When a `rat race' implies an intergenerational wealth trap

TL;DR

This paper introduces a model linking intergenerational wealth traps to individual investment behaviors, revealing how high investment levels can lead to persistent wealth disparities across generations.

Contribution

It presents the first 'rat race' theorem, establishing a fundamental link between investment levels and the existence of wealth traps in intergenerational dynamics.

Findings

High investment levels correlate with wealth traps.

A nonlinear, discontinuous competitiveness function influences wealth distribution.

The model provides criteria to infer competitiveness from investment data.

Abstract

Two critical questions about intergenerational outcomes are: one, whether significant barriers or traps exist between different social or economic strata; and two, the extent to which intergenerational outcomes do (or can be used to) affect individual investment and consumption decisions. We develop a model to explicitly relate these two questions, and prove the first such `rat race' theorem, showing that a fundamental relationship exists between high levels of individual investment and the existence of a wealth trap, which traps otherwise identical agents at a lower level of wealth. Our simple model of intergenerational wealth dynamics involves agents which balance current consumption with investment in a single descendant. Investments then determine descendant wealth via a potentially nonlinear and discontinuous competitiveness function about which we do not make concavity assumptions. From this model we demonstrate how to infer such a competitiveness function from investments, along with geometric criteria to determine individual decisions. Additionally we investigate the stability of a wealth distribution, both to local perturbations and to the introduction of new agents with no wealth.