Bias correction for quantile regression estimators

TL;DR

This paper analyzes the second-order bias in quantile regression estimators and proposes a feasible bias correction method based on higher-order stochastic expansion, improving estimation accuracy in empirical applications.

Contribution

It derives an explicit second-order bias formula for quantile regression estimators and introduces a practical bias correction procedure using finite-difference estimators.

Findings

Bias correction improves estimator accuracy in simulations

The method performs well in empirical illustration

Second-order bias is significant in finite samples

Abstract

We study the bias of classical quantile regression and instrumental variable quantile regression estimators. While being asymptotically first-order unbiased, these estimators can have non-negligible second-order biases. We derive a higher-order stochastic expansion of these estimators using empirical process theory. Based on this expansion, we derive an explicit formula for the second-order bias and propose a feasible bias correction procedure that uses finite-difference estimators of the bias components. The proposed bias correction method performs well in simulations. We provide an empirical illustration using Engel's classical data on household food expenditure.