ECON7520: Final Exam
Semester 1, 2023
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Final Exam
Exam time: For most of you, the exam should be on
Monday, June 12, 2023 at 11.15am
(10 min [reading/planning time] + 120 min + 15 min
[submission time]).
Please consult your personalized exam timetable for
definite information.
The exam is an online and open book exam.
Have your lecture and tutorial notes sorted and ready.
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Final Exam
4 questions (each with several parts/subquestions), 100
marks.
The final contains short answer and problem solving
questions.
Tutorial questions and the problem set questions can give
you a quite good idea of the type of questions I like to ask.
Mix of difficulty levels:
Some (sub-)questions should feel familiar from the tutorials
and lectures.
Others will be “new”/“more advanced” and will test your
deep understanding of the course content.
Tip: Subquestions are not necessarily ordered by difficulty.
Even if you should find part (b) difficult, read parts (c), (d)
etc. as they may be very familiar.
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Final Exam
How to prepare?
Solve all the tutorial questions and the problem set by
yourself. Make sure you understand both the analytical
derivations and the economic intuition behind them.
In addition, you need to understand all the contents
discussed in the lectures.
If you have questions, each tutor and myself will each offer
two consult hours per week in each of the next two weeks.
Please see the “Course Staff” area on blackboard for
consult times.
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ECON7520: Review of the Semester
Semester 1, 2023
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Week 1: Balance of Payments Accounts
A country’s balance of payments has two main
components:
1 Current Account (CA)
CA records exports and imports of goods and services, and
international receipts and payments of income.
Exports and income receipts enter with a plus sign and
imports and income payments enter with a minus sign.
2 Financial Account (FA)
FA records changes in a country’s net foreign asset position.
Sales of assets to foreigners are given a plus sign and
purchases of assets located abroad a minus sign.
Fundamental Balance-of-Payments Identity
Current Account Balance = −(Financial Account Balance)
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Week 1: Current Account
Current Account Balance = Trade Balance
+ Income Balance
+ Net Unilateral Transfers.
Trade Balance = Merchandise Trade Balance
+ Services Balance.
Merchandise Trade Balance: Net exports of goods
Service Balances: Net exports of services
Income Balance = Net Investment Income
+ Net International Compensation to Employees.
Net Investment Income: e.g., interests and dividends
Net International Compensation to Employees:
Compensation to domestic workers abroad minus
compensations to foreign workers
Net Unilateral Transfers = Personal Remittances +
Government Transfers
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Week 1: Financial Account
Financial Account
= Increase in Foreign-Owned Assets in Home Country
− Increase in Home-Owned Assets Abroad.
Assets include:
Securities
Currencies
Bank loans
Foreign direct investment (FDI)
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Week 2: Perpetual Trade Balance Deficit: Analysis
Given the transversality condition, we obtain
B0 = −
TB1
(1+ r)
−
TB2
(1+ r)2
. (1)
(1) provides a formal answer to our question:
1 If B0 > 0, it is possible (but not necessary) to have both
TB1 < 0 and TB2 < 0.
2 If B0 < 0, it must be that TB1 > 0 or TB2 > 0.
A country can run a perpetual trade deficit only if the
country has positive initial NIIP.
Since the U.S. is currently a net foreign debtor it will have
to run a TB surplus at some point in the future.
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Week 2: Perpetual Current Account Deficit: Analysis
Using the transversality condition (B2 = 0), we obtain
B0 = −CA1 −CA2. (2)
Equation (2) gives us the answer to our question.
1 If B0 > 0, it is possible (but not necessary) to have both
CA1 < 0 and CA2 < 0.
2 If B0 < 0, it must be true that CA1 > 0 or CA2 > 0.
A country can run a perpetual current account deficit only if
the country has positive initial NIIP.
(This result applies to economies with finitely many
periods.)
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Week 2: 1: CA as Changes in NIIP
Keep assuming that there are
1 no international compensation to employees,
2 no unilateral transfers,
3 no valuation changes of assets in this world.
We obtain
1: CA as Change in NIIP
CAt = Bt − Bt−1.
Notation:
CAt : The country’s current account in period t.
Bt : The country’s NIIP at the end of period t.
If CAt < 0 then NIIP falls because Bt − Bt−1 < 0.
If CAt > 0 then NIIP rises.
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Week 2: 2: CA as Reflections of TB and NII
We get
CA as Reflections of Trade Balance
CAt = TBt + rBt−1.
Notation:
TBt : The country’s trade balance in period t.
r : The interest rate on investments held for one period.
This is the original definition of CA.
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Week 3: Setup: Small Open Economy
Small open economy:
Open: The country trades in goods and financial assets
with the rest of the world (ROW).
Small: The country’s domestic economic conditions don’t
affect the prices of internationally traded goods, services
and financial assets.
Examples of small open economies:
Developed: Netherlands, Switzerland, Austria, New
Zealand, Australia, Canada, Norway
Emerging: Argentina, Chile, Peru, Bolivia, Greece,
Portugal, Estonia, Latvia, Thailand
Examples of large open economies:
Developed: U.S., Japan, Germany, U.K.
Emerging: China, India
Small open economy model: country + ROW.
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Week 3: Equilibrium
Exogenously given are r0,B0, r
∗,Q1 and Q2. An equilibrium is
a consumption path (C1,C2) and an interest rate r1 such that:
1 Feasibility of the intertemporal allocation
C1 +
C2
1+ r1
= (1+ r0)B0 + Q1 +
Q2
1+ r1
.
2 Optimality of the intertemporal allocation
U1(C1,C2) = (1+ r1)U2(C1,C2).
3 Interest rate parity condition
r1 = r
∗.
This is implied by free capital mobility and means that the
domestic interest rate r1 equals the world interest rate r
∗.
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Week 3: Temporary vs. Permanent Output Shocks
What is the effect on the current account of an increase or
decrease in output?
Depends on whether the shock is temporary or permanent.
For the analysis, assume:
1 Temporary shock
Output in Period 1 = Q1 −∆
Output in Period 2 = Q2
2 Permanent shock
Output in Period 1 = Q1 −∆
Output in Period 2 = Q2 −∆
The next slides assume that both C1 and C2 are normal
goods (their consumption increases with income).
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Week 3: Temporary vs. Permanent Output Shocks:
Summary
1 Temporary shock
Relatively small effect on the consumption path (C1,C2).
Temporary negative income shocks are smoothed out by
borrowing from the rest of the world.
Generally, one should expect the borrowing to move the
country’s trade balance and current account significantly.
2 Permanent shock
Relatively large effect on the consumption path (C1,C2).
Generally, one should expect permanent negative income
shocks to lead to similarly sized reductions in C1 and C2.
Generally, one should expect the country’s trade balance
and current account to not be much affected.
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Week 4: Import Tariffs: Optimality, Resource
Constraint
The optimality condition (tangency of IC and IBC) becomes
U1(C1,C2) =
1+ τ1
1+ τ2
(1+ r1)U2(C1,C2).
If τ1 = τ2, then there is no change from τ1 = τ2 = 0.
If τ1 > τ2, then C1 becomes relatively more expensive and,
assuming diminishing marginal utilities, C1 ↓ and C2 ↑.
If τ1 < τ2, then C1 becomes relatively cheaper and,
assuming diminishing marginal utilities, C1 ↑ and C2 ↓.
The economy’s resource constraint is
C1 +
C2
1+ r1
= (1+ r0)B0 + TT1Q1 +
TT2Q2
1+ r1
.
τ1 and τ2 do not enter this constraint because the import
tariff revenues are returned to the HH.
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Week 4: Firm
What does the firm do? The firm
makes investments in period t that lead to output in t + 1.
finances its investments in period t by issuing debt in t.
Production: The production in periods 1 and 2 is given by
Q1 = A1F (I0)
Q2 = A2F (I1)
where
F is a function,
At > 0 (t = 1, 2) are technology parameters,
I0 is the investment in period 0 and exogeneously given,
I1 is the investment in period 1 and chosen by the firm.
Debt: The firm issues debt Dft in period t = 0,1:
Df0 = I0 (exogenous; to be repaid in period 1),
Df1 = I1 (to be repaid in period 2) (3)
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Week 4: Investment Decision
How does the firm choose the investment level I1?
The firm maximizes its profits
Π2 = A2F (I1)− (1+ r1)D
f
1 where D
f
1 = I1
or
Π2(I1) = A2F (I1)− (1+ r1)I1.
The first-order condition for profit maximization is
Π′2(I1) = 0
⇔ A2F
′(I1) = 1+ r1
d [A2F (I1)]
dI1
= A2F
′(I1) = Marginal Product of Capital (MPK)
(1+ r1) = Marginal Cost of Capital (MCK).
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Week 5: Reaction of Households to World Interest
Rate Shocks
There are the two effects that we discussed earlier:
1 Substitution effect (SE)
Saving in period 1 becomes more attractive.
2 Income effect (IE)
r∗ ↑ makes debtors poorer and creditors richer.
In addition, there now is another income effect:
3 Additional income effect (IE2)
Π2 (= area between MPK & MCK curves) decreases.
4 Assume Bh0 = 0 and that C1 and C2 are normal goods.
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Week 5: Adjustment to a World Interest Shock
r∗ ↑ by ∆ > 0
HH = debtor (Bh1 = Π1 − C
A
1 < 0)
slope of black line = −(1+ r∗)
slope of green line = −(1+ r∗ +∆)
C1
C2
b
b
b
b
b
b
A
CA1
C
B
D
CD1
Π1
Π2
Π′2
SEIEIE2
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Week 5: Analysis
We can see:
1 Changes in G1 and G2 affect the HH’s consumption.
2 The following changes don’t affect the consumption as long
as they satisfy the government’s IBC.
Changes in the tax schedule, T1 and T2.
Related changes in the gvnmt.’s asset/debt position, B
g
1 .
Therefore, even if the government decreases T1 and B
g
1
and instead increases T2 such that the government’s IBC
remains satisfied, this won’t affect the optimal consumption
path.
Point 2 is the so called Ricardian equivalence.
The Ricardian equivalence holds because the HH reacts to
tax changes by adjusting its savings.
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Week 5: Can Government Spending Explain the CA
Deficits?
Recall that
TB1 (= X1 − IM1) = Q1 − C1 −G1 − I1︸︷︷︸
=0
,
CA1 = r0B0 + TB1
Suppose that G1 ↑.
Direct effect: G1 ↑ implies TB1 ↓ and thus CA1 ↓.
Indirect effect: G1 ↑ implies C1 ↓, which offsets the direct
effect to some extent.
If the HH has a logarithmic utility function then
−∆C1 =
1
2
∆G1 < ∆G1
and the direct effect dominates: G1 ↑ implies TB1 ↓ & CA1 ↓.
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Week 5: Failure of the Ricardian Equivalence
We consider three possible environments where the
Ricardian equivalence fails.
If the Ricardian equivalence fails, a change in tax schedule
can affect consumption choices.
The possible channels are
1 Borrowing constraints (on households)
2 Intergenerational effects
3 Distortionary taxation
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Week 6: Motivation: The Great Moderation in the U.S.
Quarterly Real Per Capita U.S. GDP Growth, 1947Q2 - 2017Q4
The volatility of the growth rate of real U.S. GDP per capita
declined significantly after (about) 1984.
This has become known has the Great Moderation.
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Week 6: Motivation: The Great Moderation in the U.S.
U.S. CA-to-GDP Ratio, 1947Q1 - 2017Q4
1947-1983: on average, CA surplus of 0.34% of GDP;
1984-2017: on average, CA deficit of 2.8% of GDP.
Any relationship with the volatility of the GDP growth?
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Week 6: Uncertainty and Household’s Saving
How does uncertainty affect the current account?
Potentially through the household saving channel.
How does uncertainty affect household’s saving?
Through a motive for precautionary saving.
1 High uncertainty about the future
People save more. The CA improves.
2 Low uncertainty about the future (Great Moderation)
People save less. The CA deteriorates.
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Week 7: Large Open Economy
Thus far: CA determination in a small open economy.
How do our result(s) change if we consider a large open
economy?
To check, we set up a two-country model:
the U.S.
the rest of the world (RW)
We then have
CAUS = −CARW
or
CAUS + CARW = 0.
A U.S. CA deficit implies a RW CA surplus, and vice versa.
Important: Now, the U.S. CA balance affects the world
interest rate.
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Week 7: Large Open Economy
Current Account Determination in a Large Open Economy
We draw the U.S.’s and RW’s current account schedules
into a symmetric graph.
The point A describes the equilibrium (CAUS = −CARW ).
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Week 7: Investment Surge in a Large Open Economy
Positive Anticipated Future Productivity Shock
in a Large Open Economy
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Week 8: The Law of One Price
The LOOP holds when a good costs the same abroad and
at home:
Law of One Price (LOOP)
The Law of One Price for a particular good holds if P = EP∗.
Here:
P = good’s domestic-currency price in the domestic country
P∗ = good’s foreign-currency price in the foreign country
E = nominal exchange rate
E is the domestic-currency price of one unit of foreign
currency.
E (or 1
E
) is what TV news report as an exchange rate.
E.g.: If 1kg of apples costs 7.33USD in the U.S., E = 1.5 &
LOOP holds, then 1kg of apples costs 11AUD in Australia.
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Week 8: The Big Mac Index: Empirical
Changes in Big Mac Real Exchange Rates, 2006-2019
The figure plots the change in eBigMac during 2006-2019
against eBigMac from 2006 for 40 countries.
We see that deviations from LOOP are persistent: most
countries were cheaper than the U.S. in 2006 and in 2019.
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Week 8: Purchasing Power Parity
Purchasing power parity (PPP) is a generalization of the
law of one price.
Real exchange rate:
Real Exchange Rate
The real exchange rate is defined as e = EP
∗
P .
Here:
P = domestic currency price of a (representative) domestic
basket of goods
P∗ = foreign price of a (representative) foreign basket of
goods
E = nominal exchange rate
Purchasing Power Parity (PPP)
We say (absolute) PPP holds when e = 1 or P = EP∗.
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Week 8: Failure of PPP and Nontradable Goods
Assume that the aggregate price level is some average of
PT and PN as given by
P = φ (PT ,PN) .
The same for the foreign price level:
P∗ = φ (P∗T ,P
∗
N) .
We assume the following property for the function φ(·, ·):
1 φ (PT ,PN) is increasing in both PT and PN .
2 For every λ > 0,
φ (λPT , λPN ) = λφ (PT ,PN) .
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Week 8: Failure of PPP and Nontradable Goods
Then, we have
e =
EP∗
P
=
Eφ
(
P∗T ,P
∗
N
)
φ (PT ,PN)
=
EP∗Tφ
(
1,P∗N/P
∗
T
)
PTφ (1,PN/PT )
=
φ
(
1,P∗N/P
∗
T
)
φ (1,PN/PT )
,
where last equality holds because by the LOOP, PT = EP
∗
T .
Observe that in general, e 6= 1:
e ≷ 1 if and only if
P∗N
P∗
T
≷ PN
PT
.
With nontradable goods, absolute PPP systematically fails.
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Week 8: Balassa-Samuelson Model
Recall that
e =
φ
(
1,P∗N/P
∗
T
)
φ (1,PN/PT )
.
By plugging in productivities, we get
e =
φ
(
1,a∗T/a
∗
N
)
φ (1,aT/aN)
.
The real exchange rate depends on the two countries’
difference in relative productivities of tradables and
nontradables.
If aTaN
↑ over time then e ↓, i.e. the real exchange rate
appreciates (towards the domestic country).
The domestic country becomes relatively more expensive.
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Week 9: Motivation: Argentina’s Sudden Stop in 2001
The data shows that Argentina experienced
1 An increase in the interest rate
2 A change in the CA balance toward surplus
3 A real exchange rate depreciation
4 A GDP reduction
We like to build a model that accounts for these four data
features.
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Week 9: Utility Function with Tradables and
Nontradables
The household obtains her utility from (CT1 ,C
N
1 ,C
T
2 ,C
N
2 ).
The utility function is defined as
U(CT1 ,C
N
1 ,C
T
2 ,C
N
2 ).
The utility function now is defined over four types of goods.
Later, for simplicity, we will assume
U(CT1 ,C
N
1 ,C
T
2 ,C
N
2 ) = lnC
T
1 + lnC
N
1 + lnC
T
2 + lnC
N
2 .
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Week 9: Equilibrium
An equilibrium requires four conditions:
1 Resource constraint
CT1 +
CT2
1+ r1
= (1+ r0)B0 + Q
T
1 +
QT2
1+ r1
.
2 Optimality of the intertemporal allocation
U1
1
=
U2
p1
=
U3
1
1+r1
=
U4
p2
1+r1
3 Interest rate parity condition
r1 = r
∗.
4 Market clearing for nontradable goods
CN1 = Q
N
1 ,
CN2 = Q
N
2 . 39 / 68
Week 9: Solution for the Logarithmic Utility Case
We can obtain
CT1 =
1
2
{
(1+ r0)B0 + Q
T
1 +
QT2
1+ r∗
}
.
Then, we can subsequently derive
CT2 =
1
2
(1+ r∗)
{
(1+ r0)B0 + Q
T
1 +
QT2
1+ r∗
}
,
CN1 = Q
N
1 ,
CN2 = Q
N
2 ,
p1 =
CT1
QN1
,
p2 =
CT1
QN2
(1+ r∗).
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Week 9: Sudden Stop Analysis
We model a sudden stop as a significant increase in the
interest rate r∗ for the country.
That is,
Foreign investors become reluctant to invest money in the
country.
Therefore, they impose a high interest rate (say 100% for
example).
To understand the effects of a sudden stop, we can
compare:
1 Normal case: r∗ = 0.10.
2 Sudden stop case: r∗ = 1.00.
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Week 9: Dynamics of A Sudden Stop
Note that CT1 depends on r
∗ as
CT1 =
1
2
{
(1+ r0)B0 + Q
T
1 +
QT2
1+ r∗
}
.
Thus, CT1 decreases as r
∗ increases sharply.
When CT1 decreases while Q
N
1 doesn’t change, the price of
nontradables relative to tradables, p1, decreases as
p1 =
CT1
QN1
.
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Week 9: Dynamics of A Sudden Stop
How about the current account?
The current account in this economy is given by as
CA1 = TB1 + r0B0
where
TB1 = Q
T
1 − C
T
1 .
Therefore, CA1 improves as C
T
1 decreases.
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Week 9: Intuition Behind the Dynamics
1 The increase in the interest rate r1 makes it harder for the
country to borrow.
2 Then, the country has to reduce the amount of tradables
that they import in period 1.
Before the sudden stop, the country enjoyed consuming a
plenty of tradables as they could borrow.
3 The reduction of imports causes the current account to
improve in period 1.
4 Thus, the amount of nontradables becomes relatively
abundant compared to tradables.
5 The price of nontradables falls relative to tradables, that
makes the real exchange rate depreciate.
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Week 9: Intuition Behind the Dynamics
Thus, a sudden stop involves
1 An improvement in the current account balance.
2 A real exchange rate depreciation.
3 A reduction in GDP.
Today’s model is not able to produce the last result.
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Week 10: Motivation: Great Recession in Peripheral
Europe
The sudden stop generated
1 Large current account reversals
2 Higher unemployment rates
3 Moderate real exchange rate (RER) depreciation
The third observation is different from other real-world
sudden stops:
Chile, 1979-1985, (close to 100% RER depreciation).
Argentina, 2001-2002, (≈ 150% RER) depreciation.
Question: Is there a mechanism to generate a moderate
real exchange rate depreciation and instead a higher
unemployment rate?
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Week 10: Downward Nominal Wage Rigidities
If nominal wages are flexible, they adjust to achieve full
employment. In that case, we have
h1 = h2 = h¯.
However, an important assumption of our model today are
downward nominal wage rigidities.
Nominal wages do not adjust downwards in the short-run.
Thus the labor market may not clear. We can have
h1 < h¯, h2 < h¯.
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Week 10: Downward Nominal Wage Rigidities
Formally, taking W0 as exogenously given, we assume:
downard nominal wage rigidity
W2 ≥ W1 ≥ W0
labor market slackness conditions
(W2 −W1)(h¯ − h2) = (W1 −W0)(h¯ − h1) = 0
In fact, to simplify our analysis, we now assume that:
E1 = E2 = E¯ . That is, the country adopts a fixed exchange
rate regime (= currency peg).
Around 2008 some peripheral European countries were
members of Euro area, others were pegged to the Euro.
Nominal wages are rigid: W2 = W1 = W0.
These assumptions imply that real wages are rigid:
w¯ ≡ w1 =
W1
PT1
=
W0
E¯
= w2 =
W2
PT2
=
W0
E¯
.
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Week 10: Equilibrium (Five Conditions)
1 Resource constraint
CT1 +
CT2
1+ r1
= (1+ r0)B0 + Q
T
1 +
QT2
1+ r1
(4)
2 Optimality of the intertemporal allocation
1
CT
1
1
=
1
CN
1
p1
=
1
CT
2
1
1+r1
=
1
CN
2
p2
1+r1
(5)
3 Interest rate parity condition
r1 = r
∗ (6)
4 Market clearing for nontradable goods
CN1 = Q
N
1 = (h1)
α , CN2 = Q
N
2 = (h2)
α (7)
5 Firm’s optimization conditions (new!)
p1α (h1)
α−1 = w¯ , p2α (h2)
α−1 = w¯ (8)
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Week 10: Solution for the Logarithmic Utility Case
We can derive:
CT1 =
1
2
(
(1+ r0)B0 + Q
T
1 +
QT2
1+ r∗
)
,
CT2 = (1+ r
∗)CT1 ,
p1 =
(
w¯
α
)
α (
CT1
)1−α
,
p2 =
(
w¯
α
)
α (
CT2
)1−α
,
h1 =
(αp1
w¯
) 1
1−α
,
h2 =
(αp2
w¯
) 1
1−α
,
CN1 = (h1)
α ,
CN2 = (h2)
α .
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Week 10: Dynamics of a Sudden Stop
CT1 decreases as r
∗ increases sharply, as
CT1 =
1
2
(
(1+ r0)B0 + Q
T
1 +
QT2
1+ r∗
)
.
When CT1 decreases, the price p1 of nontradables relative
to tradables decreases as
p1 =
(
w¯
α
)
α (
CT1
)1−α
.
Observe:
If w¯ were to decrease, p1 would decrease even more.
A further reduction of p1 would create a greater real
exchange rate depreciation.
However, because wages are rigid, these things do not
happen.
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Week 10: Dynamics of a Sudden Stop
The decrease in p1 causes a decrease in h1 as
h1 =
(αp1
w¯
) 1
1−α
.
Observe:
A reduction of w¯ generates employment.
If nominal wages were flexible then w¯ would decrease, h1
increase and we would reach full employment (h1 = h¯).
However, because wages are rigid, this does not happen.
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Week 10: Dynamics of a Sudden Stop
The current account in this economy is defined as
CA1 = TB1 + r0B0
where
TB1 = Q
T
1 − C
T
1 .
Therefore, CA1 improves as C
T
1 decreases.
In this economy, GDP1 = Q
T
1 + p1Q
N
1 = Q
T
1 + p1(h1)
α.
Therefore, GDP1 decreases as Q
N
1 goes down.
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Week 10: Intuition Behind the Dynamics
1 The increase in the interest rate r1 makes it harder for the
country to borrow.
2 The country has to reduce the amount of tradables that
they import in period 1.
3 Thus, the amount of nontradables becomes relatively
abundant compared to tradables.
4 The price of nontradables falls relative to tradables.
5 However, nominal wages are fixed. Therefore, firms reduce
employment and unemployment is generated.
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Week 11: Free Capital Mobility and CIP
The difference
(1+ it)− (1+ i
∗
t )
Ft
Et
is called the covered interest rate differential (CID).
“Covered” because the forward contract covers the investor
against exchage rate risk.
If the covered interest differential is zero then we say that
covered interest rate parity (CIP) holds.
Covered Interest Rate Parity
Under free capital mobility, (1 + it) = (1+ i
∗
t )
Ft
Et
holds.
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Week 11: Free Capital Mobility and CIP
Proof.
Suppose that (1+ it) < (1+ i
∗
t )
Ft
Et
. Then the following
transaction gives investors an arbitrage opportunity.
In period t :
Borrow 1 dollar at home at the interest rate it .
Exchange the 1 dollar to 1
Et
euros.
Invest the 1
Et
euros in foreign bonds.
Enter a forward contract to exchange (1+ i∗t )
1
Et
euros next
period.
In period t + 1:
Receive (1+ i∗t )
1
Et
euros from your foreign investment.
Execute the forward contract to receive (1+ i∗t )
Ft
Et
dollars for
those euros.
You materialize a profit of (1+ i∗t )
Ft
Et
− (1+ it ) > 0.
Under free capital mobility investors exploit all arbitrage
opportunities, so the above inequality cannot hold. 56 / 68
Week 11: Offshore-Onshore Interest Rate Differentials
Other interest rate differentials besides the CID also are
informative about he degree of capital market integration.
Eurocurrency deposits are foreign currency deposits in a
market other than the home market of the foreign currency.
e.g.: eurodollar deposits = dollar deposits outside the U.S.
Compare the interest rates on USD time deposits in New
York (onshore rate) and London (offshore rate):
offshore-onshore interest rate differential = i∗t − it ,
where
i∗t = interest rate in period t on a USD deposit in London,
it = interest rate in period t on a USD deposit in the NYC.
Under free capital mobility, the offshore-onshore differential
should be zero.
57 / 68
Week 12: Demand and Supply for Money
We assume that Ct = C for all t .
Thus
Mdt
Pt
= L(C, it).
Mt denotes the nominal supply of money.
The equilibrium condition in the money market is
Mt
Pt
= L(C, it) (9)
58 / 68
Week 12: Purchasing Power Parity
There is a single tradable good.
Absolute purchasing power parity holds:
Pt = EtP
∗
t
For simplicity, we assume P∗t = 1 for all t .
Thus
Pt = Et
and money market clearing condition (9) becomes
Mt
Et
= L(C, it)
59 / 68
Week 12: Interest Parity Condition
Let i∗t denote the foreign nominal interest rate in period t .
We assume that i∗t = i
∗ for all t .
We assume that there is free capital mobility.
We assume that there is no uncertainty.
E.g., at time t the HH knows the entire future path of
nominal exchange rates (Et , Et+1, Et+2, . . .).
We then get the interest parity condition
1+ it = (1 + i
∗
t )
Et+1
Et
60 / 68
Week 12: Government Budget Constraint
B
g
t = B
g
t−1 +
Mt −Mt−1
Pt
− (Gt − Tt − i
∗B
g
t−1)
Let
DEFt = (Gt − Tt)− i
∗B
g
t−1
Then, using Pt = Et ,
B
g
t = B
g
t−1 +
Mt −Mt−1
Et
− DEFt (10)
If DEFt > 0 then
the government creates money (Mt −Mt−1 > 0) and/or
the government’s asset position declines (B
g
t < B
g
t−1)
61 / 68
Week 12: Balance of Payments Crises
Suppose that the government pegs the nominal exchange
rate and runs fiscal deficits DEFt ≥ DEF > 0.
This is unsustainable and leads to a BOP crisis.
Empirically, right before the peg is abandoned, the central
bank often suffers a speculative attack in which it loses
vast amounts of foreign reserves in a short period of time.
Question: Can our model reproduce and explain the
mechanics of a speculative attack?
62 / 68
Week 12: Balance of Payments Crises
1 Pre-Crisis Phase: t ∈ {1, . . . ,T − 2}
The currency is pegged in the current and next period:
Et = Et+1 = E
Therefore,
Pt = E
it = i
∗
Mt = EL(C, i
∗)
Seignorage is
Mt −Mt−1
Pt
= 0
The central bank loses foreign reserves:
B
g
t = B
g
t−1 − DEF
63 / 68
Week 12: Balance of Payments Crises
3 Post-Crisis Phase: t ∈ {T ,T + 1, . . .}
B
g
t−1 = B
g
t = 0 (the government has no foreign reserves)
government prints money at rate µ to finance fiscal deficit:
Mt = (1+ µ)Mt−1
Et = (1+ µ)Et−1
Pt = (1 + µ)Pt−1
1+ it = (1+ µ)(1+ i
∗) or it = i(µ)
Mt = PtL(C, i(µ))
seignorage
Mt−Mt−1
Pt
= L(C, i(µ)) µ
1+µ
DEF = L(C, i(µ)) µ
1+µ
64 / 68
Week 12: The Dynamics of a Balance of Payments
Crisis
SUW Figure 15.3.
65 / 68
Week 12: The Dynamics of a Balance of Payments
Crisis
The depreciation rate and inflation are zero until T − 1 and
jump to a permanently higher level in T .
The nominal interest rate jumps one period earlier in T − 1
because of the anticipated depreciation in T .
The increase in the interest rate induces households to
reduce their real money holdings in T − 1.
Nominal money demand Mdt = EtL(C, it) and thus nominal
money supply Mt
drop in T − 1 as iT−1 > iT−2 while ET−1 = E ,
grow at a constant rate from T on (creating seignorage).
Foreign reserves fall by DEF per period until T − 2 and
then get depleted by a final, larger drop in T − 1.
66 / 68
Week 12: Intuition Behind the Speculative Attack
The model explains why a
speculative run against the domestic currency and
large losses of foreign reserves
often precede the end of real life currency pegs:
it rises in anticipation of a devaluation in period T .
This causes a contraction in the demand for real money
balances: people get rid of part of their domestic-currency
holdings.
Because it still defends the peg in T − 1, the central bank
must absorb the entire decline in the demand for money by
selling foreign reserves.
67 / 68
ECON7520
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