Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
ECON6002
Tutorial 7 (New Keynesian DSGE)
NOTE: The tutorial problems are covered by the online tutor. If you have any ques-
tions about the tutorial questions that are covered by the tutor, please post the ques-
tions (after you have tried working on the problems) on Ed and the tutor will respond.
Please use this as a learning mechanism and not just a channel to get the solutions.
1. Consider the purely forward-looking NKPC, pit = βEtpit+1 +κy˜t, where pit and y˜t are inflation
and the output gap, respectively. Assume that β = 1 and κ = 0.05. Also assume that y˜t
follows a first-order autoregressive (AR(1)) process y˜t = ρy˜t−1 + εt, where ρ is the persistence
parameter and εt is the innovation to the output gap (i.e., the innovation process has zero
expected value Etεt+k = 0 for all k > 0).
(a) Posit a solution for the model of the form pit = byy˜t and use the method of undetermined
coefficients to solve for by.
(b) Suppose that ρ = 0 so that output gap has zero persistence and there is a one-time −1%
shock to output gap at t = 1 (i.e., εt goes back to its zero value thereafter). Prior to
this shock, the economy was at the steady-state with 3% inflation and zero output gap.
Sketch the evolution of inflation and output gap over time, starting from t = 0 (steady
state), t = 1, 2, ..., until the economy arrives back at the steady state. (Hint: There is
no change in the steady state—all the variables will eventually go back to the old steady
state.)
(c) How does the persistence of inflation compare to the persistence of the output gap?
Why? (Hint: Persistence is defined as how long a variable tends to deviate from its
steady-state value.)
(d) Redo part (b) for ρ = 0.5 — that is, the output gap is somewhat persistent. Is inflation
also more persistent in this case as compared to when ρ = 0? Why?
2. Consider the following hybrid NKPK with β = 1: pit = γpit−1 + (1− γ)Etpit+1 + κy˜t. Assume
that γ = 0.5, so that price-setting is equally backward- and forward-looking. Assume that
y˜t follows a first-order autoregressive (AR(1)) process with ρ = 0.5 and slope of the hybrid
NKPC is κ = 0.05.
(a) Without computing precise values, guess and draw the evolution of inflation and output
gap over time under this hybrid NKPC. Is inflation more persistent under this hybrid
NKPC than a purely forward-looking NKPC? Why or why not?
1
(b) Now, suppose that the central bank announces a permanent and fully credible reduction
in its target or steady-state inflation rate from 3% to 1% at t = 1 (prior to this, the
economy was at the steady state with 3% inflation and zero output gap). Assume that
y˜t doesn’t follow an AR(1) process anymore and the central bank has some control of
the evolution of y˜t (by adjusting the policy rate, for example). Show that it is possible
to achieve immediate and costless disinflation under the purely forward-looking NKPC
(γ = 0). Show that it is not possible for the central bank to do so under the hybrid
NKPC (γ = 0.5)—that is, inflation should be reduced gradually with the cost of a
negative output gap during the transition. (Hint: Inflation will eventually reach the new
steady state of 1%, while the output gap will eventually go back to its zero level).