UNIVERSITY OF GRONINGEN
FACULTY OF ECONOMICS AND BUSINESS
Name:
Student Number:
MONETARY MACROECONOMICS (EBB130A05)
Final Exam with Answers
Program 2018-2019
November 7, 2018
18.30-21:30 hours
This exam consists of 20 multiple-choice questions and 3 open questions with several sub-questions.
To answer the multiple choice questions use the special multiple choice response sheet provided to you for
this purpose. Make sure that you read the instructions on the response sheet. No credit will be given to
answers in this booklet.
To answer the open questions use the corresponding textboxes in this booklet. We only consider answers that
are readable and correctly placed. No credit will be given to answers not in this booklet.
Both the booklet and the answer sheet have to be handed in after the exam. Do not forget to write your name
and student ID number on the two documents. The answers will be posted on Nestor as soon as the grades
have been processed. Any questions regarding this exam can be addressed to G.H. Kuper (g.h.kuper@rug.nl).
Score Part II
Question 1
Score Part II
Question 2
Score Part II
Question 3
Total Score
Part II
Part I – Multiple-Choice Questions (20 points)
Answer this part by marking your answer on the multiple choice response sheet. No credit will be given to
answers in this booklet.
1) Suppose the current one-year interest rate is 1%. Also assume that financial markets expect the
one-year interest rate next year to be 2%, and expect the one-year rate to be 4% the year after
that. Given this information, the yield to maturity on a three-year bond will be approximately
A) 1.99%.
B) 2.33%.
C) 3.51%.
D) 7.14%.
Answer: B
2) Suppose that the yield curve is initially upward sloping. Suppose that financial market investors
suddenly learn that the central bank will pursue a monetary contraction in the future. Given this
information, we would expect which of the following to occur?
A) The yield curve will become steeper.
B) The yield curve will become flatter.
C) The yield curve will become horizontal.
D) The yield curve will become downward sloping.
Answer: A
3) For this question, assume that the central bank is expected to respond to any event by keeping the
interest rate constant (i.e., equal to its initial level). An unexpected tax cut will cause
A) stock prices to fall.
B) stock prices to rise.
C) no change in stock prices.
D) an ambiguous effect on stock prices.
Answer: B
4) Consumption is most likely to respond one-for-one with changes in current income when
A) the change in current income results from a one-time bonus.
B) people believe the change in their current income is temporary.
C) the change in current income is caused by the business cycle.
D) none of the above
Answer: D
5) The "depreciation rate" tells us
A) the interest rate that should be used in present discounted value calculations.
B) the rate at which consumers deplete their total wealth in retirement.
C) the difference between current and expected income.
D) how much usefulness a machine loses from year to year.
Answer: D
6) Suppose there is a simultaneous reduction in expected future output and reduction in the future
expected interest rate. This will cause which of the following to occur?
A) the IS curve to shift left in the current period
B) the IS curve to shift right in the current period
C) the LM curve to shift down in the current period
D) an ambiguous effect on the position of the IS curve in the current period
Answer: D
7) A revaluation causes which of the following to occur in the short run in the AS-AD model?
A) A reduction in net exports.
B) A reduction in the price level.
C) A reduction in output.
D) All of the above.
Answer: D
8) Suppose a country that has been pegging its currency is faced with a situation where financial
market participants now expect some future devaluation. In such a situation, we would generally
expect which of the following to occur?
A) An increase in the domestic interest rate.
B) An announcement by the central bank that a large devaluation will occur in the near future.
C) An increase in the demand for the country's currency.
D) All of the above.
Answer: A
9) An increase in the foreign interest rate (i*) will cause
A) the UIP curve to shift to the left/up.
B) the UIP curve to shift to the right/down.
C) a movement along the UIP curve.
D) neither a shift nor movement along the UIP curve.
Answer: A
10) Assume policy makers in a fixed exchange rate regime decide to peg the exchange rate at a lower
level. This is called
A) a devaluation.
B) a revaluation.
C) a depreciation.
D) an appreciation.
Answer: A
11) Under a fixed exchange rate regime, the central bank must act to keep
A) P = P*.
B) the real exchange rate fixed.
C) i = i*.
D) E = 1.
Answer: C
12) Assume that policy makers are pursuing a fixed exchange rate regime. Now suppose that a
reduction in stock market wealth causes a decrease in consumption. Which of the following will
tend to occur in a fixed exchange rate regime?
A) A reduction in income.
B) A reduction in the money supply.
C) No change in the domestic interest rate.
D) All of the above.
Answer: D
13) Assume that uncovered interest parity holds, the future expected exchange rate is constant, the
current nominal exchange rate is 1.2, the one-year foreign interest rate is 6% and the one-year
domestic interest rate is 3%. Given this information, one can conclude that
A) financial market participants expect that the exchange rate (E) will increase by 3% over the
coming year.
B) financial market participants expect that the exchange rate (E) will decrease by 3% over the
coming year.
C) financial market participants expect that the domestic currency to depreciate by 3% over the
coming year.
D) financial market participants expect that the exchange rate (E) will increase by 20% over the
coming year.
Answer: A
14) The primary deficit is represented by which of the following?
A) G − T
B) T − G
C) iB + G − T
D) rB − G + T
Answer: A
15) A higher deficit in the current year will lead to increased debt in the future only if
A) the deficit is greater than the previous year's deficit.
B) the deficit-to-GDP ratio is greater than the debt-to-GDP ratio.
C) it causes a drop in private saving.
D) None of the above.
Answer: D
16) All else equal, a rise in the debt-to-GDP ratio implies
A) a greater ratio of interest payments to GDP.
B) a greater difference between the official deficit and the inflation-adjusted deficit as a fraction
of GDP.
C) a greater surplus is needed to prevent further rises in the debt-to-GDP ratio.
D) All of the above.
Answer: D
17) In the medium run, a tax increase that causes a reduction in the budget deficit will
A) affect only the price level.
B) not affect the price level but will alter the composition of output.
C) not affect the level of output, but will affect the composition of output.
D) affect both the level and composition of output.
Answer: C
18) If the government initially has zero debt, and runs a primary deficit in year zero of 𝐵0, and, in
year 1, decides to stabilize the debt (i.e., prevent the debt from rising any further), then in year 1
and beyond, it must run a primary surplus equal to
A) zero.
B) 𝐵0.
C) (1 + 𝑟)𝐵0.
D) 𝑟𝐵0.
Answer: D
19) If the Ricardian equivalence proposition is correct, then an increase in the deficit will lead to
A) an increase in private saving.
B) a decrease in investment spending.
C) a lower standard of living in the future.
D) All of the above.
Answer: A
20) The existence of inflation does which of the following?
A) Facilitates the downward adjustment of real wages.
B) Reduces shoe-leather costs.
C) Reduces tax distortions.
D) Reduces the costs associated with money illusion.
Answer: A
Part II – Open Questions (30 points)
Give your answers to each sub-question in the corresponding textboxes. We only consider answers that are
readable and correctly placed.
Question 1 (10 points)
Assume we are in 2018. The Greek government has issued zero coupon bonds to its creditors, the
Eurogroup, of which the total principal value equals 300 billion euros. The repayment dates are the
following: 50 billion euro has to be repaid in 2028, 50 billion has to be repaid in 2029, 50 billion has
to be repaid in 2030, 50 billion has to be repaid in 2031, 50 billion has to be repaid in 2032, and the
final 50 billion has to be repaid in 2033. Assume throughout questions a) to d) that the Greek
government will not issue new debt, and that it is capable of repaying its debt whenever it is due.
Assume that the nominal interest rate is 4%.
a) Calculate the net present value of Greek government debt. (2 points)
50
50
50
50
50
50
+
+
+
+
+
10
11
12
13
14
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)15
1
2
3
4
50
1
1
1
1
1 5
=
[1 + (
) +(
) +(
) +(
) +(
) ]
(1 + 𝑖)10
1+𝑖
1+𝑖
1+𝑖
1+𝑖
1+𝑖
1 6
1
−
(
50
1 + 𝑖 ) ) = 184
=
(
1
(1 + 𝑖)10
1−1+𝑖
Hence the net present value of Greek government debt is 184 billion euros.
𝑁𝑃𝑉 =
b) Assume that Greek GDP is equal to 180 billion euros. Calculate the debt-to-GDP ratio using
the net present value of the debt. (1 point)
debt-to-GDP = 184/180 = 1.02 or 102% of current Greek GDP.
c) Greece’s creditors, the Eurogroup, offer the possibility of shifting the debt repayment 20
years into the future, i.e. the first 50 billion is now repaid in 2048, the second 50 billion in
2049, with last repayment due in 2053. Calculate the net present value of the extended future
debt repayments, and the new debt-to-GDP ratio. (2 points)
50
50
50
50
50
50
+
+
+
+
+
30
31
32
33
34
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)35
50
1 1
1 2
1 3
1 4
1 5
=
[1
+
(
)
+
(
)
+
(
)
+
(
)
+
(
) ]
(1 + 𝑖)30
1+𝑖
1+𝑖
1+𝑖
1+𝑖
1+𝑖
1 6
1
−
(
50
1 + 𝑖 ) ) = 84
=
(
1
(1 + 𝑖)30
1−1+𝑖
Hence the net present value of Greek government debt is reduced from 184 billion euros to 84 billion
euros by shifting the repayment dates 20 years into the future.
𝑁𝑃𝑉 =
The debt-to-GDP ratio falls to debt-to-GDP = 84/180 = 0.467 or 46.7% of current Greek GDP. We
see that debt-to-GDP ratio falls from 102% to 46.7%, so yes, this constitutes a significant debt relief
by the Eurogroup.
d) The Eurogroup decides to offer an alternative to shifting the debt repayments into the future.
Instead, it proposes a haircut program under which 50% of all outstanding Greek debt is
written off (does not have to be repaid). This implies that the repayments are reduced from 50
billion per year to 25 billion per year. However, in that case the debt has to be repaid
according to the original time schedule, i.e. from 2028 to 2033. Calculate the net present
value of this alternative debt relief offer and the resulting debt-to-GDP ratio. Should the
Greeks go for maturity extension or for a haircut? Explain. (3 points)
The net present value is halved in comparison to question a:
25
25
25
25
25
25
𝑁𝑃𝑉 =
+
+
+
+
+
10
11
12
13
14
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)
(1 + 𝑖)15
6
1
1 − (1 + 𝑖 )
25
=
(
) = 92
1
(1 + 𝑖)10
1−1+𝑖
The net present value drops to 92 billion euros.
The debt-to-GDP ratio is halved, and is now equal to 51% of Greek GDP. However, maturity
extension reduced the debt-to-GDP ratio to 46.7%, which suggests that the Greeks are better off not
reducing the principal value of the debt but shifting the repayments into the future.
Note that the following questions can be answered without solving the previous exercises.
e) Assume now that Greek government debt no longer consists of zero coupon bonds, but are
regular bonds over which the Greek government has to pay interest. Suppose that inflation
equals 2%, economic growth 1% and the primary surplus 2%. Calculate the long-run debt-toGDP ratio (the ratio at which debt-to-GDP remains constant). What changes can reduce the
long-run debt-to-GDP ratio? (2 points)
The real interest rate 𝑟 equals 4 − 2 = 2%. The formula for the evolution of the debt-to-GDP ratio is
given by:
𝐵𝑡 𝐵𝑡−1
𝐵𝑡−1 𝐺𝑡 − 𝑇𝑡
−
= (𝑟 − 𝑔)
+
𝑌𝑡 𝑌𝑡−1
𝑌𝑡−1
𝑌𝑡
𝐵
In the long-run, the debt-to-GDP ratio is constant and equal to 𝑌 . Substitution of 𝑟 = 0.02, 𝑔 = 0.01
and
𝐺− 𝑇
𝑌
= −0.02 gives:
0 = (𝑟 − 𝑔)
𝐵 𝐺− 𝑇
𝐵 (𝐺 − 𝑇)/𝑌
𝐵
−0.02
+
→ =
→ =
=2
𝑌
𝑌
𝑌
𝑔−𝑟
𝑌 0.01 − 0.02
Hence the long-run debt-to-GDP ratio is 200% of Greek GDP. From the formula we infer that long
run debt-to-GDP ratio is reduced when the primary surplus is smaller, when the real interest rate is
larger, and when the growth rate is smaller.
Question 2 (10 points)
Suppose the IS relation is given by:
Y = A(Y, T, r+x, Y’e, T’e, r’e+x’e) + G
A is aggregate private spending, Y, T and G are current values of income (output), taxes and
government spending, respectively. r is the real interest rate and x is the risk premium. Index ’e
represent expected future values.
The LM relation is r = ̄r.
Suppose initially the economy is in a recession, and the risk premium is zero.
a) What is the effect on income and the borrowing rate if investors become more risk averse (the
risk premium increases)? Illustrate with a graph showing the IS-LM model (with the real
interest rate along the vertical axis) for the current period. (3 points)
The borrowing rate increases because the risk premium is positive, and current income drops. In the
future income will also be lower reducing current income. This lowers current income more. The IS
curve shifts left.
Suppose the central bank lowers the real interest rate in the current period, and that the central bank
announces that it lowers the real interest rate also in the future.
b) What is the effect on income and the real interest rate in the current period if the
announcement of a future drop in the real interest rate is not credible. Illustrate with a graph
showing the IS-LM model (with the real interest rate along the vertical axis) for the current
period. (3 points)
LM drops, increasing income and lowering the real interest rate in the current period. (move down
along IS).
c) What is the effect on income and the real interest in the current period if the announcement of
a future drop in the real interest rate is credible, and in the future investors are less risk
averse. Illustrate with a graph showing the IS-LM model (with the real interest rate along the
vertical axis) for the current period. (4 points)
LM drops also in the future, increasing income and lowering the real interest rate in the future
periods. The lower risk premium shifts the IS curve in the future to the right. This increases future
income and lowers the future real interest rate. These future effects shift the IS curve to the right in
the current period.
Question 3 (10 points)
Consider the following Keynesian model of a small open economy operating under perfect capital
mobility and flexible exchange rates:
𝐶 = 𝑐0 + 𝑐(𝑌 − 𝑇)
𝐼 = 𝑖0 + 𝑏1 𝑌 − 𝑏2 𝑖
𝐺 = 𝐺0
𝑇 = 𝑡0 + 𝑡𝑌
𝐸𝑋 = 𝑥1 𝑌 ∗ − 𝑥2 𝐸
𝐼𝑀 = 𝑚1 𝑌 + 𝑚2 𝐸
𝑖=𝑖
Where 𝐶 is consumption, 𝑐0 is autonomous consumption, 𝑐 is the marginal propensity to consume, 𝑌
is output, 𝑇 is taxes, 𝐼 is investment, 𝑖0 is autonomous investment, 𝑏1 is the marginal propensity to
invest, 𝑏2 is the sensitivity of investment to the interest rate, 𝑖 is the nominal interest rate, 𝐺 is
government spending, 𝑡0 is the autonomous part of taxes, 𝑡 is the part of taxes that depends on
income, 𝐸𝑋 is exports, 𝑥1 determines the effect of world income on exports, 𝑌 ∗ is foreign income, 𝐸
is the nominal exchange rate, 𝑥2 is the sensitivity of exports to changes in the exchange rate, 𝐼𝑀is
imports, 𝑚1 is the marginal propensity to import, and 𝑚2 is the sensitivity of imports to changes in
the exchange rate.
a) Solve for the IS, LM and UIP curves and draw the resulting graph. (3 points)
Since we have a central bank that sets the nominal interest rate, the LM curve is given by:
𝑖=𝑖
For the UIP curve, knowing the UIP condition suffices. This is given by:
1+𝑖
𝐸𝑡 = (
) 𝐸𝑒
1 + 𝑖 ∗ 𝑡+1
Saving the most intricate curve for last - to solve for the IS curve we use the goods market
equilibrium condition:
𝑌 = 𝐶 + 𝐼 + 𝐺 + 𝑁𝑋 = 𝐶 + 𝐼 + 𝐺 + 𝐸𝑋 − 𝐼𝑀
Substituting the components of output in and replacing the nominal exchange rate by the UIP
condition, we find that the IS curve is given by:
1+𝑖
𝑒
𝑐0 − 𝑐𝑡0 + 𝑖0 − 𝑏2 𝑖 + 𝐺0 + 𝑥1 𝑌 ∗ − (𝑥2 + 𝑚2 ) (1 + 𝑖 ∗ ) 𝐸𝑡+1
𝑌=
1 − (1 − 𝑡)𝑐 − 𝑏1 + 𝑚1
b) Calculate the effect of an increase in government spending (i.e. the multiplier!). Comment on
the sign of the effect. Is the government multiplier the same, smaller, or larger than one you
would find if the economy were closed? And if so, why? (2 points)
Formally, we calculate the fiscal multiplier by taking the derivative of the IS curve with respect to
government spending:
𝜕𝑌
1
=
> 0.
𝜕𝐺0 1 − (1 − 𝑡)𝑐 − 𝑏1 + 𝑚1
The sign is positive as long as 1 − (1 − 𝑡)𝑐 − 𝑏1 + 𝑚1 > 0: as the government increases its
spending, output increases. The government multiplier is smaller than in a closed economy: as
income increases, some of the additional income is spent on imports. Hence, due to import leakage
the multiplier is smaller in an open economy.
c) Calculate the effect of an expected depreciation on output. Comment on the sign of the effect
and explain the mechanism. (2 points)
We can calculate the effect of an expected depreciation by taking the derivative of the IS curve with
respect to next period’s nominal exchange rate:
1+𝑖
(𝑥2 + 𝑚2 ) (
𝜕𝑌
1
+ 𝑖 ∗ ) < 0.
=
−
𝑒
𝜕𝐸𝑡+1
1 − (1 − 𝑡)𝑐 − 𝑏1 + 𝑚1
The sign is negative as long as 1 − (1 − 𝑡)𝑐 − 𝑏1 + 𝑚1 > 0. Since an expected depreciation implies
𝑒
that 𝐸𝑡+1
decreases, we find that in this case output increases if the nominal exchange rate is
expected to depreciate: exports increase and imports decrease, causing an increase in output.
Next, let’s assume that the government decides to implement a fixed exchange rate regime, such that
𝑒
𝐸𝑡 = 𝐸𝑡+1
= 𝐸. Suppose that the government is credible and foreign investors have no doubts about
the sustainability of the fixed exchange rate regime. There is still perfect capital mobility.
d) What do these assumption imply for the uncovered interest parity condition? (1 point)
1+𝑖
𝑒
If 𝐸𝑡 = 𝐸𝑡+1
= 𝐸, then the UIP condition reduces to 1 = (1+𝑖 ∗). Hence, we know that the domestic
interest rate must equal the foreign interest rate:
𝑖 = 𝑖∗
e) Calculate the effects of contractionary monetary policy under fixed exchange rates. That is,
the effect of an increase in the nominal interest rate 𝑖. Comment on the sign of the effect and
explain the economic reason why it has this sign. (2 points)
UIP: 𝑖 = 𝑖 ∗. As a result, the IS curve becomes:
𝑐0 − 𝑐𝑇0 + 𝑖0 − 𝑏2 𝑖 ∗ + 𝐺0 + 𝑥1 𝑌 ∗ − (𝑥2 + 𝑚2 )𝐸
𝑌=
1 − (1 − 𝑡)𝑐 − 𝑏1 + 𝑚1
Finally, we calculate the effect of a contractionary monetary policy shock by taking the derivative
with respect to the domestic nominal interest rate:
𝜕𝑌
=0
𝜕𝑖
Hence, the effect on output from an increase in nominal interest rates is zero. As the country is
operating under a fixed exchange rate, the domestic interest rate must equal the foreign interest rate.
If 𝑖 > 𝑖 ∗ , then foreign investors would increase their holdings of domestic currency bonds, which
would lead to a nominal appreciation, i.e. an increase in 𝐸. This cannot be the case under fixed
exchange rates, since 𝐸 cannot increase. Hence, the effect on output is zero