Long-term firm growth properties derived from short-term laws of sales and number of employees in Japan and France
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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.
KeywordsEconophysics Firm growth Gibrat’s law Non-Gibrat’s law
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.
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Conflict of interest
The authors declare that there is no conflict of interest regarding the publication of this article.
- Aoyama H, Nagahara Y, Okazaki MP, Souma W, Takayasu H, Takayasu M (2000) Pareto’s law for income of individuals and debt of bankrupt companies. Fractals 8:293–300Google Scholar
- Bureau van Dijk. http://www.bvdinfo.com/
- Coad A (2010) Investigating the exponential age distribution of firms. Economics 4:2010–2017Google Scholar
- Coad A (2009) The growth of firms. Edward Elgar Publishing, USAGoogle Scholar
- Gibra R (1932) Les Inégalités Économique. Sirey, ParisGoogle Scholar
- Ishikawa A, Fujimoto S, Mizuno T, Watanabe T (2015) Firm age distributions and the decay rate of firm activities. In: Takayasu H, Ito N, Noda I, Takayasu M (eds) Proceedings of the international conference on social modeling and simulation, plus econophysics colloquium 2014, pp 187–194Google Scholar
- Ishikawa A, Fujimoto S, Mizuno T, Watanabe T (2015) The relation between firm age distributions and the decay rate of firm activities in the United States and Japan, Big Data (Big Data). In: 2015 IEEE international conference on date of conference, pp 2726–2731Google Scholar
- Mantegna RN, Stanley HE (1991) Introduction to econophysics: correlations and complexity in finance. Clarendon Press, OxfordGoogle Scholar
- Pareto V (1897) Cours d’Économie Politiqu. Macmillan, LondonGoogle Scholar
- Romer PM (2008) Economic growth. In: Henderson DR (ed) The concise encyclopedia of economics. Liberty Fund, IndianapolisGoogle Scholar
- Saichev A, Malevergne Y, Sornette D (2009) Theory of Zip’s law and beyond. Cambridge University Press, CambridgeGoogle Scholar
- Sornette D, Cont R (1997) Convergent multiplicative processes repelled from zero: power laws and truncated power laws. J Phys I(7):431–444Google Scholar
- Statistics Bureau, Ministry of internal affairs and communications. http://www.stat.go.jp/index.htm
- Sutton J (1997) Gibrat’s legacy. J Econ Lit 35:40–59Google Scholar
- Takayasu H, Sato A, Takayasu M (1997) Stable infinite variance fluctuations in randomly amplified Langevin systems. Phys Rev Lett 79:966–969Google Scholar