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Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms

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  • Yoshi Fujiwara
  • Corrado Di Guilmi
  • Hideaki Aoyama
  • Mauro Gallegati
  • Wataru Souma

Abstract

By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find that detailed balance holds in the large-size region for periods we investigated; the empirical probability for a firm to change its size from a value to another is statistically the same as that for its reverse process. We prove several relationships among Pareto-Zipf's law, Gibrat's law and the condition of detailed balance. As a consequence, we show that the distribution of growth rate possesses a non-trivial relation between the positive side of the distribution and the negative side, through the value of Pareto index, as is confirmed empirically.

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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/0310061.

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Date of creation: Oct 2003
Date of revision: Nov 2003
Handle: RePEc:arx:papers:cond-mat/0310061

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Web page: http://arxiv.org/

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Cited by:
  1. Xavier Gabaix & Augustin Landier, 2006. "Why Has CEO Pay Increased So Much?," 2006 Meeting Papers 518, Society for Economic Dynamics.
  2. Bottazzi, Giulio, 2009. "On the irreconcilability of Pareto and Gibrat laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1133-1136.
  3. A. Saichev & Y. Malevergne & D. Sornette, 2008. "Theory of Zipf's Law and of General Power Law Distributions with Gibrat's law of Proportional Growth," Papers 0808.1828, arXiv.org.
  4. Fujimoto, S. & Ishikawa, A. & Mizuno, T. & Watanabe, T., 2011. "A New Method for Measuring Tail Exponents of Firm Size Distributions," Working Paper Series 7, Center for Interfirm Network, Institute of Economic Research, Hitotsubashi University.
  5. Wright, Ian, 2009. "Implicit Microfoundations for Macroeconomics," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 3(19), pages 1-27.
  6. Fujimoto, Shouji & Ishikawa, Atushi & Mizuno, Takayuki & Watanabe, Tsutomu, 2011. "A new method for measuring tail exponents of firm size distributions," Economics Discussion Papers 2011-29, Kiel Institute for the World Economy.
  7. Ishikawa, Atushi, 2008. "Power-Law and Log-Normal Distributions in Firm Size Displacement Data," Economics Discussion Papers 2008-45, Kiel Institute for the World Economy.
  8. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, 05.
  9. Ian Wright, 2004. "A conjecture on the distribution of firm profit," Papers cond-mat/0407687, arXiv.org, revised Mar 2011.
  10. Xavier Gabaix, 2005. "The Granular Origins of Aggregate Fluctuations," 2005 Meeting Papers 470, Society for Economic Dynamics.
  11. Ishikawa, Atushi, 2009. "Power-Law and Log-Normal Distributions in Temporal Changes of Firm-Size Variables," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 3(11), pages 1-25.
  12. Kiyoyasu Tanaka & Naomi Hatsukano, 2011. "The size distribution of all Cambodian establishments," Economics Bulletin, AccessEcon, vol. 31(3), pages 2128-2137.
  13. Ian Wright, 2004. "The Social Architecture of Capitalism," Papers cond-mat/0401053, arXiv.org, revised Mar 2011.
  14. Yuichi Ikeda & Hideaki Aoyama & Hiroshi Iyetomi & Yoshi Fujiwara & Wataru Souma, 2008. "Correlated performance of firms in a transaction network," Journal of Economic Interaction and Coordination, Springer, vol. 3(1), pages 73-80, June.

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