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The uniqueness of firm size distribution function from tent-shaped growth rate distribution

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  • Ishikawa, Atushi

Abstract

Employing profits data of Japanese firms in 2003 and 2004, we report the proof that a Non-Gibrat's law in the middle scale region of profits is unique under the law of detailed balance. This uniquely leads to the probability distribution function (pdf) of profits. In the proof, two approximations are employed. The pdf of growth rate is described as tent-shaped exponential functions and the value of the origin of the growth rate distribution is constant. These approximations are confirmed in the database. The resultant profits pdf fits with the empirical data consistently. This guarantees the validity of the approximations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:383:y:2007:i:1:p:79-84
    DOI: 10.1016/j.physa.2007.04.089
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    References listed on IDEAS

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    1. Bottazzi, Giulio, 2009. "On the irreconcilability of Pareto and Gibrat laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1133-1136.
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    Citations

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    Cited by:

    1. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2019. "Statistical law observed in inactive rate of firms," Evolutionary and Institutional Economics Review, Springer, vol. 16(1), pages 201-212, June.
    2. Hernan Mondani & Petter Holme & Fredrik Liljeros, 2014. "Fat-Tailed Fluctuations in the Size of Organizations: The Role of Social Influence," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-9, July.
    3. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno & Tsutomu Watanabe, 2016. "Long-term firm growth properties derived from short-term laws of sales and number of employees in Japan and France," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 409-422, December.
    4. Murat ATAN & Emre BOZDAĞ, 2011. "Avrupa Karbonatlı İçecekler Piyasasında Firma Büyüklüğü Ve Büyüklük Genişleme Oranı İlişkisi," Ekonomik Yaklasim, Ekonomik Yaklasim Association, vol. 22(80), pages 19-38.
    5. Atushi Ishikawa & Takayuki Mizuno & Shouji Fujimoto, 2022. "Employee Number Dependence in Labor Productivity Distribution," The Review of Socionetwork Strategies, Springer, vol. 16(2), pages 465-477, October.
    6. Junho Na & Jeong-dong Lee & Chulwoo Baek, 2017. "Is the service sector different in size heterogeneity?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 95-120, April.
    7. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno & Tsutomu Watanabe, 2017. "Dependence of the decay rate of firm activities on firm age," Evolutionary and Institutional Economics Review, Springer, vol. 14(2), pages 351-362, December.
    8. 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).

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