J. Phys. I France
Volume 7, Numéro 4, April 1997
Page(s) 621 - 633
DOI: 10.1051/jp1:1997180
J. Phys. I France 7 (1997) 621-633

Scaling Behavior in Economics: I. Empirical Results for Company Growth

Luís A. Nunes Amaral1, 2, Sergey V. Buldyrev1, Shlomo Havlin1, 3, Heiko Leschhorn1, Philipp Maass1, Michael A. Salinger4, H. Eugene Stanley1 and Michael H.R. Stanley1

1  Center of Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA
2  Institute für Festkörperforschung, Forschungszentrum Jülich, 52425 Jülich, Germany
3  Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel
4  School of Management, Boston University, Boston, MA 02215, USA

(Received 15 November 1996, accepted 30 December 1996)

We address the question of the growth of firm size. To this end, we analyze the Compustat data base comprising all publicly-traded United States manufacturing firms within the years 1974-1993. We find that the distribution of firm sizes 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 one year, and for companies with approximately the same size S, display an exponential form, and (ii) the fluctuations in the growth rates - measured by the width of this distribution $\sigma_1$ - scale as a power with $S,\ \sigma_1\sim S^{-\beta}$. We find that the exponent $\beta$ takes the same value, within the error bars, for several measures of the size of a company. In particular, we obtain: $\beta = 0.20\pm 0.03$ for sales, $\beta = 0.18\pm 0.03$ for number of employees, $\beta = 0.18\pm 0.03$ for assets, $\beta = 0.18\pm 0.03$ for cost of goods sold, and $\beta = 0.20\pm 0.03$ for property, plant, and equipment.

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