State reduction and second-order perturbations of heterogeneous agent models - Michael Reiter (Institut für Höhere Studien - Institute for Advanced Studies (IHS), 2023)
This paper develops a method to compute second-order perturbations of discretetime heterogeneous agent models. It addresses the three main tasks to make secondorder approximations tractable: state reduction, generating sufficient smoothness, and fast computation of the quadratic terms in the perturbation solution. The method is applied to a model with divisible labor, one with indivisible labor, and to an OLG model with stochastic aging. Compared to a linearized solution, second-order perturbations achieve substantially higher accuracy if models are subject to large or medium-sized aggregate shocks. They also capture precautionary behavior with respect to aggregate shocks. A general method of state reduction is developed, called "conditional-expectations approach". In the example models, it performs better in terms of accuracy and reliability than alternative approaches.
Keywords: C63; C68; E21; 330; heterogeneous agents; model reduction; perturbation methods