Zipf's law in the distribution of Brazilian firm size

Thiago Trafane Oliveira SantosCentral Bank of Brazil, Brasília, Brazil. Department of %Economics, University of Brasilia, Brazil, Daniel Oliveira CajueiroDepartment of Economics, University of Brasilia, Brazil. National Institute of Science and Technology for Complex Systems
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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.
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巴西企业规模分布中的齐普夫定律
齐普夫定律指出,变量大于 $s$ 的概率与 $s$ 成反比。在本文中,我们对巴西按雇员人数计算的企业规模分布进行了齐普夫定律评估。我们使用了巴西地理统计局(IBGE)掌握的企业中央登记册(CEMPRE)中公开的年度分档数据,该数据涵盖了所有正规组织。值得注意的是,我们发现齐普夫定律对 1996 年至 2020 年期间每年的数据提供了一个非常好的近似值,尽管这个近似值并不完美,但对整个经济层面以及农业、工业和服务业都是如此。然而,对数正态分布的表现也很好,甚至在某些情况下优于齐普夫定律。
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