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On the Irreconcilability of Pareto and Gibrat Laws

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  • Giulio Bottazzi

Abstract

If business firms face a multiplicative growth process in which their growth rates are independent from their sizes, then these sizes cannot be distributed according to a stationary Pareto distribution. At the same time , the Laplace distribution of growth rates cannot be easily reconciled with a Pareto distribution of firm sizes. Recent contributions, using formal arguments, seems to contrast these statements. We prove that the proposed formal results are wrong.

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Bibliographic Info

Paper provided by Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy in its series LEM Papers Series with number 2007/10.

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Date of creation: 12 Mar 2007
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Handle: RePEc:ssa:lemwps:2007/10

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Keywords: Firm Growth; Gibrat's Law; Power law distribution; Laplace distribution.;

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References

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  1. Giulio Bottazzi & Angelo Secchi, 2005. "Explaining the Distribution of Firms Growth Rates," LEM Papers Series 2005/16, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  2. Fujiwara, Yoshi & Di Guilmi, Corrado & Aoyama, Hideaki & Gallegati, Mauro & Souma, Wataru, 2004. "Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 197-216.
  3. Yoshi Fujiwara & Wataru Souma & Hideaki Aoyama & Taisei Kaizoji & Masanao Aoki, 2002. "Growth and Fluctuations of Personal Income," Papers cond-mat/0208398, arXiv.org.
  4. Gatti, Domenico Delli & Guilmi, Corrado Di & Gaffeo, Edoardo & Giulioni, Gianfranco & Gallegati, Mauro & Palestrini, Antonio, 2005. "A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 489-512, April.
  5. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  6. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
  7. Aoyama, Hideaki & Souma, Wataru & Fujiwara, Yoshi, 2003. "Growth and fluctuations of personal and company's income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 352-358.
  8. Dosi Giovanni, 2008. "Statistical Regularities in the Evolution of Industries. A Guide through Some Evidence and Challenges for the Theory," L'industria, Società editrice il Mulino, issue 2, pages 185-220.
  9. L. A. N. Amaral & S. V. Buldyrev & S. Havlin & H. Leschhorn & P. Maass & M. A. Salinger & H. E. Stanley & M. H. R. Stanley, 1997. "Scaling behavior in economics: I. Empirical results for company growth," Papers cond-mat/9702082, arXiv.org.
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Cited by:
  1. Cirillo, Pasquale, 2010. "An analysis of the size distribution of Italian firms by age," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 459-466.

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