This was part of Aggregate Dynamics in Models with Heterogeneous Agents

Existence and Uniqueness of Recursive Equilibria with Aggregate and Idiosyncratic Risk

Elisabeth Proehl, University of Amsterdam
Thursday, October 28, 2021

Abstract: In this work, I study the existence and uniqueness of recursive equilibria in economies with aggregate and idiosyncratic risk. Rather than relying on compactness to establish existence, I exploit the monotonicity property of the equilibrium model and rely on arguments from convex analysis. This methodology does not only give rise to a convergent iterative procedure, but more strikingly, it also yields uniqueness. To illustrate my theoretical results, I establish sufficient conditions for the existence and uniqueness of solutions to the stochastic growth model as in Krusell and Smith (1998) and the heterogeneous-agent exchange economy as in Huggett 1993 with aggregate risk.