A first passage under resetting approach to income dynamics

Detailed knowledge of individual income dynamics is one essential ingredient for investigating the existence of the American dream, pertinent to the question Are we able to improve our income status during our working life? This key question simply boils down to observing individual status and how it moves between two thresholds: the current income and the desired income. Yet, our knowledge of these temporal properties of income remains limited since we rely on estimates coming from transition matrices which simplify income dynamics by aggregating the individual changes into quantiles and thus overlooking significant microscopic variations. Here, we bridge this gap by employing First Passage Time concepts in a baseline stochastic process with resetting used for modeling income dynamics and developing a framework that is able to crucially disaggregate the temporal properties of income to the level of an individual worker. We find analytically and illustrate numerically that our framework is orthogonal to the transition matrix approach and leads to improved and more granular estimates. Moreover, to facilitate potential empirical applications of the framework, we introduce a statistical methodology, and showcase the application using the USA income dynamics data. These results help to improve our understanding on the temporal properties of income in real economies and could potentially provide a set of tools for designing policy interventions.