双重差分模型幻灯片+-+difference+in+differences+models.ppt

1 DifferenceinDifferenceModels BillEvansSpring2008 2 Differenceindifferencemodels MaybethemostpopularidentificationstrategyinappliedworktodayAttemptstomimicrandomassignmentwithtreatmentand comparison sampleApplicationoftwo wayfixedeffectsmodel 3 Problemsetup Cross sectionalandtimeseriesdataOnegroupis treated withinterventionHavepre postdataforgroupreceivinginterventionCanexaminetime serieschangesbut unsurehowmuchofthechangeisduetosecularchanges 4 time Y t1 t2 Ya Yb Yt1 Yt2 Trueeffect Yt2 Yt1 Estimatedeffect Yb Ya ti 5 Interventionoccursattimeperiodt1TrueeffectoflawYa YbOnlyhavedataatt1andt2Ifusingtimeseries estimateYt1 Yt2Solution 6 Differenceindifferencemodels Basictwo wayfixedeffectsmodelCrosssectionandtimefixedeffectsUsetimeseriesofuntreatedgrouptoestablishwhatwouldhaveoccurredintheabsenceoftheinterventionKeyconcept cancontrolforthefactthattheinterventionismorelikelyinsometypesofstates 7 Threedifferentpresentations TabularGraphicalRegressionequation 8 DifferenceinDifference 9 time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Treatmenteffect Yt2 Yt1 Yc2 Yc1 10 KeyAssumption ControlgroupidentifiesthetimepathofoutcomesthatwouldhavehappenedintheabsenceofthetreatmentInthisexample YfallsbyYc2 Yc1evenwithouttheinterventionNotethatunderlying levels ofoutcomesarenotimportant returntothisintheregressionequation 11 time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Treatmenteffect Yt2 Yt1 Yc2 Yc1 TreatmentEffect 12 Incontrast whatiskeyisthatthetimetrendsintheabsenceoftheinterventionarethesameinbothgroupsIftheinterventionoccursinanareawithadifferenttrend willunder overstatethetreatmenteffectInthisexample supposeinterventionoccursinareawithfasterfallingY 13 time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Truetreatmenteffect Estimatedtreatment TrueTreatmentEffect 14 BasicEconometricModel Datavariesbystate i time t OutcomeisYitOnlytwoperiodsInterventionwilloccurinagroupofobservations e g states firms etc 15 ThreekeyvariablesTit 1ifobsibelongsinthestatethatwilleventuallybetreatedAit 1intheperiodswhentreatmentoccursTitAit interactionterm treatmentstatesaftertheinterventionYit 0 1Tit 2Ait 3TitAit it 16 Yit 0 1Tit 2Ait 3TitAit it 17 Moregeneralmodel Datavariesbystate i time t OutcomeisYitManyperiodsInterventionwilloccurinagroupofstatesbutatavarietyoftimes 18 uiisastateeffectvtisacompletesetofyear time effectsAnalysisofcovariancemodelYit 0 3TitAit ui t it 19 Whatisniceaboutthemodel SupposeinterventionsarenotrandombutsystematicOccurinstateswithhigherorloweraverageYOccurintimeperiodswithdifferentY sThisiscapturedbytheinclusionofthestate timeeffects allowscovariancebetweenuiandTitAit tandTitAit 20 GroupeffectsCapturedifferencesacrossgroupsthatareconstantovertimeYeareffectsCapturedifferencesovertimethatarecommontoallgroups 21 Meyeretal Workers compensationStateruninsuranceprogramCompensateworkersformedicalexpensesandlostworkduetoonthejobaccidentPremiumsPaidbyfirmsFunctionofpreviousclaimsandwagespaidBenefits ofincomew cap 22 TypicalbenefitsscheduleMin pY C P percentreplacementY earningsC cape g 65 ofearningsupto 400 month 23 Concern Moralhazard BenefitswilldiscouragereturntoworkEmpiricalquestion duration benefitsgradientPreviousestimatesRegressduration y onreplacedwages x Problem givenprogressivenatureofbenefits replacedwagesrevealalotabouttheworkersReplacementrateshigherinhigherwagestates 24 Yi Xi Ri iY duration R replacementrate Expect 0ExpectCov Ri i HigherwageworkershavelowerRandhigherduration understate HigherwagestateshavelongerdurationandlongerR overstate 25 Solution QuasiexperimentinKYandMIIncreasedtheearningscapIncreasedbenefitforhigh wageworkers Treatment Didnothingtothosealreadybeloworiginalcap comparison Comparechangeindurationofspellbeforeandafterchangeforthesetwogroups 26 27 28 Model Yit durationofspellonWCAit periodafterbenefitshikeHit highearningsgroup Income E3 Yit 0 1Hit 2Ait 3AitHit 4Xit itDiff in diffestimateis 3 29 30 Questionstoask Whatparameteri