EC3115 Monetary Economics
Section A
Answer all EIGHT questions from this section.
Indicate whether the following statements are true or false, or uncertain and give a short explanation. Points are only given for a well reasoned answer.
1. The only purpose of money is as a means of payment.
2. The banks role in transforming maturities makes them vulnerable to bank runs.
3. A halving of the velocity of money will lead to a halving of the price levels.
4. Interest rates have higher information content regarding future inflation and real output than monetary aggregates.
5. Financial accelerator refers to more frequent changes in the short term policy instrument of a central bank.
6. The appointment of a conservative central banker will entirely eliminate inflation bias.
7. Monetary policymakers who face parameter uncertainty in their models should react cautiously when reacting to economic shocks.
8. A fully anticipated future inflation does not have welfare costs.
Section B
Answer THREE out of FIVE questions from this section.
9. Consider the following reduced form. Taylor rule
Rt = α + β(yt − yt*) + γπt
,
where Rt
is the nominal interest rate, (yt − yt*) is the output gap, πt
is inflation, and α = r
∗ − (γ − 1)π*. Gerlach and Schnabel (2000) fitted this model to the EMU data over the period 1990 - 1998 and found that for the EMU
Rˆ
t = 2.40 + 0.45(yt − yt*) + 1.58πt
.
(a) (5 points) Interpret the β and γ coefficients, and explain whether the EMU esti-mates make economic sense.
(b) (5 points) Let the target inflation equal π* = 2%. If inflation is equal to the target and the output gap is zero, what does the equation above collapse to? What is implied real interest in this case?
(c) (6 points) Discuss the advantages and disadvantages of adopting a monetary policy rule
(d) (4 points) An alternative monetary rule is Friedman’s rule of constant money growth. Explain the reasoning behind the suggestion of keeping money growth constant.
10. Economic agents have to form. their forecasts in real time. Most macroeconomic data, however, needs to be revised. Consider the following structure of the data revision:
Xt
f = Xt
p + rt
f
,
where Xt
p
is the initial announcement, Xt
f
is the final value and rt
f
denotes the final revision.
(a) (4 points) Discuss the main reasons why data needs to be revised.
(b) (6 points) Outline the properties of well behaved revisions and discuss whether, empirically, actual revisions are likely to have these properties.
(c) (5 points) What is the implication for monetary policy of this data uncertainty?
(d) (5 points) Explain why central banks engage in interest rate smoothing.
11. Assume that the one year interest rates on treasury bills for the next five years are given as:
r1 5%
r2 6%
r3 7%
r4 6%
r5 5%
(a) (6 points) Assuming that the expectations theory is the correct theory of the term structure, calculate the interest rates in the term structure for maturities of one to five years, and plot the resulting yield curves for the following path of one-year interest rates over the next five years.
(b) (4 points) How would your yield curve in part (a) change if people preferred shorter-term bonds over longer-term bonds?
(c) (5 points) Explain how you might use the yield curve to extract inflation expecta-tions. What assumptions do you need to make to make it work?
(d) (5 points) Predict what will happen to interest rates on a corporations bonds if the federal government guarantees today that it will pay creditors if the corporation goes bankrupt in the future. What will happen to the interest rates on Treasury securities?
12. Suppose that the economy of Plania is characterized by the following Phillips Curve
πt = yt + aπt−1
and the IS Curve
yt = −bit + ∈t
where y is the real output, π is the rate of inflation, i is the short term interest rate set by the Central Bank and ∈ are i.i.d. shocks with ∈ ∼ N(0, σ∈2
). The Central Bank of Plania is aiming to stabilize inflation around a target inflation π* of 0 percent. The quadratic loss function of the Central Bank (which aims to minimize this loss function) takes the following form.
L = Et(πt − π*)
2
(a) (6 points) Solve for the optimal interest rate under these conditions.
(b) (8 points) Now suppose that there is parameter uncertainty, i.e. parameters a and b are time varying. The policymaker knows from which distribution these parameters are drawn. To capture this let a ∼ N(a, σa
2) and b ∼ N(b, σb
2). Now solve for the optimal interest rate setting rule.
(c) (3 points) Compare your results in (b) with those in (a), highlighting the main effects of parameter uncertainty.
(d) (3 points) What are the properties of well-behaved data revisions? What is the US evidence on data revisions according to Aruoba (2008)?
13. Consider the three equation IS-PC-MR model described in Carlin and Soskice (2006). Let the IS curve be given by
y1 = A − ar0,
where y1 is actual output in period 1, A is an autonomous expenditure variable, r0 is the real interest rate, set in period 0, and a is a constant. The simplified Phillips curve is given by
π1 = π0 + α(y1 − ye),
where π0 and π1 are inflation in period 0 and 1, respectively; ye is the ‘trend’ output associated with a constant level of inflation. Lastly, the loss function of the central bank is given by
L = β(π1 − π
T
)
2 + (y1 − ye)
2
,
with π
T defined as the target rate of inflation and where the parameter β measures the relative importance of inflation against the output gap in the loss function. Also let rs be the ‘natural real rate of interest’ that would prevail at trend output.
(a) (5 points) Derive algebraically the monetary rule (MR-AD equation) that outlines the equilibrium relation between output and inflation in period 1.
(b) (5 points) Derive algebraically the interest rate rule.
(c) (5 points) Show graphically the effect of a supply shock in the IS-PC-MR model.
(d) (5 points) How does the response of the central bank to economic shocks depend on its loss function? Show graphically.