Zipf's law in the distribution of Brazilian firm size

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.