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The beyondpareto command for optimal extreme-value index estimation

Author

Listed:
  • Johannes König

    (DIW Berlin)

  • Christian Schluter

    (Aix Marseille School of Economics)

  • Carsten Schröder

    (DIW Berlin)

  • Isabella Retter

    (DIW Berlin)

  • Mattis Beckmannshagen

    (DIW Berlin)

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.

Suggested Citation

  • Johannes König & Christian Schluter & Carsten Schröder & Isabella Retter & Mattis Beckmannshagen, 2025. "The beyondpareto command for optimal extreme-value index estimation," Stata Journal, StataCorp LLC, vol. 25(1), pages 169-188, March.
    • Handle: RePEc:tsj:stataj:v:25:y:2025:i:1:p:169-188
    DOI: 10.1177/1536867X251322969
    Note: to access software from within Stata, net describe http://www.stata-journal.com/software/sj25-1/st0770/
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