Trading-off Bias and Variance in Stratified Experiments and in Staggered Adoption Designs, Under a Boundedness Condition on the Magnitude of the Treatment Effect
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18 mars 2022
- ISIDORE Id: 10670/1.c20ead...
- hal: hal-03873919
http://creativecommons.org/licenses/by-nc/ , info:eu-repo/semantics/OpenAccess
Mots-clés
Bias-variance trade-off Average treatment effect Mean-squared error Minimaxlinear estimator Bounded normal mean model Stratified randomized experiments Differencesin-differences Staggered adoption designs Shrinkage C - Mathematical and Quantitative Methods/C.C2 - Single Equation Models • Single Variables/C.C2.C21 - Cross-Sectional Models • Spatial Models • Treatment Effect Models • Quantile Regressions C - Mathematical and Quantitative Methods/C.C2 - Single Equation Models • Single Variables/C.C2.C23 - Panel Data Models • Spatio-temporal ModelsSujets proches
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Clément de Chaisemartin, « Trading-off Bias and Variance in Stratified Experiments and in Staggered Adoption Designs, Under a Boundedness Condition on the Magnitude of the Treatment Effect », HAL SHS (Sciences de l’Homme et de la Société), ID : 10670/1.c20ead...
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I consider estimation of the average treatment effect (ATE), in a population composed of G groups, when one has unbiased and uncorrelated estimators of each group's conditional average treatment effect (CATE). These conditions are met in stratified randomized experiments. I assume that the outcome is homoscedastic, and that each CATE is bounded in absolute value by B standard deviations of the outcome, for some known B. I derive, across all linear combinations of the CATEs' estimators, the estimator of the ATE with the lowest worst-case mean-squared error. This minimax-linear estimator assigns a weight equal to group g's share in the population to the most precisely estimated CATEs, and a weight proportional to one over the estimator's variance to the least precisely estimated CATEs. I also derive the minimax-linear estimator when the CATEs' estimators are positively correlated, a condition that may be met by differences-indifferences estimators in staggered adoption designs.
