Until the advent of the rational expectations (RE) hypothesis, initially put forward by J. Muth and later propagated by Robert Lucas and Thomas Sargent, the AE hypothesis was quite popular in empirical economics. The proponents of the RE hypothesis contend that the AE hypothesis is inadequate because it relies solely on the past values of a variable in formulating expectations, whereas the RE hypothesis assumes that “individual economic agents use current available and relevant information in forming their expectations and do not rely purely upon past experience. In short, the RE hypothesis contends that expectations are ‘rational’ in the sense that they efficiently incorporate all information available at the time the expectation is formulated and not just the past information. (Gujarati, 2009 p.631)
Under rational expectations it is assumed that individuals possess completed knowledge about the functioning of the economic system and put this knowledge to the best possible use when forming their expectations together with all the available information.
X*t = E (X*t / It)
X*t is the expectations formed at time t of X in time t+1. This is dependent on the information available at time t (It).
It may turn out that actual X is not the same as expected. That is agents may make a prediction error
- Xt+1 = Xt* + ut or Xt+1-Xt*=ut
ut is the error of the expectation
E(ut)=0 The expected value of the prediction error is zero. This means that under the rational expectations hypothesis forecasts by individuals are assumed to be correct on average.
Cov (X*t, ut) should also be equal to 0. In addition, the prediction error must be uncorrelated with any information available at the time the prediction is made. If not, this would imply that the forecast has not made use of all available information. Since all available information is summed up in the variable X*t , this implies that ut must be uncorrelated with X*t.