BEWLEY–HUGGETT–AIYAGARI MODELS: COMPUTATION, SIMULATION, AND UNIQUENESS OF GENERAL EQUILIBRIUM

Abstract

This paper provides conditions under which an algorithm for the computation and simulation of Bewley–Huggett–Aiyagari models, based on state-space discretization, will converge to all true solutions. These conditions are shown to be satisfied in two standard examples: the Aiyagari model and its extension to endogenous labor. Bewley–Huggett– Aiyagari models are general equilibrium models with incomplete markets and idiosyncratic, but no aggregate, shocks. The algorithm itself is based on discretization, while the theory importantly allows for making simulations using the approximate computational solution of the value function problem rather than the true model solution. The numerical results of applying the algorithm to both models are provided and investigated in terms of replication, revealing that the Aiyagari model overestimates the degree of precautionary savings in the high-risk-and-high-risk-aversion case. The results also show that both models almost certainly have a unique general equilibrium. Theoretically, the existence of equilibria was known, but uniqueness remained an open question.