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
    File URL: https://libkey.io/10.1016/j.physa.2003.12.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boris Podobnik & Davor Horvatic & Alexander M. Petersen & Branko Urov{s}evi'c & H. Eugene Stanley, 2010. "Bankruptcy risk model and empirical tests," Papers 1011.2670, arXiv.org.
    2. Enrico Santarelli, 1998. "Start-up size and post-entry performance: the case of tourism services in Italy," Applied Economics, Taylor & Francis Journals, vol. 30(2), pages 157-163, February.
    3. John Sutton, 2001. "Rich Trades, Scarce Capabilities: Industrial Development Revisited," STICERD - Economics of Industry Papers 28, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Michael Pickford & Qing Gong Yang, 2014. "Comparing merger enforcement across jurisdictions -- New Zealand versus the European Union and the United States," New Zealand Economic Papers, Taylor & Francis Journals, vol. 48(1), pages 72-95, April.
    5. Fleischer, Manfred, 1997. "The inefficiency trap: strategy failure in the German machine tool industry," EconStor Books, ZBW - Leibniz Information Centre for Economics, number 122877, July.
    6. Derbyshire, James & Garnsey, Elizabeth, 2015. "Are firm growth paths random? A further response regarding Gambler's Ruin Theory," Journal of Business Venturing Insights, Elsevier, vol. 3(C), pages 9-11.
    7. Audretsch, David B. & Santarelli, Enrico & Vivarelli, Marco, 1999. "Start-up size and industrial dynamics: some evidence from Italian manufacturing," International Journal of Industrial Organization, Elsevier, vol. 17(7), pages 965-983, October.

    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.

    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 bibliographic 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.

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

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.