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A model for scaling in firms’ size and growth rate distribution

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  • Metzig, Cornelia
  • Gordon, Mirta B.

Abstract

We introduce a simple agent-based model which allows us to analyze three stylized facts: a fat-tailed size distribution of companies, a ‘tent-shaped’ growth rate distribution, the scaling relation of the growth rate variance with firm size, and the causality between them. This is achieved under the simple hypothesis that firms compete for a scarce quantity (either aggregate demand or workforce) which is allocated probabilistically. The model allows us to relate size and growth rate distributions. We compare the results of our model to simulations with other scaling relationships, and to similar models and relate it to existing theory. Effects arising from binning data are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:398:y:2014:i:c:p:264-279
    DOI: 10.1016/j.physa.2013.11.027
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    as
    1. Wyart, Matthieu & Bouchaud, Jean-Philippe, 2003. "Statistical models for company growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 326(1), pages 241-255.
    2. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    3. Foley Duncan K., 1994. "A Statistical Equilibrium Theory of Markets," Journal of Economic Theory, Elsevier, vol. 62(2), pages 321-345, April.
    4. Sutton, John, 2002. "The variance of firm growth rates: the ‘scaling’ puzzle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(3), pages 577-590.
    5. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    6. Giulio Bottazzi & Angelo Secchi, 2006. "Explaining the distribution of firm growth rates," RAND Journal of Economics, RAND Corporation, vol. 37(2), pages 235-256, June.
    7. 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.
    8. 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.
    9. Youngki Lee & Luis A. N. Amaral & David Canning & Martin Meyer & H. Eugene Stanley, 1998. "Universal features in the growth dynamics of complex organizations," Papers cond-mat/9804100, arXiv.org.
    10. Matteo Marsili & Sergei Maslov & Yi-Cheng Zhang, 1998. "Dynamical Optimization Theory of a Diversified Portfolio," Papers cond-mat/9801239, arXiv.org, revised Jan 1998.
    11. Giulio Bottazzi & Angelo Secchi, 2006. "Explaining the Distribution of Firm Growth Rates," RAND Journal of Economics, The RAND Corporation, vol. 37(2), pages 235-256, Summer.
    12. Einar Erlingsson & Simone Alfarano & Marco Raberto & Hlynur Stefánsson, 2013. "On the distributional properties of size, profit and growth of Icelandic firms," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(1), pages 57-74, April.
    13. Giulio Bottazzi & Davide Pirino & Federico Tamagni, 2015. "Zipf law and the firm size distribution: a critical discussion of popular estimators," Journal of Evolutionary Economics, Springer, vol. 25(3), pages 585-610, July.
    14. Nunes Amaral, Luís A & Buldyrev, Sergey V & Havlin, Shlomo & Maass, Philipp & Salinger, Michael A & Eugene Stanley, H & Stanley, Michael H.R, 1997. "Scaling behavior in economics: The problem of quantifying company growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 244(1), pages 1-24.
    15. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    16. Alfarano, Simone & Milaković, Mishael & Irle, Albrecht & Kauschke, Jonas, 2012. "A statistical equilibrium model of competitive firms," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 136-149.
    17. Marsili, Matteo & Maslov, Sergei & Zhang, Yi-Cheng, 1998. "Dynamical optimization theory of a diversified portfolio," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 403-418.
    18. Peter Richmond & Sorin Solomon, 2001. "Power Laws Are Disguised Boltzmann Laws," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 333-343.
    19. Moshe Levy & Sorin Solomon, 1996. "Power Laws Are Logarithmic Boltzmann Laws," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 595-601.
    20. Stephen Kinsella & Matthias Greiff & Edward J Nell, 2011. "Income Distribution in a Stock-Flow Consistent Model with Education and Technological Change," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 37(1), pages 134-149.
    21. Alves, Luiz G.A. & Ribeiro, Haroldo V. & Mendes, Renio S., 2013. "Scaling laws in the dynamics of crime growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2672-2679.
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    Cited by:

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    3. Williams, Michael A. & Pinto, Brijesh P. & Park, David, 2015. "Global evidence on the distribution of firm growth rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 102-107.
    4. Williams, Michael A. & Baek, Grace & Li, Yiyang & Park, Leslie Y. & Zhao, Wei, 2017. "Global evidence on the distribution of GDP growth rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 750-758.

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