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Category > Management Posted 02 Feb 2018 My Price 10.00

self-fulfilling movements

Consider the system given by (11.41).

(a) What does the system simplify to when φπ = 1? What are the eigenvalues of the system in this case? Suppose we look for self-fulfilling movements in ˜y and π of the form

for what values of λ and c does such a solution satisfy (11.41)? Thus, what form do the self-fulfilling movements in inflation and output take?

(b) Suppose φπ is slightly (that is, infinitesimally) greater than 1. Are both eigenvalues inside the unit circle? What if φπ is slightly less than 1?

(c) Suppose  What does the system simplify to in this case? What are the eigenvalues of the system in this case? Suppose we look for self-fulfilling movements in ˜y and π of the form  ε2 are independent, mean-zero shocks with variances  and where a, h, and k are positive. Policymakers want to stabilize output, but they cannot observe y or the shocks, ε1 and ε2. Assume for simplicity that p is fixed.

(a) Suppose the policymaker fixes i at some level i. What is the variance of y?

(b) Suppose the policymaker fixes m at some level m. What is the variance of y?

(c) If there are only monetary shocks (so σ2 1 = 0), does money targeting or interest-rate targeting lead to a lower variance of y?

(d) If there are only IS shocks (so σ2 2 = 0), does money or interest-rate targeting lead to a lower variance of y?

(e) Explain your results in parts (c ) and (d) intuitively.

(f) When there are only IS shocks, is there a policy that produces a variance of y that is lower than either money or interest-rate targeting? If so, what policy minimizes the variance of y? If not, why not? (Hint: Consider the money-market equilibrium condition, m − p = hy − ki.)

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Maurice Tutor
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Status NEW Posted 02 Feb 2018 07:02 PM My Price 10.00

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