ECON6002 Tutorial 8 (Monetary Policy)
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ECON6002
Tutorial 8 (Monetary Policy)
1. Consider the backward-looking “Old Keynesian” model:
IS Curve:
Phillips Curve:
IS Shock:
Assume the central bank’s loss function is E[(y - y* )2] + 入E[T2].
(a) Posit a linear form to solution of the central bank’s optimization problem given as Et[y˜t+1] = -qTt+1 . Find an expression of the unconditional expectation E[T2] as a function of the shock variances and the model parameters.
(b) Find an expression of the unconditional expectation E[(y - y* )2] as a function of the E[T2], the shock variances and the model parameters.
(c) Find the optimal q* which minimizes the central bank’s loss function? How does it compare to the baseline model in section 12.4 of Romer’s textbook which abstracts from an inflation shock?
2. Consider the forward-looking New Keynesian model:
IS Curve:
NKPC:
Clarida, Gali and Gertler (2000) show that an interest rate rule of the form
will eliminate sunspots so long as the eigenvalues lVl ≤ 1, where
(a) Suppose that oπ = 0. Show that lfl < 1.
(b) Suppose oπ is slightly (that is, infinitesimally) greater than 0. Are both eigenvalues less than 1 in absolute value? (Hint: Compute af/aoπ and evaluate it at oπ = 0). What does this imply about the possibility of sunspot fluctuations?
(c) What if oπ is slightly (that is, infinitesimally) smaller than 0? Are sunspot fluctuations possible in this case?
2023-07-13