Solution Methods for Nonlinear Models¤

Economic models are used for many purposes, including forecasting and simulation. Economic models are generally nonlinear. Even simple macroeconomic models, where all the stochastic equations in the system may be linear in logarithms, need to be completed by accounting identities that are linear in levels. As a consequence, although a model may be estimated using linear techniques, forecasts with that model (which need to take the identities into account) will normally involve using nonlinear solution techniques. Unfortunately, nonlinear models cannot in general be solved analytically and so solution techniques involve iterative numerical methods. When models include rational expectations, then solution techniques are made more complicated.