The adaptive expectations hypothesis states that economic agents will adapt their future expectations, about inflation and other phenomena, based on actual experiences in the recent past.
So, for example, if inflation last year was 4%, having risen from 3% the year before, then adaptive expectations theory would suggest that people will expect inflation next year to be in the 4% to 5% range.
The most recent value is the most important, but the direction of change is also important, so the rise in inflation over previous years will feature in some way in the expected value in future years. There is no precise adaptive expectations formula that specifies exactly how to weight these values, but the principle itself is of use in many areas of economics.
Formally, Milton Friedman has provided a formula for adaptive expectations as:
Yp = bY + (1- b)Yp(t-1)
Yp here is a given economic variable, t is a time period, and b is a measure of how responsive, or adaptive, expectations are from one period to the next. The formula can be extended to multiple time periods, but the equations start to get complex. For info, see that PDF link below to the article by Chow.
The most obvious application of the theory relates to inflation, and it forms the backbone of the 'Non-Accelerating Inflation Rate of Unemployment' and the expectations-augmented Phillips curve. For details on that, see my article at:
The key difference between the adaptive expectations hypothesis and the rational expectations hypothesis relates to the responsiveness of economic agents to circumstances. The adaptive school regards economic agents to be reactive to information as it emerges, the rational expectations school assert that economic agents will fully anticipate the effects of events and be proactive in amending their future expectations.
For example, expected inflation next year will not simply be some continuance of past levels and trends, it will depend on an assessment of current economic policy.
The rational expectations school, therefore, insists that economic agents will not be duped by stimulus spending or tax cuts, rather they will understand that such things create extra inflation. The implication is that they will react to such things with extra caution regarding their own spending behavior, thereby mitigating the intended stimulus effects.
I think, at this point, that the reader should be aware that adaptive expectations are much less stringent, and that rational expectations are much more hardcore. There may well be circumstances in which either hypothesis is more accurate, and the paper by Chow (see link below) examines this.
A more formal dividing line between the adaptive expectations school and the rational expectations school is given by the existence, or not, of 'money illusion'. Money illusion relates to the way in which people react to nominal increases in their cash balances as opposed to real increases after taking the effects of inflation into account.
If money illusion theory is correct then consumers will react to nominal changes as if they are real, meaning that governments are able to dupe people into spending more money when they want them to.
As always, the extent to which the theory is borne out in the real world will depend heavily on the specific circumstances of the day. It is, of course, entirely unsatisfactory to write that 'it depends' but this is a very common issue in economics that is much misunderstood by the profession in general.
Many mainstream economists today still use economic models and mathematical approaches that have been adapted from the hard sciences like physics. They regard people like particles, but people are not always predictable, and these models frequently fail.
At the top of the article I stated that there is no precise adaptive expectations formula, by this I meant that there is no formula that can be applied at all times with confidence.
It may be that for long periods we can use historical trends (called empirical evidence) in order to construct models of expectations. However, there comes a point at which people behave in entirely unpredictable ways.
The best example of this, sticking with inflationary expectations, comes when an economy moves from high inflation to hyperinflation. In these circumstances people can actually behave more in the manner predicted by the rational expectations school when, all of a sudden, people wake up to the reality of their situation and simply stop accepting their national currency altogether. They act rationally and realize that it is worthless paper at this point, and resort to almost any viable alternative.