1 Coursework Assignment – ECON 400
Consider the following log-linear equations of the basic New Keynesian model,
b b b bn
Yt= EtYt+1 Rt Etbt+1 r^t
; (1) bt= Etbt+1+( 1)(‘+1)Yt +u^t; (2)
^^
n
r^t = Zt Zt+1; (3)
Z^ t = Z^ t 1 + ” zt ; (4)
u^ t = u^ t 1 + ” ut ; (5) where Ybt is output, bt is ináation, Rbt is the nominal interest rate, Z^t is a demand
n shock, r^t
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) Ybt =mcct 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 “ut 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,
L =b2+#Yb2; (6) ttt
where # (‘+1) is the relative weight on output áuctuations (relative to ináa-
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, Rbt= bt where = 1:5: Discuss equations (1) and (2) and the transmission channels of monetary policy.
2. Assume that all sources of uncertainty nZ^t;u^to 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 ináation follow the same two-state Markov process as the shocks. Once the shocks return to their steady state, they remain there, with output and ináation 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
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Gali, J. (2015). ìMonetary Policy, Ináation, and the Business Cycle: An Introduction to the New Keynesian Framework and Its Applications ñ Second Editionî. Princeton University Press. Chapters 3-5.
Clarida, R, J. Gali, and M. Gertler. (1999). ìThe Science of Monetary Policy: A New Keynesian Perspectiveî. Journal of Economic Literature, 1661-1707.
Eggertsson, G. B. (2011). “What Öscal policy is e§ective at zero interest rates?.” NBER Macroeconomics Annual, 25(1), 59-112.
Nistico, S. (2007). ìThe welfare loss from unstable ináationî. Economic Letters, 96, 51-57.
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and ináation and show how they are related to both shocks with the central bank following a Taylor rule as speciÖed 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 ináation that follow. Make sure to use shock standard deviations that result in ëreasonableí annual percentage deviations in key variables.
4. Explain why the Covid-19 induced recession can be thought of as a com- bination of supply and demand 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^to1t=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. Recommended References (to start with)