Table Of ContentMatching, Regression
Discontinuity, Difference in
Differences, and Beyond
Matching, Regression
Discontinuity, Difference in
Differences, and Beyond
Myoung-jaeLee
1
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CONTENTS
Preface xv
1 BasicsofTreatmentEffectAnalysis 1
1.1 Counterfactual,Intervention,andCausalRelation 1
1.1.1 PotentialOutcomesandIntervention 1
1.1.2 CausalityandAssociation 3
1.1.3 PartialEquilibriumAnalysisandRemarks 4
1.2 VariousTreatmentEffectsandNoEffects 5
1.2.1 VariousEffects 5
1.2.2 ThreeNo-EffectConcepts 6
1.2.3 Remarks 7
1.3 Group-MeanDifferenceandRandomization 8
1.3.1 Group-MeanDifferenceandMeanEffect 8
1.3.2 ConsequencesofRandomization 10
1.3.3 CheckingOutCovariateBalance 12
1.4 OvertBias,HiddenBias,andSelectionProblems 13
1.4.1 OvertandHiddenBiases 13
1.4.2 SelectiononObservablesandUnobservables 14
1.4.3 LinearModelsandBiases 16
1.5 EstimationwithGroupMeanDifferenceandLSE 18
1.5.1 Group-MeanDifferenceandLSE 18
1.5.2 JobTrainingExample 19
1.5.3 LinkingCounterfactualstoLinearModels 21
1.6 StructuralForm,Assignment,andMarginalModel 22
1.6.1 StructuralversusReducedFormsforResponse 22
1.6.2 TreatmentStructuralFormandAssignment 23
1.6.3 MarginalStructuralModel 24
1.7 Simpson’sParadoxandFalseCovariateControl 25
2 Matching 28
2.1 BasicsofMatchingandVariousEffects 28
2.1.1 MainIdea 28
2.1.2 EffectonTreatedandEffectonPopulation 30
2.1.3 DimensionandSupportProblems 31
2.1.4 VariablestoControl 32
vii
viii Contents
2.2 ImplementingMatching 35
2.2.1 DecisionstoMakeinMatching 35
2.2.2 MatchingEstimators 37
2.2.3 AsymptoticVarianceEstimation 40
2.2.4 LaborUnionEffectonWage 44
2.3 PropensityScoreMatching(PSM) 46
2.3.1 PropensityScoreasaBalancingScore 46
2.3.2 RemovingOvertBiaswithPropensityScore 47
2.3.3 ImplementingPSMandBootstrap 48
2.3.4 PSMEmpiricalExamples 50
2.3.5 PropensityScoreSpecificationIssues* 52
2.4 FurtherRemarks 54
2.4.1 CovariateBalanceCheck 54
2.4.2 MatchingforHiddenBias 56
2.4.3 PrognosticScoreandMore* 58
3 NonmatchingandSampleSelection 61
3.1 Weighting 61
3.1.1 WeightingEstimatorforEffectonPopulation 61
3.1.2 OtherWeightingEstimatorsandRemarks 63
3.1.3 AsymptoticDistributionofWeightingEstimators* 65
3.1.4 JobTrainingEffectonUnemployment 66
3.1.5 DoublyRobustEstimator* 67
3.1.6 WeightingforMissingData* 68
3.2 RegressionImputation 69
3.2.1 LinearRegressionImputation 70
3.2.2 RegressionImputationwithPropensityScore 71
3.2.3 RegressionImputationforMultipleTreatment 72
3.2.4 RegressionImputationforContinuousTreatment* 73
3.2.5 MilitaryServiceEffectonWage 74
3.3 CompletePairingwithDoubleSum 76
3.3.1 DiscreteCovariates 77
3.3.2 ContinuousCovariates 79
3.3.3 NonparametricDistributionalEffectTests* 80
3.4 TreatmentEffectsunderSampleSelection 84
3.4.1 DifficultieswithSampleSelectionModels 85
3.4.2 Participation,Invisible,andVisibleEffects 86
3.4.3 IdentificationofThreeEffectswithMeanDifferences 87
3.4.4 ReligiosityEffectonAffairs 88
3.5 EffectDecompositioninSampleSelectionModels* 90
3.5.1 MotivationforDecomposition 90
3.5.2 DecompositionwithLinearSelectionModel 91
3.5.3 FourSpecialModels 92
3.5.4 RaceEffectonWage 94
ix Contents
4 RegressionDiscontinuity 97
4.1 IntroducingRDwithBefore-After 97
4.1.1 BAExamples 97
4.1.2 BAIdentificationAssumption 98
4.1.3 FromBAtoRD 99
4.2 RDIdentificationandFeatures 100
4.2.1 SharpRD(SRD)andFuzzyRD(FRD) 101
4.2.2 IdentificationatCutoff 102
4.2.3 RDMainFeatures 104
4.2.4 ClassSizeEffectonTestScore 106
4.3 RDEstimators 109
4.3.1 LSEforLevelEquation 109
4.3.2 IVEforRight-LeftDifferencedEquation 110
4.3.3 BandwidthChoiceandRemarks 112
4.3.4 HighSchoolCompletionEffectonFertility 113
4.4 SpecificationTests 116
4.4.1 BreaksinConditionalMeans 116
4.4.2 ContinuityinScoreDensity 117
4.5 RDTopics* 119
4.5.1 SpatialBreaks 119
4.5.2 RDforLimitedDependentVariables 120
4.5.3 MeasurementErrorinScore 121
4.5.4 RegressionKink(RK)andGeneralization 123
4.5.5 SRDwithMultipleScores 126
4.5.6 QuantileRD 129
5 DifferenceinDifferences 131
5.1 DDBasics 131
5.1.1 ExamplesforDD 132
5.1.2 Time-ConstantandTime-VaryingQualifications 133
5.1.3 DataRequirementandNotation 135
5.2 DDwithRepeatedCross-Sections 136
5.2.1 Identification 136
5.2.2 IdentificationwithParametricModels 140
5.2.3 SchoolingEffectonFertility:‘FuzzyDD’ 142
5.2.4 LinearModelEstimationforTwoPeriodsorMore 144
5.2.5 EarnedIncomeTaxCreditEffectonWork 147
5.2.6 Time-VaryingQualification* 148
5.3 DDwithPanelData 150
5.3.1 Identification 150
5.3.2 IdentificationandEstimationwithParametricModels 152
5.3.3 DaylightSavingTimeEffectonEnergy 157
5.4 PanelStayerDDforTime-VaryingQualification 158
5.4.1 Motivation 158
