IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v335y2004i1p197-216.html
   My bibliography  Save this article

Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms

Author

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

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

  • 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.
  • Handle: RePEc:eee:phsmap:v:335:y:2004:i:1:p:197-216
    DOI: 10.1016/j.physa.2003.12.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437103011294
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:335:y:2004:i:1:p:197-216. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.