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AS4:3.png

AS4:3.png

4. Consider an economy whose output behaves according to
yt = a(Tt - Te )
A policy maker sets monetary policy, but inflation cannot be controlled with perfect ac-
curacy. Specifically,
Tit = Tit + nt
where , is the inflation target and 7, is a random variable such that E[n ] = 0 and
Elm-] = 02. The private sector has rational expectations and the policy-maker sets TP so
as to minimize expected loss, which is
El(yt - y)2 + X72].
Here is the timeline of events: (i) the private sector sets , (ii) the policy-maker sets TP,
(iii) the value of the shock n is revealed and inflation and output are determined.
(a) Find the rational expectations equilibrium values of expected inflation E[ ] and
expected log output Elyt] in terms of parameters.
(b) Solve for the rational expectations equilibrium values of yt and it in terms of pa-
rameters and ,. What is the predicted slope of the empirical Phillips curve
Ay ,
AT
(c) What is the (Pearson) correlation coefficient between inflation and output?

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