Difference in difference models 计量经济学 自然实验模型 倍差分模型.ppt

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1、DifferenceinDifferenceModelsBillEvansSpring20081DifferenceindifferencemodelsMaybethemostpopularidentificationstrategyinappliedworktodayAttemptstomimicrandomassignmentwithtreatmentand“comparison”sampleApplicationoftwo-wayfixedeffectsmodel2ProblemsetupCross-sectiona

2、landtimeseriesdataOnegroupis‘treated’withinterventionHavepre-postdataforgroupreceivinginterventionCanexaminetime-serieschangesbut,unsurehowmuchofthechangeisduetosecularchanges3timeYt1t2YaYbYt1Yt2Trueeffect=Yt2-Yt1Estimatedeffect=Yb-Yati4Interventionoccursattimeper

3、iodt1TrueeffectoflawYa–YbOnlyhavedataatt1andt2Ifusingtimeseries,estimateYt1–Yt2Solution?5DifferenceindifferencemodelsBasictwo-wayfixedeffectsmodelCrosssectionandtimefixedeffectsUsetimeseriesofuntreatedgrouptoestablishwhatwouldhaveoccurredintheabsenceoftheintervent

4、ionKeyconcept:cancontrolforthefactthattheinterventionismorelikelyinsometypesofstates6ThreedifferentpresentationsTabularGraphicalRegressionequation7DifferenceinDifferenceBeforeChangeAfterChangeDifferenceGroup1(Treat)Yt1Yt2ΔYt=Yt2-Yt1Group2(Control)Yc1Yc2ΔYc=Yc2-Yc1

5、DifferenceΔΔYΔYt–ΔYc8timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)9KeyAssumptionControlgroupidentifiesthetimepathofoutcomesthatwouldhavehappenedintheabsenceofthetreatmentInthisexample,YfallsbyYc2-Yc1evenwithouttheinterventionNotethatunde

6、rlying‘levels’ofoutcomesarenotimportant(returntothisintheregressionequation)10timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)TreatmentEffect11Incontrast,whatiskeyisthatthetimetrendsintheabsenceoftheinterventionarethesameinbothgroupsIfthein

7、terventionoccursinanareawithadifferenttrend,willunder/overstatethetreatmenteffectInthisexample,supposeinterventionoccursinareawithfasterfallingY12timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2TruetreatmenteffectEstimatedtreatmentTrueTreatmentEffect13BasicEconometricModelDa

8、tavariesbystate(i)time(t)OutcomeisYitOnlytwoperiodsInterventionwilloccurinagroupofobservations(e.g.states,firms,etc.)14ThreekeyvariablesTit=1ifobsibelon