Low-rank Panel Quantile Regression: Estimation and Inference

TL;DR

This paper introduces low-rank panel quantile regression models that handle unobserved heterogeneity in slopes across individuals and time, with estimation, inference, and hypothesis testing methods validated through simulations and real data.

Contribution

It develops a novel low-rank quantile regression framework with nuclear norm regularization, sample splitting, and debiasing, along with new tests for slope constancy and additive structure.

Findings

Estimators are asymptotically normally distributed.

Proposed tests effectively detect slope structure.

Finite sample performance is validated via simulations and real data.

Abstract

In this paper, we propose a class of low-rank panel quantile regression models which allow for unobserved slope heterogeneity over both individuals and time. We estimate the heterogeneous intercept and slope matrices via nuclear norm regularization followed by sample splitting, row- and column-wise quantile regressions and debiasing. We show that the estimators of the factors and factor loadings associated with the intercept and slope matrices are asymptotically normally distributed. In addition, we develop two specification tests: one for the null hypothesis that the slope coefficient is a constant over time and/or individuals under the case that true rank of slope matrix equals one, and the other for the null hypothesis that the slope coefficient exhibits an additive structure under the case that the true rank of slope matrix equals two. We illustrate the finite sample performance of estimation and inference via Monte Carlo simulations and real datasets.