  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.

General Economics;Economics