IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i18p3837-3843.html
   My bibliography  Save this article

An analogy of the size distribution of business firms with Bose–Einstein statistics

Author

Listed:
  • Hernández-Pérez, R.

Abstract

We approach the size distribution of business firms by proposing an analogy of the firms’ ranking with a boson gas, identifying the annual revenue of the firms with energy. We found that Bose–Einstein statistics fits very well to the empirical cumulative distribution function for the firms’ ranking for different countries. The fitted values for the temperature-like parameter are compared between countries and with an index of economic development, and we found that our results support the hypothesis that the temperature of the economy can be associated with the level of economic development of a country. Moreover, for most of the countries the value obtained for the fugacity-like parameter is close to 1, suggesting that the analogy could correspond to a photon gas in which the number of particles is not conserved; this is indeed the case for real-world firms’ dynamics, where new firms arrive in the economy and other firms disappear, either by merging with others or through bankruptcy.

Suggested Citation

  • Hernández-Pérez, R., 2010. "An analogy of the size distribution of business firms with Bose–Einstein statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3837-3843.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:18:p:3837-3843
    DOI: 10.1016/j.physa.2010.05.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110004541
    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.2010.05.024?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Jianhua & Chen, Qinghua & Wang, Yougui, 2009. "Zipf distribution in top Chinese firms and an economic explanation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(10), pages 2020-2024.
    2. Ramsden, J.J. & Kiss-Haypál, Gy., 2000. "Company size distribution in different countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 220-227.
    3. Clementi, F. & Di Matteo, T. & Gallegati, M. & Kaniadakis, G., 2008. "The κ-generalized distribution: A new descriptive model for the size distribution of incomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3201-3208.
    4. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432, arXiv.org, revised Aug 2000.
    5. A. Drăgulescu & V.M. Yakovenko, 2001. "Evidence for the exponential distribution of income in the USA," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 585-589, April.
    6. Okuyama, K & Takayasu, M & Takayasu, H, 1999. "Zipf's law in income distribution of companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 125-131.
    7. Hernández-Pérez, R. & Angulo-Brown, F. & Tun, Dionisio, 2006. "Company size distribution for developing countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 607-618.
    8. D'Hulst, R. & Rodgers, G.J., 2001. "Business size distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 328-333.
    9. Gaffeo, Edoardo & Gallegati, Mauro & Palestrini, Antonio, 2003. "On the size distribution of firms: additional evidence from the G7 countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 117-123.
    10. Cirillo, Pasquale, 2010. "An analysis of the size distribution of Italian firms by age," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 459-466.
    11. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    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. Junho Na & Jeong-dong Lee & Chulwoo Baek, 2017. "Is the service sector different in size heterogeneity?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 95-120, April.
    2. Pascoal, Rui & Augusto, Mário & Monteiro, A.M., 2016. "Size distribution of Portuguese firms between 2006 and 2012," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 342-355.
    3. Hernández-Pérez, R. & Angulo-Brown, F. & Tun, Dionisio, 2006. "Company size distribution for developing countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 607-618.
    4. Fujimoto, Shouji & Ishikawa, Atushi & Mizuno, Takayuki & Watanabe, Tsutomu, 2011. "A new method for measuring tail exponents of firm size distributions," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 5, pages 1-20.
    5. Pascoal, Rui & Augusto, Mário & Monteiro, A.M., 2016. "Size distribution of Portuguese firms between 2006 and 2012," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 342-355.
    6. Petra Štamfestová & Lukáš Sobíšek & Jiří Hnilica, 2023. "Firm Size Distribution in the Central European Context," Central European Business Review, Prague University of Economics and Business, vol. 2023(5), pages 151-175.
    7. Tao, Yong, 2015. "Universal laws of human society’s income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 89-94.
    8. Kaldasch, Joachim, 2012. "Evolutionary model of the personal income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5628-5642.
    9. Gregor Semieniuk & Victor M. Yakovenko, 2020. "Historical Evolution of Global Inequality in Carbon Emissions and Footprints versus Redistributive Scenarios," Papers 2004.00111, arXiv.org.
    10. Pasquale Cirillo & Mauro Gallegati, 2012. "The Empirical Validation of an Agent-based Model," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 38(4), pages 525-547.
    11. Markus P. A. Schneider, 2018. "Revisiting the thermal and superthermal two-class distribution of incomes: A critical perspective," Papers 1804.06341, arXiv.org.
    12. Chami Figueira, F. & Moura, N.J. & Ribeiro, M.B., 2011. "The Gompertz–Pareto income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 689-698.
    13. Nikolaos Papanikolaou, 2020. "The Econophysics of Labor Income," Bulletin of Applied Economics, Risk Market Journals, vol. 7(1), pages 107-122.
    14. Kang, Sang Hoon & Jiang, Zhuhua & Cheong, Chongcheul & Yoon, Seong-Min, 2011. "Changes of firm size distribution: The case of Korea," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 319-327.
    15. Sarabia, José María & Jordá, Vanesa, 2014. "Explicit expressions of the Pietra index for the generalized function for the size distribution of income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 582-595.
    16. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno & Tsutomu Watanabe, 2017. "Dependence of the decay rate of firm activities on firm age," Evolutionary and Institutional Economics Review, Springer, vol. 14(2), pages 351-362, December.
    17. Heinrich, Torsten & Dai, Shuanping, 2016. "Diversity of firm sizes, complexity, and industry structure in the Chinese economy," Structural Change and Economic Dynamics, Elsevier, vol. 37(C), pages 90-106.
    18. Gao, Baojun & Chan, Wai Kin (Victor) & Li, Hongyi, 2015. "On the increasing inequality in size distribution of China's listed companies," China Economic Review, Elsevier, vol. 36(C), pages 25-41.
    19. Garanina, O.S. & Romanovsky, M.Yu., 2015. "New multi-parametric analytical approximations of exponential distribution with power law tails for new cars sells and other applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 1-9.
    20. Guo, Jinzhong & Xu, Qi & Chen, Qinghua & Wang, Yougui, 2013. "Firm size distribution and mobility of the top 500 firms in China, the United States and the world," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2903-2914.

    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:389:y:2010:i:18:p:3837-3843. 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.