The Emergence of Different Tail Exponents in the Distributions of Firm Size Variables
AbstractWe discuss a mechanism through which inversion symmetry (i.e., invariance of a joint probability density function under the exchange of variables) and Gibrat’s law generate power-law distributions with different tail exponents. Using a dataset of firm size variables, that is, tangible fixed assets K, the number of workers L, and sales Y , we confirm that these variables have power-law tails with different exponents, and that inversion symmetry and Gibrat’s law hold. Based on these findings, we argue that there exists a plane in the three dimensional space (log K, log L, log Y ), with respect to which the joint probability density function for the three variables is invariant under the exchange of variables. We provide empirical evidence suggesting that this plane fits the data well, and argue that the plane can be interpreted as the Cobb-Douglas production function, which has been extensively used in various areas of economics since it was first introduced almost a century ago.
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Bibliographic InfoPaper provided by University of Tokyo, Graduate School of Economics in its series UTokyo Price Project Working Paper Series with number 003.
Length: 21 pages
Date of creation: Oct 2012
Date of revision: Dec 2012
Contact details of provider:
Postal: University of Tokyo 702 Faculty of Economics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan
Web page: http://www.e.u-tokyo.ac.jp/
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econophysics; power law; Gibrat’s law; inversion symmetry;
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- Fujiwara, Yoshi & Di Guilmi, Corrado & Aoyama, Hideaki & Gallegati, Mauro & Souma, Wataru, 2004.
"Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 335(1), pages 197-216.
- Yoshi Fujiwara & Corrado Di Guilmi & Hideaki Aoyama & Mauro Gallegati & Wataru Souma, 2003. "Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms," Papers cond-mat/0310061, arXiv.org, revised Nov 2003.
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