Modeling the Origin and Possible Control of the Wealth Inequality Surge

Abstract

The rapid increase of wealth inequality in the past few decades is a most disturbing social and economic issue of our time. In order to control, and even reverse that surge, its origin and underlying mechanisms should be revealed. One of the challenges in studying these mechanisms is to incorporate realistic individual dynamics in the population level in a self-consistent manner. Our theoretical approach meets the challenge by using interacting multi-agent master-equations to model the dynamics of wealth inequality. The model is solved using stochastic multi-agent iterated maps. Taking into account growth rate, return on capital, private savings and economic mobility, we were able to capture the historical dynamics of wealth inequality in the United States during the course of the 20th century. We show that the fraction of capital income in the national income and the fraction of private savings are the critical factors that govern the wealth inequality dynamics. In addition, we found that economic mobility plays a crucial role in wealth accumulation. Notably, we found that the major decrease in private savings since the 1980s could be associated primarily with the recent surge in wealth inequality and if nothing changes in this respect we predict further increase in wealth inequality in the future. However, the 2007–08 financial crisis brought an opportunity to restrain the wealth inequality surge by increasing private savings. If this trend continues, it may lead to prevention, and even reversing, of the ongoing inequality surge.

A Fokker-Planck model for wealth inequality dynamics

“…(25), how the value of σ 1 required for the initial decrease of CV(t) is dependent onβ. These results echo the findings of Piketty [1] and others [3,10,22], showing that when the wealth-saved-income ratio is very high, and particularly when personal savings rates are low, wealth inequality is likely to increase, and vice versa. Since income is more equally distributed than wealth, a high savings rate strongly couples wealth to income, and therefore may lead to a low wealth-income ratio and to the reduction of wealth inequality, as explained in [4].…”

“…This shows that such a simplified case is inadequate for describing the dynamics of the wealth distribution. Furthermore, it demonstrates that income should be considered, which supports its well-known role in the dynamics of wealth inequality [3,10].…”

“…The model differs from previous models of wealth dynamics by the explicit inclusion of stochastic terms and by analyzing the joint income-wealth dynamics, in contrast to the models presented in refs. [3,10,12]. This allows for obtaining closed-form expressions for the wealth distribution moments, hence new analytic results and insights.…”

“…The model substantially differs from previous models of wealth dynamics, in particular refs. [3,10]. In this paper we present a much generalized model with two substantial improvements:…”

“…In previous models, such as those presented in refs. [3,10], income was taken as an external contribution to wealth and the dynamics were deterministic.…”