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Adaptive vs Rational Expectations

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Adaptive vs Rational Expectations
Differentiate between Rational and Adaptive Expectations and clearly explain their role in focusing on future macro-economic variables
1. Rational Expectations
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

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