1 ECON 400 – Coursework Assignment Consider the following log-linear equations of the New-Keynesian modelbYt= Et bYt+1 bRt Etbt+1+ b”dt (1) bt= Etbt+1+(p 1)(
+ 1) bYt + b”st (2)bRt= bt + y bYt; > 1; y0 (3)b”dt = db”dt 1 + d;t; (4)b”st = sb”st 1 + s;t (5) where bYt is output, bt is ination 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, ination 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 ination 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, ination 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
