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. Other things equal a higher level of risk on bonds increases the demand for money.

2. The Wicksell Problem can be solved with the introduction of commodity money.

3. There is more information content in interest rates than in money aggregates to explain real output variations.

4. A key assumption of New Keynesian Models is the presence of nominal rigidities.

5. To reduce inflation bias, governments are advised to set up independent central banks.

6. Cash In Advance models predict that inflation will lead to a lower output.

7. A policy maker should ignore additive uncertainty when setting policy.

8. Theoretically, upwards sloping yield curves indicate that interest rates are expected to rise in the future.

Section B

Answer THREE out of FIVE questions from this section.

9. Suppose that the economy of Krugmania is characterised by the following Phillips Curve

πt = yt + aπt−1

and the IS Curve

yt = −bit

where y is the real output, π is the rate of inflation, i is the short term interest rate set by the Central Bank. Suppose that the IS Curve is subject to i.i.d. shocks with ∈ ∼ N(0, σ∈2). The Central Bank of Krugmania 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) (7 points) Solve for the optimal interest rate under these conditions.

(b) (7 points) Now suppose that there is parameter uncertainty about parameters a and b. 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) (6 points) Compare your results in (b) with those in (a), highlighting the main effects of parameter uncertainty.

10. In an economy with n households, assume a household’s utility depends on the quantity of goods consumed, X, and on real money balances, M/P.

U = X 1/2 (M/P) 1/2

Let the household have initial endowments X0 of goods and M0 of nominal money balances. The budget constraint faced by the household is then, in nominal terms:

P X + M ≤ P X0 + M0

.

(a) (5 points) What is a potential justification of the inclusion of money in the utility function?

(b) (10 points) Derive the equilibrium and explain whether money is neutral in this economy? Discuss analytically.

(c) (5 points) If the economy was characterised by limited participation in financial markets would your results change? Provide intuition without deriving the model.

11. Consider a McCallum economy with sticky prices where the aggregate demand expression is given as:

yt = β0 + β1(mt − pt) + β2Et−1 [pt+1 − pt ] + νt ,

where yt , mt and pt are the logs of real output, nominal money balances and the price level respectively at date t, νt is an i.i.d. normal aggregate demand shock with νt ∼ (0, σν 2 ), β0, β1, β2 are positive parameters and E is the expectations operator. To construct the aggregate supply assume the following:

(i) the market clearing price is denoted by p ∗ t ;

(ii) the prices are set by firms at t − 1 and will only be effective in t; furthermore the price at date t is the expectation at date t − 1 of the market clearing price at date

t, i.e. pt = Et−1 [p ∗ t ];

(iii) real output consistent with natural rate of unemployment, (y*), is determined by the following law of motion

yt* = δ0 + δ1t + δ2yt* −1 + ut

where t is a time trend, δ0, δ1, δ2 positive parameters and ut is an i.i.d. normal aggregate supply shock with ut ∼ (0, σu 2 );

(iv) the monetary policy is described by the expression

mt = µ0 + µ1mt−1 + et

where et is an i.i.d. normal money supply shock with et ∼ (0, σe 2 ); 0 < µ1 ≤ 1.

(a) (7 points) Solve for the output gap, i.e. deviations of real output from the market clearing level.

(b) (6 points) Are anticipated monetary policy changes effective? Show analytically and provide intuition.

(c) (7 points) Can Quantitative Easing (QE) programmes be effective if the model described above is valid ? If yes, explain. If no, when can QE policies be effective policy tools?

12. Consider Lucas’ misperceptions model. Suppose the aggregate supply curve is given as:

yt = y* + δ(Pt − Et−1[Pt ]),

where yt is aggregate output, y ∗ is the full employment/market clearing level of output and Pt is the price level at date t. δ is a positive parameter. Suppose that the aggregate demand is:

yt = 1000 + 3(Mt/Pt),

where Mt is the level of money supply at date t.

(a) (5 points) Suppose that there has been no shock in the economy for some time and no changes in policy are expected in the near future. If M = 600, find y and P in terms of y*.

(b) (5 points) What happens when the monetary authorities announce (in t − 1) that M will increase to 650 in t?

(c) (10 points) Show graphically and verbally what happens if this increase is entirely unexpected? In this final part, you do not need to solve for P and y.

13. Assume that the banking sector is described as follows:

D = d0 − d1(i − iD)

L = l0 + l1(i − iL),

where L stands for bank loans, D stands for bank deposits, iL the loan rate, iD deposit rate and i is the market interest rate. Assume that banks do not have operating costs and are not required to hold reserves.

(a) (7 points) Calculate the competitive equilibrium. Illustrate the equilibrium in a diagram. How do your results change when the government sets deposit rates equal to iD = a, with a < iL. Provide intuition.

(b) (6 points) Now suppose that government introduces a mandatory reserve ratio, r ∗ , such that total reserves R is given by R = r ∗D. How do your results change? What are the implications of such a reserve ratio policy on prices and quantities? Provide intuition.

(c) (7 points) Sometimes, it is suggested that the reserve ratio policy can be an alter-native to targeting interest rates or monetary aggregates. Can this be an effective policy to stabilize output and inflation fluctuations?