Regression Discontinuity Designs Using Covariates

TL;DR

This paper explores how including covariates in regression discontinuity designs can improve estimation accuracy and inference, proposing new methods and validating them through simulations and empirical examples.

Contribution

It introduces a covariate-adjusted estimation approach for RDDs that maintains consistency and offers improved inference, with new bias correction and MSE expansion techniques.

Findings

Covariate adjustment can enhance RDD estimation accuracy.

New bias correction methods improve inference robustness.

Software implementations facilitate practical application.

Abstract

We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions, and characterize the potential for estimation and inference improvements. We also present new covariate-adjusted mean squared error expansions and robust bias-corrected inference procedures, with heteroskedasticity-consistent and cluster-robust standard errors. An empirical illustration and an extensive simulation study is presented. All methods are implemented in \texttt{R} and \texttt{Stata} software packages.