Working Papers
Existence and Uniqueness of Recursive Equilibria with Aggregate and Idiosyncratic Risk
R&R Review of Economic Studies
(paper on SSRN, online appendix, slides)
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 monotone operator theory. This methodology does not only give rise to a convergent iterative procedure, but more strikingly, it also yields uniqueness. To illustrate my theoretical results, I establish sufficient conditions for the existence and uniqueness of solutions to the stochastic growth model with heterogeneous agents as in Krusell and Smith (1998). These conditions on the model primitives are relatively weak and accommodate standard calibrations.
Approximating Equilibria with Ex-Post Heterogeneity and Aggregate Risk
(paper on SSRN, online appendix, code and other supplementary material)
This paper develops a novel global solution method for heterogeneous-agent models with idiosyncratic and aggregate risk. Departing from the bounded rationality assumption in the Krusell-Smith algorithm, I use polynomial chaos expansions to directly discretize the cross-sectional distribution. This projection technique for random variables yields a nonparametric law of motion for aggregate variables. My main contribution is the proof of the algorithm’s convergence to the recursive rational expectations equilibrium. I validate the method in the Krusell-Smith model and apply it in a nonlinear setting with an endogenous labor supply choice of the employed that depends on their wealth. The algorithm's high accuracy in nonlinear settings allows the derivation of new insights into optimal unemployment insurance. Higher UI improves equity across employment states but increases inequality among workers and distorts labor supply. The degree of market incompleteness emerges as the major driver behind the trade-off emphasizing the role of the borrowing constraint.
Work in Progress
A Global Solution Method for HACT Models with Aggregate Risk
(joint with Niklas Bonnmann, draft coming soon)
Heterogeneous agent models in continuous time (HACT) have become a workhorse in macroeconomics, but incorporating aggregate risk remains a major computational challenge. Existing methods often rely on local approximations or restrict models to stationary settings, limiting their ability to capture nonlinear macroeconomic dynamics. This paper introduces a novel approach that globally solves non-stationary HACT models with aggregate risk by leveraging the master equation. Our approach transforms this nonstandard partial
differential equation (PDE) into a high-dimensional yet standard PDE using Polynomial Chaos expansions, enabling the application of advanced but offthe-shelf deep learning techniques from the applied mathematics literature. Specifically, we adapt the Deep BSDE method to solve the master equation efficiently. To demonstrate its applicability, we not only solve a two-asset HACT model with aggregate risk featuring adjustment costs and collateral constraints but also its transition along a deterministic policy change.
Health Risk and Asset Pricing
(joint with Esther Eiling and Miguel Palacios)
An OTC Market with Heterogeneous Agents
(joint with Yenan Wang)
A Theoretical Foundation for Optimal Fiscal Policy Design in Heterogeneous Economies