On the Predictability of Economic Events - Jordan, J. S. (Econometrica, 1980)
Events by Grunberg and Modigliani [3]. Economic forecasts are made to be used, and decisions based on them may affect their ultimate realization. Grunberg and Modigliani explored this problem in a model in which future aggregate supply was influenced by current decisions based on the predicted future price. They applied the Brouwer fixed point theorem to show that if the future equilibrium price is a bounded continuous function of its currently predicted value, a exists. In [8] this result was placed in a temporary equilibrium context and the notation of a correct prediction was extended to include probabilistic predictions based on estimation procedures. Again, a fixed point theorem was applied to show that the causal influence of a forecast does not always invalidate it. Although this result is a reassuring and necessary first step, the analysis is confined to a single realization of the exogeneous variables. Thus a forecast is a single point or probability distribution rather than a function or conditional distribution whose domain is the space of observable variables. Of course, if the complete exogenous specification of the economy is observable, this is no restriction since the theorems could be applied separately to each realization. However, it is more likely that the space of observable variables contains a mixture of exogenous and endogenous variables without containing the complete set of either. Then if the exogenous variables are generated stochastically, the results of the above mentioned papers do not guarantee the existence of a statistically forecasting procedure. What is needed are general equilibrium versions of the results in [10], where, in particular, the statistically forecast of a future price is derived as a function of current and past prices. It would seem natural to approach this as a fixed point problem in the space of joint distributions of the observable variables and the