The beyondpareto command for optimal extreme-value index estimation

• König, Johannes ^[1] ; Schluter, Christian ^[2] ; Beckmannshagen, Mattis ^[1]
  1. [1] German Institute for Economic Research

     German Institute for Economic Research

     Berlin, Stadt, Alemania

     
  2. [2] University of Southampton

     University of Southampton

     GB.ENG.M4.24UJ, Reino Unido

     
• Localización: The Stata journal, ISSN 1536-867X, Vol. 25, Nº. 1, 2025, págs. 169-188
• Idioma: inglés
• DOI: 10.1177/1536867X251322969
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• Resumen

  • 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