Working Papers Approximating Equilibria with Ex-Post Heterogeneity and Aggregate Risk (Job market paper) (paper on SSRN, code, revised version 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 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. Work in Progress Existence and Uniqueness of Recursive Equilibria with Aggregate and Idiosyncratic Risk (Working paper coming soon) In this paper, I study the existence and uniqueness of recursive equilibria in production economies with aggregate risk. The economy features a continuum of agents who face idiosyncratic shocks and borrowing constraints. In particular, I establish existence for the Aiyagari-Bewley growth model Krusell and Smith (1998). In contrast to the existing literature, I do not rely on compactness to establish a fixed point. I instead exploit the monotonicity property of the equilibrium model and rely on arguments from convex analysis. Approximating Heterogeneous Agent Equilibria for Models with Trade (Working paper coming soon) The growth model in my paper "Approximating Equilibria with Ex-Post Heterogeneity and Aggregate Risk" has a rather simple equilibrium condition in that aggregate capital, i.e., the capital demand from the firm, has to equal the mean of the cross-sectional distribution, i.e., the capital supply from households. The aggregate variable is hence, explicitly defined. In models with trade, however, prices are implicitly defined through a zero- or unit-net supply condition. Here, I generalize my numerical method using generalized polynomial chaos to approximate the cross-sectional distribution. For any given cross-sectional distribution, one solves the agent’s optimization problem given a set of fixed prices. In a second step, one solves the equilibrium condition to select the appropriate price. Distributional Effects in a Macroeconomic Model with a Financial Sector This study 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. |