Unified Extreme Value Estimation for Heterogeneous Data

30 Pages Posted: 8 Oct 2020

See all articles by John H. J. Einmahl

John H. J. Einmahl

Tilburg University - Department of Econometrics & Operations Research

Yi He

University of Amsterdam - Amsterdam School of Economics (ASE)

Multiple version iconThere are 2 versions of this paper

Date Written: September 24, 2020

Abstract

We develop a universal econometric formulation of the empirical power laws possibly driven by parameter heterogeneity. Our approach extends classical extreme value theory to specifying the behavior of the empirical distribution of a general data set with possibly heterogeneous marginal distributions and a complex dependence structure. The main assumption is that in the intermediate tail the empirical distribution approaches some heavy-tailed distribution with a positive extreme value index. In this setup the Hill estimator consistently estimates this extreme value index and, on a log-scale, extreme quantiles are consistently estimated. We discuss several model examples that satisfy our conditions and demonstrate in simulations how heterogeneity may generate the dynamics of empirical power laws. We observe a dynamic cross-sectional power law for the new confirmed COVID-19 cases and deaths per million people across countries, and show that this international inequality is largely driven by the heterogeneity of the countries' scale parameters.

Keywords: Power law; Extreme values; Heterogeneous data; COVID-19; Inequality

JEL Classification: C14, C21, I19

Suggested Citation

Einmahl, John H. J. and He, Yi, Unified Extreme Value Estimation for Heterogeneous Data (September 24, 2020). Available at SSRN: https://ssrn.com/abstract=3699676 or http://dx.doi.org/10.2139/ssrn.3699676

John H. J. Einmahl

Tilburg University - Department of Econometrics & Operations Research ( email )

P.O. Box 90153
5000 LE Tilburg
Netherlands

Yi He (Contact Author)

University of Amsterdam - Amsterdam School of Economics (ASE) ( email )

Roetersstraat 11
Amsterdam, North Holland 1018 WB
Netherlands

HOME PAGE: http://yihe.nl

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
7
Abstract Views
77
PlumX Metrics