The fate of the American dream: A first passage under resetting approach to income dynamics

TL;DR

This paper introduces a novel framework using First Passage Time with resetting to analyze individual income dynamics, providing more detailed insights than traditional transition matrix methods, and applies it to US income data.

Contribution

It develops a new stochastic modeling approach for income dynamics that disaggregates individual income changes and offers a publicly available methodology for empirical analysis.

Findings

Framework improves granularity of income dynamics analysis

Analytical and numerical results demonstrate advantages over traditional methods

Application to US data illustrates practical utility

Abstract

Detailed knowledge of individual income dynamics is crucial for investigating the existence of the American dream: 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 empirical applications of the framework, we introduce a publicly available 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 provide a set of tools for designing policy interventions.