Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks

TL;DR

This paper develops practical inference methods for extremal conditional quantile models using extreme value theory, with applications to stock return fluctuations and low birthweight analysis.

Contribution

It introduces feasible inference tools for extremal quantile regression based on extreme value approximations, applicable in various empirical contexts.

Findings

Effective inference methods for tail quantiles

Application to stock return extremes

Analysis of low birthweight percentiles

Abstract

Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many economic and financial applications, such as conditional value-at-risk, production efficiency, and adjustment bands in (S,s) models. In this paper we provide feasible inference tools for extremal conditional quantile models that rely upon extreme value approximations to the distribution of self-normalized quantile regression statistics. The methods are simple to implement and can be of independent interest even in the non-regression case. We illustrate the results with two empirical examples analyzing extreme fluctuations of a stock return and extremely low percentiles of live infants' birthweights in the range between 250 and 1500 grams.