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A New Method for Measuring Tail Exponents of Firm Size Distributions

Author

Listed:
  • Fujimoto, S.
  • Ishikawa, A.
  • Mizuno, T.
  • Watanabe, T.
  • 渡辺, 努
  • ワタナベ, ツトム

Abstract

We propose a new method for estimating the power-law exponents of firm size variables. Our focus is on how to empirically identify a range in which a firm size variable follows a power-law distribution. As is well known, a firm size variable follows a power-law distribution only beyond some threshold. On the other hand, in almost all empirical exercises, the right end part of a distribution deviates from a power-law due to finite size effect. We modify the method proposed by Malevergne et al. (2011) so that we can identify both of the lower and the upper thresholds and then estimate the power-law exponent using observations only in the range defined by the two thresholds. We apply this new method to various firm size variables, including annual sales, the number of workers, and tangible fixed assets for firms in more than thirty countries.

Suggested Citation

  • Fujimoto, S. & Ishikawa, A. & Mizuno, T. & Watanabe, T. & 渡辺, 努 & ワタナベ, ツトム, 2011. "A New Method for Measuring Tail Exponents of Firm Size Distributions," Working Paper Series 7, Center for Interfirm Network, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:cinwps:7
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. 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.
    5. Hisano, Ryohei & Mizuno, Takayuki, 2011. "Sales distribution of consumer electronics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 309-318.
    6. Stanley, Michael H. R. & Buldyrev, Sergey V. & Havlin, Shlomo & Mantegna, Rosario N. & Salinger, Michael A. & Eugene Stanley, H., 1995. "Zipf plots and the size distribution of firms," Economics Letters, Elsevier, vol. 49(4), pages 453-457, October.
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    Cited by:

    1. Ishikawa, Atushi & 石川, 温 & イシカワ, アツシ & Fujimoto, Shoji & 藤本, 祥二 & フジモト, ショウジ & Watanabe, Tsutomu & 渡辺, 努 & ワタナベ, ツトム & Mizuno, Takayuki & 水野, 貴之 & ミズノ, タカユキ, 2011. "Emergence of power laws with different power-law exponents from reversal quasi-symmetry and Gibrat’s law," Working Paper Series 9, Center for Interfirm Network, Institute of Economic Research, Hitotsubashi University.
    2. Shouji Fujimoto & Takayuki Mizuno & Atushi Ishikawa, 2022. "Interpolation of non-random missing values in financial statements’ big data using CatBoost," Journal of Computational Social Science, Springer, vol. 5(2), pages 1281-1301, November.
    3. 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.
    4. Vitezić Vanja & Srhoj Stjepan & Perić Marko, 2018. "Investigating Industry Dynamics in a Recessionary Transition Economy," South East European Journal of Economics and Business, Sciendo, vol. 13(1), pages 43-67, June.
    5. Takayuki Mizuno & Takaaki Ohnishi & Tsutomu Watanabe, 2016. "Power laws in market capitalization during the dot-com and Shanghai bubble periods," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 445-454, December.
    6. Takayuki Mizuno & Takaaki Ohnishi & Tsutomu Watanabe, 2016. "Power laws in market capitalization during the Dot-com and Shanghai bubble periods," UTokyo Price Project Working Paper Series 070, University of Tokyo, Graduate School of Economics.
    7. Shouji Fujimoto & Atushi Ishikawa & Takayuki Mizuno, 2022. "Copula-Based Synthetic Data Generation in Firm-Size Variables," The Review of Socionetwork Strategies, Springer, vol. 16(2), pages 479-492, October.
    8. 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.
    9. Takayuki Mizuno & Takaaki Ohnishi & Tsutomu Watanabe, 2016. "Power laws in market capitalization during the Dot-com and Shanghai bubble periods," CARF F-Series CARF-F-392, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    10. Mizuno, Takayuki & Ohnishi, Takaaki & Watanabe, Tsutomu, 2016. "Power law in market capitalization during Dot-com and Shanghai bubble periods," HIT-REFINED Working Paper Series 60, Institute of Economic Research, Hitotsubashi University.
    11. Gualandi, Stefano & Toscani, Giuseppe, 2018. "Pareto tails in socio-economic phenomena: A kinetic description," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-17.
    12. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.

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    More about this item

    Keywords

    Econophysics; power-law distributions; power-law exponents; firm size variables; finite size effect;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • D20 - Microeconomics - - Production and Organizations - - - General
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production

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