Solving Rational Expectations Models

In this chapter, we present theoretical foundations of main methods solving rational expectations models with a special focus on perturbation approaches. We restrict our attention to models with a finite number of state variables. We first give some insights on the solution methods for linear models. Second, we show how to use the perturbation approach for solving non-linear models. We then document the limits of this approach. The perturbation approach, while it is the most common solution method in the macroeconomic literature, is inappropriate in a context of large fluctuations (large shocks or regime switching) and of strong non-linearities (e.g. occasionally binding constraints). The former case is then illustrated extensively by studying regime switching models. We also illustrate the latter case by studying existing methods for solving rational expectations models under the Zero Lower Bound constraint, i.e. the condition of non negativity of the nominal interest rate. Finally, we end up with a brief presentation of global methods which are alternatives when the perturbation approach fails in solving models.