Excerpts from the report Introduction: Rational expectations are becoming increasingly popular as a means of generating unobservable explanatory variables in econometric models. The intuitive attractiveness of the rational expectations hypothesis advanced by Muth has been evident for some time. However, problems of implementing the hypothesis in applied contexts have limited its use. Specifically, for more than highly simplified constructs, methods of obtaining estimates of the unobservable explanatory variables implied by the systematic component of the model, and thus rational, but permitting consistent estimation of the structural parameters have not been available. This difficulty with the application of the rational expectations hypothesis in econometric models was highlighted in a recent exchange by Nelson and McCallum. Moreover, building on the results by Nelson, McCallum was able to show that an instrumental variables approach using extrapolative prediction for the unobservable variables would produce consistent estimates for the structure of a model incorporating "partially" rational expectations. The expectations are termed partial because the extrapolative process for generating the instruments does not incorporate all of the restrictions on the unobservable variables which are implied by the structure. The present paper extends these results by showing that the extrapolative process imposed by McCallum for obtaining consistent estimates of the structural parameters with a rational expectations hypothesis on the unobservable variables is unnecessary. Namely, more direct methods for producing the required unobservables and correspondingly consistent estimates of the structural parameters can be derived. These include the unobservable variables, instrumental variables, and iterated instrumental variables estimation methods. Each of the methods provides an operational means of obtaining consistent estimates in models with rational expectations.
