Despite the theoretical appeal of the rational expectations hypothesis, practical problems arising in the estimation and testing of models that incorporate it have yet to be resolved. Many alternatives have been proposed, but even though these approaches have been extensively examined and compared on a theoretical level, little is known about their estimation properties. This paper attempts to provide preliminary Monte-Carlo evidence on the empirical properties of the ‘reduced-torm’ and ‘structural-form’ estimators proposed as alternatives in the implementation of the substitution approach. When applied to the basic models, the two solution methods yield similar results. However, under autocorrelated errors, the structural form estimator performs much better. An alternative adaptive estimator is also examined and found to be far superior to the off-line estimation method when the parameters vary over time.