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.

Format:

Book

Author/Creator:

de Chaisemartin, Clément.

Contributor:

National Bureau of Economic Research.

Series:

Working Paper Series (National Bureau of Economic Research) no. w29879.

NBER working paper series no. w29879

Language:

English

Physical Description:

1 online resource: illustrations (black and white);

Place of Publication:

Cambridge, Mass. National Bureau of Economic Research 2022.

Summary:

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.

Notes:

Print version record

March 2022.