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 existence of uncertainty is a key reason for the existence of money as a means of exchange.

2. Other things equal a higher return on assets increases the individual demand for money.

3. Monetary authorities can fairly easily control the total supply of money by setting the base money and deposit ratio.

4. Inverse yield curves often signify upcoming recessions.

5. When the net worth of a firm increases, the external risk premium it has to pay in order to borrow also increases.

6. To reduce inflation bias, governments are advised to exert strong control over their central banks.

7. A downside of money in utility models is that they assume people derive utility from something that is intrinsically worthless.

8. A policy maker should ignore uncertainties when setting its policies.

Section B

Answer THREE out of FIVE questions from this section.

9. Friedman and Schwartz (1963) stated that ‘Inflation is always and everywhere a mone-tary phenomenon’.

(a) (5 points) Explain what is meant by the above phrase . Use the Quantity Theory of Money to support your answer.

(b) (5 points) Discuss two hypotheses that can be tested to check whether inflation is ‘always and everywhere a monetary phenomenon’.

(c) (10 points) Discuss the empirical evidence relating to the statement that ‘Inflation is always and everywhere a monetary phenomenon’.

10. Suppose a country with 20 people is set up so that everybody supplies 5 unit of labour per period (no matter what). There are 50 identical competitive firms maximising their profit function

Πi = YiP − W Ni

where Yi is output per firm, P is the price of output, W is the nominal wage and Ni is the number of units of labour. Both firms have a production function equal to Yi = ln Ni.

(a) (5 points) Derive the demand for labour of one firm, its output and the aggregate demand for labour in the economy.

(b) (5 points) Draw on a graph the aggregate demand and supply of labour. Compute algebraically the equilibrium wage (W/P) ∗ and equilibrium level of labour supply N*.

(c) (5 points) Suppose that the demand for real money balances is given by

M/P = 0.5Y*

and the money supply is equal to 20. What is the aggregate supply function for goods in the economy? Calculate the equilibrium level of output, Y* and the equilibrium price level, P*.

(d) (5 points) Suppose that the government doubles, once and for all, the money sup-ply. Does this improve the position of the workers in the economy?

11. 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 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) (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.

12. Consider a McCallum economy with sticky prices where the aggregate demand expression 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) Prices for date t are set by firms at t−1. The price at time t is equal to the expected market clearing price, that is pt = Et−1[p*t];

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

y*t = δ0 + δ1t + δ2yt* −1 + ut

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

(iv) Monetary policy is characterised by the expression

mt = µ0 + µ1mt−1 + et

where et is an i.i.d. normal money supply shock with et ∼ (0, σe 2 ).

(a) (5 points) Solve for the output gap, i.e. deviations of real output from the market clearing level.

(b) (5 points) Are unanticipated monetary policy changes effective? Show analytically and provide intuition.

(c) (5 points) Are anticipated monetary policy changes effective? Show analytically and provide intuition.

(d) (5 points) What is the Lucas critique? Evaluate the critique based on the output gap equation you have derived above.

13. Suppose that the Brainard-land is characterized by an aggregate supply equation (Phillips Curve):

πt = yt + aπt−1

and an aggregate demand equation (IS Curve):

yt = −bit + εt

with

ε ∼ (0, σε 2 ),

where π stands for inflation, y for the business cycle component of real output (or income), i for the short term interest rate that the policy maker can control and ε for the stochastic demand shocks hitting the economy; a and b are constants. The parameters of the system are known by the policy maker. The policy maker also cares about inflation stabilisation. Suppose that the expected loss function of the central bank takes the following form.

E(L) = E (πt − π*)2

where π* represents the target inflation.

(a) (10 points) What is the optimal central bank rate when the only source of uncer-tainty are additive shocks. Explain the concept ”certainty equivalence”.

(b) (10 points) The economic environment is the same as in the previous section except that the parameter b of the aggregate demand equation is allowed to vary over time, thus uncertain. Specifically, yt = −btit + εt, with ε ∼ (0, σε 2 ) and the parameter b ∼ (bb, σb 2 ). What would the be optimal central bank response in the presence of parameter uncertainty?