ECOS 2002
Assignment 4
1. Dual Mandate: Suppose the central bank has a dual mandate. This implies the
following IS-MP-AS model:
IS : Y˜t = a¯− b¯(Rt − r¯)
MP : Rt − r¯ = m¯(πt − π¯) + d¯Y˜t
AS : πt = πt−1 + v¯Y˜t + o¯
(a) Why does the above model represent a dual mandate?
(b) Solve for the AD curve of this economy.
(c) Compare the slope of the AD curve in this economy to the slope of an AD
curve in an economy with a single mandate (i.e. set d¯ = 0.). Does the slope
make sense given the central bank’s objectives? Explain using a graph.
2. Rational Expectations: Consider the following IS-MP-AS model:
IS : Y˜t = a¯− b¯(Rt − r¯)
MP : Rt − r¯ = m¯(πt − π¯) + d¯Y˜t
AS : πt = π
e + v¯Y˜t + o¯
(a) Solve for the AD curve and substitute it into the AS curve. Then, solve for
πt.
(b) Under the assumption of rational expectations, the agents in the economy are
assumed to know the actual value of πt at every point in time. This implies
that πe = πt. Using this fact solve for the rational expectations value of π
e.
Does your answer make intuitive sense? Explain your solution.
3. Dynamic IS-MP-AS: For this exercise you will need to download the spreadsheet
IS MP AS Q2.xlsx.
(a) Simulate a supply shock by changing the “bar o” cell from zero to one. De-
scribe the effect of the supply shock.
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(b) Simulate a demand shock by changing the “bar o” cell from one to zero and
the “bar a” cell from zero to one. Based on the path of output, inflation,
and the interest rates is it possible to distinguish a supply shock (your answer
from part (a)) from a demand shock? Explain.
(c) Finally, consider a central bank with a dual mandate i.e.
MP : Rt − r¯ = m¯(πt−1 − π¯) + x¯ ˜Yt−1.
Assume that x¯ = 0.2. Modify the spreadsheet to reflect this assumption.
What is the effect of this change on the prediction for the effect of a demand
shock (a¯ = 1)? Explain and include a picture of the dynamics. (Note: I
do not want the whole spreadsheet, just the picture of the path of output,
inflation, and the interest rate.)
4. Monetary Policy and the Taylor Rule: In class we learned that one way to sum-
marize monetary policy is to think about interest rates set according to a Taylor
rule:
it = r¯ + πt + ϕπ(πt − π¯) + ϕy(yt − y¯). (1)
Download the spreadsheet Australian Data.xlsx and test whether the RBA’s pol-
icy can be approximated by a Taylor rule. Assume ϕπ = 1.5, ϕy = 1, r¯ = 2,
π¯ = 2.5 and y¯ = 3. (Hint: In a new column code the equation from the Taylor
rule. It is easier to “hard” code the parameter of the model like is done in the
IS MP AS Q2.xlsx spreadsheet. To do this you simply click on the cell you want
and press F4. Pressing F4 will put dollars signs ($) in and around the cell name
and will hold that parameter fixed as you drag the equation to a new cell to create
the predictions. You can also just place $’s in the equation as well. This should
work in all spreadsheet software. Use IS MP AS Q2.xlsx as an example, if you are
having trouble getting started.)
(a) Provide a graph of the predicted cash rate, a four quarter moving average of
the cash predicted cash rate, and the actual cash rate.
(b) Does it appear the RBA policy is approximated by the Taylor rule?
(c) Does it appear that the RBA has been constrained by the zero lower bound?
(d) If the RBA is following the Taylor rule, does the graph predict that interest
rates should be rising or falling in the near future?