Extremal Quantile Regression: An Overview

TL;DR

Extremal quantile regression focuses on the tails of the distribution, with recent advances improving estimation accuracy and inference, especially in finance and economics, through extreme value theory and bootstrap methods.

Contribution

This overview introduces recent theoretical and empirical developments in extremal quantile regression, emphasizing extreme value approximations and bias correction techniques.

Findings

Extreme value laws outperform Gaussian laws at distribution tails.

Bias correction methods improve estimation accuracy.

Empirical examples demonstrate applications in finance and economics.

Abstract

Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants of low infant birth weights, and auction models. This chapter provides an overview of recent developments in the theory and empirics of extremal quantile regression. The advances in the theory have relied on the use of extreme value approximations to the law of the Koenker and Bassett (1978) quantile regression estimator. Extreme value laws not only have been shown to provide more accurate approximations than Gaussian laws at the tails, but also have served as the basis to develop bias corrected estimators and inference methods using simulation and suitable variations of bootstrap and subsampling. The applicability of these methods is illustrated with two empirical examples on conditional value-at-risk and financial contagion.