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The careful distinction between an economic law and a forecasting rule was the necessary step to obtain a proper description of an economic dynamical system in a Markovian environment. The results of this chapter demonstrate that the property of rational expectations along orbits of an economic dynamical system imposes structural restrictions on the economic fundamentals which are embodied in an economic law. A remarkable phenomenon in economic systems with expectational leads is the notion of an unbiased no-updating forecasting rule. Within the class of possible unbiased forecasting rules, these yield the most precise forecasts as forecasts are best least-squares predictions conditional on information which is not available at the stage in which they were issued. An economic implication of this chapter is that agents who know an unbiased forecasting rule also know how their forecasts influence the economy. In principle, these agents could try to strategically exploit this information. How this could be achieved is an interesting avenue for future research.

The careful distinction between an economic law and a forecasting rule was the necessary step to obtain a proper description of an economic dynamical system in a Markovian environment. The results of this chapter demonstrate that the property of rational expectations along orbits of an economic dynamical system imposes structural restrictions on the economic fundamentals which are embodied in an economic law. A remarkable phenomenon in economic systems with expectational leads is the notion of an unbiased no-updating forecasting rule. Within the class of possible unbiased forecasting rules, these yield the most precise forecasts as forecasts are best least-squares predictions conditional on information which is not available at the stage in which they were issued. An economic implication of this chapter is that agents who know an unbiased forecasting rule also know how their forecasts influence the economy. In principle, these agents could try to strategically exploit this information. How this could be achieved is an interesting avenue for future research.

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.

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.

The careful distinction between an economic law and a forecasting rule was the necessary step to obtain a proper description of an economic dynamical system in a Markovian environment. The results of this chapter demonstrate that the property of rational expectations along orbits of an economic dynamical system imposes structural restrictions on the economic fundamentals which are embodied in an economic law. A remarkable phenomenon in economic systems with expectational leads is the notion of an unbiased no-updating forecasting rule. Within the class of possible unbiased forecasting rules, these yield the most precise forecasts as forecasts are best least-squares predictions conditional on information which is not available at the stage in which they were issued. An economic implication of this chapter is that agents who know an unbiased forecasting rule also know how their forecasts influence the economy. In principle, these agents could try to strategically exploit this information. How this could be achieved is an interesting avenue for future research.

The fact that perfect foresight is possible in a random environment of an exchange economy seems to have been overlooked in the literature. This chapter demonstrates that forecasting rules which generate perfect foresight exist under standard assumptions. Using the methodology of Chapter 5, these socalled perfect forecasting rules can successfully be estimated from historical data by means of nonparametric estimations. The censoring of the approximated forecasting rules assures that the system is kept stable at all stages of the estimation procedure and that the resulting process satisfies the necessary stochastic properties. It should be noted that the method required neither the existence of a perfect forecasting rule nor its contraction property.

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.