The Italian primary school-size distribution and the city-size: a complex nexus

We characterize the statistical law according to which Italian primary school-size distributes. We find that the school-size can be approximated by a log-normal distribution, with a fat lower tail that collects a large number of very small schools. The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF. These distributions are similar to those observed for firms and are consistent with a Bose-Einstein preferential attachment process. The body of the distribution features a bimodal shape suggesting some source of heterogeneity in the school organization that we uncover by an in-depth analysis of the relation between schools-size and city-size. We propose a novel cluster methodology and a new spatial interaction approach among schools which outline the variety of policies implemented in Italy. Different regional policies are also discussed shedding lights on the relation between policy and geographical features.