Existence and Uniqueness of Recursive Equilibria With Aggregate and Idiosyncratic Risk
59 Pages Posted: 10 Oct 2018 Last revised: 19 Sep 2023
Date Written: September 19, 2023
Abstract
In this paper, 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.
Keywords: Existence, Uniqueness, Dynamic stochastic general equilibrium, Incomplete markets, Heterogeneous agents, Aggregate uncertainty, Convergence
JEL Classification: C61, C62, D51, D52, E21
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