Correlation between Gini index and mobility in a stochastic kinetic model of economic exchange

Abstract

Starting from a class of stochastically driven kinetic models of economic exchange, here we present results highlighting the correlation of the Gini inequality index with the social mobility rate, close to dynamical equilibrium. Except for the “canonical-additive case”, our numerical results consistently indicate negative values of the correlation coefficient, in agreement with empirical evidence. This confirms that growing inequality is not conducive to social mobility which then requires an “external source” to sustain its dynamics. On the other hand, the sign of the correlation between inequality and total income in the canonical ensemble depends on the way wealth enters or leaves the system. At a technical level, the approach involves a generalization of a stochastic dynamical system formulation, that further paves the way for a probabilistic formulation of perturbed economic exchange models. Keywords: Langevin, Gini index, Ornstein-Uhlenbeck, Fokker-Planck, Hurst exponent