Approximating Equilibria with Ex-Post Heterogeneity and Aggregate Risk

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 have assumed bounded rationality in terms of a parametric law of motion of aggregate variables in order to reduce dimensionality. In this paper, we remove that assumption and compute a fully rational equilibrium dependent on the whole cross-sectional distribution. Dimensionality is tackled by polynomial chaos expansions, a projection technique for square-integrable random variables, resulting in a nonparametric law of motion. We establish conditions under which our method converges and approximation error bounds. Economically, we find that the bounded rationality assumption leads to significantly more inequality than in a fully rational equilibrium. Furthermore, more risk sharing in form of redistribution can lead to higher systemic risk.