Throughout our lives, we make decisions based on our views of the world. Our views keep changing as the circumstances around us change. We form views based on a lot of variables. We also make predictions about the future based on those views. Once we act on those predictions or meet the actual future we might get some errors or disappointments. These disappointments tell us that our predictions were in error OR the other way around our view of the world was in error. In this perspective, adaptive expectations is the theory of how people make future predictions based on their past experiences, circumstances, and errors in their earlier predictions. So prediction after prediction, each influenced by the past prediction, is actually the theory of adaptive expectations.
One such example is the inflation. If one expects that inflation will be lower, but in fact, it happens to be higher and their prediction went wrong. They will make another prediction by solely seeing their error in the past prediction. Let’s say x1 is the next year’s prediction of inflation, x2 is the current year’s expectation (which was expected last year), and let x3 be the ‘actual’ inflation rate of the current year. The following formula will bind them together in the case of adaptive expectations.
x1 = x2 + h(x3 - x2)
In the above equation, ‘h’ is the constant factor between 0 and 1. The second term which is added to x2 is the error term. This equation tells exactly how adaptive expectations work in true mathematical terms. This can be extended to year on year expectations in the past.
The important factor of past events in adaptive expectation plays a central role in all the future predictions. The prediction and expectation are very much different terms but people tend to predict what they exact or they tend to expect what they predict. Which path to follow is something that you need to crack. I believe we should make a prediction of future based on past event, current context, a mathematical model, and consensus. Once that is done we can give a description of such prediction in terms of expectations. Raw expectations are dangerous.
Adaptive expectations is really a simple model which only sees the past events and also somewhat the same type of past events. But in the real world, there are more factors than the past or the type of events in the past that influence future. So bear in mind that adaptive expectation is good for simplistic understanding but you need to add more variables in order to come up with something solid. Also, do not rely on adaptive expectations for the decision making as well. For solid decision making, you need to consider Rational Expectations.