# Rational Expectations Hypothesis Essay

Let the value a variable ‘y’ takes in period t depend upon, or be a function f (.) of, the value of other variables, x1, x2 and x3 have taken in some previous periods. But let y also be influenced by a random event, u. So the true nature of the world is the following: yt = f (x1t-1----- x1t-n, x2t-1----- x2t-n, x3t-1----- x3t-n) + ut ------------------------------------------ ( 2.1)

Here the state of the world is

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Consider the following example. Suppose the aggregate supply function is defined as, yt = mt +mt-1 +yt-1 +t ------------------------------------------ ( 2.7)

Where m¬t is the money supply, yt is output, and t is an error term. By lagging this relationship and repeatedly substituting it back into the equation to eliminate lagged output terms, output can be shown to be a function of past money supply. yt = mt +( +)mt-1 +-----------+ t ------------------------- (2.8).

A systematic money supply rule based on the previous level of money supply, mt-1, and a random component ut, such as mt= mt - 1 + ut --------------------------------- (2.9) would be influenced on output. Consider now the equation above rating output to lagged money supply, we know that Et - 1 mt = mt – 1 ------------------------------------------