Summary
Following the work of Okuyama, Takayasu and Takayasu [Okuyama, Takayasu and Takayasu 1999] we analyze huge databases of Japanese companies’ financial figures and confirm that the Zipf’s law, a power law distribution with the exponent -1, has been maintained over 30 years in the income distribution of Japanese companies with very high precision. Similar power laws are found not only in income distribution of company’s income, but also in the distributions of capital, sales and number of employees.
From the data we find an important time evolutionary property that the growth rate of income is approximately independent of the value of income, namely, small companies and large ones have similar statistical chances of growth. This observational fact suggests the applicability of the theory of multiplicative stochastic processes developed in statistical physics. We introduce a discrete version of Langevin equation with additive and multiplicative noises as a simple time evolution model of company’s income. We test the validity of the TakayasuSato-Takayasu condition [Takayasu, Sato and Takayasu 1997] for having an asymptotic power law distribution as a unique statistically steady solution. Directly estimated power law exponents and theoretically evaluated ones are compared resulting a reasonable fit by introducing a normalization to reduce the effect of gross economic change.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
K Okuyama, M Takaysu, H Takayasu (1999) Zipf’s law in income distribution of companies. Physica A269: 125–131
H Aoyama, Y Nagahara, M P Okazaki, W Souma, H Takayasu, M Takayasu (Sept.2000) Pareto’s law for income of individuals and debt of bankrupt companies. Fractale 8: 293–300 [cond-mat 10006038]
M H R Stanley, L A N Amaral, S V Buldyrev, S Havlin, H Leschhorn, P Maass, M A Salinger, H E Stanley (1996) Scaling behavior in the growth of companies. Nature 379: 804–806
Y Lee, L A N Amaral, D Canning, M Meyer, H E Stanley (1998) Universal Features in the Growth Dynamics of Complex Organizations. Phys Rev Lett 81: 3275–3278
H Takayasu, A H Sato, M Takayasu (1997) Stable Infinite Variance Fluctuations in Randomly Amplified Langevin Systems. Phys Rev Lett 79: 966–969
Yuji Ijiri, Herbert A Simon (1977) Skew distributions and the sizes of business firms. Amsterdam: North Holland Publishing
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Japan
About this paper
Cite this paper
Mizuno, T., Katori, M., Takayasu, H., Takayasu, M. (2002). Statistical Laws in the Income of Japanese Companies. In: Takayasu, H. (eds) Empirical Science of Financial Fluctuations. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66993-7_35
Download citation
DOI: https://doi.org/10.1007/978-4-431-66993-7_35
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-66995-1
Online ISBN: 978-4-431-66993-7
eBook Packages: Springer Book Archive