Find a solution for πt, yt and r₺ as function of the disturbances and the pa- rameters of the model. What are the effects of an unfavorable inflation shock (i.e. u increases) on output, interest rate and inflation in this case? Interpret your answer.

Exploring Economics
8th Edition
ISBN:9781544336329
Author:Robert L. Sexton
Publisher:Robert L. Sexton
Chapter27: Issues In Macroeconomic Theory And Policy
Section: Chapter Questions
Problem 13P
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Suppose now the economy is described by a New Keynesian Model, where we
assume rational expectations. The equilibrium is described by the following three
equations, in order the Dynamic IS, the New Keynesian PC and the Monetary
Policy Rule:
1
Y₁ = E₁Y₁+1 = = rt+u!S;
Yt Etyt+1
(1)
T4+ = BETCH+1+ky tuổi
(2)
rt = Y¬πt + YyYt + UMP
(3)
where u¹S, u and u
IS
MP are white noise, iid disturbances identifying output, infla-
tion and interest rate shocks, respectively. Then, 0, ß, к are positive model's (con-
volution of) structural parameters and 4 and yy are positive policy parameters.
Because of the absence of any backward-looking elements and any information
about the future values of the disturbances, Ett+1 = Etyt+1 = 0.
Transcribed Image Text:Suppose now the economy is described by a New Keynesian Model, where we assume rational expectations. The equilibrium is described by the following three equations, in order the Dynamic IS, the New Keynesian PC and the Monetary Policy Rule: 1 Y₁ = E₁Y₁+1 = = rt+u!S; Yt Etyt+1 (1) T4+ = BETCH+1+ky tuổi (2) rt = Y¬πt + YyYt + UMP (3) where u¹S, u and u IS MP are white noise, iid disturbances identifying output, infla- tion and interest rate shocks, respectively. Then, 0, ß, к are positive model's (con- volution of) structural parameters and 4 and yy are positive policy parameters. Because of the absence of any backward-looking elements and any information about the future values of the disturbances, Ett+1 = Etyt+1 = 0.
Find a solution for πt, уt and r₁ as function of the disturbances and the pa-
rameters of the model. What are the effects of an unfavorable inflation shock
(i.e. uŢ increases) on output, interest rate and inflation in this case? Interpret
your answer.
Transcribed Image Text:Find a solution for πt, уt and r₁ as function of the disturbances and the pa- rameters of the model. What are the effects of an unfavorable inflation shock (i.e. uŢ increases) on output, interest rate and inflation in this case? Interpret your answer.
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