The Estimation of 'Surprise' Models and the 'Surprise' Consumption Function

In the first part of the paper we outline a method for estimating a class of models in which news or surprises appear and expectations are formed rationally. The method is an extension of the errors-in-variables method of McCallum and Wickens. As a by-product some of Pagan's results on the circumstances under which the commonly use two-step method of estimating surprise models is efficient are shown to be a consequence of well-known theorems on the efficiency of sub-system estimation when a subset of equations is exactly identified. In the second part of the paper the method is applied to Hall's random-walk model of consumption, which is extended to allow for stochastic interest rates and for leisure and government spending to be substitutes for private spending. The extended formulation is a great deal more successful at capturing the salient features of the data. We also derive approximate restrictions across the parameters of the model due to the rational expectations hypothesis but find that they are marginally rejected by the data. Finally, we evaluate the ability of the life-cycle with rational expectations model to encompass alternative models.