Working Paper Discretizing the Infinite-Dimensional Space of Distributions to Approximate Markov Equilibria with Ex-Post Heterogeneity and Aggregate Risk (paper on SSRN, code coming soon) 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 assume bounded rationality in terms of a parametric law of motion of aggregate variables to reduce dimensionality. In this paper, we do not take that assumption and compute a fully rational equilibrium depending 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 existence of the computed recursive equilibrium and theoretical convergence results. Economically, we find that idiosyncratic risk does not aggregate in our fully rational approximate equilibrium, which contrasts the well-known approximate aggregation result for the bounded rational approximate equilibrium by Krusell and Smith (1998). Work in Progress Distributional Effects in a Macroeconomic Model with a Financial Sector This work looks at combining nonlinear amplification effects due to occasionally binding constraints, as proposed by Brunnermeier and Sannikov (2014), with the heterogeneous agent literature focusing on distributional effects as for instance in Kaplan, Moll and Violante (2017). The goal is to evaluate the effects of volatile crises episodes driven by asset illiquidity on the wealth distribution, e.g. what are distributional effects when transitioning in and out of a crisis and what are the mechanisms behind. This study is methodologically challenging as it combines heterogeneity due to idiosyncratic risks with significant aggregate risks. Generic Existence of Recursive Equilibria for Models with Idiosyncratic and Aggregate Risk In my paper "Discretizing the Infinite-Dimensional Space of Distributions to Approximate Markov Equilibria with Ex-Post Heterogeneity and Aggregate Risk", I use a non-standard approach to show existence of simple recursive equilibria for the Aiyagari-Bewly growth model with aggregate risk. Rather than using a fixed point argument based on compactness of the state space, I exploit the monotonicity features of the equilibrium problem. In this work, I explore extensions of this approach to more generic equilibrium models featuring trade, which leads to equilibrium conditions of zero- or unit-net supply and hence, an implicit definition of prices. |