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The beyondpareto command for optimal extreme-value index estimation

Author

Listed:
  • 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)

  • Carsten Schröder

    (DIW Berlin - Deutsches Institut für Wirtschaftsforschung)

  • Isabella Retter

    (DIW Berlin - Deutsche Institut für Wirtschaftsforschung = German Institute for Economic Research)

  • Mattis Beckmannshagen

    (DIW Berlin - Deutsches Institut für Wirtschaftsforschung)

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.

Suggested Citation

  • Johannes König & Christian Schluter & Carsten Schröder & Isabella Retter & Mattis Beckmannshagen, 2025. "The beyondpareto command for optimal extreme-value index estimation," Post-Print hal-05085219, HAL.
    • Handle: RePEc:hal:journl:hal-05085219
    DOI: 10.1177/1536867X251322969
    as

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