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Size distributions reconsidered

Author

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  • Christian Schluter
  • Mark Trede

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," Econometric Reviews, Taylor & Francis Journals, vol. 38(6), pages 695-710, July.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:6:p:695-710
    DOI: 10.1080/07474938.2017.1417732
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    Cited by:

    1. Arturo Ramos & Till Massing & Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2024. "Mixtures of log-normal distributions in the mid-scale range of firm-size variables," Evolutionary and Institutional Economics Review, Springer, vol. 21(2), pages 249-260, September.
    2. Rocco Rante & Federico Trionfetti & Priyam Verma, 2025. "Geography and City Size: From Remains of Bukhara to the Modern US," Working Papers 2025.13, International Network for Economic Research - INFER.
    3. Rocco Rante & Federico Trionfetti & Priyam Verma, 2024. "The Size Distribution of Cities: Evidence from the Lab," Working Papers hal-04556678, HAL.
    4. 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.
    5. Christian Schluter, 2021. "On Zipf’s law and the bias of Zipf regressions," Empirical Economics, Springer, vol. 61(2), pages 529-548, August.

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