Firm dynamics in a closed, conserved economy: A model of size distribution of employment and related statistics
We address the issue of the distribution of firm size. To this end we propose a model of firms in a closed, conserved economy populated with zero-intelligence agents who continuously move from one firm to another. We then analyze the size distribution and related statistics obtained from the model. Our ultimate goal is to reproduce the well known statistical features obtained from the panel study of the firms i.e., the power law in size (in terms of income and/or employment), the Laplace distribution in the growth rates and the slowly declining standard deviation of the growth rates conditional on the firm size. First, we show that the model generalizes the usual kinetic exchange models with binary interaction to interactions between an arbitrary number of agents. When the number of interacting agents is in the order of the system itself, it is possible to decouple the model. We provide some exact results on the distributions. Our model easily reproduces the power law. The fluctuations in the growth rate falls with increasing size following a power law (with an exponent 1 whereas the data suggests that the exponent is around 1/6). However, the distribution of the difference of the firm-size in this model has Laplace distribution whereas the real data suggests that the difference of the log sizes has the same distribution.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- L. A. N. Amaral & S. V. Buldyrev & S. Havlin & H. Leschhorn & P. Maass & M. A. Salinger & H. E. Stanley & M. H. R. Stanley, 1997. "Scaling behavior in economics: I. Empirical results for company growth," Papers cond-mat/9702082, arXiv.org.
- Arnab Chatterjee & Bikas K. Chakrabarti, 2007. "Kinetic Exchange Models for Income and Wealth Distributions," Papers 0709.1543, arXiv.org, revised Nov 2007.
- Kordecki, Wojciech, 1997. "Reliability bounds for multistage structures with independent components," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 43-51, May.
- Aoyama, Hideaki & Fujiwara, Yoshi & Souma, Wataru, 2004. "Kinematics and dynamics of Pareto–Zipf's law and Gibrat's law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 117-121.
- S. V. Buldyrev & L. A. N. Amaral & S. Havlin & H. Leschhorn & P. Maass & M. A. Salinger & H. E. Stanley & M. H. R. Stanley, 1997. "Scaling behavior in economics: II. Modeling of company growth," Papers cond-mat/9702085, arXiv.org.
- Repetowicz, Przemysław & Hutzler, Stefan & Richmond, Peter, 2005. "Dynamics of money and income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 641-654.
- Marco Patriarca & Anirban Chakraborti & Kimmo Kaski & Guido Germano, 2005. "Kinetic theory models for the distribution of wealth: power law from overlap of exponentials," Papers physics/0504153, arXiv.org, revised May 2005.
- P. K. Mohanty, 2006. "Generic features of the wealth distribution in ideal-gas-like markets," Papers physics/0603141, arXiv.org, revised Jul 2006.
- Dunne, T. & Roberts, M.J. & Samuelson, L., 1988.
"The Growth And Failure Of U.S. Manufacturing Plants,"
1-87-5, Pennsylvania State - Department of Economics.
- Timothy Dunne & Mark J. Roberts & Larry Samuelson, 1989. "The Growth and Failure of U. S. Manufacturing Plants," The Quarterly Journal of Economics, Oxford University Press, vol. 104(4), pages 671-698.
- Singh, Ajit & Whittington, Geoffrey, 1975.
"The Size and Growth of Firms,"
51715, University Library of Munich, Germany.
- Alex Coad, 2006. "A Closer Look at Serial Growth Rate Correlation," LEM Papers Series 2006/29, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
- Steven J. Davis & John Haltiwanger, 1992.
"Gross Job Creation, Gross Job Destruction, and Employment Reallocation,"
The Quarterly Journal of Economics,
Oxford University Press, vol. 107(3), pages 819-863.
- Steve J. Davis & John Haltiwanger, 1991. "Gross Job Creation, Gross Job Destruction and Employment Reallocation," NBER Working Papers 3728, National Bureau of Economic Research, Inc.
- Steve J. Davis & John Haltiwanger, 1991. "Gross job creation, gross job destruction and employment reallocation," Working Paper Series, Macroeconomic Issues 91-5, Federal Reserve Bank of Chicago.
- Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
- Jovanovic, Boyan, 1979.
"Job Matching and the Theory of Turnover,"
Journal of Political Economy,
University of Chicago Press, vol. 87(5), pages 972-990, October.
- Alex Coad, 2007. "A Closer Look at Serial Growth Rate Correlation," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 31(1), pages 69-82, August.
- Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2009. "Microeconomics of the ideal gas like market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4151-4158.
- A. Chatterjee & B. K. Chakrabarti, 2007. "Kinetic exchange models for income and wealth distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(2), pages 135-149, November.
- Ishikawa, Atushi, 2005. "Pareto law and Pareto index in the income distribution of Japanese companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 597-608.
- Stanley, Michael H. R. & Buldyrev, Sergey V. & Havlin, Shlomo & Mantegna, Rosario N. & Salinger, Michael A. & Eugene Stanley, H., 1995. "Zipf plots and the size distribution of firms," Economics Letters, Elsevier, vol. 49(4), pages 453-457, October.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1112.2168. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.