Approximating Equilibria with Ex-Post Heterogeneity and Aggregate Risk
45 Pages Posted: 21 Jun 2015 Last revised: 13 Feb 2019
Date Written: February 12, 2019
Dynamic stochastic general equilibrium models with ex-post heterogeneity due to idiosyncratic risk have to be solved numerically. This is a nontrivial task as the cross-sectional distribution of endogenous variables becomes an element of the state space due to aggregate risk. Existing global solution methods often assume bounded rationality in terms of a parametric law of motion of aggregate variables in order to reduce dimensionality. I do not make this assumption and tackle dimensionality by polynomial chaos expansions, a projection technique for square-integrable random variables. This approach results in a nonparametric law of motion of aggregate variables. Moreover, I establish convergence of the proposed algorithm to the rational expectations equilibrium. Economically, I find that higher levels of idiosyncratic risk sharing lead to higher systemic risk, i.e., higher volatility within the ergodic state distribution, and second, heterogeneity leads to an amplification of aggregate risk for sufficiently high levels of risk sharing.
Keywords: Dynamic stochastic general equilibrium, Incomplete markets, Heterogeneous agents, Aggregate uncertainty, Convergence, Numerical solutions, Polynomial chaos
JEL Classification: C62, C63, D31, D52, E21
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