1 Tour of the book |
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1 | (6) |
2 Basics of treatment effect analysis |
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7 | (36) |
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2.1 Treatment intervention, counter-factual, and causal relation |
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7 | (4) |
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2.1.1 Potential outcomes and intervention |
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7 | (2) |
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2.1.2 Causality and association |
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9 | (1) |
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2.1.3 Partial equilibrium analysis and remarks |
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10 | (1) |
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2.2 Various treatment effects and no effects |
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11 | (5) |
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11 | (2) |
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2.2.2 Three no-effect concepts |
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13 | (1) |
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14 | (2) |
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2.3 Group-mean difference and randomization |
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16 | (5) |
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2.3.1 Group-mean difference and mean effect |
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16 | (2) |
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2.3.2 Consequences of randomization |
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18 | (1) |
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2.3.3 Checking out covariate balance |
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19 | (2) |
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2.4 Overt bias, hidden (covert) bias, and selection problems |
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21 | (5) |
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2.4.1 Overt and hidden biases |
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21 | (1) |
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2.4.2 Selection on observables and unobservables |
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22 | (3) |
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2.4.3 Linear models and biases |
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25 | (1) |
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2.5 Estimation with group mean difference and LSE |
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26 | (6) |
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2.5.1 Group-mean difference and LSE |
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26 | (2) |
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2.5.2 A job-training example |
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28 | (2) |
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2.5.3 Linking counter-factuals to linear models |
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30 | (2) |
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2.6 Structural form equations and treatment effect |
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32 | (3) |
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2.7 On mean independence and independence |
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35 | (3) |
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2.7.1 Independence and conditional independence |
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35 | (1) |
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2.7.2 Symmetric and asymmetric mean-independence |
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36 | (1) |
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2.7.3 Joint and marginal independence |
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37 | (1) |
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2.8 Illustration of biases and Simpson's Paradox |
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38 | (5) |
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2.8.1 Illustration of biases |
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38 | (2) |
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2.8.2 Source of overt bias |
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40 | (1) |
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41 | (2) |
3 Controlling for covariates |
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43 | (36) |
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3.1 Variables to control for |
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43 | (6) |
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44 | (1) |
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45 | (1) |
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46 | (1) |
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47 | (1) |
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48 | (1) |
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3.2 Comparison group and controlling for observed variables |
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49 | (7) |
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3.2.1 Comparison group bias |
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49 | (2) |
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3.2.2 Dimension and support problems in conditioning |
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51 | (2) |
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3.2.3 Parametric models to avoid dimension and support problems |
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53 | (1) |
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3.2.4 Two-stage method for a semi-linear model |
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54 | (2) |
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3.3 Regression discontinuity design (RDD) and before-after (BA) |
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56 | (9) |
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3.3.1 Parametric regression discontinuity |
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56 | (2) |
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3.3.2 Sharp nonparametric regression discontinuity |
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58 | (3) |
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3.3.3 Fuzzy nonparametric regression discontinuity |
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61 | (3) |
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64 | (1) |
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3.4 Treatment effect estimator with weighting |
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65 | (7) |
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3.4.1 Effect on the untreated |
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67 | (1) |
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3.4.2 Effects on the treated and on the population |
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68 | (1) |
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3.4.3 Efficiency bounds and efficient estimators |
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69 | (2) |
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3.4.4 An empirical example |
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71 | (1) |
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3.5 Complete pairing with double sums |
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72 | (7) |
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3.5.1 Discrete covariates |
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72 | (2) |
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3.5.2 Continuous or mixed (continuous or discrete) covariates |
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74 | (2) |
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3.5.3 An empirical example |
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76 | (3) |
4 Matching |
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79 | (38) |
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4.1 Estimators with matching |
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80 | (5) |
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4.1.1 Effects on the treated |
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80 | (2) |
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4.1.2 Effects on the population |
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82 | (2) |
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4.1.3 Estimating asymptotic variance |
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84 | (1) |
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4.2 Implementing matching |
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85 | (7) |
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4.2.1 Decisions to make in matching |
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85 | (3) |
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4.2.2 Evaluating matching success |
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88 | (2) |
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90 | (2) |
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4.3 Propensity score matching |
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92 | (5) |
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4.3.1 Balancing observables with propensity score |
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93 | (1) |
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4.3.2 Removing overt bias with propensity-score |
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93 | (2) |
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95 | (2) |
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4.4 Matching for hidden bias |
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97 | (2) |
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4.5 Difference in differences (DD) |
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99 | (12) |
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4.5.1 Mixture of before-after and matching |
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99 | (1) |
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4.5.2 DD for post-treatment treated in no-mover panels |
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100 | (3) |
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4.5.3 DD with repeated cross-sections or panels with movers |
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103 | (2) |
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4.5.4 Linear models for DD |
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105 | (3) |
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108 | (3) |
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4.6 Triple differences (TD) |
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111 | (6) |
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4.6.1 TD for qualified post-treatment treated |
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112 | (1) |
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4.6.2 Linear models for TD |
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113 | (2) |
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4.6.3 An empirical example |
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115 | (2) |
5 Design and instrument for hidden bias |
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117 | (30) |
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5.1 Conditions for zero hidden bias |
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117 | (2) |
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5.2 Multiple ordered treatment groups |
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119 | (4) |
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119 | (3) |
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122 | (1) |
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123 | (2) |
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5.4 Multiple control groups |
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125 | (4) |
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5.5 Instrumental variable estimator (IVE) |
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129 | (7) |
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5.5.1 Potential treatments |
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129 | (2) |
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5.5.2 Sources for instruments |
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131 | (3) |
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5.5.3 Relation to regression discontinuity design |
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134 | (2) |
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5.6 Wald estimator, IVE, and compliers |
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136 | (11) |
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5.6.1 Wald estimator under constant effects |
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136 | (2) |
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5.6.2 IVE for heterogenous effects |
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138 | (1) |
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5.6.3 Wald estimator as effect on compliers |
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139 | (3) |
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5.6.4 Weighting estimators for complier effects |
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142 | (5) |
6 Other approaches for hidden bias |
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147 | (24) |
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147 | (13) |
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6.1.1 Unobserved confounder affecting treatment |
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148 | (4) |
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6.1.2 Unobserved confounder affecting treatment and response |
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152 | (5) |
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6.1.3 Average of ratios of biased to true effects |
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157 | (3) |
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6.2 Selection correction methods |
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160 | (3) |
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6.3 Nonparametric bounding approaches |
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163 | (4) |
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6.4 Controlling for post-treatment variables to avoid confounder |
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167 | (4) |
7 Multiple and dynamic treatments |
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171 | (20) |
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171 | (6) |
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7.1.1 Parameters of interest |
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172 | (2) |
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7.1.2 Balancing score and propensity score matching |
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174 | (3) |
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7.2 Treatment duration effects with time-varying covariates |
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177 | (4) |
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7.3 Dynamic treatment effects with interim outcomes |
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181 | (10) |
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7.3.1 Motivation with two-period linear models |
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181 | (5) |
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7.3.2 G algorithm under no unobserved confounder |
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186 | (2) |
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7.3.3 G algorithm for three or more periods |
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188 | (3) |
Appendix |
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191 | (42) |
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A.1 Kernel nonparametric regression |
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191 | (5) |
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A.2 Appendix for Chapter 2 |
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196 | (5) |
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A.2.1 Comparison to a probabilistic causality |
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196 | (2) |
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A.2.2 Learning about joint distribution from marginals |
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198 | (3) |
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A.3 Appendix for Chapter 3 |
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201 | (3) |
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A.3.1 Derivation for a semi-linear model |
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201 | (1) |
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A.3.2 Derivation for weighting estimators |
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202 | (2) |
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A.4 Appendix for Chapter 4 |
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204 | (10) |
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A.4.1 Non-sequential matching with network flow algorithm |
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204 | (2) |
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A.4.2 Greedy non-sequential multiple matching |
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206 | (3) |
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A.4.3 Nonparametric matching and support discrepancy |
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209 | (5) |
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A.5 Appendix for Chapter 5 |
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214 | (7) |
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A.5.1 Some remarks on LATE |
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214 | (2) |
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A.5.2 Outcome distributions for compliers |
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216 | (3) |
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A.5.3 Median treatment effect |
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219 | (2) |
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A.6 Appendix for Chapter 6 |
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221 | (5) |
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A.6.1 Controlling for affected covariates in a linear model |
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221 | (3) |
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A.6.2 Controlling for affected mean-surrogates |
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224 | (2) |
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A.7 Appendix for Chapter 7 |
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226 | (7) |
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A.7.1 Regression models for discrete cardinal treatments |
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226 | (2) |
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A.7.2 Complete pairing for censored responses |
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228 | (5) |
References |
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233 | (12) |
Index |
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245 | |