A Fokker-Planck Model for Wealth Inequality Dynamics (Vol. 48, No. 5-6)
The growing wealth inequality in most western countries during the past several decades led to an increased interest in the nature of wealth inequality dynamics – particularly, what has driven wealth inequality upwards? Statistical mechanics can be used for addressing this question. We present a simple stochastic model for wealth and income and derive from it a Fokker-Planck equation – a standard tool in non-equilibrium statistical mechanics for studying the evolution of a distribution. Using this equation we are able to calculate the joint wealth-income distribution and its dynamics. Our analysis supports empirical findings on the dynamics of wealth inequality. We find that wealth inequality inevitably tends to increase in the long run. However, even if inequality eventually goes up, we find a criterion for its possible short run decrease. This criterion is most likely to be fulfilled if the correlation between wealth and income is very low. The conditions for such a decrease are found to be met at several points during the 20th century, coinciding indeed with an observed decrease in wealth inequality.
Y. Berman, Y. Shapira and M. Schwartz, A Fokker-Planck model for wealth inequality dynamics, EPL 118, 38004 (2017)