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We explore the role of non-ergodicity in the relationship between incomeinequality, the extent of concentration in the income distribution, andmobility, the feasibility of an individual to change their position in theincome distribution. For this purpose, we explore the properties of anestablished model for income growth that includes "resetting" as a stabilisingforce which ensures stationary dynamics. We find that the dynamics ofinequality is regime-dependent and may range from a strictly non-ergodic statewhere this phenomenon has an increasing trend, up to a stable regime whereinequality is steady and the system efficiently mimics ergodic behaviour.Mobility measures, conversely, are always stable over time, but the stationaryvalue is dependent on the regime, suggesting that economies become less mobilein non-ergodic regimes. By fitting the model to empirical data for the dynamicsof income share of the top earners in the United States, we provide evidencethat the income dynamics in this country is consistently in a regime in whichnon-ergodicity characterises inequality and immobility dynamics. Our resultscan serve as a simple rationale for the observed real world income dynamics andas such aid in addressing non-ergodicity in various empirical settings acrossthe globe.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

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