Economic Models Subject to Stationary Noise

Concluding Remarks

Extending and confirming results of Chapter 2 to the case of stationary noise, it was shown that the class of unbiased forecasting rules which generate rational expectations are themselves time-invariant functions. The most remarkable phenomenon in stationary economic systems with expectational leads is the notion of an unbiased no-updating forecasting rule which yields the most precise forecasts in the sense that forecast errors vanish conditional on information which was not available at the stage in which they were issued.

The existence of unbiased forecasting rules was reduced to the existence of a global inverse of the mean error function associated with the system. This error function depends exclusively on the fundamentals of the economy and is independent of any expectations formation procedure. The information necessary to construct an unbiased forecasting rule requires detailed knowledge of the whole economic system and amounts to the ability of computing the global inverse of the mean error function. The static nature of this error function, however, opens up the possibility to estimate and approximate unbiased forecasting rules from historical data, whenever they exist.