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 language | English |
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Pages (from-to) | 255-269 |
Journal | Journal of Business & Economic Statistics |
Volume | 41 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2023 |
Keywords
- power law
- extreme values
- heterogeneous data
- COVD-19
- inequality