IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i4p741-756.html
   My bibliography  Save this article

Relations between allometric scalings and fluctuations in complex systems: The case of Japanese firms

Author

Listed:
  • Watanabe, Hayafumi
  • Takayasu, Hideki
  • Takayasu, Misako

Abstract

To elucidate allometric scaling in complex systems, we investigated the underlying scaling relationships between typical three-scale indicators for approximately 500,000 Japanese firms; namely, annual sales, number of employees, and number of business partners. First, new scaling relations including the distributions of fluctuations were discovered by systematically analyzing conditional statistics. Second, we introduced simple probabilistic models that reproduce all these scaling relations, and we derived relations between scaling exponents and the magnitude of fluctuations.

Suggested Citation

  • Watanabe, Hayafumi & Takayasu, Hideki & Takayasu, Misako, 2013. "Relations between allometric scalings and fluctuations in complex systems: The case of Japanese firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 741-756.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:741-756
    DOI: 10.1016/j.physa.2012.10.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112009168
    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.2012.10.020?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. Watanabe, Tsutomu & Mizuno, Takayuki & Ishikawa, Atsushi & Fujimoto, Shoji, 2011. "A New Method for Specifying Functional Forms of Production Functions," Economic Review, Hitotsubashi University, vol. 62(3), pages 193-208, July.
    2. 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.
    3. Samaniego, Horacio & Moses, Melanie E., 2008. "Cities as Organisms: Allometric Scaling of Urban Road Networks," The Journal of Transport and Land Use, Center for Transportation Studies, University of Minnesota, vol. 1(1), pages 21-39.
    4. 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.
    5. 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.
    6. Zhang, Jiang & Yu, Tongkui, 2010. "Allometric scaling of countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4887-4896.
    7. Hideaki Aoyama & Yuichi Nagahara & Mitsuhiro P. Okazaki & Wataru Souma & Hideki Takayasu & Misako Takayasu, 2000. "Pareto's Law for Income of Individuals and Debt of Bankrupt Companies," Papers cond-mat/0006038, arXiv.org.
    8. Saito, Yukiko Umeno & Watanabe, Tsutomu & Iwamura, Mitsuru, 2007. "Do larger firms have more interfirm relationships?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 158-163.
    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. Geoffrey B. West & James H. Brown & Brian J. Enquist, 1997. "A General Model for the Origin of Allometric Scaling Laws in Biology," Working Papers 97-03-019, Santa Fe Institute.
    11. 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.
    12. Luís M A Bettencourt & José Lobo & Deborah Strumsky & Geoffrey B West, 2010. "Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-9, November.
    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 & Tsutomu Watanabe, 2014. "Analytical Derivation of Power Laws in Firm Size Variables from Gibrat’s Law and Quasi-inversion Symmetry: A Geomorphological Approach," UTokyo Price Project Working Paper Series 019, University of Tokyo, Graduate School of Economics.
    2. MIZUNO Takayuki & SOUMA Wataru & WATANABE Tsutomu, 2015. "Buyer-Supplier Networks and Aggregate Volatility," Discussion papers 15056, Research Institute of Economy, Trade and Industry (RIETI).
    3. 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.
    4. Takayuki Mizuno & Wataru Souma & Tsutomu Watanabe, 2014. "Buyer-Supplier Networks and Aggregate Volatility," CARF F-Series CARF-F-353, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Hayafumi Watanabe, 2014. "Mean Field Approximation for Biased Diffusion on Japanese Inter-Firm Trading Network," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-5, March.
    6. Jun’ichi Ozaki & Hideki Takayasu & Misako Takayasu, 2019. "Estimation of sales decrease caused by a disaster: Hokkaido blackout after earthquake in 2018," Journal of Computational Social Science, Springer, vol. 2(1), pages 47-51, January.
    7. Takayuki Mizuno & Wataru Souma & Tsutomu Watanabe, 2014. "The Structure and Evolution of Buyer-Supplier Networks," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-10, July.
    8. Lang, Wei & Long, Ying & Chen, Tingting & Li, Xun, 2019. "Reinvestigating China’s urbanization through the lens of allometric scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1429-1439.
    9. Takayuki Mizuno & Wataru Souma & Tsutomu Watanabe, 2014. "The Structure and Evolution of Buyer-Supplier Networks," CARF F-Series CARF-F-339, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    10. Mizuno, Takayuki & Souma, Wataru & Watanabe, Tsutomu, 2014. "The Structure and Evolution of Buyer-Supplier Networks," Working Paper Series 27, Center for Interfirm Network, Institute of Economic Research, Hitotsubashi University.
    11. Takayuki Mizuno & Wataru Souma & Tsutomu Watanabe, 2014. "Buyer-Supplier Networks and Aggregate Volatility," UTokyo Price Project Working Paper Series 033, University of Tokyo, Graduate School of Economics.
    12. 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.
    13. Carolina Mattsson & Frank W. Takes & Eelke M. Heemskerk & Cees Diks & Gert Buiten & Albert Faber & Peter M. A. Sloot, 2021. "Functional structure in production networks," Papers 2103.15777, arXiv.org.

    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. Chen, Yanguang, 2017. "Multi-scaling allometric analysis for urban and regional development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 673-689.
    2. 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.
    3. 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.
    4. Dion R J O’Neale & Shaun C Hendy, 2012. "Power Law Distributions of Patents as Indicators of Innovation," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-9, December.
    5. Brinkley, Catherine & Raj, Subhashni, 2022. "Perfusion and urban thickness: The shape of cities," Land Use Policy, Elsevier, vol. 115(C).
    6. Pierpaolo Andriani & Bill McKelvey, 2009. "Perspective ---From Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations," Organization Science, INFORMS, vol. 20(6), pages 1053-1071, December.
    7. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    8. Hsiehchen, David & Espinoza, Magdalena & Hsieh, Antony, 2016. "Hypoallometric scaling in international collaborations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 188-193.
    9. 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.
    10. 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.
    11. Chen, Yanguang & Wang, Yihan & Li, Xijing, 2019. "Fractal dimensions derived from spatial allometric scaling of urban form," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 122-134.
    12. 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.
    13. 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.
    14. Dalgaard, Carl-Johan & Strulik, Holger, 2011. "Energy distribution and economic growth," Resource and Energy Economics, Elsevier, vol. 33(4), pages 782-797.
    15. David Levinson, 2012. "Network Structure and City Size," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-11, January.
    16. Ausloos, M. & Bronlet, Ph., 2003. "Strategy for investments from Zipf law(s)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 30-37.
    17. Xu, Yan & Wang, Yougui & Tao, Xiaobo & Ližbetinová, Lenka, 2017. "Evidence of Chinese income dynamics and its effects on income scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 143-152.
    18. 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.
    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.

    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:392:y:2013:i:4:p:741-756. 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.