Shape of Growth Rate Distribution Determines the Type of Non-Gibrat's Property

TL;DR

This paper investigates how the shape of growth rate distributions influences the type of Non-Gibrat's property in firm size data, revealing distinct behaviors for profits and sales through empirical and analytical methods.

Contribution

It introduces a detailed analysis of growth-rate distribution shapes and their relation to Non-Gibrat's properties, supported by empirical data from Japanese firms.

Findings

Growth-rate distributions of sales have wider tails than profits.

Different Non-Gibrat's properties are observed for profits and sales.

Analytic derivation of distributions from Non-Gibrat's properties and detailed balance.

Abstract

In this study, the authors examine exhaustive business data on Japanese firms, which cover nearly all companies in the mid- and large-scale ranges in terms of firm size, to reach several key findings on profits/sales distribution and business growth trends. First, detailed balance is observed not only in profits data but also in sales data. Furthermore, the growth-rate distribution of sales has wider tails than the linear growth-rate distribution of profits in log-log scale. On the one hand, in the mid-scale range of profits, the probability of positive growth decreases and the probability of negative growth increases symmetrically as the initial value increases. This is called Non-Gibrat's First Property. On the other hand, in the mid-scale range of sales, the probability of positive growth decreases as the initial value increases, while the probability of negative growth hardly changes. This is called Non-Gibrat's Second Property. Under detailed balance, Non-Gibrat's First and Second Properties are analytically derived from the linear and quadratic growth-rate distributions in log-log scale, respectively. In both cases, the log-normal distribution is inferred from Non-Gibrat's Properties and detailed balance. These analytic results are verified by empirical data. Consequently, this clarifies the notion that the difference in shapes between growth-rate distributions of sales and profits is closely related to the difference between the two Non-Gibrat's Properties in the mid-scale range.