Difference in Differences and Beyond

이명재

ProfessorMyoung-jaeLeeisaneconometricianandstatisticianatKoreaUniversity.HereceivedhisPh.D.ineconomicsfromUniversityofWisconsin-Madisonin1989.Sincethen,heheldregularpositionsinvariousuniversitiesaroundtheworld,includingPennsylvaniaStateUniversity,TilburgUniversity,SingaporeManagementUniversity,ChineseUniversityofHongKong,andAustralianNationalUniversity.Hepublishedmorethan80papersoneconomics,statistics,politicalscience,sociology,transportationresearch,andmedicalscience.Hispapersappearedinmanytop-ratedjournalssuchasEconometrica,JournaloftheRoyalStatisticalSociety(SeriesB),Biometrika,TransportationResearch(PartB),PoliticalAnalysis,andSociologicalMethods&Research.Myoung-jaeLeealsopublishedfivesingle-authoredbooksfromSpringer,AcademicPressandOxfordUniversityPress,includingMicro-econometricsforpolicy,program,andtreatmenteffects(2005),Micro-Econometrics(2010),andMatching,regressiondiscontinuity,differenceindifferences,andbeyond(2016).

Chapter1:Introduction...1

1.BasicsandThreeExamples...1
1.1.Example1:PlasticSurgeryonBeauty...2
1.2.Example2:ThreeStrikeLawonCrimeRate...3
1.3.Example3:InfluxofCheapLaboronUnemployment...4
2.Notation...5
2.1.TimePeriodsandTreatment...5
2.2.PotentialResponses,CovariatesandOthers...6
3.FromBAtoDDandtoTD...7
3.1.Before-After(BA)...7
3.2.DifferenceinDifferences(DD)...9
3.3.TripleDifferences(TD)...10
3.4.ExplicitlyControllingCovariates*...12

Chapter2:DDwithPanelData...15

1.IdentificationwithPanelData...15
1.1.IdentificationBasics...15
1.2.RemarksonIdentification*...16
2.GraphicalDemonstrations...18
2.1.ConstantEffectandConstantTiming...18
2.2.VaryingEffectandConstantTiming...20
3.EstimationwithPanelLinearModels...22
3.1.TwoWavesOnly...22
3.2.EmpiricalExample:HighwayDevelopmentProgram...23
3.3.MorethanTwoWaves...25
3.3.1LevelandDifferencedModels...25
3.3.2Time-WiseDD...27
3.4.EmpiricalExample:TayoBusStory...28
3.4.1TayoBusPolicy,ParallelTrendsandMainFindings...29
3.4.2PanelOLSforTayoBusRidership*...33
3.4.3EmpiricalResultsforTayoBusEffects*...34
3.5.TreatmentEndogeneityAllowedinDD*...36
4.GeneralizationsofPanelLinearModels...37
4.1.Duration-DependentEffectandOne-ShotTreatment...38
4.2.TreatmentDose/Intensity...39
5.DDversusLaggedResponseRegressor...40
5.1.NeitherisMoreGeneral...41
5.2.LaggedResponseandQualificationDummyRelation...42
5.3.CommonFactorandFalseMeanReversion...44
6.NoObviousQualificationVariable*...46
6.1.ArtificialGroupingandTime-VaryingEffect...46
6.2.EstimationDetails...47
6.3.DDtoRemoveTimeandIndividualEffects...49

Chapter3:DDwithRepeatedCross-Sections...53

1.RandomSamplingEveryPeriod...53
2.IdentificationwithRCS...54
2.1.CovariatesImplicit...55
2.2.CovariatesExplicit*...57
2.3.IdentificationViewedfromLinearModel*...59
3.EstimationwithRCS...61
3.1.SingleEquationDerivationwithRCS...62
3.1.1ConstantEffectandConstantTiming...62
3.1.2Duration-VaryingEffectandVaryingTiming*...63
3.2.EmpiricalExamples:Health-BookandEITC...65
3.3.Remarks...66
3.4.EmpiricalExample:AbilityMixing...67
3.4.1BackgroundandData...67
3.4.2EmpiricalResultsforAbilityMixing...69
3.4.3CausalityProbleminQuantileRegression...70
4.DDwithCross-SectionData...72
4.1.InteractionEffectsinCross-SectionData...72
4.2.Double-ScoreRegressionDiscontinuity(RD)*...74
4.2.1PartialEffects...74
4.2.2FourPotentialResponses...75
5.DDwithLimitedDependentVariables(LDV)...77
5.1.EffectforLatentVariableandEffectforLDV...77
5.2.BinaryandCountResponses...78
5.2.1DDwithProbit...78
5.2.2RatioinRatios(RR)forCounts...79
5.2.3Odds-RatioinOdds-Ratios(RRR)forLogit*...80
5.3.EmpiricalExample:ScreenDoortoPreventSuicide...81
6.FuzzyDD...82

Chapter4:TopicsforDD...85

1.DDinReverse(DDR)...85
1.1.DDRBasics...85
1.2.DDRIdentification...86
1.3.DDREstimationwithOLS...89
1.4.EmpiricalExample:WorkHourReductionLaw...90
2.SyntheticControl...93
2.1.MainIdea...93
2.2.InferencewithPermutationTest...94
2.3.ApplicationsandRemarks...96
3.TripleDifferences(TD)...98
3.1.TDBasics...98
3.2.TDwithPanelData...100
3.2.1TDIdentificationwithPanelData...100
3.2.2TDEstimationwithPanelLinearModel...102
3.2.3EmpiricalExample:Tax-inclusivePriceonDemand...103
3.3.TDwithRCS...105
3.3.1TDIdentificationwithRCS...105
3.3.2TDEstimationwithRCS...106
3.3.3EmpiricalExample:MandatedBenefitonWage...108
4.GeneralizedDifferenceinDifferences(GDD)...110
4.1.MotivationforGDDandBeyond...111
4.2.OLSforDD,GDDandQD...113
4.3.EmpiricalExample:SulfaDrugonMortality...113
4.3.1SulfaDrugBackground...113
4.3.2EmpiricalResultsforSulfaDrugData...115
5.PanelStayerDDforTime-VaryingQualification...117
5.1.Motivations...117
5.2.EffectonIn-Stayer...119
5.3.IdentificationandEstimationwithPanelLinearModel...120
5.3.1UntreatedMovingEffectversusTreatmentEffects...120
5.3.2AshenfelterDipandPath-DependentMovingEffect*...121
5.4.EmpiricalExample:PensionEffectonExpenditure...122

AppendixforTreatmentEffectBasicsandChapters...125

1.ReducedForm(RF)andPropensityScore(PS)...125
2.TreatmentEffectBasicsandConfounding...127
2.1.OvertBiasandHiddenBias...127
2.2.OvertandHiddenBiasesinLinearModels...128
2.3.InstrumentalResidualEstimator*...129
3.VariousEffectsandSimpson’sParadox...133
3.1.EffectonTreated...133
3.2.EffectonUntreatedandEffectonPopulation...134
3.3.Simpson’sParadox...135
4.CovariatestoControl...137
5.TreatmentEffectEstimators...140
5.1.PropensityScoreMatching(PSM)Estimators...141
5.2.RegressionAdjustment/ImputationEstimators...144
5.3.PropensityScoreResidualEstimator(PSR)...146
5.4.InverseProbabilityWeightingEstimators(IPW)...148
6.Work-HourReductionLawandRandomization...149
7.Endogeneity,IVEandComplierEffect...152
7.1.LinearProjection