The Krusell-Smith Algorithm: Are Self-fulfilling Equilibria Likely?

I investigate whether the popular Krusell and Smith algorithm used to solve heterogeneous-agent economies with aggregate uncertainty and in- complete markets is likely to be subject to multiple self-fullling equilibria. In a benchmark economy, the parameters representing the equilibrium ag- gregate law of motion are randomly perturbed 500 times, and are used as the new initial guess to compute the equilibrium with this algorithm. In a sequence of cases, diering only in the magnitude of the perturbations, I do not nd evidence of multiple self-fullling equilibria. The economic reason behind the result lies in a self-correcting mechanism present in the algorithm: compared to the equilibrium law of motion, a candidate one implying a higher (lower) expected future capital reduces (increases) the equilibrium interest rates, increasing (reducing) the savings of the wealth- rich agents only. These, on the other hand, account for a small fraction of the population and cannot compensate for the opposite change triggered by the wealth-poor agents, who enjoy higher (lower) future wages and increase (reduce) their current consumption. Quantitatively, the change in behavior of the wealth-rich agents has a negligible impact on the de- termination of the change in the aggregate savings, inducing stability in the algorithm as a by-product.