2.1 The Rational Expectations Hypothesis The rational expectations hypothesis is the hypothesis that, when forming expectations about any variable, people will make optimal use of the available information. This information includes the actual value of certain variables and, more widely, the nature or structure of the world in which people are operating.
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 …show more content…
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 ------------------------------------------
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 …show more content…
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 ------------------------------------------