Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2016, Article ID 9303480, 6 pages
http://dx.doi.org/10.1155/2016/9303480
Research Article

Firm Growth Function and Extended-Gibrat’s Property

1Kanazawa Gakuin University, 10 Sue, Kanazawa, Ishikawa 920-1392, Japan
2National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
3Department of Informatics, The Graduate University for Advanced Studies, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
4PRESTO, Japan Science and Technology Agency, 7 Gobancho, Chiyodaku, Tokyo 102-0076, Japan
5Graduate School of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
6The Canon Institute for Global Studies, 5-1 Marunouchi 1-chome, Chiyoda-ku, Tokyo 100-6511, Japan

Received 21 September 2015; Accepted 6 March 2016

Academic Editor: Doojin Ryu

Copyright © 2016 Atushi Ishikawa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. N. Mantegna and H. E. Stanley, Introduction to Econophysics: Correlations and Complexity in Finance, Clarendon Press, Oxford, UK, 1991.
  2. A. Saichev, Y. Malevergne, and D. Sornette, Theory of Zip's Law and Beyond, Cambridge University Press, Cambridge, UK, 2009.
  3. V. Pareto, Cours d'Economie Politique, Macmillan, London, UK, 1897.
  4. M. E. J. Newman, “Power laws, Pareto distributions and Zipf's law,” Contemporary Physics, vol. 46, no. 5, pp. 323–351, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Clauset, C. R. Shalizi, and M. E. J. Newman, “Power-law distributions in empirical data,” SIAM Review, vol. 51, no. 4, pp. 661–703, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. E. Bonabeau and L. Dagorn, “Possible universality in the size distribution of fish schools,” Physical Review E, vol. 51, no. 6, pp. R5220–R5223, 1995. View at Publisher · View at Google Scholar · View at Scopus
  7. S. Redner, “How popular is your paper? An empirical study of the citation distribution,” European Physical Journal B, vol. 4, no. 2, pp. 131–134, 1998. View at Publisher · View at Google Scholar · View at Scopus
  8. Y. Fujiwara and H. Aoyama, “Large-scale structure of a nation-wide production network,” European Physical Journal B, vol. 77, no. 4, pp. 565–580, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. H. Aoyama, W. Souma, Y. Nagahara, M. P. Okazaki, H. Takayasu, and M. Takayasu, “Pareto's law for income of individuals and debt of bankrupt companies,” Fractals, vol. 8, no. 3, pp. 293–300, 2000. View at Google Scholar · View at Scopus
  10. T. Yamano, “Distribution of the Japanese posted land price and the generalized entropy,” European Physical Journal B, vol. 38, no. 4, pp. 665–669, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. R. N. Mantegna and H. E. Stanley, “Scaling Behaviour in the dynamics of an economic index,” Nature, vol. 376, no. 6535, pp. 46–49, 1995. View at Publisher · View at Google Scholar · View at Scopus
  12. R. L. Axtell, “Zipf distribution of U.S. firm sizes,” Science, vol. 293, no. 5536, pp. 1818–1820, 2001. View at Publisher · View at Google Scholar · View at Scopus
  13. B. Podobnik, D. Horvatic, A. M. Petersen, B. Urošević, and H. E. Stanley, “Bankruptcy risk model and empirical tests,” Proceedings of the National Academy of Sciences of the United States of America, vol. 107, no. 43, pp. 18325–18330, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. D. Fu, F. Pammolli, S. V. Buldyrev et al., “The growth of business firms: theoretical framework and empirical evidence,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 52, pp. 18801–18806, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. B. Podobnik, D. Horvatic, F. Pammolli, F. Wang, H. E. Stanley, and I. Grosse, “Size-dependent standard deviation for growth rates: empirical results and theoretical modeling,” Physical Review E, vol. 77, no. 5, Article ID 056102, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. K. Okuyama, M. Takayasu, and H. Takayasu, “Zipf's law in income distribution of companies,” Physica A, vol. 269, no. 1, pp. 125–131, 1999. View at Publisher · View at Google Scholar · View at Scopus
  17. P. Gopikrishnan, M. Meyer, L. A. N. Amaral, and H. E. Stanley, “Inverse cubic law for the distribution of stock price variations,” European Physical Journal B, vol. 3, no. 2, pp. 139–140, 1998. View at Google Scholar · View at Scopus
  18. T. Mizuno, M. Katori, H. Takayasu, and M. Takayasu, “Statistical laws in the income of Japanese companies,” in Empirical Science of Financial Fluctuations, pp. 321–330, Springer, Tokyo, Japan, 2002. View at Google Scholar
  19. M. Nirei and W. Souma, “A two factor model of income distribution dynamics,” Review of Income and Wealth, vol. 53, no. 3, pp. 440–459, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. H. Iyetomi, H. Aoyama, Y. Fujiwara, Y. Ikeda, and W. Souma, “A paradigm shift from production function to production copula: statistical description of production activity of firms,” Quantitative Finance, vol. 12, no. 9, pp. 1453–1466, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. M. Levy and S. Solomon, “Power laws are logarithmic Boltzmann laws,” International Journal of Modern Physics C, vol. 7, no. 4, pp. 595–601, 1996. View at Publisher · View at Google Scholar · View at Scopus
  22. D. Sornette and R. Cont, “Convergent multiplicative processes repelled from zero: power laws and truncated power laws,” Journal de Physique I, vol. 7, pp. 431–444, 1997. View at Google Scholar
  23. H. Takayasu, A.-H. Sato, and M. Takayasu, “Stable infinite variance fluctuations in randomly amplified langevin systems,” Physical Review Letters, vol. 79, no. 6, pp. 966–969, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. Y. Fujiwara, W. Souma, H. Aoyama, T. Kaizoji, and M. Aoki, “Growth and fluctuations of personal income,” Physica A, vol. 321, no. 3-4, pp. 598–604, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. Y. Fujiwara, C. Di Guilmi, H. Aoyama, M. Gallegati, and W. Souma, “Do Pareto-Zipf and Gibrat laws hold true? An analysis with European firms,” Physica A, vol. 335, no. 1-2, pp. 197–216, 2004. View at Publisher · View at Google Scholar · View at Scopus
  26. A. Ishikawa, “Annual change of Pareto index dynamically deduced from the law of detailed quasi-balance,” Physica A: Statistical Mechanics and its Applications, vol. 371, no. 2, pp. 525–535, 2006. View at Publisher · View at Google Scholar · View at Scopus
  27. A. Ishikawa, “Quasi-statically varying power-law and log-normal distributions in the large and the middle scale regions of japanese land prices,” Progress of Theoretical Physics Supplement, vol. 179, pp. 103–113, 2009. View at Google Scholar · View at Scopus
  28. A. Ishikawa, “Derivation of the distribution from extended Gibrat's law,” Physica A, vol. 367, pp. 425–434, 2006. View at Publisher · View at Google Scholar · View at Scopus
  29. A. Ishikawa, “The uniqueness of firm size distribution function from tent-shaped growth rate distribution,” Physica A: Statistical Mechanics and its Applications, vol. 383, no. 1, pp. 79–84, 2007. View at Publisher · View at Google Scholar · View at Scopus
  30. M. Tomoyose, S. Fujimoto, and A. Ishikawa, “Non-Gibrat's law in the middle scale region,” Progress of Theoretical Physics Supplements, vol. 179, pp. 114–122, 2009. View at Google Scholar
  31. A. Ishikawa, S. Fujimoto, and T. Mizuno, “Shape of growth rate distribution determines the type of Non-Gibrat's property,” Physica A, vol. 390, no. 23-24, pp. 4273–4285, 2011. View at Publisher · View at Google Scholar · View at Scopus
  32. R. Gibra, Les Inégalités Économique, Sirey, Paris, France, 1932.
  33. J. Sutton, “Gibrat's legacy,” Journal of Economic Literature, vol. 35, no. 1, pp. 40–59, 1997. View at Google Scholar
  34. W. Miura, H. Takayasu, and M. Takayasu, “Effect of coagulation of nodes in an evolving complex network,” Physical Review Letters, vol. 108, no. 16, Article ID 168701, 2012. View at Publisher · View at Google Scholar · View at Scopus
  35. T. Mizuno, W. Souma, and T. Watanabe, “The structure and evolution of buyer-supplier networks,” PLoS ONE, vol. 9, no. 7, Article ID e100712, 2014. View at Publisher · View at Google Scholar · View at Scopus
  36. E. G. J. Luttmer, “On the mechanics of firm growth,” Review of Economic Studies, vol. 78, no. 3, pp. 1042–1068, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  37. A. M. Petersena, M. Riccaboni, H. E. Stanley, and F. Pammolli, “Persistence and uncertainty in the academic career,” Proceedings of the National Academy of Sciences of the United States of America, vol. 109, no. 14, pp. 5213–5218, 2012. View at Publisher · View at Google Scholar · View at Scopus
  38. A. Coad, The Growth of Firms, Edward Elgar, 2009.
  39. Bureau van Dijk, http://www.bvdinfo.com/Home.aspx/.
  40. Statistics Bureau, “Ministry of Internal Affairs and Communications,” http://www.stat.go.jp/english/index.htm.