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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.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:cond-mat/0310061
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    1. Sutton, John, 1995. "The size distribution of businesses, part I: a benchmark case," LSE Research Online Documents on Economics 2289, London School of Economics and Political Science, LSE Library.
    2. John Sutton, 1995. "The Size Distribution of Businesses, Part I: A Benchmark Case," STICERD - Economics of Industry Papers 09, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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