Scaling behavior in economics: The problem of quantifying company growth
Inspired by work of both Widom and Mandelbrot, we analyze the Computstat database comprising all publicly traded United States manufacturing companies in the years 1974–1993. We find that the distribution of company size remains stable for the 20 years we study, i.e., the mean value and standard deviation remain approximately constant. We study the distribution of sizes of the “new” companies in each year and find it to be well approximated by a log- normal. We find (i) the distribution of the logarithm of the growth rates, for a fixed growth period of T years, and for companies with approximately the same size S displays an exponential “tent-shaped” form rather than the bell-shaped Gaussian, one would expect for a log-normal distribution, and (ii) the fluctuations in the growth rates — measured by the width of this distribution σT — decrease with company size and increase with time T. We find that for annual growth rates (T = 1), σT ∼ S−β, and that the exponent β takes the same value, within the error bars, for several measures of the size of a company. In particular, we obtain β = 0.20 ± 0.03 for sales, β = 0.18 ± 0.03 for number of employees, β = 0.18±0.03 for assets, β = 0.18 ± 0.03 for cost of goods sold, and β = 0.20 ± 0.03 for propert, plant, and equipment. We propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an “optimal” size. That model leads to an exponential distribution of the logarithm of growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate β to parameters of a company structure. We find that β = −1n Π/1nz, where z defines the mean branching ratio of the hierarchical tree and Π is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the output distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically. We also discuss the time dependence of the shape of the distribution of the growth rates.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 244 (1997)
Issue (Month): 1 ()
|Contact details of provider:|| Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/|
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.:
- P. Bak & M. Paczuski & M. Shubik, 1996.
"Price Variations in a Stock Market with Many Agents,"
96-09-075, Santa Fe Institute.
- Bak, P. & Paczuski, M. & Shubik, M., 1997. "Price variations in a stock market with many agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 430-453.
- P. Bak & M. Paczuski & Martin Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Cowles Foundation Discussion Papers 1132, Cowles Foundation for Research in Economics, Yale University.
- Liu, Yanhui & Cizeau, Pierre & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Correlations in economic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 437-440.
- Yanhui Liu & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1997. "Correlations in Economic Time Series," Papers cond-mat/9706021, arXiv.org.
- Galluccio, S. & Caldarelli, G. & Marsili, M. & Zhang, Y.-C., 1997. "Scaling in currency exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 423-436.
When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:244:y:1997:i:1:p:1-24. 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: (Zhang, Lei)
If references are entirely missing, you can add them using this form.