Two-way Clustering Robust Variance Estimator in Quantile Regression Models

TL;DR

This paper develops a new two-way cluster-robust variance estimator for linear quantile regression models with clustered data, providing theoretical guarantees and highlighting limitations in non-Gaussian regimes.

Contribution

It introduces a novel variance estimator tailored for two-way clustered data in quantile regression, with rigorous theoretical validation and insights into inference limitations.

Findings

Proposes a consistent two-way cluster-robust variance estimator.

Establishes Gaussian approximation and inference validity.

Identifies impossibility of uniform inference in non-Gaussian regimes.

Abstract

We study inference for linear quantile regression with two-way clustered data. Using a separately exchangeable array framework and a projection decomposition of the quantile score, we characterize regime-dependent convergence rates and establish a self-normalized Gaussian approximation. We propose a two-way cluster-robust sandwich variance estimator with a kernel-based density ``bread'' and a projection-matched ``meat'', and prove consistency and validity of inference in Gaussian regimes. We also show an impossibility result for uniform inference in a non-Gaussian interaction regime.