1 ECON 400 - Coursework Assignment
Consider the following log-linear equations of the New-Keynesian modelbYt= Et bYt+1 bRtEtbt+1+ b"dt (1)
bt= Etbt+1+(p1)( + 1)

bYt + b"st (2)bRt= bt + y bYt; > 1; y0 (3)b"dt = db"dt1 + d;t; (4)b"st = sb"st1 + s;t (5)
where bYt is output, bt is in‡ation bRt is the nominal interest rate and b"dt andb"st are the shock process for demand and supply shocks. The term = 0:99 is
the discount factor, p = 6 is the price elasticity of substitution, = 80 is an
adjustment cost parameter and = 5. Finally, d;t; s;t represent a mean-zero,
serially uncorrelated demand and supply shocks, respectively.
Please answer the following questions (all parts carry equal weights):
1. Assume that the central bank belived that the …nancial crisis was caused
by a negative demand shock d;t with persistence, d = 0:7:
i) Compare the dynamics of output, in‡ation and the policy rate for
this adverse demand shock with a standard Taylor Rule weight of = 1:5
but with y = 0 (use a 1% negative shock)
ii) Assume the central bank aims to only minimize in‡ation in the
loss function such that:
L =b2t
is the weight of = 1:5 and y = 0 optimal? If not what weight would
you recomend? Explain your answer.
2. Suppose a collapse in the exchange rate follows more closely a supply
shock,(an increase in s;t) with s = 0:75. Find the optimal policy and
plot the responses of output, in‡ation and the policy rate following a 1%
shock when the central bank has a loss function of
L =b2t + 0:1bY 2t :
when
i) is set optimally with y = 0.
ii) Both and y are set optimally.
iii) Explain why your results change (or instead why they do not
change) in parts i) and ii).
1