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Statistical models for company growth

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  • Wyart, Matthieu
  • Bouchaud, Jean-Philippe

Abstract

We study Sutton's ‘microcanonical’ model for the internal organization of firms, that leads to non-trivial scaling properties for the statistics of growth rates. We show that the growth rates are asymptotically Gaussian in this model, whereas empirical results suggest that the kurtosis of the distribution increases with size. We also obtain the conditional distribution of the number and size of sub-sectors in Sutton's model. We formulate and solve an alternative model, based on the assumption that the sector sizes follow a power-law distribution. We find in this new model both anomalous scaling of the variance of growth rates and non-Gaussian asymptotic distributions. We give some testable predictions of the two models that would differentiate them further. We also discuss why the growth rate statistics at the country level and at the company level should be identical.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:326:y:2003:i:1:p:241-255
    DOI: 10.1016/S0378-4371(03)00267-X
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    Citations

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    Cited by:

    1. Thesmar , David & Landier , Augustin, 2014. "Instabilities in Large Economies: Aggregate Volatility Without Idiosyncratic Shocks," HEC Research Papers Series 1052, HEC Paris.
    2. Xavier Gabaix, 2004. "Power laws and the origins of aggregate fluctuations," Econometric Society 2004 North American Summer Meetings 484, Econometric Society.
    3. Hernan Mondani & Petter Holme & Fredrik Liljeros, 2014. "Fat-Tailed Fluctuations in the Size of Organizations: The Role of Social Influence," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-9, July.
    4. 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.
    5. 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.
    6. Luca Fontanelli, 2023. "Theories of market selection: a survey," LEM Papers Series 2023/22, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    7. Chen Yeh, 2017. "Are firm-level idiosyncratic shocks important for U.S. aggregate volatility?," Working Papers 17-23, Center for Economic Studies, U.S. Census Bureau.
    8. Aloys Prinz & Jan Piening & Thomas Ehrmann, 2015. "The success of art galleries: a dynamic model with competition and information effects," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 39(2), pages 153-176, May.
    9. Kemp, Jordan T. & Bettencourt, Luís M.A., 2022. "Statistical dynamics of wealth inequality in stochastic models of growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    10. Eugene Larsen-Hallock & Adam Rej & David Thesmar, 2022. "Expectations Formation with Fat-tailed Processes: Evidence from Sales Forecasts," Papers 2210.10169, arXiv.org.
    11. Sandro Claudio Lera & Didier Sornette, 2017. "Quantification of the evolution of firm size distributions due to mergers and acquisitions," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-16, August.
    12. Xie, Wen-Jie & Gu, Gao-Feng & Zhou, Wei-Xing, 2010. "On the growth of primary industry and population of China’s counties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3876-3882.
    13. Olivier Guedj & Jean-Philippe Bouchaud, 2004. "Experts' earning forecasts: bias, herding and gossamer information," Papers cond-mat/0410079, arXiv.org.
    14. Chen Yeh, 2016. "Are firm-level idiosyncratic shocks important for U.S. aggregate volatility?," Working Papers 16-47, Center for Economic Studies, U.S. Census Bureau.

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