Trading-off Bias and Variance in Stratified Experiments and in Staggered Adoption Designs, Under a Boundedness Condition on the Magnitude of the Treatment Effect

Clément de Chaisemartin

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Abstract: 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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2022-03-18
New Economics Papers: this item is included in nep-exp
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Related works:
Working Paper: Trading-off Bias and Variance in Stratified Experiments and in Staggered Adoption Designs, Under a Boundedness Condition on the Magnitude of the Treatment Effect (2022)
Working Paper: Trading-off Bias and Variance in Stratified Experiments and in Staggered Adoption Designs, Under a Boundedness Condition on the Magnitude of the Treatment Effect (2022)
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