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 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.
Existence and Uniqueness of Recursive Equilibria with Aggregate and Idiosyncratic Risk
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. In particular, I establish sufficient conditions for 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.
Work in Progress
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.