Huggett Economies with Multiple Stationary Equilibria

Abstract

I obtain a closed-form solution to a Huggett economy with constant absolute risk aversion (CARA) utility when the vector of individual state variables follows a VAR(1) process with an arbitrary shock distribution. The stationary equilibrium is unique if the income process is AR(1), but not necessarily so otherwise. With Gaussian shocks, I provide general sufficient conditions for the existence of at least three equilibria when the income process is either ARMA(1,1), AR(2), or has a persistent-transitory (PT) representation with negatively correlated shocks. The possibility of multiple equilibria calls for caution in comparative statics exercises and policy analyses using heterogeneous-agent models. As an illustration I provide an example in which the welfare implication of changing the income risk goes in opposite directions depending on the choice of equilibrium.

Keywords: CARA utility, income fluctuation problem, persistent-transitory representation

JEL Classification: C62, D52, D58, E21