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Power-Law and Log-Normal Distributions in Firm Size Displacement Data

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  • Ishikawa, Atushi

Abstract

We have shown that firm size signed displacement data follow not only power-law in the large scale region but also the log-normal distribution in the middle scale one. In the analyses, we employ three databases: high-income data, high-sales data and positive-profits data of Japanese firms. It is particularly worth noting that the growth rate distributions of the firm size displacement have no wide tail which is observed in assets, sales of firms, the number of employees and personal income data. An extended-Gibrat's law is also found in the growth rate distributions. This leads the power-law and the log-normal distributions of the firm size displacement under the detailed balance.

Suggested Citation

  • Ishikawa, Atushi, 2008. "Power-Law and Log-Normal Distributions in Firm Size Displacement Data," Economics Discussion Papers 2008-45, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwedp:7466
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    References listed on IDEAS

    as
    1. Masashi Tomoyose & Shouji Fujimoto & Atushi Ishikawa, 2008. "Non-Gibrat's law in the middle scale region," Papers 0809.3060, arXiv.org.
    2. Fujiwara, Yoshi & Di Guilmi, Corrado & Aoyama, Hideaki & Gallegati, Mauro & Souma, Wataru, 2004. "Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 197-216.
    3. Ishikawa, Atushi, 2006. "Annual change of Pareto index dynamically deduced from the law of detailed quasi-balance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 525-535.
    4. Atushi Ishikawa, 2007. "The uniqueness of company size distribution function from tent-shaped growth rate distribution," Papers physics/0702248, arXiv.org.
    5. Ishikawa, Atushi, 2006. "Derivation of the distribution from extended Gibrat's law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 425-434.
    6. Atushi Ishikawa, 2007. "Quasistatically varying log-normal distribution in the middle scale region of Japanese land prices," Papers 0710.1893, arXiv.org.
    7. Kaushik Matia & Dongfeng Fu & Sergey V. Buldyrev & Fabio Pammolli & Massimo Riccaboni & H. Eugene Stanley, 2005. "Statistical Properties of Business Firms Structure and Growth," Papers physics/0502081, arXiv.org.
    8. Ishikawa, Atushi, 2007. "The uniqueness of firm size distribution function from tent-shaped growth rate distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 79-84.
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    Cited by:

    1. Segarra, Agustí & Teruel, Mercedes, 2012. "An appraisal of firm size distribution: Does sample size matter?," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 314-328.
    2. Gao, Baojun & Chan, Wai Kin (Victor) & Li, Hongyi, 2015. "On the increasing inequality in size distribution of China's listed companies," China Economic Review, Elsevier, vol. 36(C), pages 25-41.

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    More about this item

    Keywords

    Econophysics; firm size displacement distribution; Pareto's law; log-normal distribution; (non-)Gibrat's law; detailed balance;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D30 - Microeconomics - - Distribution - - - General
    • D39 - Microeconomics - - Distribution - - - Other

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