  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.
