Empirical Likelihood Covariate Adjustment for Regression Discontinuity Designs

This paper proposes a novel approach to incorporate covariates in regression discontinuity (RD) designs. We represent the covariate balance condition as overidentifying moment restrictions. The empirical likelihood (EL) RD estimator efficiently incorporates the information from covariate balance and thus has an asymptotic variance no larger than that of the standard estimator without covariates. It achieves efficiency gain under weak conditions. We resolve the indeterminacy raised by Calonico, Cattaneo, Farrell, and Titiunik (2019, Page 448) regarding the asymptotic efficiency gain from incorporating covariates to RD estimator, as their estimator has the same asymptotic variance as ours. We then propose a robust corrected EL (RCEL) confidence set which achieves the fast n^(-1) coverage error decay rate even though the point estimator converges at a nonparametric rate. In addition, the coverage accuracy of the RCEL confidence set is automatically robust against slight perturbation to the covariate balance condition, which may happen in cases such as data contamination and misspecified "unaffected" outcomes used as covariates. We also show a uniform-in-bandwidth Wilks theorem, which is useful in sensitivity analysis for the proposed RCEL confidence set in the sense of Armstrong and Kolesar (2018). We conduct Monte Carlo simulations to assess the finite-sample performance of our method and also apply it to a real dataset.Comment: 61 pages, 7 figure