Existence of Generalized Recursive Equilibrium in Krusell and Smith (1998)

Abstract

In this paper, I define and show the existence of a generalized recursive equilibrium in Krusell and Smith (1998)’s economy with both aggregate and idiosyncratic shocks. The method to establish existence using finite horizon approximation applies equally well to economies with a finite number of agents or with a continuum of agents. With a continuum of agents, my proof relies on the compactness of the space of probability measures over a bounded interval endowed with weak topology and of the space of Lipschitz continuous value functions and weakly increasing policy functions. These properties enable the use of the Kakutani-Glicksberg-Fan Fixed Point Theorem for infinite dimensional spaces. The existence proof suggests a numerical algorithm to compute a global nonlinear recursive equilibrium. I implement the algorithm and analyze its numerical solutions for two-agent economies.