Where Gibrat meets Zipf: Scale and scope of French firms

The proper characterization of the size distribution and growth of firms represents an important issue in economics and business. We use the Maximum Entropy approach to assess the plausibility of the assumption that firm size follows Lognormal or Pareto distributions, which underlies most recent works on the subject. A comprehensive dataset covering the universe of French firms allows us to draw two major conclusions. First, the Pareto hypothesis for the whole distribution should be rejected. Second, by discriminating across firms based on the number of products sold and markets served, we find that, within the class of multi-product companies active in multiple markets, the distribution converges to a Zipf's law. Conversely, Lognormal distribution is a good benchmark for small single-product firms. The size distribution of firms largely depends on firms' diversification patterns.