Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms

TL;DR

This paper empirically tests the validity of Pareto-Zipf and Gibrat's laws for European firms, confirming their applicability in the large-size region and exploring the relationship with detailed balance and growth rate distributions.

Contribution

It provides empirical evidence supporting Pareto-Zipf and Gibrat's laws for large firms and establishes their theoretical relationships with detailed balance and growth rate distributions.

Findings

Upper-tail of firm size follows a power-law (Pareto-Zipf law)

Growth rate is independent of firm size (Gibrat's law) in the large-size region

Detailed balance holds for large firms during the studied periods

Abstract

By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find that detailed balance holds in the large-size region for periods we investigated; the empirical probability for a firm to change its size from a value to another is statistically the same as that for its reverse process. We prove several relationships among Pareto-Zipf's law, Gibrat's law and the condition of detailed balance. As a consequence, we show that the distribution of growth rate possesses a non-trivial relation between the positive side of the distribution and the negative side, through the value of Pareto index, as is confirmed empirically.