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Generalizing Gibrat. Reasonable Multiplicative Models of Firm Dynamics

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  • Matteo Richiardi

    (LABORatorio Riccardo Revelli Centre for Employment Studies)

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 which modifications to the standard multiplicative model of firm dynamics lead to stable (and reasonable) distributions of firm size. An agent-based simulation study is performed, and a methodology is proposed to recover the (aggregate) laws governing the system by estimating the reduced form, i.e. the local data generating process, on the artificial data resulting from a number of artificial experiments. 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. While other particular, ad hoc, entry and exit mechanisms could be imagined, 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.

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Bibliographic Info

Paper provided by EconWPA in its series Industrial Organization with number 0304004.

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Date of creation: 07 Apr 2003
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Handle: RePEc:wpa:wuwpio:0304004

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Web page: http://128.118.178.162

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Keywords: Firm growth Gibrat Entry Exit Simulation;

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  1. Bronwyn H. Hall, 1986. "The Relationship Between Firm Size and Firm Growth in the U.S. Manufacturing Sector," NBER Working Papers 1965, National Bureau of Economic Research, Inc.
  2. McCloughan, Patrick, 1995. "Simulation of Concentration Development from Modified Gibrat Growth-Entry-Exit Processes," Journal of Industrial Economics, Wiley Blackwell, vol. 43(4), pages 405-33, December.
  3. Harhoff, Dietmar & Stahl, Konrad O. & Woywode, Michael, 1996. "Legal Form, Growth and Exit of West German Firms - Empirical Results for Manufacturing, Construction, Trade and Service Industries," CEPR Discussion Papers 1401, C.E.P.R. Discussion Papers.
  4. Variyam, Jayachandran N. & Kraybill, David S., 1992. "Empirical evidence on determinants of firm growth," Economics Letters, Elsevier, vol. 38(1), pages 31-36, January.
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  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.
  7. 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.
  8. Evans, David S, 1987. "Tests of Alternative Theories of Firm Growth," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 657-74, August.
  9. Cordoba, Juan, 2001. "Balanced City Growth and Zipf's Law," Working Papers 2002-03, Rice University, Department of Economics.
  10. Peter Hart & Nicholas Oulton, 1999. "Gibrat, Galton and Job Generation," International Journal of the Economics of Business, Taylor & Francis Journals, vol. 6(2), pages 149-164.
  11. Singh, Ajit & Whittington, Geoffrey, 1975. "The Size and Growth of Firms," MPRA Paper 51715, University Library of Munich, Germany.
  12. Rudi Vander Vennet, 2001. "The law of proportionate effect and OECD bank sectors," Applied Economics, Taylor & Francis Journals, vol. 33(4), pages 539-546.
  13. José Fariñas & Lourdes Moreno, 2000. "Firms' Growth, Size and Age: A Nonparametric Approach," Review of Industrial Organization, Springer, vol. 17(3), pages 249-265, November.
  14. Kumar, M S, 1985. "Growth, Acquisition Activity and Firm Size: Evidence from the United Kingdom," Journal of Industrial Economics, Wiley Blackwell, vol. 33(3), pages 327-38, March.
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Cited by:
  1. Fioretti, Guido, 2007. "The production function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 707-714.
  2. Delli Gatti, Domenico & Di Guilmi, Corrado & Gaffeo, Edoardo & Gallegati, Mauro, 2004. "Bankruptcy as an exit mechanism for systems with a variable number of components," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 8-13.
  3. Navarro-Barrientos, Jesús Emeterio & Cantero-Álvarez, Rubén & Matias Rodrigues, João F. & Schweitzer, Frank, 2008. "Investments in random environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2035-2046.
  4. Segarra, Agustí & Teruel, Mercedes, 2012. "An appraisal of firm size distribution: Does sample size matter?," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 314-328.
  5. Guido Fioretti, 2005. "The Production Function," Papers physics/0511191, arXiv.org.

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