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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Zhang, Jiang & Yu, Tongkui, 2010. "Allometric scaling of countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4887-4896.
    9. 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.
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    Citations

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    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. 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.
    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.

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