Recursive equilibrium in Krusell and Smith (1998)

Abstract

This paper uses the tools developed in the literature on dynamically incomplete markets with finite agents to study the large economy with a continuum of agents and both aggregate and idiosyncratic shocks in Krusell and Smith (1998). It establishes the existence of sequential competitive equilibrium, generalized recursive equilibrium, recursive equilibrium with an extended-state space, and characterizes several important properties of the equilibrium variables. The equilibrium process admits an ergodic measure, which enables the application of the ergodic theorem for simulating and calibrating the model. Without aggregate shocks, the existence and some characterization results carry over to economies with only idiosyncratic shocks such as Huggett (1997)'s economy. However, the existence of recursive equilibrium with the natural minimal state space in Krusell and Smith's economy remains elusive, as in finite-agent incomplete markets economies.