Flexible Covariate Adjustments in Regression Discontinuity Designs

Abstract: Empirical regression discontinuity (RD) studies often include covariates in their specifications to increase the precision of their estimates. In this paper, we propose a novel class of estimators that use such covariate information more efficiently than existing methods and can accommodate many covariates. Our estimators are simple to implement and involve running a standard RD analysis after subtracting a function of the covariates from the original outcome variable. We characterize the function of the covariates that minimizes the asymptotic variance of these estimators. We also show that the conventional RD framework gives rise to a special robustness property which implies that the optimal adjustment function can be estimated flexibly via modern machine learning techniques without affecting the first-order properties of the final RD estimator. We demonstrate our methods' scope for efficiency improvements by reanalyzing data from a large number of recently published empirical studies.