9.14. Money versus interest-rate targeting. (Poole, 1970.) Suppose the econ- omy is described by linear IS and LM curves that are subject to distur bances: y cai is, mp hy ki +EIM, where IS and L are independent, mean-zero shocks with variances of and M, and where

a, h,

and k are positive. Policymakers want to stabilize output, but they cannot observe y or the shocks, EIS and ELM. Assume for simplicity that p is fixed.

(a) Suppose the policymaker fixes i at some level 7. 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 LM shocks (so = 0), does money targeting or interest- rate targeting lead to a lower variance of y?

(d) If there are only IS shocks (so = 0), does money or interest-rate tar- geting 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 LM curve, m-p=hy - ki.)