Do firms share the same functional form of their growth rate distribution? A statistical test

We propose a hypothesis testing procedure to investigate whether the same growth rate distribution is shared by all the firms in a balanced panel or, more generally, whether they share the same functional form for this distribution, without necessarily sharing the same parameters. We apply the test to panels of US and European Union publicly quoted manufacturing firms, both at the sectoral and at the subsectoral NAICS level. We consider the following null hypotheses about the growth rate distribution of the individual firms: (i) an unknown shape common to all firms, with all the firms sharing also the same parameters, or with the firm variance related to its firm size through a scaling relationship, and (ii) several functional shapes described by the Subbotin family of distributions. Our empirical results indicate that firms do not have a common shape of the growth rate distribution at the sectorial NAICS level, whereas firms may typically be described by the same shape of the distribution at the subsectorial level, even if the specific shape may not be the same for different subsectors.