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A Model for Scaling in Firms' Size and Growth Rate Distribution

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  • Cornelia Metzig
  • Mirta B. Gordon

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

  • Cornelia Metzig & Mirta B. Gordon, 2013. "A Model for Scaling in Firms' Size and Growth Rate Distribution," Papers 1304.4311, arXiv.org, revised Nov 2013.
  • Handle: RePEc:arx:papers:1304.4311
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    References listed on IDEAS

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    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. 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.
    3. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    4. Palestrini, Antonio, 2007. "Analysis of industrial dynamics: A note on the relationship between firms' size and growth rate," Economics Letters, Elsevier, vol. 94(3), pages 367-371, March.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Stephen Hymer & Peter Pashigian, 1962. "Firm Size and Rate of Growth," Journal of Political Economy, University of Chicago Press, vol. 70, pages 556-556.
    10. 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.
    11. West, Geoffrey B., 1999. "The origin of universal scaling laws in biology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 104-113.
    12. repec:spr:lnecms:978-3-642-02946-2 is not listed on IDEAS
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