IDEAS home Printed from https://ideas.repec.org/p/arx/papers/physics-0702248.html
   My bibliography  Save this paper

The uniqueness of company size distribution function from tent-shaped growth rate distribution

Author

Listed:
  • Atushi Ishikawa

Abstract

We report the proof that the extension of Gibrat's law in the middle scale region is unique and the probability distribution function (pdf) is also uniquely derived from the extended Gibrat's law and the law of detailed balance. In the proof, two approximations are employed. The pdf of growth rate is described as tent-shaped exponential functions and the value of the origin of the growth rate distribution is constant. These approximations are confirmed in profits data of Japanese companies 2003 and 2004. The resultant profits pdf fits with the empirical data with high accuracy. This guarantees the validity of the approximations.

Suggested Citation

  • Atushi Ishikawa, 2007. "The uniqueness of company size distribution function from tent-shaped growth rate distribution," Papers physics/0702248, arXiv.org.
    • Handle: RePEc:arx:papers:physics/0702248
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/physics/0702248
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2019. "Statistical law observed in inactive rate of firms," Evolutionary and Institutional Economics Review, Springer, vol. 16(1), pages 201-212, June.
    2. 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.
    3. 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.
    4. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno & Tsutomu Watanabe, 2016. "Long-term firm growth properties derived from short-term laws of sales and number of employees in Japan and France," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 409-422, December.
    5. 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.
    6. Ishikawa, Atushi, 2008. "Power-Law and Log-Normal Distributions in Firm Size Displacement Data," Economics Discussion Papers 2008-45, Kiel Institute for the World Economy (IfW Kiel).
    7. Murat ATAN & Emre BOZDAĞ, 2011. "Avrupa Karbonatlı İçecekler Piyasasında Firma Büyüklüğü Ve Büyüklük Genişleme Oranı İlişkisi," Ekonomik Yaklasim, Ekonomik Yaklasim Association, vol. 22(80), pages 19-38.
    8. Atushi Ishikawa & Takayuki Mizuno & Shouji Fujimoto, 2022. "Employee Number Dependence in Labor Productivity Distribution," The Review of Socionetwork Strategies, Springer, vol. 16(2), pages 465-477, October.

    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. 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.
    2. Segarra, Agustí & Teruel, Mercedes, 2012. "An appraisal of firm size distribution: Does sample size matter?," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 314-328.
    3. Lyócsa, Štefan & Výrost, Tomáš, 2018. "Scale-free distribution of firm-size distribution in emerging economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 501-505.
    4. Massing, Till & Puente-Ajovín, Miguel & Ramos, Arturo, 2020. "On the parametric description of log-growth rates of cities’ sizes of four European countries and the USA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    5. Keiichi Kishi, 2016. "Technology Diffusion, Pareto Distribution, and Patent Policy," Discussion Papers in Economics and Business 16-31, Osaka University, Graduate School of Economics.
    6. Musa, Hussam & Krištofík, Peter & Medzihorský, Juraj & Klieštik, Tomáš, 2024. "The development of firm size distribution – Evidence from four Central European countries," International Review of Economics & Finance, Elsevier, vol. 91(C), pages 98-110.
    7. Stefano Battiston & Joao F. Rodrigues & Hamza Zeytinoglu, 2007. "The Network Of Inter-Regional Direct Investment Stocks Across Europe," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 29-51.
    8. Wang, Yuanjun & You, Shibing, 2016. "An alternative method for modeling the size distribution of top wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 443-453.
    9. Atushi Ishikawa, 2007. "Quasistatically varying log-normal distribution in the middle scale region of Japanese land prices," Papers 0710.1893, arXiv.org.
    10. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, February.
    11. Giuseppe Toscani, 2016. "Kinetic and mean field description of Gibrat's law," Papers 1606.04796, arXiv.org.
    12. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 49-100.
    13. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2021. "Why does production function take the Cobb–Douglas form?," Evolutionary and Institutional Economics Review, Springer, vol. 18(1), pages 79-102, April.
    14. Wright, Ian, 2009. "Implicit Microfoundations for Macroeconomics," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-27.
    15. Atushi Ishikawa & Takayuki Mizuno & Shouji Fujimoto, 2022. "Employee Number Dependence in Labor Productivity Distribution," The Review of Socionetwork Strategies, Springer, vol. 16(2), pages 465-477, October.
    16. Ramón Rufín & Cayetano Medina, 2008. "Market delimitation, firm survival and growth in service industries," The Service Industries Journal, Taylor & Francis Journals, vol. 30(9), pages 1401-1417, September.
    17. Atushi Ishikawa, 2007. "The log-normal distribution from Non-Gibrat's law in the middle scale region of profits," Papers 0705.1056, arXiv.org.
    18. Fujimoto, Shouji & Ishikawa, Atushi & Mizuno, Takayuki & Watanabe, Tsutomu, 2011. "A new method for measuring tail exponents of firm size distributions," Economics Discussion Papers 2011-29, Kiel Institute for the World Economy (IfW Kiel).
    19. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    20. Atushi Ishikawa & Shouji Fujimoto & Tsutomu Watanabe & Takayuki Mizuno, 2012. "The Emergence of Different Tail Exponents in the Distributions of Firm Size Variables," UTokyo Price Project Working Paper Series 003, University of Tokyo, Graduate School of Economics, revised Dec 2012.

    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:physics/0702248. 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.