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Generalizing Gibrat. Reasonable Multiplicative Models of Firm Dynamics

  • Matteo Richiardi

    (LABORatorio Riccardo Revelli Centre for Employment Studies)

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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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
Note: Type of Document - ; figures: included
Contact details of provider: Web page: http://128.118.178.162

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  1. Variyam, Jayachandran N. & Kraybill, David S., 1992. "Empirical evidence on determinants of firm growth," Economics Letters, Elsevier, vol. 38(1), pages 31-36, January.
  2. 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.
  3. Geroski, Paul A & Samiei, Hossein & Urga, Giovanni, 1997. "Are Differences in Firm Size Transitory or Permanent?," CEPR Discussion Papers 1691, C.E.P.R. Discussion Papers.
  4. 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.
  5. Evans, David S., 1986. "The Relationship Between Firm Growth, Size, and Age: Estimates for 100 Manufacturing Industries," Working Papers 86-33, C.V. Starr Center for Applied Economics, New York University.
  6. 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.
  7. Singh, Ajit & Whittington, Geoffrey, 1975. "The Size and Growth of Firms," MPRA Paper 51715, University Library of Munich, Germany.
  8. Rudi Vander Vennet, 2001. "The law of proportionate effect and OECD bank sectors," Applied Economics, Taylor & Francis Journals, vol. 33(4), pages 539-546.
  9. 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.
  10. Harhoff, Dietmar & Stahl, Konrad & 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.
  11. 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.
  12. Cordoba, Juan, 2001. "Balanced City Growth and Zipf's Law," Working Papers 2002-03, Rice University, Department of Economics.
  13. 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.
  14. 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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