Economic inequality and mobility in kinetic models for social sciences

TL;DR

This paper investigates the relationship between economic inequality and mobility using kinetic models, confirming a negative correlation through analytical and numerical analysis, which aligns with empirical observations.

Contribution

It extends previous kinetic models by analyzing how parameters affect both inequality and mobility, providing a theoretical explanation for their negative correlation.

Findings

Negative correlation between inequality and mobility confirmed

Parameters like taxation and savings influence both inequality and mobility

Numerical solutions support the theoretical analysis

Abstract

Statistical evaluations of the economic mobility of a society are more difficult than measurements of the income distribution, because they require to follow the evolution of the individuals' income for at least one or two generations. In micro-to-macro theoretical models of economic exchanges based on kinetic equations, the income distribution depends only on the asymptotic equilibrium solutions, while mobility estimates also involve the detailed structure of the transition probabilities of the model, and are thus an important tool for assessing its validity. Empirical data show a remarkably general negative correlation between economic inequality and mobility, whose explanation is still unclear. It is therefore particularly interesting to study this correlation in analytical models. In previous work we investigated the behavior of the Gini inequality index in kinetic models in dependence on several parameters which define the binary interactions and the taxation and redistribution processes: saving propensity, taxation rates gap, tax evasion rate, welfare means-testing etc. Here, we check the correlation of mobility with inequality by analyzing the mobility dependence from the same parameters. According to several numerical solutions, the correlation is confirmed to be negative.