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A comment on the relationship between firms' size and growth rate

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  • Giulio Bottazzi

Abstract

Since the seminal work of Pareto, many empirical analyses suggested that the distribution of firms size is characterized by an asymptotic power like behavior. At the same time, recent investigations show that the distribution of annual growth rates of business firms displays a remarkable double-exponential shape. A recent letter propose a possible connection between these two empirical regularities. By assuming a bivariate Marshall-Olkin power-like distribution for the size of firms in subsequent time steps, and performing a qualitative asymptotic analysis, it is suggested that the implied growth rates distribution takes a Laplace shape. By performing a complete analytical investigation, I show that this statement is not correct. The implied distribution does in general possess a non-continuous component and becomes degenerate when perfect correlation is assumed between size levels at different time steps. Essentially, the approach is faulty as it treats firm size levels as stationary stochastic variables and neglects the integrated nature of the growth process.

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Bibliographic Info

Paper provided by Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy in its series LEM Papers Series with number 2007/11.

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Date of creation: 27 Mar 2007
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Handle: RePEc:ssa:lemwps:2007/11

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Keywords: Firm Growth; Size distribution; Power law; Laplace distribution.;

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  1. Brock, W A, 1999. "Scaling in Economics: A Reader's Guide," Industrial and Corporate Change, Oxford University Press, vol. 8(3), pages 409-46, September.
  2. Giulio Bottazzi & Angelo Secchi, 2005. "Explaining the Distribution of Firms Growth Rates," LEM Papers Series, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy 2005/16, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  3. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 114(3), pages 739-767, August.
  4. Palestrini, Antonio, 2007. "Analysis of industrial dynamics: A note on the relationship between firms' size and growth rate," Economics Letters, Elsevier, Elsevier, vol. 94(3), pages 367-371, March.
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