Statistical regularity of firm size distribution: the Pareto IV and truncated Yule for Italian SCI manufacturing

In this paper we model the firm size distribution (FSD) of Italian manufacturing firms of SCI, the GDP survey of ISTAT, by a continuous and a discrete distribution: the Pareto IV distribution on total assets and the Yule distribution on Number of Employees. The Pareto IV distribution is characterized by four parameters and shows a better fit than both the Lognormal and Pareto 1, which are the distributions more frequently applied to model firm size. The Pareto IV is inconsistent with Gibrat's Law according to which the different segments of an Industry are characterized by proportionate growth and the distribution of size is Lognormal. A truncation of the Yule distribution has been necessary because the dataset is characterized by firms with at least 20 employees. The truncated Yule distribution shows a good fit for medium-large firms (firms with more than 50 employees). The partition of the dataset in innovative and non-innovative firms - both of which are well described by the Pareto IV - reveals a beneficial effect of scale on innovation. Finally, the good fit of both distributions holds not only for the composite industry, but for the single sectors too.