We present an algorithm and software routines for computing nth order 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 first- or second-order) 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 first- through 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.
Levin, Andrew T., Eric T. Swanson, and Gary S. Anderson. 2006. “Higher-Order Perturbation Solutions to Dynamic, Discrete-Time Rational Expectations Models,” Federal Reserve Bank of San Francisco Working Paper 2006-01. Available at https://doi.org/10.24148/wp2006-01