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The Size Variance Relationship of Business Firm Growth Rates

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  • Massimo Riccaboni
  • Fabio Pammolli
  • Sergey V. Buldyrev
  • Linda Ponta
  • H. Eugene Stanley

Abstract

The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior σ(S) similar to S^-β(S) where S is the firm size and β(S) almost equal to 0.2 is an exponent weakly dependent on S. Here we show how a model of proportional growth which treats firms as classes composed of various number of units of variable size, can explain this size-variance dependence. In general, the model predicts that β(S) must exhibit a crossover from β(0) = 0 to β(∞) = 1/2. For a realistic set of parameters, β(S) is approximately constant and can vary in the range from 0.14 to 0.2 depending on the average number of units in the firm. We test the model with a unique industry specific database in which firm sales are given in terms of the sum of the sales of all their products. We find that the model is consistent with the empirically observed size-variance relationship.

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Bibliographic Info

Paper provided by Department of Computer and Management Sciences, University of Trento, Italy in its series DISA Working Papers with number 0901.

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Length: 27 pages
Date of creation: Jun 2009
Date of revision: 11 Jun 2009
Handle: RePEc:trt:disawp:0901

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Cited by:
  1. Massimo Riccaboni & Stefano Schiavo, 2010. "The Structure and Growth of International Trade," DEGIT Conference Papers c015_032, DEGIT, Dynamics, Economic Growth, and International Trade.
  2. Misako Takayasu & Hayafumi Watanabe & Hideki Takayasu, 2013. "Generalised central limit theorems for growth rate distribution of complex systems," Papers 1301.2728, arXiv.org, revised Jan 2014.
  3. Anindya S. Chakrabarti, 2013. "Bimodality in the firm size distributions: a kinetic exchange model approach," Papers 1302.3818, arXiv.org, revised May 2013.
  4. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of Weighted Networks," Papers 0908.0348, arXiv.org, revised Dec 2009.

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