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Size distributions reconsidered

Author

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  • 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)

  • Mark Trede

    (WWU - Westfälische Wilhelms-Universität Münster = University of Münster)

Abstract

We consider tests of the hypothesis that the tail of size distributions decays faster than any power function. These are based on a single parameter that emerges from the Fisher–Tippett limit theorem, and discriminate between leading laws considered in the literature without requiring fully parametric models/specifications. We study the proposed tests taking into account the higher order regular variation of the size distribution that can lead to catastrophic distortions. The theoretical bias corrections realign successfully nominal and empirical test behavior, and inform a sensitivity analysis for practical work. The methods are used in an examination of the size distribution of cities and firms.

Suggested Citation

  • Christian Schluter & Mark Trede, 2019. "Size distributions reconsidered," Post-Print hal-01994353, HAL.
    • Handle: RePEc:hal:journl:hal-01994353
    DOI: 10.1080/07474938.2017.1417732
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-01994353
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    References listed on IDEAS

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    1. Christian Schluter, 2021. "On Zipf’s law and the bias of Zipf regressions," Empirical Economics, Springer, vol. 61(2), pages 529-548, August.
    2. Arturo Ramos & Till Massing & Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2023. "Composite distributions in the social sciences: A comparative empirical study of firms' sales distribution for France, Germany, Italy, Japan, South Korea, and Spain," Papers 2301.09438, arXiv.org.

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    Keywords

    regular variation; power law; Extreme value index; size distribution; tail behavior;
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