A Perturbational Approach for Approximating Heterogeneous-Agent Models
Abstract:
We develop a novel pertur bational technique to approximate a broad class of stochastich eterogeneous -agent (HA) models that is scalable to the second and higher orders of appr oximation and that can be applied to economies that have recursive represen tations with very complex state spaces, such as multi-dimensional endogenou s 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 rec ursive mathematical structure, which allows us to derive exact analytical e xpressions for approximating coefficients as solutions to a small-dimension al linear system of equations. Computationally, to the first order of appro ximation, our method is as fast and precise as existing state-of-the-art te chniques that linearized HA models using so-called “MIT shocks,” but our ap proach is easily scalable to higher orders of approximation. We also show h ow our techniques can be used to obtain quick and efficient approximations to models with stochastic volatility and portfolio problems and study welfa re in HA environments
DTSTAMP:20260407T005158Z DTSTART:20230306T143000Z DTEND:20230306T160000Z SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR