Unified Extreme Value Estimation for Heterogeneous Data

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages31
Volume2020-025
Publication statusPublished - 30 Sep 2020

Publication series

NameCentER Discussion Paper
Volume2020-025

Keywords

  • Power law;
  • Extreme values
  • Heterogeneous data
  • COVID-19
  • Inequality

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