Consider the following problem, based on a simplified version of Poole (1970),
(William Poole, 1970. 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 variances, σ
2
u and σv
2
, respectively. y0 and m0 are constant terms
in these two equations respectively. Assume that the central bank wants to
minimize the loss function,
Lt = E (yt)
2
. (3)
1. Explain these equations [6 marks];
2. Find analytically the minimum loss obtainable under an interest rate tar_xfffe_geting regime [22 marks];
3. Find analytically the minimum loss obtainable under a monetary targeting
regime [22 marks];
4. Using your results in 2 and 3 above, discuss how the choice of the optimal
policy instrument depends on the nature of the shocks, and discuss the
policy implications of these results. [50 marks].
Particular attention must be given to the theoretical explanation and eco nomic intuition of all your equations and results. Please provide the full deriva tion of your results, with explanations of all steps taken to arrive at each solu tion. Results without evidence of their derivation, even if correct, will receive
no credit.
IMPORTANT NOTES
1. This assessed coursework counts for 25% of your final mark for this
course.
1
2. Your essay must be typed and be less than 1500 words in MS Word office
for the whole document and including everything.
3. Your must provide a word limit that has been counted in MS Word for
the whole document and place this at the end of your work. I will use this
as your word count, (although this is subject to checks).
4. If you do not state clearly a word limit at the end of your work, I will use
Turnitin’s limit which, in any case should not never exceed 1750 words,
for the whole document.
5. You are not allowed to use images of text. If you do, the penalty will be
according to the discretion of the examiners.
6. Your work must be submitted in one combined file in PDF form. The
UG office has asked us for this, because if you try to submit a word
file Turnitin automatically converts it into a PDF file. However, any
characters or equations that are corrupted in the process will be treated
as a mistake by examiners. This is why we strongly urge you to have your
word converted into a pdf and check it thoroughly before you submit it.
7. For every 100 words you exceed the limit there will be 3 marks deducted.
