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The variance of firm growth rates: the ‘scaling’ puzzle


  • Sutton, John


Recent evidence suggests that a power-law relationship exists between a firm's size and the variance of its growth rate. The flatness of the relation is regarded as puzzling, in that it suggests that large firms are not much more stable than small firms. It has been suggested that the power-law nature of the relationship reflects the presence of some form of correlation of growth rates across the firm's constituent businesses. Here, it is shown that a model of independent businesses which allows for the fact that these businesses vary in size, as modelled by a simple ‘partitions of integers’ model, provides a good representation of what is observed empirically.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:phsmap:v:312:y:2002:i:3:p:577-590 DOI: 10.1016/S0378-4371(02)00852-X

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    References listed on IDEAS

    1. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    2. 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,
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    Cited by:

    1. University of Minnesota & Erzo G.J. Luttmer, 2007. "New Goods and the Size Distribution of Firms," 2007 Meeting Papers 266, Society for Economic Dynamics.
    2. 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.
    3. Aoki, Masanao, 2008. "Thermodynamic limits of macroeconomic or financial models: One- and two-parameter Poisson-Dirichlet models," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 66-84, January.
    4. Alviarez, Vanessa & Cravino, Javier & Levchenko, Andrei A., 2017. "The growth of multinational firms in the Great Recession," Journal of Monetary Economics, Elsevier, vol. 85(C), pages 50-64.
    5. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters,in: Handbook of Research on Complexity, chapter 9 Edward Elgar Publishing.
    6. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW).
    7. Cefis, Elena & Ciccarelli, Matteo & Orsenigo, Luigi, 2007. "Testing Gibrat's legacy: A Bayesian approach to study the growth of firms," Structural Change and Economic Dynamics, Elsevier, vol. 18(3), pages 348-369, September.
    8. Stanley, H.Eugene, 2003. "Statistical physics and economic fluctuations: do outliers exist?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(1), pages 279-292.
    9. Buldyrev, Sergey V. & Salinger, Michael A. & Stanley, H. Eugene, 2016. "A statistical physics implementation of Coase׳s theory of the firm," Research in Economics, Elsevier, vol. 70(4), pages 536-557.
    10. Masanao Aoki & Hiroshi Yoshikawa, 2007. "Non-Self-Averaging in Macroeconomic Models: A Criticism of Modern Micro-founded Macroeconomics," CIRJE F-Series CIRJE-F-493, CIRJE, Faculty of Economics, University of Tokyo.
    11. Cornelia Metzig & Mirta B. Gordon, 2013. "A Model for Scaling in Firms' Size and Growth Rate Distribution," Papers 1304.4311,, revised Nov 2013.
    12. Daniela MAGGIONI & Alessia LO TURCO & Mauro GALLEGATI, 2014. "Does export complexity matter for firms' output volatility?," Working Papers 407, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    13. Şeker, Murat, 2012. "A structural model of firm and industry evolution: Evidence from Chile," Journal of Economic Dynamics and Control, Elsevier, vol. 36(6), pages 891-913.
    14. 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.
    15. James Christopher Westland & Jin Xing Hao & Xinping Xiao & Siqing Shan, 2016. "Substitutes, Complements and Network Effects in Instant Messaging Services," Networks and Spatial Economics, Springer, vol. 16(2), pages 525-543, June.
    16. Tai-Young Kim & Jeroen G. Kuilman, 2013. "The Demography of Resources," Journal of Management Studies, Wiley Blackwell, vol. 50(7), pages 1155-1184, November.
    17. Manas, Arnaud, 2012. "The Laplace illusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3963-3970.
    18. Thomas Lux, 2006. "Applications of Statistical Physics in Finance and Economics," Working Papers wpn06-07, Warwick Business School, Finance Group.
    19. 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.
    20. Alex Coad, 2008. "Firm growth and scaling of growth rate variance in multiplant firms," Economics Bulletin, AccessEcon, vol. 12(9), pages 1-15.
    21. Masanao Aoki, 2006. "Growth Patterns of Two Types of Macro-Models: Limiting Behavior of One-and Two-Parameter Poisson-Dirichlet Models," CIRJE F-Series CIRJE-F-446, CIRJE, Faculty of Economics, University of Tokyo.
    22. Maggioni, Daniela & Lo Turco, Alessia & Gallegati, Mauro, 2016. "Does product complexity matter for firms' output volatility?," Journal of Development Economics, Elsevier, vol. 121(C), pages 94-109.
    23. Manas, Arnaud, 2009. "French butchers don't do quantum physics," Economics Letters, Elsevier, vol. 103(2), pages 101-106, May.
    24. repec:spr:scient:v:60:y:2004:i:3:d:10.1023_b:scie.0000034374.79769.ed is not listed on IDEAS


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