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

TL;DR

This paper analyzes the distribution of Italian primary school sizes, revealing a log-normal pattern with heterogeneity influenced by regional policies and city sizes, using novel clustering and spatial interaction methods.

Contribution

It introduces a new cluster methodology and spatial interaction approach to analyze school size distribution and policy effects in Italy.

Findings

School sizes follow a log-normal distribution with a fat lower tail.

Upper tail of school size decreases exponentially.

Regional policies influence school size and distribution patterns.

Abstract

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.