The beyondpareto command for optimal extreme-value index estimation

Johannes König (), Christian Schluter, Carsten Schröder, Isabella Retter () and Mattis Beckmannshagen ()
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Johannes König: DIW Berlin
Isabella Retter: DIW Berlin
Mattis Beckmannshagen: DIW Berlin

Stata Journal, 2025, vol. 25, issue 1, 169-188

Abstract: In this article, we introduce the command beyondpareto, which estimates the extreme-value index for distributions that are Pareto-like, that is, whose upper tails are regularly varying and eventually become Pareto. The estimation is based on rank-size regressions, and the threshold value for the upper-order statis- tics included in the final regression is determined optimally by minimizing the asymptotic mean squared error. An essential diagnostic tool for evaluating the fit of the estimated extreme-value index is the Pareto quantile–quantile plot, pro- vided in the accompanying command pqqplot. The usefulness of our estimation approach is illustrated in several real-world examples focusing on the upper tail of German wealth and city-size distributions.

Keywords: beyondpareto; pqqplot; rank-size regression; extreme value index; Pareto; Zipf’s law; heavy tails; bias (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1177/1536867X251322969

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