This chapter presents theoretical foundations of main methods of solving rational expectations models with a special focus on perturbation approaches. First, it gives some insights into the solution methods for linear models. Second, it shows how to use the perturbation approach for solving nonlinear models. It then documents the limits of this approach. The perturbation approach, though the most common solution method in the macroeconomic literature, is inappropriate in contexts of large fluctuations (large shocks or regime switching) and of strong nonlinearities (e.g., occasionally binding constraints). The former case is illustrated by regime switching models. The latter case is illustrated by a study of existing methods for solving rational expectations models under the zero lower bound constraint, that is, the condition of non-negativity of the nominal interest rate. The chapter concludes with a presentation of global methods available when the perturbation approach fails in solving models.
System Reduction and Finite-Order VAR Solution Methods for Linear Rational Expectations Models