgroups21Questionstoask?Whatparameterisidentifiedbythequasi-experiment?Isthisaneconomicallymeani