Cluster-Robust Bootstrap Inference in Quantile Regression Models

TL;DR

This paper introduces a wild bootstrap method for reliable cluster-robust inference in linear quantile regression, effective with many small, heterogeneous clusters, and validated through theoretical proofs and an application to educational data.

Contribution

It develops a simple, effective bootstrap procedure for cluster-robust inference in quantile regression, valid with many small clusters and demonstrated through theoretical and empirical analysis.

Findings

Bootstrap provides asymptotically valid inference for the entire quantile process.

Method performs well even with fewer clusters than sample size.

Application to Project STAR data illustrates practical utility.

Abstract

In this paper I develop a wild bootstrap procedure for cluster-robust inference in linear quantile regression models. I show that the bootstrap leads to asymptotically valid inference on the entire quantile regression process in a setting with a large number of small, heterogeneous clusters and provides consistent estimates of the asymptotic covariance function of that process. The proposed bootstrap procedure is easy to implement and performs well even when the number of clusters is much smaller than the sample size. An application to Project STAR data is provided.