具有随机重置的几何布朗运动中的收入不平等和流动性：理论结果和非遍历性的经验证据
Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity
摘要：
我们探讨了非遍历性在收入不平等（收入分配集中程度）与流动性（个人改变收入分配地位的可行性）之间的关系中的作用。为此，我们探讨了一个既定的收入增长模型，其中包括“重置”作为一个稳定的力量，确保静态动态的属性。我们发现，不平等的动态是政权依赖的，范围可以从一个严格的非遍历状态，这种现象有一个增加的趋势，到一个稳定的制度，不平等是稳定的，系统有效地模仿遍历行为。相反，流动性的措施，总是稳定的，随着时间的推移，但固定值是依赖于制度，这表明，经济变得不那么流动，在非遍历制度。通过拟合模型的经验数据，在美国的高收入者的收入份额的动态，我们提供的证据表明，在这个国家的收入动态是一贯的制度，其中非遍历性的特点不平等和不流动的动态。我们的研究结果可以作为一个简单的理由，观察到的现实世界的收入动态，并在解决非遍历性在全球各地的各种经验设置这样的援助。
英文摘要：
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.
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