DID方法

1DifferenceinDifferenceModelsWhatisDID•HowcanweestimatetheeffectsofhighereducationreforminChina?•YangandChen(2009)23Problemsetup•Cross-sectionalandtimeseriesdata•Onegroupis‘treated’withintervention•Havepre-postdataforgroupreceivingintervention•Canexaminetime-serieschangesbut,unsurehowmuchofthechangeisduetosecularchanges4timeYt1t2YaYbYt1Yt2Trueeffect=Yb-YaEstimatedeffect=Yt2-Yt1ti5•Interventionoccursattimeperiodt1•Trueeffectoflaw–Ya–Yb•Onlyhavedataatt1andt2–Ifusingtimeseries,estimateYt1–Yt2•Solution?6Differenceindifferencemodels•Basictwo-wayfixedeffectsmodel–Crosssectionandtimefixedeffects•Usetimeseriesofuntreatedgrouptoestablishwhatwouldhaveoccurredintheabsenceoftheintervention•Keyconcept:cancontrolforthefactthattheinterventionismorelikelyinsometypesofstates7timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)8DifferenceinDifferenceBeforeChangeAfterChangeDifferenceGroup1(Treat)Yt1Yt2ΔYt=Yt2-Yt1Group2(Control)Yc1Yc2ΔYc=Yc2-Yc1DifferenceΔΔYΔYt–ΔYc9KeyAssumption•Controlgroupidentifiesthetimepathofoutcomesthatwouldhavehappenedintheabsenceofthetreatment•Inthisexample,YfallsbyYc2-Yc1evenwithouttheintervention•Notethatunderlying‘levels’ofoutcomesarenotimportant(returntothisintheregressionequation)10timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)TreatmentEffect11•Incontrast,whatiskeyisthatthetimetrendsintheabsenceoftheinterventionarethesameinbothgroups•Iftheinterventionoccursinanareawithadifferenttrend,willunder/overstatethetreatmenteffect•Inthisexample,supposeinterventionoccursinareawithfasterfallingY12timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2TruetreatmenteffectEstimatedtreatmentTrueTreatmentEffect13BasicEconometricModel•Datavariesby–state(i)–time(t)–OutcomeisYit•Onlytwoperiods•Interventionwilloccurinagroupofobservations(e.g.states,firms,etc.)14•Threekeyvariables–Tit=1ifobsibelongsinthestatethatwilleventuallybetreated–Ait=1intheperiodswhentreatmentoccurs–TitAit--interactionterm,treatmentstatesaftertheintervention•Yit=β0+β1Tit+β2Ait+β3TitAit+εit15Yit=β0+β1Tit+β2Ait+β3TitAit+εitBeforeChangeAfterChangeDifferenceGroup1(Treat)β0+β1β0+β1+β2+β3ΔYt=β2+β3Group2(Control)β0β0+β2ΔYc=β2DifferenceΔΔY=β316Moregeneralmodel•Datavariesby–state(i)–time(t)–OutcomeisYit•Manyperiods•Interventionwilloccurinagroupofstatesbutatavarietyoftimes17•uiisastateeffect•vtisacompletesetofyear(time)effects•Analysisofcovariancemodel•Yit=β0+β3TitAit+ui+λt+εit18Whatisniceaboutthemodel•Supposeinterventionsarenotrandombutsystematic–OccurinstateswithhigherorloweraverageY–OccurintimeperiodswithdifferentY’s•Thisiscapturedbytheinclusionofthestate/timeeffects–allowscovariancebetween–uiandTitAit–λtandTitAit19•Groupeffects–Capturedifferencesacrossgroupsthatareconstantovertime•Yeareffects–Capturedifferencesovertimethatarecommontoallgroups20Questionstoask?•Whatparameterisidentifiedbythequasi-experiment?Isthisaneconomicallymeaningfulparameter?•Whatassumptionsmustbetrueinorderforthemodeltoprovideandunbiasedestimateofβ3?•Dotheauthorsprovideanyevidencesupportingtheseassumptions?