To Adjust or not to Adjust? Estimating the Average Treatment Effect in Randomized Experiments with Missing Covariates

Randomized experiments allow for consistent estimation of the average treatment effect based on difference in mean outcomes without strong modeling assumptions. Appropriate use pretreatment covariates can further improve efficiency. Missingness is nevertheless common practice, and raises an important question: should we adjust subject to missingness, if so, how? The unadjusted means always unbiased. complete-covariate analysis adjusts all completely observed covariates, asymptotically more efficient than at least one covariate predictive outcome. Then what additional gain adjusting missingness? To reconcile conflicting recommendations literature, analyze compare five strategies handling missing randomized under design-based framework, recommend missingness-indicator method, as a known but not so popular strategy due its multiple advantages. First, it removes dependence regression-adjusted estimators imputed values covariates. Second, does require missingness mechanism, yields even when mechanism related unobservable potential outcomes. Third, ensures large-sample efficiency over only Lastly, easy implement via squares. We also propose modifications asymptotic finite sample considerations. Importantly, our theory views randomization basis inference, impose any assumptions data-generating process or mechanism. Supplementary materials this article are available online.