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A Theoretical Foundation for Understanding Firm Size Distributions and Gibrat's Law

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  • Christopher A Laincz
  • Ana Sofia Domingues Rodrigues

Abstract

This paper presents a dynamic model of the firm size distribution. Empirical studies of the firm size distribution often compare the moments to a log-normal distribution as implied by Gibrat's Law and note important deviations. Thus, the first, and basic questions we ask are how well does the dynamic industry model reproduce Gibrat's Law and how well does it match the deviations uncovered in the literature. We show that the model reproduces these results when testing the simulated output using the techniques of the empirical literature. We then use the model to study how structural parameters affect the firm size distribution. We find that, among other things, fixed and sunk costs increase both the mean and variance of the firm size distribution while generally decreasing the skewness and kurtosis. The rate of growth in an industry also raises the mean and variance, but has non-monotonic effects on the higher moments.

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Paper provided by Department of Economics, University of York in its series Discussion Papers with number 05/34.

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Handle: RePEc:yor:yorken:05/34

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Keywords: Firm size distribution; Gibrat's Law; R&D.;

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References

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  1. Roy Thurik & Enrico Santarelli & David Audretsch & Luuk Klomp, 2002. "Gibrat's Law: Are the Services Different?," Scales Research Reports H200201, EIM Business and Policy Research.
  2. Singh, Ajit & Whittington, Geoffrey, 1975. "The Size and Growth of Firms," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 42(1), pages 15-26, January.
  3. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, Econometric Society, vol. 50(3), pages 649-70, May.
  4. Steven Klepper, 2002. "Firm Survival and the Evolution of Oligopoly," RAND Journal of Economics, The RAND Corporation, vol. 33(1), pages 37-61, Spring.
  5. Evans, David S., 1986. "The Relationship Between Firm Growth, Size, and Age: Estimates for 100 Manufacturing Industries," Working Papers, C.V. Starr Center for Applied Economics, New York University 86-33, C.V. Starr Center for Applied Economics, New York University.
  6. F. Lotti & E. Santarelli, 2001. "Industry Dynamics and the Distiribution of Firm Sizes: A Non-Parametric Apporoach," Working Papers 406, Dipartimento Scienze Economiche, Universita' di Bologna.
  7. Mansfield, Edwin, 1985. "How Rapidly Does New Industrial Technology Leak Out?," Journal of Industrial Economics, Wiley Blackwell, vol. 34(2), pages 217-23, December.
  8. Mansfield, Edwin & Schwartz, Mark & Wagner, Samuel, 1981. "Imitation Costs and Patents: An Empirical Study," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 91(364), pages 907-18, December.
  9. Hart, Peter E & Oulton, Nicholas, 1996. "Growth and Size of Firms," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 106(438), pages 1242-52, September.
  10. 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.
  11. 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.
  12. 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.
  13. Pakes, Ariel & Ericson, Richard, 1998. "Empirical Implications of Alternative Models of Firm Dynamics," Journal of Economic Theory, Elsevier, vol. 79(1), pages 1-45, March.
  14. Giulio Bottazzi & Elena Cefis & Giovanni Dosi & Angelo Secchi, 2003. "Invariances and Diversities in the Evolution of Manufacturing Industries," LEM Papers Series 2003/21, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  15. Laincz, Christopher A., 2005. "Market structure and endogenous productivity growth: how do R&D subsidies affect market structure?," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 187-223, January.
  16. Jose A. F. Machado & Jose Mata, 2000. "Box-Cox quantile regression and the distribution of firm sizes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 15(3), pages 253-274.
  17. Francesca Lotti & Enrico Santarelli, 2004. "Industry Dynamics and the Distribution of Firm Sizes: A Nonparametric Approach," Southern Economic Journal, Southern Economic Association, vol. 70(3), pages 443-466, January.
  18. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 62(1), pages 53-82, January.
  19. Giulio Bottazzi & Angelo Secchi, 2003. "Sectoral Specifities in the Dynamics of U.S. Manufacturing Firms," LEM Papers Series 2003/18, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
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Cited by:
  1. Qi Li & Patrick Paul Walsh, 2009. "The Firm Size Distribution in a Small Open Economy: Theory and Evidence," Working Papers, Geary Institute, University College Dublin 200920, Geary Institute, University College Dublin.

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