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Generalizing Gibrat Reasonable Stochastic Multiplicative Models of Firm Dynamics with Entry and Exit

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  • Matteo Richiardi

Abstract

Multiplicative models of firm dynamics ‘à la Gibrat’ have become a standard reference in industrial organization. However, some unpleasant properties of their implied dynamics – namely, their explosive or implosive behaviour (firm size and number collapsing to zero or increasing indefinitely) - have been given only very little attention. In this paper I investigate using simulations which modifications to the standard multiplicative model of firm dynamics lead to stable (and reasonable) distributions of firm size. I show that in order to obtain stable systems for a wide range of average growth rate, either heteroskedasticity in the growth rates has to be assumed, or entry and exit mechanisms included. In particular I show that combining the broad class of threshold entry mechanisms and the more restricted class of threshold exit mechanisms with overcapacity penalizing all firms (where entry and exit are determined with reference to an exogenously defined total capacity of the market), lead to stable distributions even in the case of growth rate homoskedasticity, given a non-zero minimum threshold for firm size.

Suggested Citation

  • Matteo Richiardi, 2003. "Generalizing Gibrat Reasonable Stochastic Multiplicative Models of Firm Dynamics with Entry and Exit," LABORatorio R. Revelli Working Papers Series 21, LABORatorio R. Revelli, Centre for Employment Studies.
  • Handle: RePEc:cca:wplabo:21
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    File URL: http://www.laboratoriorevelli.it/_pdf/wp21.pdf
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    References listed on IDEAS

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    1. D.B. Audretsch & L. Klomp & E. Santarelli & A.R. Thurik, 2004. "Gibrat's Law: Are the Services Different?," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 24(3), pages 301-324, May.
    2. G. Urga & P. A. Geroski & S. Lazarova & C. F. Walters, 2003. "Are differences in firm size transitory or permanent?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 47-59.
    3. L. A. N. Amaral & S. V. Buldyrev & S. Havlin & H. Leschhorn & P. Maass & M. A. Salinger & H. E. Stanley & M. H. R. Stanley, 1997. "Scaling behavior in economics: I. Empirical results for company growth," Papers cond-mat/9702082, arXiv.org.
    4. Cordoba, Juan, 2001. "Balanced City Growth and Zipf's Law," Working Papers 2002-03, Rice University, Department of Economics.
    5. José Fariñas & Lourdes Moreno, 2000. "Firms' Growth, Size and Age: A Nonparametric Approach," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 17(3), pages 249-265, November.
    6. Delmar, Frederic & Davidsson, Per & Gartner, William B., 2003. "Arriving at the high-growth firm," Journal of Business Venturing, Elsevier, vol. 18(2), pages 189-216, March.
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    More about this item

    Keywords

    Firm growth; Gibrat’s Law; Entry; Exit; Simulation.;

    JEL classification:

    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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