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

TL;DR

This paper develops a theory for covariate adjustment in randomized experiments with many covariates, proposing a bias-corrected estimator that remains consistent and normal without strong model assumptions.

Contribution

It introduces a bias-corrected covariate adjustment method for experiments with diverging covariates, based solely on randomization principles.

Findings

The proposed estimator is consistent and asymptotically normal.

The theory applies under weaker conditions than traditional models.

New concentration inequalities for sampling without replacement are developed.

Abstract

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. Our theory is purely randomization-based without imposing any parametric outcome model assumptions. To prove the theoretical results, we develop novel vector and matrix concentration inequalities for sampling without replacement.