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

No 29879, NBER Working Papers from National Bureau of Economic Research, Inc

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-in-differences estimators in staggered adoption designs.

JEL-codes: C21 C23 (search for similar items in EconPapers)
Date: 2022-03
New Economics Papers: this item is included in nep-ecm
Note: CF CH DEV ED EEE EH IFM IO ITI LS PE POL TWP
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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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