Evolutionary and Institutional Economics Review

, Volume 13, Issue 2, pp 409–422 | Cite as

Long-term firm growth properties derived from short-term laws of sales and number of employees in Japan and France

  • Atushi IshikawaEmail author
  • Shouji Fujimoto
  • Takayuki Mizuno
  • Tsutomu Watanabe


In Japan, we observed rapid power law growth in the first 10 years of the existence of firms and subsequent slow exponential growth on their ages not only in their sales but also in their number of employees. We also confirmed similar long-term properties in France. These observations were found by employing around one million bits of exhaustive financial data of firms in Japan and France from 2004 to 2013. Comparing the parameters, the power law and exponential growth indices of sales are larger than those of the number of employees. Such long-term growth is derived from non-Gibrat’s law in the middle-scale range and Gibrat’s law in the large-scale range. We observed both non-Gibrat’s law and Gibrat’s law, which denotes the dependence of the growth rate distributions on the initial values, for two successive years in the short-term. By introducing a stochastic model based on the short-term laws, we showed that non-Gibrat’s law and Gibrat’s law lead to power law growth and the subsequent exponential growth, respectively.


Econophysics Firm growth Gibrat’s law Non-Gibrat’s law 

JEL Classification




The authors thank the Yukawa Institute for Theoretical Physics at Kyoto University. Discussions during the YITP workshop YITP-W-15-15 on “Econophysics 2015” were useful to complete this work. This study was supported by JSPS KAKENHI Grants Numbers 24510212 and 24710156.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this article.


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Copyright information

© Japan Association for Evolutionary Economics 2016

Authors and Affiliations

  1. 1.Kanazawa Gakuin UniversityKanazawaJapan
  2. 2.National Institute of InformaticsTokyoJapan
  3. 3.The Graduate University for Advanced Studies [SOKENDAI]TokyoJapan
  4. 4.JST PRESTOTokyoJapan
  5. 5.University of TokyoTokyoJapan

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