The Size Variance Relationship of Business Firm Growth Rates
AbstractThe 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 InfoPaper provided by Department of Computer and Management Sciences, University of Trento, Italy in its series DISA Working Papers with number 0901.
Length: 27 pages
Date of creation: Jun 2009
Date of revision: 11 Jun 2009
Postal: DISA Università degli Studi di Trento via Inama, 5 I-38122 Trento TN Italy
Other versions of this item:
- Massimo Riccaboni & Fabio Pammolli & Sergey V. Buldyrev & Linda Ponta & H. Eugene Stanley, 2009. "The Size Variance Relationship of Business Firm Growth Rates," ROCK Working Papers 052, Department of Computer and Management Sciences, University of Trento, Italy, revised 11 Jun 2009.
- Massimo Riccaboni & Fabio Pammolli & Sergey V. Buldyrev & Linda Ponta & H. Eugene Stanley, 2009. "The Size Variance Relationship of Business Firm Growth Rates," Papers 0904.1404, arXiv.org, revised Apr 2009.
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- Massimo Riccaboni & Stefano Schiavo, 2010.
"The Structure and Growth of International Trade,"
DEGIT Conference Papers
c015_032, DEGIT, Dynamics, Economic Growth, and International Trade.
- Massimo Riccaboni & Stefano Schiavo, 2010. "The Structure and Growth of International Trade," Department of Economics Working Papers 1005, Department of Economics, University of Trento, Italia.
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- 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.
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