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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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  • Clément de Chaisemartin

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.

Suggested Citation

  • Clément de Chaisemartin, 2022. "Trading-off Bias and Variance in Stratified Experiments and in Staggered Adoption Designs, Under a Boundedness Condition on the Magnitude of the Treatment Effect," NBER Working Papers 29879, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:29879
    Note: CF CH DEV ED EEE EH IFM IO ITI LS PE POL TWP
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    References listed on IDEAS

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    1. Clément de Chaisemartin & Luc Behaghel, 2020. "Estimating the Effect of Treatments Allocated by Randomized Waiting Lists," Econometrica, Econometric Society, vol. 88(4), pages 1453-1477, July.
    2. Luc Behaghel & Clément de Chaisemartin & Marc Gurgand, 2017. "Ready for Boarding? The Effects of a Boarding School for Disadvantaged Students," American Economic Journal: Applied Economics, American Economic Association, vol. 9(1), pages 140-164, January.
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    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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