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 incomplete markets is likely to be subject to multiple self-fulfilling equilibria. In a benchmark economy, the parameters representing the equilibrium aggregate 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, differing only in the magnitude of the perturbations, I do not find evidence of multiple self-fulfilling 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 determination of the change in the aggregate savings, inducing stability in the algorithm as a by-product.