The theory of rational expectations was first proposed by John F. Muth of Indiana University in the early 1960s. He used the term to describe the many economic situations in which the outcome depends partly on what people expect to happen. Rational expectations theory is an assumption in a model that the agent under study uses a forecasting mechanism that is as good as is possible given the stochastic (random) processes and information available to the agent. Rational expectations is thus a theory used to model the determination of expectations of future events by economic agents and it defines these kinds of expectations as being identical to the best guess of the future (the optimal forecast) that uses all available information. The theory makes the assumption that people do not keep making the same mistakes over and over again when predicting future events and that deviations form foresight are only random. In an economic model, this is typically modelled by assuming that the expected value of a variable is equal to the expected value predicted by the model. Example.

Suppose P is the equilibrium price in a simple market determined by the forces of supply and demand. Then, the theory of rational expectations says that actual price only deviates from the expectations if there is an “information shock” caused by information unforeseen at the time expectations were formed The ex ante actual price is equal to its rational expectations. P = P* + ε

E[P] = P*

Where P* is the rational expectation and ε is the random error term; which has an expected value of zero and is independent of P*. Further, rational expectations hypothesis assumes that future expectations are based not just on past trends but on an understanding of how the economic system works. For instance, to form their expectations on the inflation rate, rational expectations theorist will use all available information including past inflation rates, the impact of expected policy actions and their knowledge of macro economic relationships within the economy. II. Adaptive Expectations

The adaptive expectations approach dominated work on inflation and macro economics in the early 1960s. The adaptive expectation hypothesis is based on the assumption that the best indicator of the future is what happened in the past.` Under this theory, agents form expectations about the future values of variables using the previous or lagged values of the same variable, that is, regardless of new information available, agents rely on past information, updating their beliefs in a form of moving average. For example, suppose that price level has been rising at an annual rate of 6% for the last three years. Under adaptive expectations, people will expect prices to rise by about 6% in year 4. Now suppose that in year 4 the rate of price rise (inflation) increases to 9%. They will predict about 7% rise in year 5. Under adaptive expectations, forecasts of the future rate of inflation may be right on the money, but they may also exhibit systematic errors. When inflation is accelerating, forecasts will tend to be too low and when inflation is decelerating, the forecasts tend to be too high.

A simple version of adaptive expectations is stated below.

Let Pe be next year’s rate of inflation that is currently expected. Pe-1 be this year’s rate of inflation that was expected last year and P is this year’s actual rate of inflation. Then, Pe = Pe-1+ (P-1 - Pe-1)

Where is between zero and one.

The above equation says that current expectations of future inflation reflects past expectations and an “error adjustment” (partial adjustment) term in which current expectations are raised or lowered according to the gap between actual inflation and previous expectations. This theory can be applied to all previous periods so that current...