Firm Size Distribution and Power Laws in Brazil: Some Empirical Evidence by Marcelo Resende, Vicente Cardoso published by IE/UFRJ (2022).
The paper investigates the prevalence of power laws for firm size distribution in Brazil during the 1999-2019 period, taking as reference the 1000, 500 and 100 largest firms considered in terms of net revenue shares. In contrast with the previous related literature, one does not assume the initial validity of a simpler power law pattern associated with a Pareto type I or yet with the stricter case of the Zipf law. In fact, the simpler models are nested within either a more general model concerning a Pareto type II or a Pareto type IV model. The evidence, based on the testing of restricted models under a maximum likelihood setting, only suggests a stronger support for power law patterns for the case of the extreme upper tail of the distributions when the 100 largest firms are assessed relatively to a Pareto type II model. Even so, the patterns are not completely uniform and prevail for at most 86% of the studied years for Pareto type I embedded in a Pareto type II model, whereas the consistency with the stricter case of the Zipf law would be observed for 86%, with mostly coinciding years, of the investigated time period. However, the consideration of model nested within a more general alternative Pareto type IV model indicates favorable evidence only in 29% of the investigated years. Thus, one cannot disregard the possibility that more complex models that are not necessarily driven by a single shape parameter in terms of a power law may characterize firm size distribution in Brazil.
