EC3115 Monetary Economics

Summer 2020

Section A

Answer all EIGHT questions from this section. Each question is worth 5 marks.

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. Money is typically a good store of value.

2. Money demand is higher when there is a lot of uncertainty.

3. A doubling of the velocity of circulation results in the price level doubling.

4. The Phillips curve provides a justification for the relevance of monetary policy in the short run.

5. US monetary aggregates have lost their informational content for inflation and real output in recent times.

6. Empirical evidence suggests that money is super-neutral.

7. In Lucas’ misperceptions model real effects of monetary policy persist in the long-run.

8. Under the segmentation hypothesis, the yield curve can be used to make predictions about expected inflation.

Section B

Answer THREE out of FIVE questions from this section. Each question is worth 20 marks.

9. Consider the Cagan(1956) model of hyperinflation. Let the money demand function be

mt − pt = αy − βRt ,

and the Fisher equation is given as

Rt = r + (p e t+1 − pt),

where mt is the log of money, pt and p e t+1 are the current and expected log price levels; Rt is the nominal interest rate. Log output, y, and the real interest rate, r, can be assumed constant. Define the growth rate of money as ∆mt = µ.

(a) (5 points) Derive, mathematically, the inflation rate, given some level of µ.

(b) (5 points) Explain how hyperinflation can arise in this model and how it affects the demand for money.

(c) (5 points) Explain why a government may wish to engage in money creation and how this can lead to hyperinflation.

(d) (5 points) A more recent phenomenon is the widespread experience of a very rapid, but non-explosive inflation as a result of a continuing government deficit, see for example the experience of Argentina and some other Latin American countries. Explain how this can be a stable equilibrium outcome; you may wish to show graphically.

10. Consider a Real Business Cycle model with money in the utility. The representative agent derives utility from consumption goods, Ct , and real money balances, Mt/Pt , but also from leisure, defined as (1 − lt) where lt is labour supplied. Utility is obtained from these variables not only today but into the future, discounted at rate β. Assume a lifetime utility function of the form.

where ζ and γ are constant preference parameters. The individual maximises utility subject to a budget constraint given in real terms.

The left-hand side comprises of consumption, Ct , real money balances, Mt/Pt , and sav-ings, Bt+1/Pt . The right-hand side comprises of real wage income, Wt/Pt lt , capital income,(1+rt−1) Bt/Pt—where Rt−1 is the nominal rate of return on savings, (Bt), from the previous period—and real money balances, Mt/Pt−1, carried over from the previous period.

(a) (4 points) Write down the dynamic Lagrangian.

(b) (5 points) Solve for the optimal consumption in t as a function of consumption in t + 1, rate of return rt and discount rate β. Comment.

(c) (5 points) Solve for optimal labour supply lt as a function real wages Wt/Pt and con-sumption Ct . Comment. Would your results change if the consumer would not derive utility from real money balances?

(d) (6 points) Solve for the real money demand Mt/Pt as a function of Ct and Rt . Comment.

11. Consider a classical Patinkin economy where a representative household utility is a func-tion of consumption, C, and real money balances, M/P, such that

Ut = Ct α (Mt/Pt) 1−α ,

and the household is subject to a budget constraint given by

Ct + Mt/Pt ≤ Yt + Mt−1/Pt .

Yt is the endowment and Mt−1 are the money balances accrued in the previous period.

(a) (6 points) What is the justification of adding money balances to the utility func-tion?

(b) (8 points) Calculate optimal goods and money demand. Provide intuition. If ele-ments in the utility function were additive of the form,

Ut = Ct α + (Mt/Pt) 1−α ,

instead of multiplicative, would your results change qualitatively? Discuss briefly using the new first order conditions?

(c) (6 points) Is there a role for monetary policy in this setting? What happens when the economy faces a money supply increase? Show graphically and provide intuition.

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) the prices are set by firms at t−1 and will only be effective in t; furthermore prices are equal to the expected to be market clearing price at time 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

y*t = δ0 + δ1t + δ2y*t−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, σu2);

(iv) the monetary policy is characterized by the expression

mt = µ0 + µ1mt−1 + et

where et is an i.i.d. normal money supply shock with et ∼ (0, σe2).

(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) Can Quantitative Easing (QE) programmes be effective if the model described above is indeed reflecting the reality? If yes, explain. If no, when can QE policies be effective policy tools?

13. Consider the aggregate supply curve

yt = y*+ α (πt − Et−1[πt ]) + Et .

where y* is the market clearing level of output, πt is inflation rate and Et is a productivity shock term where its mean is set equal to zero. Suppose that the monetary authority chooses the inflation rate directly and tries to minimise the following loss function:

L = πt 2 + λ(yt − ky*)2      where k > 1.

λ shows the authority’s preference for output fluctuations relative to inflation fluctua-tions. Assume that k > 1 so that a level of output greater than the market clearing level is desired reflecting political biases towards higher output.

(a) (5 points) Show graphically that in this environment the monetary authority with-out inflation commitment has an inflation bias. Discuss.

(b) (5 points) Show analytically the size of the inflation bias.

(c) (5 points) Discuss three elements that determine the level of inflation bias.

(d) (5 points) Suppose that the central banker would be penalised, by way of reduced salary, for allowing any inflation above the socially desired level, set in this case at zero. Suppose Ψ parameter reflects this penalty in the contract. The loss function that would be minimised would then be:

L Contract = πt 2 + λ(yt − ky*) 2 + Ψπt .

So that the central bank’s loss depends on the level of inflation through the Ψ parameter as well as squared inflation and squared output deviations. Show the size of the Ψ that would reduce the inflation bias to zero.