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 convex analysis. 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 as in Krusell and Smith (1998) and the heterogeneous-agent exchange economy as in Huggett (1993) with aggregate risk.
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 square-integrable 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, creating a benchmark for assessing alternative equilibrium concepts. I validate the method in the Krusell-Smith model and apply it in a more nonlinear setting to study optimal unemployment insurance. The model reveals a central equity-efficiency trade-off: higher UI improves equity across employment states but distorts labor supply and increases inequality among workers. The cyclicality of UI depends critically on the degree of market incompleteness, offering a unifying explanation for previously conflicting results on optimal UI policy over the business cycle.