IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v57y2007i2p131-138.html
   My bibliography  Save this article

A generalized preferential attachment model for business firms growth rates

Author

Listed:
  • S. V. Buldyrev
  • F. Pammolli
  • M. Riccaboni
  • K. Yamasaki
  • D.-F. Fu
  • K. Matia
  • H. E. Stanley

Abstract

We present a preferential attachment growth model to obtain the distribution P(K) of number of units K in the classes which may represent business firms or other socio-economic entities. We found that P(K) is described in its central part by a power law with an exponent ϕ=2+b/(1-b) which depends on the probability of entry of new classes, b. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution P(K) is exponential. Using analytical form of P(K) and assuming proportional growth for units, we derive P(g), the distribution of business firm growth rates. The model predicts that P(g) has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent ζ=3. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • S. V. Buldyrev & F. Pammolli & M. Riccaboni & K. Yamasaki & D.-F. Fu & K. Matia & H. E. Stanley, 2007. "A generalized preferential attachment model for business firms growth rates," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 131-138, May.
    • Handle: RePEc:spr:eurphb:v:57:y:2007:i:2:p:131-138
    DOI: 10.1140/epjb/e2007-00165-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1140/epjb/e2007-00165-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1140/epjb/e2007-00165-8?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:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuichi Ikeda & Hideaki Aoyama & Hiroshi Iyetomi & Yoshi Fujiwara & Wataru Souma, 2008. "Correlated performance of firms in a transaction network," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 3(1), pages 73-80, June.
    2. Kaldasch, Joachim, 2012. "Evolutionary model of the personal income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5628-5642.
    3. Jakub Growiec & Fabio Pammolli & Massimo Riccaboni, 2020. "Innovation and Corporate Dynamics: A Theoretical Framework," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(1), pages 1-45, March.
    4. ARATA Yoshiyuki, 2014. "Firm Growth and Laplace Distribution: The importance of large jumps," Discussion papers 14033, Research Institute of Economy, Trade and Industry (RIETI).
    5. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2017. "Where Gibrat meets Zipf: Scale and scope of French firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 265-275.
    6. Alfarano, Simone & Milaković, Mishael & Irle, Albrecht & Kauschke, Jonas, 2012. "A statistical equilibrium model of competitive firms," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 136-149.
    7. Alfarano, Simone & Milakovic, Mishael, 2008. "Does classical competition explain the statistical features of firm growth?," Economics Letters, Elsevier, vol. 101(3), pages 272-274, December.
    8. Arata, Yoshiyuki, 2019. "Firm growth and Laplace distribution: The importance of large jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 103(C), pages 63-82.
    9. Hisano, Ryohei & Mizuno, Takayuki, 2011. "Sales distribution of consumer electronics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 309-318.
    10. Wagner, Friedrich & Milaković, Mishael & Alfarano, Simone, 2010. "Firm profitability and the network of organizational capabilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4769-4775.
    11. Xie, Wen-Jie & Gu, Gao-Feng & Zhou, Wei-Xing, 2010. "On the growth of primary industry and population of China’s counties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3876-3882.

    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:spr:eurphb:v:57:y:2007:i:2:p:131-138. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.