When talking about rational expectations all of us know immediately what we mean, this was my belief until some months ago. However it seems to me that many people have a vague idea about the concept, but they fail to clearly state the most important underlying assumptions.
Rational Expectations were initially introduced by Muth (1961), however only Lucas and Sargent implemented them into macroeconomic theory.
The framework of New Classical Theory incorporates, additionally to the Walrasian assumptions, microeconomic principles and applies them on a macro level. One of the most important of these principles is rational expectations. The introduction of expectations into the macroeconomic theory is not a renewal, already Keynes and Friedman stressed the importance of expectations. However, in contrary to Keynes and Friedman, expectations enter in a more dynamic way and are not threated ad hoc or exogenously anymore.
So what do we mean now when talking about rational expectations?
When we have rational expectations in our model economic agents will make the best use of their available information. The available information are entering the model through the information set Ω. In every period agents will have some kind of available information Ωt. Given their information they will maximize their utility. The important thing is that the concept of rational expectations does not put any assumptions on the information set. The information set can include all the information we want to give the agents, so we could give them the knowledge of all the relevant factors in period t, but we could also limit them and give the agents very little information.
Given a certain variable xt the rational expectation of xt+1 is E(xt+1| Ωt). This means nothing else as already stated above, the agent will maximize its utility according to his expectations of the future, which are defined by the information it has. Furthermore this implies that given its information the agent will have an expected forecast error of zero. Let εt+1=E(xt+1| Ωt)-xt+1 be the forecast error, then if the forecast was formed rationally, we have E(εt+1)=0.
The beauty of this approach is that even if agents have a very limited information set they will still form rational expectations. Let’s assume for example that the information set tells our agent that inflation is determined by the rate of money growth, in this case our agents will make the best use of this information and form a rational expectation of the future inflation according to the rate of money growth.