Economic inequality and mobility for stochastic models with multiplicative noise

TL;DR

This paper introduces a stochastic economic model with multiplicative noise that self-consistently conserves population and wealth, analyzing how mobility and total income influence income inequality measured by the Gini index.

Contribution

The paper develops a self-consistent stochastic model with multiplicative noise, extending beyond Langevin-type equations, to analyze income inequality and mobility correlations.

Findings

Multiplicative noise significantly impacts income inequality.

Correlations between mobility, total income, and inequality are characterized.

The model highlights the importance of multiplicative noise in economic inequality analysis.

Abstract

In this article, we discuss a dynamical stochastic model that represents the time evolution of income distribution of a population, where the dynamics develop from an interplay of multiple economic exchanges in the presence of multiplicative noise. The model remit stretches beyond the conventional framework of a Langevin-type kinetic equation in that our model dynamics is self-consistently constrained by dynamical conservation laws emerging from population and wealth conservation. This model is numerically solved and analyzed to interpret the inequality of income as a function of relevant dynamical parameters like the {\it mobility} $M$ and the {\it total income} $\mu$. In our model, inequality is quantified by the {\it Gini index} $G$. In particular, correlations between any two of the mobility index $M$ and/or the total income $\mu$ with the Gini index $G$ are investigated and compared with the analogous correlations resulting from an equivalent additive noise model. Our findings highlight the importance of a multiplicative noise based economic modeling structure in the analysis of inequality. The model also depicts the nature of correlation between mobility and total income of a population from the perspective of inequality measure.