Share density‐based clustering of income data

Abstract

The Lorenz curve is a fundamental tool for analyzing income and wealth distribution and inequality. Indeed, the Lorenz curve and its derivative, the so‐called share density, provide valuable information regarding inequality. There is a widely recognized connection between the Lorenz curve and elements from information theory field. Starting from this evidence, the aim of this work is to compare the income inequality of different subgroups, by using a proper dissimilarity measure, borrowed from information theory, between parametric share densities. This measure is then considered for clustering purposes. To this end, a dynamic clustering algorithm is considered to group unconventional data, such as density functions. Finally, an application, regarding data from Survey on Households Income and Wealth (SHIW) by Bank of Italy, is shown.