High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing

TL;DR

This paper introduces a novel high-dimensional panel quantile regression model that combines sparse covariate effects with low-rank latent factors, addressing limitations of traditional methods and applied to asset pricing.

Contribution

It develops a new estimation method using ADMM with combined regularization to accurately estimate sparse and low-rank components in high-dimensional panel data.

Findings

Characteristics have reduced predictive power after controlling for latent factors.

Latent factors and coefficients differ across quantiles, especially at the extremes.

The proposed estimator is consistent under general conditions.

Abstract

We propose a generalization of the linear panel quantile regression model to accommodate both \textit{sparse} and \textit{dense} parts: sparse means while the number of covariates available is large, potentially only a much smaller number of them have a nonzero impact on each conditional quantile of the response variable; while the dense part is represent by a low-rank matrix that can be approximated by latent factors and their loadings. Such a structure poses problems for traditional sparse estimators, such as the $\ell_1$-penalised Quantile Regression, and for traditional latent factor estimator, such as PCA. We propose a new estimation procedure, based on the ADMM algorithm, consists of combining the quantile loss function with $\ell_1$ \textit{and} nuclear norm regularization. We show, under general conditions, that our estimator can consistently estimate both the nonzero coefficients of the covariates and the latent low-rank matrix. Our proposed model has a "Characteristics + Latent Factors" Asset Pricing Model interpretation: we apply our model and estimator with a large-dimensional panel of financial data and find that (i) characteristics have sparser predictive power once latent factors were controlled (ii) the factors and coefficients at upper and lower quantiles are different from the median.