Is It Worth Refining Linear Approximations to Non-Linear Rational Expectations Models?

We characterize the balanced growth path of the basic neoclassical growth economy using standard numerical solution methods which solve a linear or log-linear approximation to the economic model, as well as methods which preserve the nonlinearity in the original model. We also apply the same methods adding indivisible labor to the basic model, and to a monetary version of that economy, subject to a cash-in-advance constraint. In a unified framework, we show that log-linear approximations should generally be preferred to linear approximations. We also provide evidence that preserving the original nonlinear structure of the model when computing the numerical solution generally yields minor gains in accuracy. Methods that use either a linear or a log-linear approximation to the model can produce solutions as accurate as the parameterized expectations method. However, in extreme parametric cases, the solution may be rather sensible to small numerical errors, and even a log-linear approximation may then be inappropriate. Methods using the nonlinear structure of the original model can then perform significantly better.