ECON 6002 Problem Set 3
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Problem Set 3 (NK and Monetary Policy)
ECON 6002
1. Optimal monetary policy at the zero lower bound under discretion. Consider the standard New Keynesian model with a zero lower bound constraint
xt = Etxt+1 − θ − 1 (it − Etπt+1 − rt)
πt = βEtπt+1 + κxt
it = max[0,rt+ ϕππt+ ϕ北xt]
Assume that rt follows a two state Markov process
P = ) ,
where 0 < δ < 1, rt = rL < 0 in the low state and rt = rH > 0 in the high state.
(a) Show that when we are in the high state such that rt = rH it must be the case that xt = 0, πt = 0, and it = rH .
(b) Show that when we are in low state such that rt = rL < 0 that the zero lower bound must bind.
(c) When the economy is in the low state, expectations can be calculated as Etπt+1 = (1 − δ)πL + δπH ,
Etxt+1 = (1 − δ)xL + δxH .
Or, in other words, when in the low state, there is a 1 − δ probability of remaining in the low state next period and a δ probability of returning to the high state. Using Equations (1) and (2) and the above expectations, solve for xL and πL as functions of parmeters. HINT: from (a) it follows that πH = xH = 0.
(d) Using your answer to (c), how does δ, the probability of exiting the low state, affect inflation and the output gap? If δ becomes smaller, i.e. the low state is expected to last longer, does the recession get better or worse?
2. Technology shocks in the New Keynesian Model: In this question, you will analyze technology shocks in the New Keynesian model following Ireland (2004; available on Canvas). You will need to download the .mod file Ireland NK.mod for this exercise. You will also need to download a copy of Ireland’s paper.
(a) How does Ireland model nominal rigidity?
(b) The taylor rule in Ireland’s models is given by
rt − ρrrt − 1 = ρππt + ρggt + ρ北xt + ϵr,t
Explain in words what the central bank is targeting with this rule.
(c) Compare the IRFs of a technology shock and the variance decomposition of the shock when ρg = 0.25 and ρg = 0. Based on these results should monetary policy respond to gt?
(d) Now consider the case where monetary policy responds to expected output growth rather than current growth (Etgt+1 as apposed to gt). Change the code to reflect this change.
i. Compare the IRFs of a technology shock and demand shock (ea,t). Attach a figure to your assignment.
ii. Does this specification improve economic outcomes? I.e. explain whether this ap- pears to be a better or worse policy.
2022-10-28