An Impossibility Theorem for Wealth in Heterogeneous-agent Models with Limited Heterogeneity

TL;DR

This paper proves that standard heterogeneous-agent models with certain assumptions cannot generate wealth distributions with heavier tails than income, confirming a long-standing conjecture and highlighting the need for more complex models.

Contribution

It establishes an impossibility theorem showing that under common assumptions, wealth inherits the tail behavior of income, thus explaining why standard models fail to produce heavy-tailed wealth distributions.

Findings

Wealth inherits the tail behavior of income shocks under the model assumptions.

Relaxing any of the key assumptions can produce heavy-tailed wealth distributions.

Standard models are insufficient to explain empirical heavy tails in wealth.

Abstract

It has been conjectured that canonical Bewley--Huggett--Aiyagari heterogeneous-agent models cannot explain the joint distribution of income and wealth. The results stated below verify this conjecture and clarify its implications under very general conditions. We show in particular that if (i) agents are infinitely-lived, (ii) saving is risk-free, and (iii) agents have constant discount factors, then the wealth distribution inherits the tail behavior of income shocks (e.g., light-tailedness or the Pareto exponent). Our restrictions on utility require only that relative risk aversion is bounded, and a large variety of income processes are admitted. Our results show conclusively that it is necessary to go beyond standard models to explain the empirical fact that wealth is heavier-tailed than income. We demonstrate through examples that relaxing any of the above three conditions can generate Pareto tails.