The complex behavior of firms’ size dynamics

This paper’s aim is to shed some light to the complex dynamics of firms’ size distribution (FSD). In particular we give an alternative explanation to the Cabral and Mata (2003) finding. In that paper they show that the distribution of surviving firms tends to the log-normal distribution. As an explanation they consider the “small-firms selection” argument and introduce the “financial constraint” model. We give an alternative explanation based on a “sample selection bias” argumentation. In other terms, a cohort of surviving firms may have a positive average rate of growth. This simple fact breaks the assumptions needed in order to have an asymptotic Pareto FSD. Furthermore, we show how a simple modification of a well-known multiplicative process of firms’ growth, taking into account common and idiosyncratic elements, may reconcile an old aggregate-sector puzzle (Quandt, 1966) on firms’ size distribution reported in the literature. The paper shows the possibility to have aggregate Pareto distributed FSD and non-Pareto distributed sectors.