Download Examiners` commentaries 2016 - University of London International

Examiners’ commentaries 2016
Examiners’ commentaries 2016
EC3115 Monetary economics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2015–16. The format and structure of the examination may change in future years,
and any such changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide and the Essential reading
references
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2015).
You should always attempt to use the most recent edition of any Essential reading textbook, even if
the commentary and/or online reading list and/or subject guide refer to an earlier edition. If
different editions of Essential reading are listed, please check the VLE for reading supplements – if
none are available, please use the contents list and index of the new edition to find the relevant
section.
General remarks
Learning outcomes
At the end of this course and having completed the Essential reading and activities you should be
able to:
•
explain and discuss why people hold money and why it is used in the trading process
•
solve macroeconomic models and assess the role and efficacy of monetary policy for various
types of models in both the Classical and Keynesian set-ups
•
describe and explain the main channels of the monetary transmission mechanism, through
which monetary policy can have real effects on the economy
•
discuss the merits and disadvantages of different monetary policies used by central banks
•
introduce the concepts of data and parameter uncertainty and discuss the policy under
uncertainty.
Format of the examination
This course is intended to take an analytical approach to monetary economics. Candidates are
expected to have mastered the main principles, in the form of a number of key theoretical models.
They should be able to use these flexibly, as tools to analyse economic issues and data. They are
also expected to have some knowledge of the empirical evidence on these models.
The paper contains 13 questions in total with eight in Section A and five in Section B. The format of
Section A now requires candidates to answer all eight questions from this section. These questions
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EC3115 Monetary economics
are intended to test your knowledge of important concepts and understanding of key analytical
points. A brief answer is expected, and candidates need to be selective in order to focus their answers
on the most important points, since, for some of these questions, a very long answer could be given.
Section B consists of five questions, three of which must be answered by the candidate. The
questions in Section B can be of three different types. They are intended to test the candidate’s
ability to understand and interpret empirical data and relate them to relevant theories where
possible. Some general knowledge of recent economic events is sometimes helpful in answering these
questions. The sub-sections of this type of question will typically relate to a single concept or model.
The second type of question that can appear in Section B will require the candidate to carry out
calculations and problem solving in relation to specific models. Finally, the third type of question
can be essay-type questions that test the candidate’s ability to discriminate and evaluate; these will
be intended to test whether the candidate has done further reading beyond the core text/subject
guide. All the question types in Section B will typically relate to a single concept or model.
The subject guide contains brief notes on the main topics in the syllabus, and gives
recommendations on textbooks and other readings. It is very important that candidates study
widely, using textbooks and other readings, particularly those items marked Essential reading. The
subject guide alone is not sufficient – it is not intended as a textbook, but as a guide to the relevant
literature. Candidates should aim to understand the key analytical principles with enough condence
to be able to use them as a set of tools to apply to a wide range of economic questions. General
knowledge of recent events relating to macroeconomics is valuable, particularly when commenting on
economic data in Section B of the examination.
Planning your time in the examination
The examination is divided into two parts. As mentioned above, Section A requires answers to all
eight questions and Section B requires answers to three out of five questions. Candidates should
allow ten minutes for careful reading to ensure that they understand the questions and make
appropriate choices in Section B. Each question in Section A is worth five marks, and candidates
should plan to spend ten minutes on each question, one hour and 20 minutes on the section. Each
question in Section B is worth 20 marks and 30 minutes should be allowed for each, or 90 minutes
for the whole section. Planning your time in an examination like this, where there are different
sections and questions of different lengths, is important. It is easy for candidates to spend too long
on Section A, and to have to skimp on Section B. Section A answers must be brief and to the point.
What are the examiners looking for?
The examiners are looking for answers that show an understanding and ability to apply economic
principles, combined, where appropriate, with factual knowledge. The use of diagrams to illustrate
points is welcomed by the examiners. Candidates are expected to show independent critical
judgement, for example in Section A where the statements given may be true or false or somewhere
in-between. Candidates should be able to distinguish between true and false, or partially true and
partially false, claims. In the data-based questions in Section B, the examiners are looking for
comments based on a close examination of the data provided. Candidates’ comments should reflect
appropriate economic principles and theoretical ideas. Comments should, where this is relevant, be
supported by some knowledge of other facts and circumstances beyond those shown in the question
paper. It is not expected that candidates will have studied in detail the data for the countries, the
variables, or the time period that are mentioned in the question. However, it is expected that they
will have some general knowledge of a wide range of recent economic events. The essay-type
questions in Section B are intended to test whether the candidate has done further reading beyond
the core text/subject guide.
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Examiners’ commentaries 2016
Key steps to improvement
In general, in the examination scripts for the 2016 examinations, many candidates did not set out
their answers in as much depth as the examiners expect for a final year optional course that forms
part of a degree programme. Candidates are encouraged to use diagrams to illustrate their
arguments where appropriate. They are also expected to explain in words the economic significance
of algebraic derivations. A significant group of candidates, of course, performed very well, and wrote
lucid, detailed, well-illustrated answers that showed good technical skills, understanding of the
economic principles and good knowledge of relevant recent economic events.
Key steps for improvement include the following.
•
Allow yourself time to read the questions and carefully manage your time in the
examination.
•
Answer the question on the paper directly. Do not make use of set piece answers to other,
possibly similar, questions. Do not write irrelevant material just for the sake of lengthening
your answers.
•
Make full use of diagrams where possible.
•
Combine manipulations of algebraic models with explanations in words of relevant economic
principles.
Examination revision strategy
Many candidates are disappointed to find that their examination performance is poorer than they
expected. This may be due to a number of reasons. The Examiners’ commentaries suggest ways of
addressing common problems and improving your performance. One particular failing is ‘question
spotting’, that is, confining your examination preparation to a few questions and/or topics which
have come up in past papers for the course. This can have serious consequences.
We recognise that candidates may not cover all topics in the syllabus in the same depth, but you
need to be aware that the examiners are free to set questions on any aspect of the syllabus. This
means that you need to study enough of the syllabus to enable you to answer the required number of
examination questions.
The syllabus can be found in the Course information sheet in the section of the VLE dedicated to
each course. You should read the syllabus carefully and ensure that you cover sufficient material in
preparation for the examination. Examiners will vary the topics and questions from year to year and
may well set questions that have not appeared in past papers. Examination papers may legitimately
include questions on any topic in the syllabus. So, although past papers can be helpful during your
revision, you cannot assume that topics or specific questions that have come up in past examinations
will occur again.
If you rely on a question-spotting strategy, it is likely you will find yourself in difficulties
when you sit the examination. We strongly advise you not to adopt this strategy.
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EC3115 Monetary economics
Examiners’ commentaries 2016
EC3115 Monetary economics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2015–16. The format and structure of the examination may change in future years,
and any such changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide and the Essential reading
references
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2015).
You should always attempt to use the most recent edition of any Essential reading textbook, even if
the commentary and/or online reading list and/or subject guide refer to an earlier edition. If
different editions of Essential reading are listed, please check the VLE for reading supplements – if
none are available, please use the contents list and index of the new edition to find the relevant
section.
Comments on specific questions – Zone A
Candidates should answer ELEVEN of the following THIRTEEN questions: all EIGHT from
Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are strongly
advised to divide their time accordingly.
If more questions are answered than requested, only the first answers attempted will be counted.
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.
Question 1
The existence of uncertainty is a key reason for the existence of money as a means
of exchange.
Reading for this question
Goodhart (1989), Chapter 2 (pp. 29–30).
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Examiners’ commentaries 2016
Approaching the question
True.
There are three main motives for money demand: transactionary, precautionary and speculative.
The transactionary motive is the only motive of these three that does not depend on uncertainty.
A good answer describes all three motives and discusses how precautionary and speculative
demand depend on uncertainty.
Question 2
Other things equal a higher return on assets increases the individual demand for
money.
Reading for this question
Subject guide, Chapter 3.
Approaching the question
False.
Good answers highlight the determinants of individual money demand. Higher interest rates lead
to higher opportunity costs for holding money and hence reduce the individual demand.
Question 3
Monetary authorities can fairly easily control the total supply of money by setting
the base money and deposit ratio.
Reading for this question
Subject guide, Chapter 4.
Goodhart (1989).
Approaching the question
False.
Theoretically, to directly control the total supply of money, a central bank would need to set the
absolute level of reserves held, and not just the reserve ratio. Furthermore, a good answer would
point out that in reality even then controlling the total supply of money is by no means
straightforward (see for example Goodhart for a discussion).
Question 4
Inverse yield curves often signify upcoming recessions.
Reading for this question
Subject guide, Chapter 13.
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EC3115 Monetary economics
Approaching the question
True.
A good answer uses the expectations theory or the preferred habitat theory of yield curves
combined with the Fisher equation to show that inverse yield curves indicate an expected
slowdown in inflation and link that to recessions.
Question 5
When the net worth of a firm increases, the external risk premium it has to pay in
order to borrow also increases.
Reading for this question
Subject Guide, Chapter 10.
Approaching the question
False.
A good answer should refer to financial accelerator models and argue that there is an inverse
relationship between external risk premia and firms’ net worth in the presence of asymmetric
information between lenders and entrepreneurs.
Question 6
To reduce inflation bias, governments are advised to exert strong control over their
central banks.
Reading for this question
Subject guide, Chapter 11.
Approaching the question
False.
The converse. A good answer discusses what inflation bias is and indicates that one of the
possible solutions to decrease inflation bias is an independent central bank with a clear mandate.
Question 7
A downside of money in utility models is that they assume people derive utility
from something that is intrinsically worthless.
Reading for this question
Subject guide, Chapter 8.
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Examiners’ commentaries 2016
Approaching the question
True.
A good answer discussed money in utility models and points out an alternative, such as
cash-in-advance models, that do not suffer from this drawback.
Question 8
A policy maker should ignore uncertainties when setting its policies.
Reading for this question
Subject guide, Chapter 12.
Approaching the question
False/uncertain.
A good answer discusses different sources of uncertainty and how they affect policy setting. If
there is only additive uncertainty, policy setting remains unchanged, but with parameter
uncertainty, a central bank should be more conservative than otherwise (Brainard conservatism).
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EC3115 Monetary economics
Section B
Answer THREE out of FIVE questions from this section.
Question 9
Friedman and Schwartz (1963) stated that ‘Inflation is always and everywhere a
monetary phenomenon’.
(a) Explain what is meant by the above phrase. Use the Quantity Theory of Money
to support your answer.
(5 marks)
(b) Discuss two hypotheses that can be tested to check whether inflation is ‘always
and everywhere a monetary phenomenon’.
(5 marks)
(c) Discuss the empirical evidence relating to the statement that ‘Inflation is always
and everywhere a monetary phenomenon’.
(10 marks)
Reading for this question
Subject guide, Chapter 6.
De Grauwe and Polan (2005) ‘Is inflation always and everywhere a monetary phenomenon?’
Scandinavian Journal of Economics, 107(2), pp. 239–59.
Approaching the question
(a) Variations in money lead to variations in inflation. Rewriting the Quantity Theory of
Money in log-differences gives:
p = m − y + v.
If changes in output y and velocity v are taken as exogenous, then any changes in m will
lead to proportional changes in p.
(b) Following de Grauwe and Polan (2005) one can rewrite the above relation as an econometric
model:
pt = α + β1 mt + β2 yt + ut
where changes in the volatility (vt ) are subsumed in the error term ut as they are assumed
unobservable. Using this framework, the following two hypotheses can be tested: the
‘proportionality proposition’ that movements in inflation are proportional to movements in
the growth of money, i.e. β1 = 1, and the ‘orthogonality proposition’ (or ‘neutrality
proposition’) that states that output and volatility are exogenous, i.e. β2 = 0.
(c) This discussion can draw on many different papers such as de Grauwe and Polan (2005),
which is part of the required reading list. Candidates are expected to discuss empirical
evidence on both of the propositions highlighted in part (b). De Grauwe and Polan (2005)
find partial support for the above statement. Their findings can be summarised as follows.
1. They find little evidence for the ‘proportionality proposition’. There is a strong relation
between the long-run growth rate of money and inflation; this relation is not
proportional. This strong link is wholly due to high-inflation countries.
2. In low-inflation countries, the ‘neutrality proposition’ holds; in the long run, inflation
and money growth are independent of each other.
3. It seems that volatility increases with higher inflation.
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Examiners’ commentaries 2016
4. The time it takes for the long-run effects of monetary expansions to be realised depends
on the level of inflation. For high-inflation countries the transmission may happen within
a year.
5. In low-inflation countries money growth and inflation are inversely related; while in
high-inflation countries they are positively related.
The above imply that using the money stock as a guide for steering price stability might not
be useful for low-inflation countries.
Question 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 = Yi P − 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) Derive the demand for labour of one firm, its output and the aggregate demand
for labour in the economy.
(5 marks)
(b) 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 ∗ .
(5 marks)
(c) 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 ∗ .
(5 marks)
(d) Suppose that the government doubles, once and for all, the money supply. Does
this improve the position of the workers in the economy?
(5 marks)
Reading for this question
Subject guide, Chapter 9.
Approaching the question
(a) To solve for the demand of labour of a firm, solve the profit maximisation problem:
max Π = Yi P − W Ni
Ni
giving the firm a level of demand for labour as:
Ni = P/W
and firm output as:
Yi = ln(P/W ) = − ln(W/P )
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EC3115 Monetary economics
and aggregate demand for labour as:
N ∗ = kP/W = 50P/W
where k = 50 is the number of firms in the economy.
(b) The supply of labour is fixed at N D = 20 × 5 = 100 = N ∗ . Equating the supply of labour to
the aggregate demand for labour gives:
N ∗ = 100
N ∗ = 50P ∗ /W ∗ → W ∗ /P ∗ = 0.5.
(c) Output is not dependent on demand, as N ∗ = N D = 100 is fixed. Solving for Y ∗ , we have:
Y ∗ = kYi = 50 ln(100/50) ≈ 34.66.
Substituting the above into the demand for real money balances and solving for P ∗ gives:
M/P ∗ = 0.5Y ∗
20/P ∗ = 0.5 × 34.66
P ∗ = 20/17.33 ≈ 1.15.
(d) No, their position remains unchanged. As labour supply and aggregate output are fixed, the
increase in the money supply will lead to a one-for-one increase in prices and nominal wages
and leave the real wages unchanged. Therefore, money is neutral in this setting and workers
are indifferent to the monetary shock.
Question 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 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) Derive algebraically the monetary rule (MR-AD equation) that outlines the
equilibrium relation between output and inflation in period 1.
(5 marks)
(b) Derive algebraically the interest rate rule.
(5 marks)
(c) Show graphically the effect of a supply shock in the IS-PC-MR model.
(5 marks)
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Examiners’ commentaries 2016
(d) How does the response of the central bank to economic shocks depend on its
loss function? Show graphically.
(5 marks)
Reading for this question
Subject guide, Chapter 10.
Carlin and Soskice (2006). Macroeconomics: Imperfections, Institutions and Policies. Chapters
3, 5 and 15.
Approaching the question
(a) We have:
(y1 − ye ) = −αβ(π1 − π T ).
See Carlin and Soskice for the derivation.
(b) We have:
(r0 − rs ) =
1
(π0 − π T ).
a(α + 1/(αβ))
See Carlin and Soskice for the derivation.
(c) With a supply shock the long-run Phillips curve shifts (say to the right) and inflation drops.
The central bank forecasts the new Phillips curve and moves along the IS curve to lower the
interest rate (the stabilising rate has also decreased). This leads to an increase in output;
inflation will still be below its original level initially. See Carlin and Soskice for the full
derivation and a graphical representation.
(d) The inflation rate chosen on the forecasted Phillips curve will depend on the indifference
curves of the central bank. If the central bank is more inflation averse, it will target the
output gap less aggressively. See Carlin and Soskice for details and a graphical
representation of different realisations of the central bank loss function.
Question 12
Consider a McCallum economy with sticky prices where the aggregate demand
expression given as:
yt = β0 + β1 (mt − pt ) + β2 Et−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, σν2 . 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
∗
yt∗ = δ0 + δ1 t + δ2 yt−1
+ ut
where t being time trend, δ0 , δ1 , δ2 positive
parameters and ut is an i.i.d. normal
2
aggregate supply shock with ut ∼ 0, σu
;
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EC3115 Monetary economics
(iv) Monetary policy is characterised by the expression
mt = µ0 + µ1 mt−1 + et
where et is an i.i.d. normal money supply shock with et ∼ 0, σe2 .
(a) Solve for the output gap, i.e. deviations of real output from the market clearing
level.
(5 marks)
(b) Are unanticipated monetary policy changes effective? Show analytically and
provide intuition.
(5 marks)
(c) Are anticipated monetary policy changes effective? Show analytically and
provide intuition.
(5 marks)
(d) What is the Lucas critique? Evaluate the critique based on the output gap
equation you have derived above.
(5 marks)
Reading for this question
Subject guide, Chapter 9.
McCallum (1989), Chapters 9 and 10.
Approaching the question
(a) The solution is:
yt − yt∗ = β1 (mt − Et−1 [mt ]) + vt − ut .
For a full derivation see McCallum, Chapter 10. A basic intuition is given below.
By combining the IS and LM equations, we can derive an AD expression of the form:
yt = β0 + β1 (mt − pt ) + β2 Et−1 [pt+1 − pt ] + vt .
Let yt∗ be the market-clearing output; yt∗ must equal the demand when pt = p∗t , hence:
yt∗ = β0 + β1 (mt − p∗t ) + β2 Et−1 [pt+1 − p∗t ] + vt .
Rearranging to obtain p∗t on the left-hand side gives:
p∗t =
β0 − yt∗ + β1 mt + β2 Et−1 [pt+1 ] + vt
β1 + β2
We now need an expression telling us how the market-clearing/full-employment level of
output, yt∗ , evolves over time.
Take expectations of the third condition conditional on information available at date t − 1:
Et−1 [yt∗ ]
⇒ Et−1 [yt∗ ]
∗
= δ0 + δ1 t + δ2 yt−1
= yt∗ − ut .
Do the same for the second condition, noting that Et−1 [vt ] = 0:
Et−1 [yt∗ ] = β0 + β1 Et−1 [mt − p∗t ] + β2 Et−1 [pt+1 − p∗t ].
Equating these two equations and exploiting that Et−1 p∗t = p gives:
yt∗ = β0 + β1 (Et−1 [mt ] − pt ) + β2 (Et−1 [pt+1 ] − pt ) + ut .
Now we have all the ingredients needed to define the solution yt − yt∗ (i.e. deviations of
output from the market-clearing level).
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Examiners’ commentaries 2016
(b) First show how the output gap responds to monetary policy (using the monetary policy
rule):
yt − yt∗ = β1 et + vt − ut
then show that the random component of monetary policy, the monetary policy shock et ,
will have real effects.
(c) First reiterate the relation between the output gap and monetary policy, derived in part (b):
yt − yt∗ = β1 et + vt − ut .
Then show that the anticipated component of monetary does not affect the output gap.
Good answers might wish to link this answer to the ‘policy ineffectiveness proposition’.
(d) The Lucas critique refers to the instability of reduced-form expressions used for policy
making or policy appraisal.
In the context of the model above:
yt − yt∗ = β1 et + vt − ut .
Instead of et , write mt = Et−1 [mt ] = mt − µ0 − µ1 mt−1 . We have:
yt − yt∗ = −β1 µ0 + β1 mt − β1 µ1 mt−1 + (vt − ut ).
If this equation were given to an econometrician, he or she would run a regression of the
form:
yt − yt∗ = γ0 + γ1 mt + γ2 mt−1 + η1 .
Since γ1 > 0, we may then think that an increase in the money supply should cause an
increase in output above yt∗ . For example, if γ1 was found to equal 0.5, then increasing the
money supply by 2% should cause a 1% increase in output.
In reality, the change in people’s expectations associated with this policy change will cause
the reduced form to break down. If the authorities increased the money supply by increasing
µ0 , indeed this will have a positive effect on output, via γ1 , but it will also have a negative
effect on output since γ0 = −β1 µ0 . The effect of an expansionary monetary policy will be
purely inflationary.
Question 13
Suppose that the Brainard-land is characterised by an aggregate supply equation
(Phillips Curve):
πt = yt + aπt−1
and an aggregate demand equation (IS Curve):
yt = −bit + εt
with
ε ∼ (0, σε2 ),
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:
2
E(L) = E (πt − π ∗ )
where π ∗ represents the target inflation.
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EC3115 Monetary economics
(a) What is the optimal central bank rate when the only source of uncertainty are
additive shocks. Explain the concept ‘certainty equivalence’.
(10 marks)
(b) 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 = −bt it + εt , with ε ∼ (0, σε2 ) and the parameter
b ∼ (b
b, σb2 ). What would the be optimal central bank response in the presence of
parameter uncertainty?
(10 marks)
Reading for this question
Subject guide, Chapter 12.
Brainard, W. (1967), Uncertainty and effectiveness of policy, American Economic Review
(papers and proceedings), 57 (2), pp. 411–25.
Approaching the question
(a) The case with additive uncertainty. The only source of uncertainty is the presence of
stochastic shocks. Given that the policy maker knows the nature of the shocks with a mean
of zero (E(ε) = 0) and a constant variance (E(ε2 ) = σε2 ), it will form an expectation about
these. Substitute the perceived structure of the economy into the objective function of the
central bank:
2
Le = E (aπt−1 − bit + εt − π ∗ )
or:
Le
2
= a2 πt−1
+ b2 i2t + E ε2 + π ∗2 − 2aπt−1 bit + 2aπt−1 E(εt )
| {z }
| {z }
0
σε2
∗
∗
∗
−2aπt−1 π − 2bit E(εt ) + 2bit π − 2E(εt )π .
| {z }
| {z }
0
0
Note that, by setting E(ε) = 0 and E(ε2 ) = σε2 we have inserted the policy maker’s
expectations about the shocks. The policy maker’s job is to minimise the loss with the use
of the monetary policy instrument it . We have:
∂Le
∂it
=
2b2 it + 2bπ ∗ − 2aπt−1 b = 0
it
=
−π ∗ + aπt−1
.
b
It is important to notice that the policy rate set by the policy maker is the same as the one
that it would set if there were no shocks hitting the economy. This is the certainty
equivalence result. This means additive shocks do not affect the way monetary policy is
conducted. The best the policy maker can do is simply to ignore them.
(b) The case with parameter uncertainty. Now, we can include a bit of complication. The
economic environment is the same as in the previous part except that the parameter b of the
real income equation is allowed to vary over time. We capture this by adding a time
subscript to parameter b. Specifically:
yt = −bt it + εt
with:
ε ∼ (0, σε2 ),
b ∼ (bb, σb2 )
where the shocks are still additive, however we also see that the parameter b has a certain
distribution such that its mean is bb and its variance is σb2 . It is important to note that this
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Examiners’ commentaries 2016
information is available to the policy maker such that it can form expectations about the
value of the parameter b.
By substituting we obtain again an expression for current inflation as a function of past
inflation, the policy rate, the shocks hitting the economy and the novel element of the
time-varying parameter b. We have:
πt = aπt−1 − bt it + εt .
The problem of the central bank now becomes:
Le
=
=
2
E (aπt−1 − bt it + εt − π ∗ )
2
a2 πt−1
+ E(b2t )i2t + E ε2 + π ∗2 − 2aπt−1 E(bt )it + 2aπt−1 E(εt )
| {z }
| {z }
0
σε2
∗
∗
+2aπt−1 π + 2E(bt )it E(εt ) − 2E(bt )it π − 2E(εt )π
| {z }
| {z }
0
∗
0
Remember that you can write the variance of b as σb2 = E(bt − bb)2 = E(b2t − 2btbb + bb2 ). Given
that E(bt ) = bb that is equal to σb2 = E(b2t ) − E(bb2 ). This allows us to rewrite the Le as:
Le
2
= a2 πt−1
+ E(b2t )i2t + σε2 + π ∗2 − 2aπt−1 E(bt )it + 2aπt−1 π ∗ + 2E(bt )it π ∗




2
= a2 πt−1
+ σb2 + E(bb2 ) i2t + σε2 + π ∗2 − 2aπt−1 E(bt )it + 2aπt−1 π ∗ + 2E(bt )it π ∗
| {z }
| {z }
| {z }
b
b2
b
b
b
b
2
= a2 πt−1
+ σb2 i2t + σε2 − 2aπt−1bbit + 2aπt−1 π ∗ + bb2 i2t + π ∗2 + 2bbit π ∗ .
We can now solve the policy maker’s optimisation problem that is:
∂Le
∂it
=
2σb2 it − 2aπt−1bb + 2 bbit + π ∗ bb = 0
it
=
(aπt−1 − π ∗ ) bb
σb2 + bb2
=
(aπt−1 − π ∗ )
.
(σb2 +bb2 )
b
b
The expression σb /bb refers to the coefficient of variation. It represents the trade-off between
returning inflation to target and increasing uncertainty about inflation depends on the
variance of the parameter relative to its mean level. A large coefficient of variation means
for a small reduction in the inflation bias the central bank induces a large variance into
future inflation. Once parameter uncertainty is taken into account, inflation variance
depends on the interest rate reactions. A policy maker’s decisions affect uncertainty of
future inflation. Hence rather than a strong reaction or ‘cold turkey’, gradualism (sustained
policy reaction) is preferable (Brainard conservatism).
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EC3115 Monetary economics
Examiners’ commentaries 2016
EC3115 Monetary economics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2015–16. The format and structure of the examination may change in future years,
and any such changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide and the Essential reading
references
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2015).
You should always attempt to use the most recent edition of any Essential reading textbook, even if
the commentary and/or online reading list and/or subject guide refer to an earlier edition. If
different editions of Essential reading are listed, please check the VLE for reading supplements – if
none are available, please use the contents list and index of the new edition to find the relevant
section.
Comments on specific questions – Zone B
Candidates should answer ELEVEN of the following THIRTEEN questions: all EIGHT from
Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are strongly
advised to divide their time accordingly.
If more questions are answered than requested, only the first answers attempted will be counted.
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.
Question 1
An advantage of indirect barter over fiat money is that indirect barter does not
require trust between individuals.
Reading for this question
Subject guide, Chapter 1.
Approaching the question
False.
A good answer will point out that both indirect barter and fiat money will require trust.
16
Examiners’ commentaries 2016
However, while indirect barter requires trust between individuals (a good answer could highlight
the Wicksell problem); fiat money mainly requires trust in the issuing authority.
Fiat money is generally seen as an evolution (and improvement) of indirect barter and
commodity money.
Question 2
The transactions demand for money can be thought of as the demand for money
that remains if there is no uncertainty.
Reading for this question
Subject guide, Chapter 3.
Goodhart(1989), Chapter 3 (page 53).
Approaching the question
True.
There are three main motives for money demand: transactionary, precautionary and speculative.
The transactionary motive is the only motive of these three that does not depend on uncertainty.
A good answer describes all three motives and discusses how precautionary and speculative
demand depend on uncertainty.
Question 3
Real business cycle models give a good explanation of the high observed volatility of
investments compared to consumption volatility.
Reading for this question
Subject guide, Chapter 8.
Approaching the question
True.
A good answer centres around the fact that in real business cycle models risk-averse consumers
smooth their consumption and this consumption smoothing leads to higher investment volatility.
Question 4
‘Wet’ central banks do not care about their reputation.
Reading for this question
Subject guide, Chapter 11.
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EC3115 Monetary economics
Approaching the question
False.
Wet central banks try to exploit short-term relations; in order to do so they need a reputation.
As such they may act like a ‘hard-nosed’ central bank and act tough on inflation to build up a
reputation.
Good answers explain what constitutes ‘wet’ and ‘hard-nosed’ central banks and may wish to
frame the above problem in a multi-period game setting to show why reputation affects the
ability of a central bank to ‘move along the Philips curve’.
Question 5
If market interest rates go up, bond prices tend to rise as they have now become
more attractive.
Reading for this question
Subject guide, Chapter 13.
Approaching the question
False.
The opposite. Rising interest rates make existing bonds (with fixed interest rates) less attractive,
leading to lower prices.
This can be easily demonstrated by writing out the formula of a console bond and evaluating the
price of the console by increasing the interest rate (but keeping the coupon rate constant).
Question 6
Government regulation on deposit rates can lead to profits for banks.
Reading for this question
Subject guide, Chapter 4.
Approaching the question
True.
The key observation is that rl > rd . See Figure 4.2 in the subject guide, and surrounding text,
for an illustration of how lower deposit rates can lead to bank profits.
Question 7
Central banks tend to smooth interest rates because of additive uncertainty in their
models.
Reading for this question
Subject guide, Chapter 12.
18
Examiners’ commentaries 2016
Approaching the question
False.
Central banks do smooth their interest rates (see for example Figure 12.5 of the subject guide),
but not because of additive uncertainty; rather they smooth because of uncertainty about the
structural parameters of their models and the true state of the economy.
Good answers discuss both the certainty equivalence and the effects of parameter uncertainty.
Question 8
Friedman suggested a constant money growth rule, mainly because of the time
inconsistency of monetary policy.
Reading for this question
Subject guide, Chapter 10.
Approaching the question
False.
The constant money growth rule was not levelled against time inconsistency (or neutrality).
Rather Friedman worried about the long and variable lags of activist monetary policy. Good
answers discuss the concepts of time inconsistency, the time lags and the constant money growth
rule.
19
EC3115 Monetary economics
Section B
Answer THREE out of FIVE questions from this section.
Question 9
In their article ‘Money, income, prices and interest rates’ Friedman and Kuttner
(1992) discuss the information content of variations in a range of US monetary
aggregates and short-term interest rates regarding the macroeconomy.
(a) Explain what is meant in this context by the ‘information content’ of monetary
aggregates and short-term interest rates.
(5 marks)
(b) Discuss the empirical evidence regarding the information content of monetary
aggregates and short-term interest rates.
(10 marks)
(c) Most central banks focus their monetary policy announcements on short-term
interest rates rather than monetary aggregates. Is this approach supported or
disputed by your answers in (a) and (b)? Explain your answer.
(5 marks)
Reading for this question
Subject guide, Chapter 6.
Friedman and Kuttner (1992) ‘Money, income, prices and interest rates’ American Economic
Review 82, pp. 472–92.
Aksoy and Piskorski (2006), ‘US domestic money, inflation and output’, Journal of Monetary
Economics, pp. 183–97.
Approaching the question
(a) In the context of Friedman and Kuttner (1992), the information content of policy
instruments can be defined as the extent to which they are regularly and reliably associated
with variations in relevant macroeconomic variables such as income, prices, employment, or
other variables that the central bank is trying to influence.
(b) A good answer discusses both sides of the argument regarding the information content of
money. Natural choices would be the results found in Friedman and Kuttner (1992) and the
results of Aksoy and Piskorski (2006), both of which are required reading in the subject
guide.
Friedman and Kuttner (1992) show that the information content of money has been
drastically reduced since the 1980s and can no longer explain variations in US GDP and
inflation. Short-term interest rates retain their information content throughout the entire
sample.
On the other hand, Aksoy and Piskorski (2006) argue that there is in fact a relation between
money growth and macroeconomic fundamentals (in the US), but this is obscured by the
way money aggregates are measured. Once money aggregates are redefined/measured as
domestic money aggregates, money aggregates do contain valuable information about
macroeconomic fundamentals.
(c) This approach is supported based on information content arguments for most advanced
economies. As interest rates currently have a better and stable informational content to
explain variations in real output and to some extent inflation than monetary aggregates,
these are the natural focus for monetary policy announcements. In any case, setting policy
rates is done through money markets (open market operations), therefore policy
implementation will directly affect liquidity conditions, thus monetary aggregates.
20
Examiners’ commentaries 2016
Question 10
Suppose a country with 10 people is set up so that everybody supplies 1 unit of
labour per period (no matter what). There are 2 identical competitive firms
maximising their profit function
Πi = Yi P − 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) Derive the demand for labour of one firm, its output and the aggregate demand
for labour in the economy.
(5 marks)
(b) 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 ∗ .
(5 marks)
(c) Suppose that the demand for real money balances is given by
M/P = 0.5Y
and the money supply is equal to 5. What is the aggregate supply function for
goods in the economy? Calculate Y ∗ and P ∗
(5 marks)
(d) Supposed that the government doubles, once and for all, the money supply.
Does this improve the position of the workers in the economy?
(5 marks)
Reading for this question
Subject guide, Chapter 9.
Approaching the question
(a) To solve for the demand of labour of a firm, solve the profit maximization problem:
max Π = Yi P − W Ni
Ni
giving the firm a level of demand for labour as:
Ni = P/W
and firm output as:
Yi = ln(P/W ) = − ln(W/P )
and aggregate demand for labour as:
N ∗ = kW ∗ /P ∗ = 2W ∗ /P ∗
where k = 2 is the number of firms in the economy.
(b) The supply of labour is fixed at N D = 10 × 1 = 10 = N ∗ . Equating the supply of labour to
the aggregate demand for labour gives:
N ∗ = 10
N ∗ = 2P ∗ /W ∗ → W ∗ /P ∗ = 0.2.
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EC3115 Monetary economics
(c) Output is not dependent on demand, as N ∗ = N D = 100 is fixed. Solving for Y ∗
Y ∗ = kYi = 2 ln(10/2) ≈ 3.22.
Substituting the above into the demand for real money balances and solving for P ∗ gives:
M/P ∗ = 0.5Y ∗
5/P ∗ = 0.5 × 3.22
P ∗ = 5/1.61 ≈ 3.11.
(d) No, their position remains unchanged. As labour supply and aggregate output are fixed, the
increase in the money supply will lead to a one-for-one increase in prices and nominal wages
and leave the real wages unchanged. Therefore, money is neutral in this setting and workers
are indifferent to the monetary shock.
Question 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 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) Derive algebraically the monetary rule (MR-AD equation) that outlines the
equilibrium relation between output and inflation in period 1.
(5 marks)
(b) Derive algebraically the interest rate rule.
(5 marks)
(c) What is the role of forecasting, by the central bank, in the IS-PC-MR model?
(5 marks)
(d) Show graphically the effect of a demand shock in the IS-PC-MR model.
(5 marks)
Reading for this question
Subject guide, Chapter 10.
Carlin and Soskice (2006). Macroeconomics: Imperfections, Institutions and Policies. Chapters
3, 5 and 15.
22
Examiners’ commentaries 2016
Approaching the question
(a) We have:
(y1 − ye ) = −αβ(π1 − π T ).
See Carlin and Soskice for the derivation.
(b) We have:
(r0 − rs ) =
1
(π0 − π T ).
a(α + 1/(αβ))
See Carlin and Soskice for the derivation.
(c) The central bank must forecast the Phillips curve and the IS curve that it will face next
period. See Carlin and Soskice for details.
(d) Without loss of generality assume the IS shock has pushed y0 above ye . The central bank
will forecast the Phillips curve and choose the inflation output pair that minimises its loss
function. The central bank will then set the optimal interest rate based on its forecast of the
IS curve. In the absence of further shocks, inflation will start to fall and output converges to
ye as the central bank repeats the above steps to update the optimal interest rate. See
Carlin and Soskice for details and graphical representations.
Question 12
Suppose that the economy is characterized by an expectations augmented Phillips
curve given by:
yt = y ∗ + α(πt − Et−1 πt ) + εt ,
where yt is the current real output, y ∗ is the trend output, πt is inflation, π ∗ is the
target inflation and ε is an aggregate demand shock with ε ∼ iid N (0, σε2 ). Suppose
that the Central Bank can control inflation directly and attempts to minimize a
quadratic loss function given as:
2
L = (1 − λ)(πt − π ∗ )2 + λ (yt − ky ∗ ) ,
with k > 1. Parameter λ represents the Central Bank’s preference parameter
reflecting her preference for stabilizing output fluctuations relative to inflation
fluctuations.
(a) Calculate the inflation bias.
(5 marks)
(b) Show the inflation bias graphically.
(5 marks)
(c) Can the inflation bias be entirely eliminated if monetary policy is delegated to a
conservative central banker? If not, what determines the size of the bias?
(5 marks)
(d) Discuss another way to reduce the inflation bias. Show analytically this
alternative way works.
(5 marks)
Reading for this question
Subject guide, Chapter 11.
Barro, R.J. and D.B. Gordon (1983), A positive theory of monetary policy in a natural rate
model, Journal of Political Economy, 91(4), pp. 589–610.
23
EC3115 Monetary economics
Approaching the question
(a) Note that the loss function defined above differs subtly from the loss function given in the
subject guide. Solving the problem using the wrong loss function will only give partial credit
at best.
To calculate the inflation bias, substitute the Phillips curve into the loss function, and
differentiate this with respect to the choice variable, π,. Take expectations and set the
first-order condition to zero.
The inflation bias is then given by:
Et−1 [πt − π ∗ ] = α
λ
(k − 1)y ∗ .
1−λ
(b) See for example Figure 11.1 in the subject guide; the inflation bias is represented by the
vertical distance AE in the figure.
(c) If the role of monetary policy was delegated to a conservative central bank who is less
concerned with output variations than society, in other words, has a loss function of the
form, where µ < 1:
LCB = (1 − µ)πt2 + µ(yt − ky ∗ )2
then we will still be faced with an inflation bias but the bias will be of the form
αµ/(1 − µ))(k − 1)y ∗ , and since µ < λ, the inflation bias will be lower.
(d) An alternative is an inflation contract for the central bank.
Suppose the central banker was penalised, say by way of a reduced salary, for allowing any
inflation above the socially-desired level, set in this case at zero. The loss function that
would be minimised would then be:
LContract = (1 − λ)πt2 + 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. If we substitute the Phillips curve
into this loss function and minimise it by choosing πt the inflation bias, Et−1 [πt ], is given by:
Ψ
∗
∗
Et−1 [πt − π ] = αλ(k − 1)y −
/(1 − λ).
2
Therefore, if the contract was written for the central bank such that Ψ= 2αλ(k − 1)y ∗ , then
the inflation bias would be zero and one would achieve the point of highest attainable
welfare as a time-consistent equilibrium.
Question 13
Let there be a country where prices are perfectly flexible and output is always at its
full employment level, Y . Assume that the ‘Quantity Theory of Money (QTM)’ is
valid. The velocity of circulation of money is constant, and the stock of money, M ,
grows at a constant rate, m. Aggregate demand, the IS curve, is given by
Y d = A − b(R − π e ), where R is the nominal rate of interest and π e is the expected
rate of inflation. A and b are constant parameters.
(a) What is the inflation rate, π?
(5 marks)
(b) If the population has perfect foresight, what is the effect of increasing the
growth rate of the money supply on real and nominal interest rates?
(5 marks)
24
Examiners’ commentaries 2016
(c) Is the stock of real money balances affected by the rate of growth of the money
supply?
(5 marks)
(d) Imagine now that, due to an increase in financial sophistication, the demand for
money becomes sensitive to the interest rate so that in place of the quantity
theory equation, we have (M/P )d = H − kR, where d, H and k are constant
parameters. How are your answers to parts (a) to (c) above affected by this
development? Is money neutral, and/or superneutral?
(5 marks)
Reading for this question
Subject guide, Chapter 5.
Approaching the question
(a) The Quantity Theory of Money states that M V = P Q. Taking logs and differentiating with
respect to t yields:
∂p ∂q
∂m ∂v
+
=
+
∂t
∂t
∂t
∂t
and:
µ = π.
(b) We have:
Y d = a − b(R − π e )
also:
Rreal = (R − π e ) = (Y d − a)/b
also:
R = (Y d − a)/b + µ
and:
∂R/∂µ = 1.
Therefore, the real interest rate is always constant as Y d is assumed constant and
π e = π = µ. The nominal interest rate will increase one-for-one with the increase in the
growth rate of money.
(c) We have:
M
Q
=
P
V
and:
∂(M/P )
∂(Q/V )
=
= 0.
∂t
∂t
As the money supply and the price level both grow at the same rate, real money balances
will remain constant.
(d) Money is neutral: increasing the level of the money supply does not change real variables.
However, money is no longer superneutral as real money balances are affected by the change
in nominal interest rates. However, note that the real interest rate is unaffected.
To see this, consider (M/P )d = H − kR. Take logs and differentiate with respect to t to
obtain:
∂ ln(h − kR)
∂m ∂p
−
=
=0
∂t
∂t
∂t
and:
µ = π.
We know that R goes up when µ goes up. From the money demand function we can see
that real money demand goes down when R goes up. Therefore, the price level, P , will jump
to achieve this, after an increase in µ.
25