1 Coursework Assignment - ECON 324
Consider the following log-linear equations of the basic New Keynesian model,
bYt= Et bYt+1 bRtEtbt+1r^nt ; (1)
bt= Etbt+1+( 1) ('+ 1)

bYt + u^t; (2)
r^nt = Z^tZ^t+1; (3)
Z^t = Z^t1 + "zt ; (4)
u^t = u^t1 + "ut ; (5)
where bYt is output, bt is in‡ation, bRt is the nominal interest rate, Z^t is a demand
shock, r^nt is the natural rate of interest, and u^t is a cost-push supply shock. The
term = 0:99 is the discount factor, = 6 is the price elasticity of substitution,
= 80 is the price adjustment cost parameter, ' = 0:5 is the inverse of the
Frisch elasticity of labour supply from the utility function, ('+ 1) bYt =cmct is the
log-linear marginal cost represented as a function of output, and (1)('+1)
is the slope of the New Keynesian Phillips Curve (NKPC). Equations (4) and (5)
determine the shock processes, with = 0:7 measuring the common persistence
of both shocks and "zt and "
u
t representing the mean-zero, serially uncorrelated
demand and supply shocks, respectively. The policy maker may operate under
discretion and has the objective of minimizing the period-t welfare-based loss
function,
Lt = b2t + #bY 2t ; (6)
where # ('+1) is the relative weight on output ‡uctuations (relative to in‡a-
tion) in the microfounded welfare loss-function.
Please answer the following questions:
1. Assume the central bank initially follows a simple Taylor (1993) policy
rule, bRt= bt where = 1:5: Discuss equations (1) and (2) and the
transmission channels of monetary policy.
2. Assume that all sources of uncertainty
n
Z^t; u^t
o
follow an identical two-
state Markov process. Following Eggertsson (2011), each shock process
persists with probability and reverts to its long-run level fZ; ug with a
probability of 1 every period. The dynamics of output and in‡ation
follow the same two-state Markov process as the shocks. Once the shocks
return to their steady state, they remain there, with output and in‡ation
also lapsing into their long-run levels (bt = Y^t = 0). Hence, for each
endogenous variable you can use EtX^t+1 = X^t: Using these assumptions
about the nature of the shocks, derive the closed-form solutions for output
1
and in‡ation and show how they are related to both shocks with the
central bank following a Taylor rule as speci…ed in question (1). Explain
the importance of :
3. Using Matlab and Dynare, and employing the calibration values provided
in the question, compare the dynamics of the model following a supply
shock, a demand shock and a combination of both shocks - all in one set
of impulse response functions. Explain the transmission channels of the
individual shocks and the dynamics of output and in‡ation that follow.
Make sure to use shock standard deviations that result in ‘reasonable’
annual percentage deviations in key variables.
4. Explain why the Covid-19 induced recession can be thought of as a com-
bination of both demand and supply shocks?
5. Discuss the economic and model-consistent rationale for the loss-function
given in (6).
6. Assume the economy is now only subject to demand shocks. Derive and
explain the optimal targeting rule under discretionary policy, and calculate
the optimal sequence of
nbt; Y^to1
t=0
using the Eggertsson (2011) method
used in question (2).
7. Using Matlab and Dynare, compare the dynamics of the model under the
discretionary policy derived above with the dynamics of the model under a
simple Taylor (1993) rule following a decline in Z^t:Which policy performs
better in terms of economic stabilization and welfare? What should be
the optimal ? Explain your answer.
Note: Please attach your Dynare / Matlab code in your submitted work.
2 Recommended References (to start with)
Gali, J. (2015). “Monetary Policy, In‡ation, and the Business Cycle: An
Introduction to the New Keynesian Framework and Its Applications –
Second Edition”. Princeton University Press. Chapters 3-5.
Clarida, R, J. Gali, and M. Gertler. (1999). “The Science of Monetary
Policy: A New Keynesian Perspective”. Journal of Economic Literature,
1661-1707.
Eggertsson, G. B. (2011). "What …scal policy is e¤ective at zero interest
rates?." NBER Macroeconomics Annual, 25(1), 59-112.
Nistico, S. (2007). “The welfare loss from unstable in‡ation”. Economic
Letters, 96, 51-57.
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