Regression adjustment in completely randomized experiments with a diverging number of covariates

Understand

Randomized experiments have become important tools in empirical research.

• In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate adjustment can further improve the efficiency without assuming a correctly specified outcome model.
• In modern applications, experimenters often have access to many covariates, motivating the need for a theory of covariate adjustment under the asymptotic regime with a diverging number of covariates.
• We study the asymptotic properties of covariate adjustment under the potential outcomes model and propose a bias-corrected estimator that is consistent and asymptotically normal under weaker conditions.