Dynamic models of the relations between economic variables often rest on theories about how unobservable expectations are formed. In this paper the "adaptive expectations" and "rational expectations" hypotheses are compared and contrasted. The main distinctions concern the size of information set on which expectations are based, and the optimality or otherwise of expectations, given that information set. Expectations that are optimal with respect to the given information may be defined as rational. With this definition, some bivariate dynamical rational expectations models are presented, incorporating the approximate time series forecasting rules for either a single forecast or an infinite sum of discounted forecasts. Model identification problems are discussed, and it is shown how they may be resolved by joint estimation of the bivariate process.
