Advertisement

Statistical Laws in the Income of Japanese Companies

  • Takayuki Mizuno
  • Makoto Katori
  • Hideki Takayasu
  • Misako Takayasu
Conference paper

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.

Key words

Zipf’s law Income distribution Random multiplicative process Discrete Langevin equation Takayasu-Sato-Takayasu condition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K Okuyama, M Takaysu, H Takayasu (1999) Zipf’s law in income distribution of companies. Physica A269: 125–131CrossRefGoogle Scholar
  2. 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]Google Scholar
  3. 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: 804–806ADSCrossRefGoogle Scholar
  4. 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: 3275–3278ADSCrossRefGoogle Scholar
  5. H Takayasu, A H Sato, M Takayasu (1997) Stable Infinite Variance Fluctuations in Randomly Amplified Langevin Systems. Phys Rev Lett 79: 966–969ADSzbMATHCrossRefGoogle Scholar
  6. Yuji Ijiri, Herbert A Simon (1977) Skew distributions and the sizes of business firms. Amsterdam: North Holland PublishingzbMATHGoogle Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Takayuki Mizuno
    • 1
  • Makoto Katori
    • 1
  • Hideki Takayasu
    • 2
  • Misako Takayasu
    • 3
  1. 1.Department of Physics, Faculty of Science and EngineeringChuo UniversityKasuga, Bunkyo-ku, TokyoJapan
  2. 2.Sony Computer Science Laboratories Inc.Shinagawa-ku, TokyoJapan
  3. 3.Department of Complex SystemsFuture University-HakodateHakodate, HokkaidoJapan

Personalised recommendations