Higher-Order Perturbation Solutions to Dynamic, Discrete-Time Rational Expectations Models

We present an algorithm and software routines for computing nthorder Taylor series approximate solutions to dynamic, discrete-time rational expectations models around a nonstochastic steady state. The primary advantage of higher-order (as opposed to firstor secondorder) approximations is that they are valid not just locally, but often globally (i.e., over nonlocal, possibly very large compact sets) in a rigorous sense that we specify. We apply our routines to compute firstthrough seventh-order approximate solutions to two standard macroeconomic models, a stochastic growth model and a life-cycle consumption model, and discuss the quality and global properties of these solutions. JEL Classification: C61, C63, E37 This Version: July 8, 2005 First Version: December 2002 The first version of this paper was prepared for the 2003 AEA Meetings in a session on perturbation methods and applications. We thank Ken Judd, Chris Sims, Michel Juillard, Jinill Kim, and seminar participants at the AEA Meetings, ES Meetings, SCE Meetings, SED Meetings, SITE, and the University of Maryland for helpful discussions, comments, and suggestions. The views expressed in this paper, and all errors and omissions, should be regarded as those solely of the authors, and do not necessarily represent those of the individuals or groups listed above, the Federal Reserve System, or its Board of Governors.