Pseudospectral methods for continuous-time heterogeneous-agent models

Abstract

We propose a pseudospectral method to solve heterogeneous-agent models in continuous time. The solution is approximated as a sum of smooth global basis functions, in our case polynomials represented by their values at Chebyshev nodes. We illustrate the method by applying it to a Krusell-Smith model. It solves the differential equations characterizing the steady-state efficiently and precisely, despite using only very few nodes. System dynamics are then automatically differentiated to simulate a linearized model. The full solution takes a third of a second and only uses standard software. A benchmark against finite differences shows that pseudospectral methods achieve far greater precision for a given number of nodes and for a given runtime. We conclude by discussing the methods' applicability, which is promising for smooth multi-dimensional models.