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Generalizing Gibrat: Reasonable Multiplicative Models of Firm Dynamics

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Abstract

Multiplicative models of firm dynamics � 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.

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Bibliographic Info

Article provided by Journal of Artificial Societies and Social Simulation in its journal Journal of Artificial Societies and Social Simulation.

Volume (Year): 7 (2004)
Issue (Month): 1 ()
Pages: 2

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Handle: RePEc:jas:jasssj:2003-16-2

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Keywords: Firm Growth; Gibrat's Law; Entry; Exit;

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References

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  1. 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.
  2. 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.
  3. 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.
  4. Evans, David S, 1987. "The Relationship between Firm Growth, Size, and Age: Estimates for 100 Manufacturing Industries," Journal of Industrial Economics, Wiley Blackwell, vol. 35(4), pages 567-81, June.
  5. Harhoff, Dietmar & Stahl, Konrad & Woywode, Michael, 1998. "Legal Form, Growth and Exit of West German Firms--Empirical Results for Manufacturing, Construction, Trade and Service Industries," Journal of Industrial Economics, Wiley Blackwell, vol. 46(4), pages 453-88, December.
  6. Singh, Ajit & Whittington, Geoffrey, 1975. "The Size and Growth of Firms," MPRA Paper 51715, University Library of Munich, Germany.
  7. 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.
  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. 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.
  10. Hall, Bronwyn H, 1987. "The Relationship between Firm Size and Firm Growth in the U.S. Manufacturing Sector," Journal of Industrial Economics, Wiley Blackwell, vol. 35(4), pages 583-606, June.
  11. Cordoba, Juan, 2001. "Balanced City Growth and Zipf's Law," Working Papers 2002-03, Rice University, Department of Economics.
  12. 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.
  13. Variyam, Jayachandran N. & Kraybill, David S., 1992. "Empirical evidence on determinants of firm growth," Economics Letters, Elsevier, vol. 38(1), pages 31-36, January.
  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. Emeterio Navarro & Ruben Cantero & Joao Rodrigues & Frank Schweitzer, 2007. "Investments in Random Environments," Papers 0709.3630, arXiv.org, revised Sep 2008.
  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. Guido Fioretti, 2005. "The Production Function," Papers physics/0511191, arXiv.org.

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