Local Composite Quantile Regression for Regression Discontinuity

TL;DR

This paper introduces local composite quantile regression (LCQR) for causal inference in regression discontinuity designs, demonstrating its boundary performance, proposing bias correction and inference methods, and providing practical tools and simulations.

Contribution

It develops LCQR for RD, showing its effectiveness and providing bias correction, inference procedures, bandwidth selection, and an R package for implementation.

Findings

LCQR achieves accurate treatment effect estimation at boundaries.

The proposed t-test provides reliable confidence intervals.

Simulation and real data examples validate the method's effectiveness.

Abstract

We introduce the local composite quantile regression (LCQR) to causal inference in regression discontinuity (RD) designs. Kai et al. (2010) study the efficiency property of LCQR, while we show that its nice boundary performance translates to accurate estimation of treatment effects in RD under a variety of data generating processes. Moreover, we propose a bias-corrected and standard error-adjusted t-test for inference, which leads to confidence intervals with good coverage probabilities. A bandwidth selector is also discussed. For illustration, we conduct a simulation study and revisit a classic example from Lee (2008). A companion R package rdcqr is developed.