  This paper is concerned with estimation and inference on average treatment
effects in randomized controlled trials when researchers observe potentially
many covariates. By employing Neyman's (1923) finite population perspective, we
propose a bias-corrected regression adjustment estimator using cross-fitting,
and show that the proposed estimator has favorable properties over existing
alternatives. For inference, we derive the first and second order terms in the
stochastic component of the regression adjustment estimators, study higher
order properties of the existing inference methods, and propose a
bias-corrected version of the HC3 standard error. The proposed methods readily
extend to stratified experiments with large strata. Simulation studies show our
cross-fitted estimator, combined with the bias-corrected HC3, delivers precise
point estimates and robust size controls over a wide range of DGPs. To
illustrate, the proposed methods are applied to real dataset on randomized
experiments of incentives and services for college achievement following
Angrist, Lang, and Oreopoulos (2009).
