雙重差分模型教學(xué)課件differenceindifferencesmodels課件

DifferenceinDifferenceModelsBillEvansSpring20191DifferenceinDifferenceModelDifferenceindifferencemodelsMaybethemostpopularidentificationstrategyinappliedworktodayAttemptstomimicrandomassignmentwithtreatmentand“comparison”sampleApplicationoftwo-wayfixedeffectsmodel2DifferenceindifferencemodelProblemsetupCross-sectionalandtimeseriesdataOnegroupis‘treated’withinterventionHavepre-postdataforgroupreceivinginterventionCanexaminetime-serieschangesbut,unsurehowmuchofthechangeisduetosecularchanges3ProblemsetupCross-sectionaltimeYt1t2YaYbYt1Yt2Trueeffect=Yt2-Yt1Estimatedeffect=Yb-Yati4timeYt1t2YaYbYt1Yt2TrueeffectInterventionoccursattimeperiodt1TrueeffectoflawYa–YbOnlyhavedataatt1andt2Ifusingtimeseries,estimateYt1–Yt2Solution?55DifferenceindifferencemodelsBasictwo-wayfixedeffectsmodelCrosssectionandtimefixedeffectsUsetimeseriesofuntreatedgrouptoestablishwhatwouldhaveoccurredintheabsenceoftheinterventionKeyconcept:cancontrolforthefactthattheinterventionismorelikelyinsometypesofstates6DifferenceindifferencemodelThreedifferentpresentationsTabularGraphicalRegressionequation7ThreedifferentpresentationsTDifferenceinDifferenceBeforeChangeAfterChangeDifferenceGroup1(Treat)Yt1Yt2ΔYt=Yt2-Yt1Group2(Control)Yc1Yc2ΔYc=Yc2-Yc1DifferenceΔΔYΔYt–ΔYc8DifferenceinDifferenceBeforetimeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)9timeYt1t2Yt1Yt2treatmentcontroKeyAssumptionControlgroupidentifiesthetimepathofoutcomesthatwouldhavehappenedintheabsenceofthetreatmentInthisexample,YfallsbyYc2-Yc1evenwithouttheinterventionNotethatunderlying‘levels’ofoutcomesarenotimportant(returntothisintheregressionequation)10KeyAssumptionControlgroupidtimeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)TreatmentEffect11timeYt1t2Yt1Yt2treatmentcontroIncontrast,whatiskeyisthatthetimetrendsintheabsenceoftheinterventionarethesameinbothgroupsIftheinterventionoccursinanareawithadifferenttrend,willunder/overstatethetreatmenteffectInthisexample,supposeinterventionoccursinareawithfasterfallingY12Incontrast,whatiskeyisthtimeYt1t2Yt1Yt2treatmentcontrolYc1Yc2TruetreatmenteffectEstimatedtreatmentTrueTreatmentEffect13timeYt1t2Yt1Yt2treatmentcontroBasicEconometricModelDatavariesbystate(i)time(t)OutcomeisYitOnlytwoperiodsInterventionwilloccurinagroupofobservations(e.g.states,firms,etc.)14BasicEconometricModelDatavaThreekeyvariablesTit=1ifobsibelongsinthestatethatwilleventuallybetreatedAit=1intheperiodswhentreatmentoccursTitAit--interactionterm,treatmentstatesaftertheinterventionYit=β0+β1Tit+β2Ait+β3TitAit+εit15Threekeyvariables15Yit=β0+β1Tit+β2Ait+β3TitAit+εitBeforeChangeAfterChangeDifferenceGroup1(Treat)β0+β1β0+β1+β2+β3ΔYt

=β2+β3Group2(Control)β0β0+β2ΔYc=β2DifferenceΔΔY=β316Yit=β0+β1Tit+β2Ait+β3TMoregeneralmodelDatavariesbystate(i)time(t)OutcomeisYitManyperiodsInterventionwilloccurinagroupofstatesbutatavarietyoftimes17MoregeneralmodelDatavariesuiisastateeffectvtisacompletesetofyear(time)effectsAnalysisofcovariancemodelYit=β0+β3TitAit+ui+λt+εit18uiisastateeffect18WhatisniceaboutthemodelSupposeinterventionsarenotrandombutsystematicOccurinstateswithhigherorloweraverageYOccurintimeperiodswithdifferentY’sThisiscapturedbytheinclusionofthestate/timeeffects–allowscovariancebetweenuiandTitAitλtandTitAit19WhatisniceaboutthemodelSuGroupeffectsCapturedifferencesacrossgroupsthatareconstantovertimeYeareffectsCapturedifferencesovertimethatarecommontoallgroups20Groupeffects20Meyeretal.Workers’compensationStateruninsuranceprogramCompensateworkersformedicalexpensesandlostworkduetoonthejobaccidentPremiumsPaidbyfirmsFunctionofpreviousclaimsandwagespaidBenefits--%ofincomew/cap21Meyeretal.Workers’compensatTypicalbenefitsscheduleMin(pY,C)P=percentreplacementY=earningsC=cape.g.,65%ofearningsupto$400/month22Typicalbenefitsschedule22Concern:Moralhazard.BenefitswilldiscouragereturntoworkEmpiricalquestion:duration/benefitsgradientPreviousestimatesRegressduration(y)onreplacedwages(x)Problem:givenprogressivenatureofbenefits,replacedwagesrevealalotabouttheworkersReplacementrateshigherinhigherwagestates23Concern:23Yi=Xiβ+αRi+εiY(duration)R(replacementrate)Expectα>0ExpectCov(Ri,εi)HigherwageworkershavelowerRandhigherduration(understate)HigherwagestateshavelongerdurationandlongerR(overstate)24Yi=Xiβ+αRi+εi24SolutionQuasiexperimentinKYandMIIncreasedtheearningscapIncreasedbenefitforhigh-wageworkers(Treatment)Didnothingtothosealreadybeloworiginalcap(comparison)Comparechangeindurationofspellbeforeandafterchangeforthesetwogroups25SolutionQuasiexperimentinKY26262727ModelYit=durationofspellonWCAit=periodafterbenefitshikeHit=highearningsgroup(Income>E3)Yit=β0+β1Hit+β2Ait+β3AitHit+β4Xit’+εitDiff-in-diffestimateisβ328ModelYit=durationofspello2929Questionstoask?Whatparameterisidentifiedbythequasi-experiment?Isthisaneconomicallymeaningfulparameter?Whatassumptionsmustbetrueinorderforthemodeltoprovideandunbiasedestimateofβ3?Dotheauthorsprovideanyevidencesupportingtheseassumptions?30Questionstoask?Whatparamete雙重差分模型教學(xué)課件differenceindifferencesmodels課件DifferenceinDifferenceModelsBillEvansSpring201932DifferenceinDifferenceModelDifferenceindifferencemodelsMaybethemostpopularidentificationstrategyinappliedworktodayAttemptstomimicrandomassignmentwithtreatmentand“comparison”sampleApplicationoftwo-wayfixedeffectsmodel33DifferenceindifferencemodelProblemsetupCross-sectionalandtimeseriesdataOnegroupis‘treated’withinterventionHavepre-postdataforgroupreceivinginterventionCanexaminetime-serieschangesbut,unsurehowmuchofthechangeisduetosecularchanges34ProblemsetupCross-sectionaltimeYt1t2YaYbYt1Yt2Trueeffect=Yt2-Yt1Estimatedeffect=Yb-Yati35timeYt1t2YaYbYt1Yt2TrueeffectInterventionoccursattimeperiodt1TrueeffectoflawYa–YbOnlyhavedataatt1andt2Ifusingtimeseries,estimateYt1–Yt2Solution?365DifferenceindifferencemodelsBasictwo-wayfixedeffectsmodelCrosssectionandtimefixedeffectsUsetimeseriesofuntreatedgrouptoestablishwhatwouldhaveoccurredintheabsenceoftheinterventionKeyconcept:cancontrolforthefactthattheinterventionismorelikelyinsometypesofstates37DifferenceindifferencemodelThreedifferentpresentationsTabularGraphicalRegressionequation38ThreedifferentpresentationsTDifferenceinDifferenceBeforeChangeAfterChangeDifferenceGroup1(Treat)Yt1Yt2ΔYt=Yt2-Yt1Group2(Control)Yc1Yc2ΔYc=Yc2-Yc1DifferenceΔΔYΔYt–ΔYc39DifferenceinDifferenceBeforetimeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)40timeYt1t2Yt1Yt2treatmentcontroKeyAssumptionControlgroupidentifiesthetimepathofoutcomesthatwouldhavehappenedintheabsenceofthetreatmentInthisexample,YfallsbyYc2-Yc1evenwithouttheinterventionNotethatunderlying‘levels’ofoutcomesarenotimportant(returntothisintheregressionequation)41KeyAssumptionControlgroupidtimeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatmenteffect=(Yt2-Yt1)–(Yc2-Yc1)TreatmentEffect42timeYt1t2Yt1Yt2treatmentcontroIncontrast,whatiskeyisthatthetimetrendsintheabsenceoftheinterventionarethesameinbothgroupsIftheinterventionoccursinanareawithadifferenttrend,willunder/overstatethetreatmenteffectInthisexample,supposeinterventionoccursinareawithfasterfallingY43Incontrast,whatiskeyisthtimeYt1t2Yt1Yt2treatmentcontrolYc1Yc2TruetreatmenteffectEstimatedtreatmentTrueTreatmentEffect44timeYt1t2Yt1Yt2treatmentcontroBasicEconometricModelDatavariesbystate(i)time(t)OutcomeisYitOnlytwoperiodsInterventionwilloccurinagroupofobservations(e.g.states,firms,etc.)45BasicEconometricModelDatavaThreekeyvariablesTit=1ifobsibelongsinthestatethatwilleventuallybetreatedAit=1intheperiodswhentreatmentoccursTitAit--interactionterm,treatmentstatesaftertheinterventionYit=β0+β1Tit+β2Ait+β3TitAit+εit46Threekeyvariables15Yit=β0+β1Tit+β2Ait+β3TitAit+εitBeforeChangeAfterChangeDifferenceGroup1(Treat)β0+β1β0+β1+β2+β3ΔYt

=β2+β3Group2(Control)β0β0+β2ΔYc=β2DifferenceΔΔY=β347Yit=β0+β1Tit+β2Ait+β3TMoregeneralmodelDatavariesbystate(i)time(t)OutcomeisYitManyperiodsInterventionwilloccurinagroupofstatesbutatavarietyoftimes48MoregeneralmodelDatavariesuiisastateeffectvtisacompletesetofyear(time)effectsAnalysisofcovariancemodelYit=β0+β3TitAit+ui+λt+εit49uiisastateeffect18WhatisniceaboutthemodelSupposeinterventionsarenotrandombutsystematicOccurinstateswithhigherorloweraverageYOccurintimeperiodswithdifferentY’sThisiscapturedbytheinclusionofthestate/timeeffects–allowscovariancebetweenuiandTitAitλtandTitAit50WhatisniceaboutthemodelSuGroupeffectsCapturedifferencesacrossgroupsthatareconstantovertimeYeareffectsCapturedifferencesovertimethatarecommontoallgroups51Groupeffects20Meyeretal.Workers’compensationStateruninsuranceprogramCompensateworkersformedicalexpensesandlostworkduetoonthejobaccidentPremiumsPaidbyfirmsFunctionofpreviousclaimsandwagespaidBenefits--%ofincomew/cap52Meyeretal.Workers’compensatTypicalbenefitsscheduleMin(pY,C)P=percentreplacementY=earningsC=cape.g.,65%ofearningsupto$400/month53Typicalbenefitsschedule22Concern:Moralhazard.BenefitswilldiscouragereturntoworkEmpiricalquestion:duration/benefitsgradientPreviousestimatesRegressduration(y)onreplacedwages(x)Problem:givenprogressivenatureofbenefits,replacedwagesrevealalotabouttheworkers