DID双重差分回归.ppt

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1、1DifferenceinDifferenceModelsWhatisDIDHowcanweestimatetheeffectsofhighereducationreforminChina?YangandChen(2009)23ProblemsetupCross-sectionalandtimeseriesdataOnegroupis‘treated’withinterventionHavepre-postdataforgroupreceivinginterventionCanexaminetime-serieschangesbut,unsur

2、ehowmuchofthechangeisduetosecularchanges4timeYt1t2YaYbYt1Yt2Trueeffect=Yb-YaEstimatedeffect=Yt2-Yt1ti5Interventionoccursattimeperiodt1TrueeffectoflawYa–YbOnlyhavedataatt1andt2Ifusingtimeseries,estimateYt1–Yt2Solution?6DifferenceindifferencemodelsBasictwo-wayfixedeffectsmodel

3、CrosssectionandtimefixedeffectsUsetimeseriesofuntreatedgrouptoestablishwhatwouldhaveoccurredintheabsenceoftheinterventionKeyconcept:cancontrolforthefactthattheinterventionismorelikelyinsometypesofstates7timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)

4、8DifferenceinDifferenceBeforeChangeAfterChangeDifferenceGroup1(Treat)Yt1Yt2ΔYt=Yt2-Yt1Group2(Control)Yc1Yc2ΔYc=Yc2-Yc1DifferenceΔΔYΔYt–ΔYc9KeyAssumptionControlgroupidentifiesthetimepathofoutcomesthatwouldhavehappenedintheabsenceofthetreatmentInthisexample,YfallsbyYc2-Yc1even

5、withouttheinterventionNotethatunderlying‘levels’ofoutcomesarenotimportant(returntothisintheregressionequation)10timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)TreatmentEffect11Incontrast,whatiskeyisthatthetimetrendsintheabsenceoftheinterventionarethe

6、sameinbothgroupsIftheinterventionoccursinanareawithadifferenttrend,willunder/overstatethetreatmenteffectInthisexample,supposeinterventionoccursinareawithfasterfallingY12timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2TruetreatmenteffectEstimatedtreatmentTrueTreatmentEffect13BasicEconom

7、etricModelDatavariesbystate(i)time(t)OutcomeisYitOnlytwoperiodsInterventionwilloccurinagroupofobservations(e.g.states,firms,etc.)14ThreekeyvariablesTit=1ifobsibelongsinthestatethatwilleventuallybetreatedAit=1intheperiodswhentreatmentoccursTitAit--interactionterm,treatmentsta

8、tesaftertheinterventionYit=β0+β1Tit+β2Ait+β3TitAit+εit15Yit=β0+β1Tit+β2Ait+