Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity

TL;DR

This paper investigates how non-ergodicity influences income inequality and mobility using a stochastic model with resetting, providing theoretical insights and empirical evidence from US income data.

Contribution

It introduces a model incorporating stochastic resetting to analyze non-ergodic income dynamics and empirically demonstrates its relevance to US income inequality and mobility.

Findings

Inequality dynamics are regime-dependent, ranging from increasing to stable.

Mobility measures are stable over time but vary with the regime.

US income data suggests non-ergodic inequality and immobility regimes.

Abstract

We explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and mobility, the feasibility of an individual to change their position in the income distribution. For this purpose, we explore the properties of an established model for income growth that includes "resetting" as a stabilising force which ensures stationary dynamics. We find that the dynamics of inequality is regime-dependent and may range from a strictly non-ergodic state where this phenomenon has an increasing trend, up to a stable regime where inequality is steady and the system efficiently mimics ergodic behaviour. Mobility measures, conversely, are always stable over time, but the stationary value is dependent on the regime, suggesting that economies become less mobile in non-ergodic regimes. By fitting the model to empirical data for the dynamics of income share of the top earners in the United States, we provide evidence that the income dynamics in this country is consistently in a regime in which non-ergodicity characterises inequality and immobility dynamics. Our results can serve as a simple rationale for the observed real world income dynamics and as such aid in addressing non-ergodicity in various empirical settings across the globe.