Primary Submission Category: Randomized Studies
Design based variance estimation for Hajek estimators of average causal effects in finely stratified, potentially clustered designs
Authors: Xinhe Wang, Ben Hansen,
Presenting Author: Xinhe Wang*
Clustered randomized controlled trials are commonly used to evaluate the effectiveness of one or more treatments. Frequently, stratified or paired designs are adopted in practice. In this setting, the difference of intervention and control group means is properly construed as a Hajek estimator, at least when the means are appropriately computed with weights reflecting cluster sizes and inverse assignment probabilities. Despite the ubiquity of these designs and estimators, suitable design-based variance estimation does not appear to be available in the literature. Fogarty (2018, JRSS-B) gave such estimates for finely stratified designs, but not with clustering or variation in size; Schochet et al (2022, JASA) address clustering, but only for large-stratum designs. In this work, we derive the finite-population variance-covariance matrix and establish asymptotic normality. We propose asymptotically conservative sandwich variance estimators and covariance interval estimators. These estimators are suitable both for the large-stratum designs considered by Schochet and colleagues and in the many-small-strata scenarios considered by Pashley and Miratrix (2021, J. Educ. Behav. Stat.). In contrast to the analogous standard error for impacts estimated using stratum fixed effects, ours is consistently conservative even as the number of strata grows without bound, a theoretical finding supported by our simulation experiments.