EC3115 Monetary economics
Section A
Answer all SIX 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. Without asymmetric information, there would be no need for financial intermediaries.
2. The optimal inflation rate is equal to zero.
3. Data revisions provided by the US Federal Reserve Bank tend to not be well-behaved.
4. In most countries Fiat money has replaced Credit money.
5. An unemployment-averse central bank will always try to exploit short-term Phillips curves to increase output, at the cost of higher inflation.
6. According to the Real Business Cycle model, investment is more volatile than consump-tion.
Section B
Answer TWO out of THREE questions from this section.
7. Suppose that the economy is characterised by the following aggregate supply (π) and aggregate demand (y) equations.
πt = ayt
yt = yt−1 − bit + εt
where y is the output gap, π is the inflation and i is the short term nominal rates the monetary authority controls. a and b are structural parameters of the model. The persistent output gap equation is subject to a shock ε t that is not observed in period t. This shock is distributed i.i.d. normally and ε ~ (0, σ2ε) and its statistical properties are known to the monetary authority. Suppose that the monetary authority has an expected loss function given by
Le = E[(πt − π*)2 + (yt − y*)2]
Note that the monetary authority cares both about inflation stabilisation around a target rate π* = 0 and output stabilisation around a target rate y
∗ = 0. Having this structure in mind answer the following questions.
(a) (13 points) Suppose the economy is subject to only additive shocks (ε). How should the monetary authority set the interest rate? What does the concept of certainty equivalence mean? Comment also on the relevance of the output persistence in the determination of the policy response.
(b) (13 points) Ever since the work by Brainard (1967) it is understood that structural relationships between key macroeconomic variables governed by the structural pa-rameters may change over time.
yt = yt−1 − btit
The policymaker knows from which distribution b parameter is drawn. Let b ∼ N(b, σb2). How do your results change? Interpret carefully the optimal interest rate policy response. What does the coefficient of variation represent?
(c) (6 points) Can you think of recent examples in monetary policymaking decisions where parameter uncertainty may have played a role?
8. The figure on the next page provides the Bank of England’s Spot Curve, estimated in both August 2021 (dotted line) and January 2022 (solid line). The horizontal axis is expressed in years to maturity. The table below provides selected information on the spot curve for January 2022.
|
Maturity (years)
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1
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2
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3
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4
|
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Spot Curve
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0.87
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1.01
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1.04
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1.07
|
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Break Even Inflation
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4.53
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4.94
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4.63
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4.42
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(a) (10 points) Interpret the data in the graph. Discuss what the shape and relative change of the two yield curves may tell us about the market outlook for the UK economy.
(b) (10 points) Using the data from January 2022, calculate the nominal and real for-ward rates.
(c) (6 points) How would your answers to (b) change qualitatively if there were risk premia.
(d) (6 points) Outline three theories of the yield curve and discuss how they can (or cannot) explain the main three empirical features of the yield curve.
9. 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, set in period 0, and a is a constant. The simplified Phillips curve is given by
π1 = π0 + α(y1 − ye),
where π1 is inflation in period 1 and π0 is the inflation in period 0; 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 − πT)2 + (y1 − ye)2,
with πT 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) (8 points) Derive algebraically the monetary rule (MR-AD equation) that outlines the equilibrium relation between output and inflation in period 1.
(b) (8 points) Derive algebraically the interest rate (IR) rule that outlines the relation between the equilibrium interest rate and deviations from target inflation.
(c) (8 points) Discuss a situation in which an interest rate rule is unlikely to be effective in stabilizing the economy.
(d) (8 points) Show graphically the effect of a demand shock in the IS-PC-MR model. Make sure to explain what the time path of the variables is.