Recursive Equilibrium in Krusell and Smith (1998)

This paper combines the tools developed in two important and independent literatures - one on large economies started with Aumann (1964) and the other on dynamically incomplete markets, notably Duffie et al (1994)- to study Krusell and Smith’s incomplete markets economy with both idiosyncratic and aggregate shocks. 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 the simulation and calibration of 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.