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 - Deutsche Institut für Wirtschaftsforschung = German Institute for Economic Research
Christian Schluter: AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, University of Southampton
Isabella Retter: DIW Berlin - Deutsche Institut für Wirtschaftsforschung = German Institute for Economic Research
Mattis Beckmannshagen: DIW Berlin - Deutsches Institut für Wirtschaftsforschung

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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 statistics 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 extrerme-value index is the Pareto quantile–quantile plot, provided 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.

Date: 2025-03-24
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Published in The Stata Journal, 2025, 25 (1), pp.169-188. ⟨10.1177/1536867X251322969⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05085219

DOI: 10.1177/1536867X251322969

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