A simple but powerful tail index regression

Abstract

This paper introduces a flexible framework for the estimation of the conditional tail index of heavy tailed distributions. In this framework, the tail index is computed from an auxiliary linear regression model that facilitates estimation and inference based on established econometric methods, such as ordinary least squares (OLS), least absolute deviations, or M-estimation. We show theoretically and via simulations that OLS provides interesting results. Our Monte Carlo results highlight the adequate finite sample properties of the OLS tail index estimator computed from the proposed new framework and contrast its behavior to that of tail index estimates obtained by maximum likelihood estimation of exponential regression models, which is one of the approaches currently in use in the literature. An empirical analysis of the impact of determinants of the conditional left- and right-tail indexes of commodities' return distributions highlights the empirical relevance of our proposed approach. The novel framework's flexibility allows for extensions and generalizations in various directions, empowering researchers and practitioners to straightforwardly explore a wide range of research questions.