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

  • Christopher A Laincz
  • Ana Sofia Domingues Rodrigues

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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  1. 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.
  2. 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.
  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. Mansfield, Edwin & Schwartz, Mark & Wagner, Samuel, 1981. "Imitation Costs and Patents: An Empirical Study," Economic Journal, Royal Economic Society, vol. 91(364), pages 907-18, December.
  5. 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.
  6. Mansfield, Edwin, 1985. "How Rapidly Does New Industrial Technology Leak Out?," Journal of Industrial Economics, Wiley Blackwell, vol. 34(2), pages 217-23, December.
  7. 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.
  8. Singh, Ajit & Whittington, Geoffrey, 1975. "The Size and Growth of Firms," MPRA Paper 51715, University Library of Munich, Germany.
  9. 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.
  10. Hart, Peter E & Oulton, Nicholas, 1996. "Growth and Size of Firms," Economic Journal, Royal Economic Society, vol. 106(438), pages 1242-52, September.
  11. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-70, May.
  12. Steven Klepper, 2002. "Firm Survival and the Evolution of Oligopoly," RAND Journal of Economics, The RAND Corporation, vol. 33(1), pages 37-61, Spring.
  13. Audretsch, D.B. & Klomp, L. & Thurik, A.R., 2002. "Gibrat's Law: are the services different?," ERIM Report Series Research in Management ERS-2002-04-STR, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
  14. Pakes, A. & Ericson, R., 1990. "Empirical Implications Of Alternative Models Of Firm Dynamics," Papers 594, Yale - Economic Growth Center.
  15. 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.
  16. 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.
  17. 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.
  18. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 53-82, January.
  19. 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., vol. 15(3), pages 253-274.
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