Scaling behavior in economics: I. Empirical results for company growth

TL;DR

This study analyzes the growth patterns of US manufacturing firms from 1974 to 1993, revealing stable size distributions, log-normal initial sizes, and a power-law scaling of growth rate fluctuations across various firm measures.

Contribution

It provides empirical evidence of stable firm size distributions and identifies a universal power-law scaling of growth rate fluctuations across multiple company metrics.

Findings

Firm size distribution remains stable over 20 years.

Growth rate fluctuations scale as a power law with firm size.

The scaling exponent is approximately 0.2 across different measures.

Abstract

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 $S$ displays an exponential form, and (ii) the fluctuations in the growth rates -- measured by the width of this distribution $\sigma_1$ -- scale as a power law 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: $\beta=0.20\pm0.03$ for sales, $\beta=0.18\pm0.03$ for number of employees, $\beta=0.18\pm0.03$ for assets, $\beta=0.18\pm0.03$ for cost of goods sold, and $\beta=0.20\pm0.03$ for property, plant, & equipment.