Covariate adjustment in stratified experiments

• 成果类型: Article
• 署名作者: Cytrynbaum, Max
• 署名单位: Yale University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE2475
• 发表日期: 2024
• 页码: 971-998
• 关键词: Matched pairs; analysis of covariance; blocking; robust standard error; treatment effects; C10; C14; C90

摘要

This paper studies covariate adjusted estimation of the average treatment effect in stratified experiments. We work in a general framework that includes matched tuples designs, coarse stratification, and complete randomization as special cases. Regression adjustment with treatment-covariate interactions is known to weakly improve efficiency for completely randomized designs. By contrast, we show that for stratified designs such regression estimators are generically inefficient, potentially even increasing estimator variance relative to the unadjusted benchmark. Motivated by this result, we derive the asymptotically optimal linear covariate adjustment for a given stratification. We construct several feasible estimators that implement this efficient adjustment in large samples. In the special case of matched pairs, for example, the regression including treatment, covariates, and pair fixed effects is asymptotically optimal. We also provide novel asymptotically exact inference methods that allow researchers to report smaller confidence intervals, fully reflecting the efficiency gains from both stratification and adjustment. Simulations and an empirical application demonstrate the value of our proposed methods.