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Power-Law and Log-Normal Distributions in Temporal Changes of Firm-Size Variables

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  • Ishikawa, Atushi
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    Abstract

    In this paper the author shows that signed temporal changes of firm size variables follow the power-law for large changes; while, for middle changes a log-normal distribution is found. In the analyses, the author employed three databases: highincome data, high-sales data and positive-profits data of Japanese firms. It is particularly worth noting that the growth rate distributions in temporal changes of the firm size data have no wide tail, unlike the distributions observed in assets and sales of firms, the number of employees and personal income data. An Extended-Gibrat's Law was also found in the growth rate distributions of temporal changes of firm size variables, which induces both the power-law and the log-normal distributions in the temporal changes of firm size under the Detailed Balance. --

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    File URL: http://dx.doi.org/10.5018/economics-ejournal.ja.2009-11
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    File URL: http://econstor.eu/bitstream/10419/27531/1/economics_2009-11.pdf
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    Bibliographic Info

    Article provided by Kiel Institute for the World Economy in its journal Economics: The Open-Access, Open-Assessment E-Journal.

    Volume (Year): 3 (2009)
    Issue (Month): 11 ()
    Pages: 1-25

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    Handle: RePEc:zbw:ifweej:7597

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    Related research

    Keywords: Econophysics; temporal change of firm size; Pareto's law; log-normal distribution; (non-)Gibrat's law; detailed balance;

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    References

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    1. Yoshi Fujiwara & Corrado Di Guilmi & Hideaki Aoyama & Mauro Gallegati & Wataru Souma, 2003. "Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms," Papers cond-mat/0310061, arXiv.org, revised Nov 2003.
    2. 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.
    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. Canning, D. & Amaral, L. A. N. & Lee, Y. & Meyer, M. & Stanley, H. E., 1998. "Scaling the volatility of GDP growth rates," Economics Letters, Elsevier, vol. 60(3), pages 335-341, September.
    5. Xavier Gabaix, 2009. "The Granular Origins of Aggregate Fluctuations," NBER Working Papers 15286, National Bureau of Economic Research, Inc.
    6. Atushi Ishikawa, 2007. "Quasistatically varying log-normal distribution in the middle scale region of Japanese land prices," Papers 0710.1893, arXiv.org.
    7. 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.
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