Zipf's law in the distribution of Brazilian firm size

TL;DR

This paper evaluates how well Zipf's law describes the distribution of firm sizes in Brazil, using extensive data from 1996 to 2020, and compares it with alternative models like the lognormal distribution.

Contribution

It provides empirical evidence that Zipf's law closely fits Brazilian firm size data over multiple years and sectors, with comparisons to other distributions.

Findings

Zipf's law approximates firm size distribution well across years and sectors

Lognormal distribution also fits data and sometimes outperforms Zipf's law

The fit remains consistent over a 24-year period

Abstract

Zipf's law states that the probability of a variable being larger than $s$ is roughly inversely proportional to $s$. In this paper, we evaluate Zipf's law for the distribution of firm size by the number of employees in Brazil. We use publicly available binned annual data from the Central Register of Enterprises (CEMPRE), which is held by the Brazilian Institute of Geography and Statistics (IBGE) and covers all formal organizations. Remarkably, we find that Zipf's law provides a very good, although not perfect, approximation to data for each year between 1996 and 2020 at the economy-wide level and also for agriculture, industry, and services alone. However, a lognormal distribution also performs well and even outperforms Zipf's law in certain cases.