Simultaneous Selection of Optimal Bandwidths for the Sharp Regression Discontinuity Estimator

TL;DR

This paper introduces a novel bandwidth selection rule for sharp regression discontinuity estimators that improves mean squared error performance by using different bandwidths on either side of the cutoff, supported by theoretical and simulation evidence.

Contribution

It proposes a new bandwidth selection method that optimally chooses different bandwidths on each side of the cutoff for sharper estimates in regression discontinuity designs.

Findings

Proposed method reduces asymptotic mean squared error.

Simulation results confirm theoretical advantages across various sample sizes.

Method outperforms existing bandwidth selection rules.

Abstract

A new bandwidth selection rule that uses different bandwidths for the local linear regression estimators on the left and the right of the cut-off point is proposed for the sharp regression discontinuity estimator of the mean program impact at the cut-off point. The asymptotic mean squared error of the estimator using the proposed bandwidth selection rule is shown to be smaller than other bandwidth selection rules proposed in the literature. An extensive simulation study shows that the proposed method's performances for the sample sizes 500, 2000, and 5000 closely match the theoretical predictions.