A Perturbational Approach for Approximating Heterogeneous-Agent Models

Abstract:

We develop a novel perturbational technique to approximate a broad class of stochastich eterogeneous-agent (HA) models that is scalable to the second and higher orders of approximation and that can be applied to economies that have recursive representations with very complex state spaces, such as multi-dimensional endogenous distributions. The central insight of our approach is that it is possible to analytically characterize any order of approximation for the stochastic process that governs this state. These characterizations have a linear recursive mathematical structure, which allows us to derive exact analytical expressions for approximating coefficients as solutions to a small-dimensional linear system of equations. Computationally, to the first order of approximation, our method is as fast and precise as existing state-of-the-art techniques that linearized HA models using so-called “MIT shocks,” but our approach is easily scalable to higher orders of approximation. We also show how our techniques can be used to obtain quick and efficient approximations to models with stochastic volatility and portfolio problems and study welfare in HA environments