Consider the Poole (1970) model (W. Poole, Optimal choice of monetary
policy instruments in a simple stochastic macro model, Quarterly Journal of
Economics 84, 197-216):
yt = y0
ait + ut (1)
mt = m0 + byt
cit + vt (2)
where ut and vt are independent random variables (i.e., Cov(u; v) = 0) with zero
mean, and y0 and m0 are constant terms in the IS and LM curve respectively.
Assume that the central bank wants to minimize the loss function
Lt = E (yt)
2
: (3)
Find analytically:
1. The minimum loss obtainable under an interest rate targeting regime (30
marks);
2. The minimum loss obtainable under a monetary targeting regime (30
marks);
3. Using your results in 1 and 2 above, discuss how the choice of the optimal
policy instrument depends on the nature of the shock (40 marks).
IMPORTANT NOTES:
1. Particular attention should be given to the theoretical explanation and
economic intuition of your results.
2. Please provide the full derivation of your results, with explanations of the
steps taken to arrive at each solution. Results without evidence of their
derivation, even if correct, will receive no credit.
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3. Your work must be submitted via Turnitin. At this level students are
expected to type their assignments. However, if this proves di¢ cult, you
might want to scan diagrams, algebraic derivations, etc. In either case,
there should be one piece of assignment submitted per student. If your
assignment is in various pages, or pdf Öles, please make sure that it is all
submitted in one combined pdf Öle (i.e. you could select all Öles, right
click and press “Combine Öles in Acrobat” to join them all in one pdf Öle).
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