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
R&R Quantitative Economics
(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 available upon request)
We develop a method to compute global solutions to continuous-time heterogeneous agent (HACT) models with aggregate risk, non-stationarity, and financial constraints. When the cross-sectional distribution evolves stochastically, the associated master equation describing equilibrium becomes second order. First, we provide a heuristic derivation of this second-order master equation and show how its distributional derivatives can be approximated using a polynomial chaos expansion, thereby transforming it into a standard, albeit high-dimensional, partial differential equation (PDE). Second, building on the Deep BSDE approach for high-dimensional PDEs, we develop a general-equilibrium extension — GE-Deep BSDE — that jointly solves for value functions, equilibrium prices, and distributional consistency using multi-objective deep learning. Applying the method to a two-asset model, we show that while total factor productivity shocks fail to generate sufficient risk premia, stochastic capital depreciation with collateral constraints produces endogenous risk and helps reconcile microeconomic wealth dispersion with macro-finance evidence.
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