IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1301.2728.html
   My bibliography  Save this paper

Generalised central limit theorems for growth rate distribution of complex systems

Author

Listed:
  • Misako Takayasu
  • Hayafumi Watanabe
  • Hideki Takayasu

Abstract

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety of fields can be derived from this basic physical model. Statistical data of growth rates for about 1 million business firms are analysed as a real-world example of randomly growing systems. Not only are the scaling relations consistent with the theoretical solution, but the entire functional form of the growth rate distribution is fitted with a theoretical distribution that has a power-law tail.

Suggested Citation

  • Misako Takayasu & Hayafumi Watanabe & Hideki Takayasu, 2013. "Generalised central limit theorems for growth rate distribution of complex systems," Papers 1301.2728, arXiv.org, revised Jan 2014.
    • Handle: RePEc:arx:papers:1301.2728
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1301.2728
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sergey V. Buldyrev & Jakub Growiec & Fabio Pammolli & Massimo Riccaboni & H. Eugene Stanley, 2007. "The Growth of Business Firms: Facts and Theory," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 574-584, 04-05.
    2. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    3. De Fabritiis, G. & Pammolli, F. & Riccaboni, M., 2003. "On size and growth of business firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 38-44.
    4. Bottazzi, Giulio & Dosi, Giovanni & Lippi, Marco & Pammolli, Fabio & Riccaboni, Massimo, 2001. "Innovation and corporate growth in the evolution of the drug industry," International Journal of Industrial Organization, Elsevier, vol. 19(7), pages 1161-1187, July.
    5. Fu, Dongfeng & Pammolli, Fabio & Buldyrev, Sergey V. & Riccaboni, Massimo & Matia, Kaushik & Yamasaki, Kazuko & Stanley, H. Eugene, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," MPRA Paper 15905, University Library of Munich, Germany.
    6. Youngki Lee & Luis A. N. Amaral & David Canning & Martin Meyer & H. Eugene Stanley, 1998. "Universal features in the growth dynamics of complex organizations," Papers cond-mat/9804100, arXiv.org.
    7. 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.
    8. Aoyama,Hideaki & Fujiwara,Yoshi & Ikeda,Yuichi & Iyetomi,Hiroshi & Souma,Wataru Preface by-Name:Yoshikawa,Hiroshi, 2011. "Econophysics and Companies," Cambridge Books, Cambridge University Press, number 9781107403482, September.
    9. Timothy H. Keitt & H. Eugene Stanley, 1998. "Dynamics of North American breeding bird populations," Nature, Nature, vol. 393(6682), pages 257-260, May.
    10. Massimo Riccaboni & Fabio Pammolli & Sergey V. Buldyrev & Linda Ponta & H. Eugene Stanley, 2009. "The Size Variance Relationship of Business Firm Growth Rates," Papers 0904.1404, arXiv.org, revised Apr 2009.
    11. Alex Saichev & Yannick Malevergne & Didier Sornette, 2010. "Theory of Zipf's Law and Beyond," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02946-2, October.
    12. Fujiwara, Yoshi & Aoyama, Hideaki & Di Guilmi, Corrado & Souma, Wataru & Gallegati, Mauro, 2004. "Gibrat and Pareto–Zipf revisited with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 112-116.
    13. Vasiliki Plerou & Luís A. Nunes Amaral & Parameswaran Gopikrishnan & Martin Meyer & H. Eugene Stanley, 1999. "Similarities between the growth dynamics of university research and of competitive economic activities," Nature, Nature, vol. 400(6743), pages 433-437, July.
    14. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    15. Yamasaki, Kazuko & Matia, Kaushik & Buldyrev, Sergey V. & Fu, Dongfeng & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2004. "Preferential attachment and growth dynamics in complex systems," MPRA Paper 15908, University Library of Munich, Germany, revised 06 Feb 2006.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Thesmar , David & Landier , Augustin, 2014. "Instabilities in Large Economies: Aggregate Volatility Without Idiosyncratic Shocks," HEC Research Papers Series 1052, HEC Paris.
    2. Hayato Goto & Eduardo Viegas & Hideki Takayasu & Misako Takayasu & Henrik Jeldtoft Jensen, 2019. "Dynamics of essential interaction between firms on financial reports," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-16, December.
    3. Hayato Goto & Hideki Takayasu & Misako Takayasu, 2017. "Estimating risk propagation between interacting firms on inter-firm complex network," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-12, October.
    4. Eduardo Viegas & Orr Levy & Shlomo Havlin & Hideki Takayasu & Misako Takayasu, 2024. "Spatial Constraints on Economic Interactions: A Complexity Approach to the Japanese Inter-Firm Trade Network," Mathematics, MDPI, vol. 12(8), pages 1-25, April.
    5. Sandro Claudio Lera & Didier Sornette, 2017. "Quantification of the evolution of firm size distributions due to mergers and acquisitions," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-16, August.

    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. 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.
    2. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.
    3. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    4. Buldyrev, Sergey V. & Salinger, Michael A. & Stanley, H. Eugene, 2016. "A statistical physics implementation of Coase׳s theory of the firm," Research in Economics, Elsevier, vol. 70(4), pages 536-557.
    5. Hernan Mondani & Petter Holme & Fredrik Liljeros, 2014. "Fat-Tailed Fluctuations in the Size of Organizations: The Role of Social Influence," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-9, July.
    6. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of Weighted Networks," Papers 0908.0348, arXiv.org, revised Dec 2009.
    7. Amaral, L.A.N. & Gopikrishnan, P. & Plerou, V. & Stanley, H.E., 2001. "A model for the growth dynamics of economic organizations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 127-136.
    8. Growiec, Jakub & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2008. "On the size distribution of business firms," Economics Letters, Elsevier, vol. 98(2), pages 207-212, February.
    9. 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.
    10. Dongfeng Fu & Fabio Pammolli & S. V. Buldyrev & Massimo Riccaboni & Kaushik Matia & Kazuko Yamasaki & H. E. Stanley, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," Papers physics/0512005, arXiv.org.
    11. Fabio Pammolli & Dongfeng Fu & S. V. Buldyrev & Massimo Riccaboni & Kaushik Matia & Kazuko Yamasaki & H. E. Stanley, 2006. "A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence," Papers physics/0609011, arXiv.org.
    12. Kaldasch, Joachim, 2012. "Evolutionary model of the growth and size of firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(14), pages 3751-3769.
    13. Stanley, H.E. & Gopikrishnan, P. & Plerou, V. & Amaral, L.A.N., 2000. "Quantifying fluctuations in economic systems by adapting methods of statistical physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 339-361.
    14. 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.
    15. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of International Trade," Documents de Travail de l'OFCE 2009-24, Observatoire Francais des Conjonctures Economiques (OFCE).
    16. ARATA Yoshiyuki, 2014. "Firm Growth and Laplace Distribution: The importance of large jumps," Discussion papers 14033, Research Institute of Economy, Trade and Industry (RIETI).
    17. Stanley, H.E & Amaral, L.A.N & Gopikrishnan, P & Ivanov, P.Ch & Keitt, T.H & Plerou, V, 2000. "Scale invariance and universality: organizing principles in complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 60-68.
    18. Stanley, H.E & Amaral, L.A.N & Gopikrishnan, P & Plerou, V, 2000. "Scale invariance and universality of economic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(1), pages 31-41.
    19. Stanley, H.Eugene, 2000. "Exotic statistical physics: Applications to biology, medicine, and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 1-17.
    20. Metzig, Cornelia & Gordon, Mirta B., 2014. "A model for scaling in firms’ size and growth rate distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 264-279.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:1301.2728. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.