Optimal Income Crossover for Two-Class Model Using Particle Swarm Optimization

TL;DR

This paper introduces an optimization-based method to accurately determine the income crossover point between two distribution classes in income data, providing insights into inequality dynamics, applied to Brazilian data stratified by demographic groups.

Contribution

It presents the first optimization approach to identify a continuous two-class income distribution and its parameters, linking inequality measures to distribution characteristics.

Findings

The method successfully identified income crossover points in Brazilian data.

The model revealed temporal dynamics between Pareto index and high-income population percentage.

Analysis showed differences in income distribution parameters across demographic groups.

Abstract

Personal income distribution may exhibit a two-class structure, such that the lower income class of the population (85-98%) is described by exponential Boltzmann-Gibbs distribution, whereas the upper income class (15-2%) has a Pareto power-law distribution. We propose a method, based on a theoretical and numerical optimization scheme, which allows us to determine the crossover income between the distributions, the temperature of the Boltzmann-Gibbs distribution and the Pareto index. Using this method, the Brazilian income distribution data provided by the National Household Sample Survey was studied. The data was stratified into two dichotomies (sex/gender and color/race), so the model was tested using different subsets along with accessing the economic differences between these groups. Lastly, we analyse the temporal evolution of the parameters of our model and the Gini coefficient discussing the implication on the Brazilian income inequality. To our knowledge, for the first time an optimization method is proposed in order to find a continuous two-class income distribution, which is able to delimit the boundaries of the two distributions. It also gives a measure of inequality which is a function that depends only on the Pareto index and the percentage of people in the high income region. It was found a temporal dynamics relation, that may be general, between the Pareto and the percentage of people described by the Pareto tail.