Optimal Bandwidth Choice for Robust Bias Corrected Inference in Regression Discontinuity Designs

TL;DR

This paper develops new bandwidth selection methods for robust bias corrected inference in regression discontinuity designs, improving confidence interval coverage accuracy over traditional MSE-optimal choices.

Contribution

It introduces optimal bandwidth choices specifically for RBC confidence intervals, addressing the suboptimal coverage error of standard MSE-optimal bandwidths in RD analysis.

Findings

Standard MSE-optimal bandwidths are too large for RBC inference.

New bandwidths minimize coverage error for RBC confidence intervals.

RBC inference provides higher-order refinements over undersmoothing.

Abstract

Modern empirical work in Regression Discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment effect estimator, but is by construction invalid for inference. Robust bias corrected (RBC) inference methods are valid when using the MSE-optimal bandwidth, but we show they yield suboptimal confidence intervals in terms of coverage error. We establish valid coverage error expansions for RBC confidence interval estimators and use these results to propose new inference-optimal bandwidth choices for forming these intervals. We find that the standard MSE-optimal bandwidth for the RD point estimator is too large when the goal is to construct RBC confidence intervals with the smallest coverage error. We further optimize the constant terms behind the coverage error to derive new optimal choices for the auxiliary bandwidth required for RBC inference. Our expansions also establish that RBC inference yields higher-order refinements (relative to traditional undersmoothing) in the context of RD designs. Our main results cover sharp and sharp kink RD designs under conditional heteroskedasticity, and we discuss extensions to fuzzy and other RD designs, clustered sampling, and pre-intervention covariates adjustments. The theoretical findings are illustrated with a Monte Carlo experiment and an empirical application, and the main methodological results are available in \texttt{R} and \texttt{Stata} packages.