Regression Discontinuity Designs Using Covariates

We study identification, estimation, and inference in Regression Discontinuity (RD) designs when additional covariates are included in the estimation. Standard RD estimation and inference is based on local polynomial... [ view full abstract ]

We study identification, estimation, and inference in Regression Discontinuity (RD) designs when additional covariates are included in the estimation. Standard RD estimation and inference is based on local polynomial regression methods using the outcome and running variables that determines treatment assignment. Applied researchers often include specifications with additional covariates to increase efficiency. However, no results justifying this adjustment have been formally derived, leaving little practical guidance and a proliferation of ad-hoc methods that may result in invalid estimation and inference. We examine the properties of local polynomial estimators that incorporates covariates in an additive separable, linear-in-parameters way, imposing a common effect on both sides of the cutoff. Under minimal assumptions, we show that this covariate-adjusted RD estimator remains consistent for the RD treatment effect and characterize the potential improvements. We show that including interactions between treatment status and covariates leads to an estimator that is inconsistent in general. We present asymptotic mean squared error expansions, optimal bandwidth choices, optimal point estimators, robust nonparametric inference procedures based on bias-correction techniques, and heteroskedasticity-consistent standard errors. Our results cover sharp, fuzzy, kink RD designs, and clustered data.