Equilibrium Multiplicity in Aiyagari and Krusell-Smith

Repeatedly solving the Aiyagari (1994) model with random parameters, we construct hundreds of examples with multiple stationary equilibria. We never find multiplicity with risk aversion less than ≈ 1.49, depreciation less than ≈ 0.19, or income persistence less than ≈ 0.47, and multiplicity requires a disaster state for income. In cases with multiplicity, the lowest rental rate occurs near depreciation times the capital share. It is possible for the economy, without a change in fundamentals, to transition rationally from a higher-rate equilibrium to one with a lower rental rate, lower inequality, and lower welfare (for most agents). We also construct the first Krusell and Smith (1998) examples with multiple recursive competitive equilibria.