Scaling behavior in economics: II. Modeling of company growth

TL;DR

This paper models company growth using scaling laws, proposing hierarchical and optimal size models that align with empirical data on growth rate distributions of US manufacturing firms.

Contribution

It introduces hierarchical and optimal size models to explain the scaling behavior of company growth rates, linking model parameters to empirical scaling exponents.

Findings

Growth rate distribution follows an exponential form.

Hierarchical model relates parameters to the scaling exponent β.

Models are consistent with empirical growth rate data.

Abstract

In the preceding paper we presented empirical results describing the growth of publicly-traded United States manufacturing firms within the years 1974--1993. Our results suggest that the data can be described by a scaling approach. Here, 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 the growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate the two parameters of the model to the exponent $\beta$, which describes the dependence of the standard deviation of the distribution of growth rates on size. We find that $\beta = -\ln \Pi / \ln z$, where $z$ defines the mean branching ratio of the hierarchical tree and $\Pi$ is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically.