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On the irreconcilability of Pareto and Gibrat laws

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  • Bottazzi, Giulio

Abstract

If business firms face a multiplicative growth process in which their growth rates are Laplace distributed and independent from their sizes, the size cannot be distributed according to a stationary Pareto distribution. Recent contributions, using formal arguments, seem to contrast with these statements. We prove that the proposed formal results are wrong.

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File URL: http://www.sciencedirect.com/science/article/pii/S0378437108010212
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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 388 (2009)
Issue (Month): 7 ()
Pages: 1133-1136

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Handle: RePEc:eee:phsmap:v:388:y:2009:i:7:p:1133-1136

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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

Related research

Keywords: Firm growth; Gibrat’s law; Power law distribution; Laplace distribution;

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  1. Yoshi Fujiwara & Wataru Souma & Hideaki Aoyama & Taisei Kaizoji & Masanao Aoki, 2002. "Growth and Fluctuations of Personal Income," Papers cond-mat/0208398, arXiv.org.
  2. 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.
  3. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  4. 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.
  5. Yoshi Fujiwara & Corrado Di Guilmi & Hideaki Aoyama & Mauro Gallegati & Wataru Souma, 2003. "Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms," Papers cond-mat/0310061, arXiv.org, revised Nov 2003.
  6. 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.
  7. Giulio Bottazzi & Angelo Secchi, 2006. "Explaining the distribution of firm growth rates," RAND Journal of Economics, RAND Corporation, vol. 37(2), pages 235-256, 06.
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