ECON7520: A Sudden Stop and Real
Exchange Rates
Semester 1, 2023
1 / 36
Motivation: Argentina’s Sudden Stop in 2001
Argentina U.S. Interest Spread
SUW Figure 10.5. Displayed is the interest rate spread of Argentine dollar-denominated bonds over U.S. Treasuries
between 1994 and 2001.
The interest rate differential between Argentina and the
U.S. sharply increased in 2001.
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Motivation: Argentina’s Sudden Stop in 2001
SUW Figure 10.5. Displayed is the Argentine CA to GDP ratio from 1991 to 2002.
The current account balance moved towards a surplus.
3 / 36
Motivation: Argentina’s Sudden Stop in 2001
SUW Figure 10.5.
The peso depreciated in real terms ≈ 150% against the
dollar.
That is, within a few month, the U.S. became 2.5 times as
expensive relative to Argentina as before the sudden stop.
4 / 36
Motivation: Argentina’s Sudden Stop in 2001
SUW Figure 10.5. Displayed is the Argentine CA to GDP ratio from 1991 to 2002.
The real GDP of Argentina decreased.
5 / 36
Motivation: Argentina’s Sudden Stop in 2001
In 2001, Argentina fell into a crisis that culminated in
default and devaluation.
The default lead to a cutoff from international capital
markets and hence capital inflows stopped abruptly.
Such a phenomenon is called a sudden stop.
Questions:
1 What are the effects of a sudden stop on the economy?
2 What are the mechanism of the effects?
6 / 36
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.
7 / 36
ECON7520
A Model of A Sudden Stop
8 / 36
Main Points
We study a model of a sudden stop
The sudden stop is modeled as:
A sharp increase in the interest rate for borrowing, r1.
This will make it harder (= more expensive) for the country
to borrow from the rest of the world (ROW).
The model will generate an interesting dynamics of the CA
balance and real exchange rate.
9 / 36
Setup
Time periods: 1 and 2.
Agent: There is a representative household in the country.
Good: There are tradable and nontradable consumption
goods in this world.
Asset: There is a single asset, a bond, in this world
The household holds B0 units of the bond at the beginning.
Interest Rates: r0 for the initial asset holdings, and r1 for
the assets held at the end of period 1.
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Setup
Endowment: The household is endowed with:
QT1 units of tradables and Q
N
1 units of nontradables in
period 1.
QT2 units of tradables and Q
N
2 units of nontradables in
period 2.
Consumption: The household’s consumption choices are
CT1 for tradables and C
N
1 for nontradables in period 1.
CT2 for tradables and C
N
2 for nontradables in period 2.
Price of goods are determined in equilibrium:
p1 = price of nontradables relative to that of tradables in
period 1.
p2 = price of nontradables relative to that of tradables in
period 2.
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Real Exchange Rate
The real exchange rate in each period (t = 1,2) is defined
as
et =
EtP
∗
t
Pt
Pt ≡ φ
(
PTt ,P
N
t
)
is the aggregate price level for the home
country.
P∗t ≡ φ
(
PT∗t ,P
N∗
t
)
is the aggregate price level for the rest of
the world.
We assume that the function φ(·, ·) has the following
properties:
1 φ
(
PTt ,P
N
t
)
is increasing in both PTt and P
N
t .
2 For every λ > 0, we have
φ
(
λPTt , λP
N
t
)
= λφ
(
PTt ,P
N
t
)
.
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Real Exchange Rate
Then, we have
et =
EtP
∗
t
Pt
=
Etφ
(
PT∗t ,P
N∗
t
)
φ
(
PTt ,P
N
t
)
=
EtP
∗
Tφ
(
1,PN∗t /P
T∗
t
)
PTφ
(
1,PNt /P
T
t
) = φ (1,PN∗t /PT∗t )
φ
(
1,PNt /P
T
t
) = φ (1,1)
φ (1,pt)
,
Here we assumed that the price ratio of nontradables and
tradables in the ROW is constant; in particular:
PN∗t
PT∗t
= 1 for all t = 1,2.
Note also that we have, by definition,
PNt
PTt
= pt for all t = 1,2
13 / 36
Household’s Budget Constraint
The budget constraint is expressed in tradable goods as
the unit of measure.
Therefore, we have
CT1 + p1C
N
1 + B1 =(1+ r0)B0 + Q
T
1 + p1Q
N
1 , (1)
CT2 + p2C
N
2 =(1+ r1)B1 + Q
T
2 + p2Q
N
2 . (2)
By combining (1) and (2), we can derive the household’s
intertemporal budget constraint
CT1 +p1C
N
1 +
CT2 + p2C
N
2
1+ r1
= (1+ r0)B0+Q
T
1 +p1Q
N
1 +
QT2 + p2Q
N
2
1+ r1
.
14 / 36
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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Utility Maximization: The Case of Four Goods
In the two-good case, we had
−
U1 (C1,C2)
U2 (C1,C2)︸ ︷︷ ︸
(IC’sSlope)
= −(1+ r1)︸ ︷︷ ︸
(BC’sSlope)
where U1 (C1,C2) =
∂U(C1,C2)
∂C1
and U2 (C1,C2) =
∂U(C1,C2)
∂C2
.
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Utility Maximization: The Case of Four Goods
We extend this idea to the four-good case as
−
U1
U2
= −
1
p1
−
U1
U3
= − (1+ r1)
−
U1
U4
= −
1
p2
(1+ r1)
where
U1 =
∂U
(
CT1 ,C
N
1 ,C
T
2 ,C
N
2
)
∂CT1
, U2 =
∂U
(
CT1 ,C
N
1 ,C
T
2 ,C
N
2
)
∂CN1
U3 =
∂U
(
CT1 ,C
N
1 ,C
T
2 ,C
N
2
)
∂CT2
, U4 =
∂U
(
CT1 ,C
N
1 ,C
T
2 ,C
N
2
)
∂CN2
.
17 / 36
Market Clearing Conditions for Nontradables
In our setup, all the nontradables are consumed within the
country.
Thus, we need additional conditions to ensure that.
These conditions are so-called market clearing conditions:
CN1 = Q
N
1 ,
CN2 = Q
N
2 .
Under these conditions, all the nontradable goods are
consumed within the country.
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Resource Constraint
Plugging in the market clearing conditions for nontradables
into the intertemporal budget constraint
CT1 +p1C
N
1 +
CT2 + p2C
N
2
1+ r1
= (1+ r0)B0+Q
T
1 +p1Q
N
1 +
QT2 + p2Q
N
2
1+ r1
yields the economy’s resource constraint
CT1 +
CT2
1+ r1
= (1+ r0)B0 + Q
T
1 +
QT2
1+ r1
.
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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 . 20 / 36
Logarithmic Utility Function
We can easily solve out for an equilibrium if the household
has the logarithmic utility function given by
U(CT1 ,C
N
1 ,C
T
2 ,C
N
2 ) = lnC
T
1 + lnC
N
1 + lnC
T
2 + lnC
N
2 .
Using the derivative formula,
d(ln x)
dx =
1
x , we can get
U1 =
∂
(
lnCT1 + lnC
N
1 + lnC
T
2 + lnC
N
2
)
∂CT1
=
1
CT1
,
U2 =
∂
(
lnCT1 + lnC
N
1 + lnC
T
2 + lnC
N
2
)
∂CN1
=
1
CN1
,
U3 =
∂
(
lnCT1 + lnC
N
1 + lnC
T
2 + lnC
N
2
)
∂CN2
=
1
CT2
,
U4 =
∂
(
lnCT1 + lnC
N
1 + lnC
T
2 + lnC
N
2
)
∂CT2
=
1
CN2
,
Substitute the above conditions into the optimality
condition.
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Equilibrium under Logarithmic Utility Function
Now, the equilibrium requires the following conditions:
1 Resource constraint
C
T
1 +
CT2
1+ r1
= (1+ r0)B0 + Q
T
1 +
QT2
1+ r1
.
2 Optimality of the intertemporal allocation
−
CN1
CT1
= −
1
p1
(3)
−
CT2
CT1
= − (1+ r1) (4)
−
CN2
CT1
= −
1
p2
(1+ r1) (5)
3 Interest rate parity condition
r1 = r
∗
.
4 Market clearing for nontradable goods
C
N
1 = Q
N
1 , C
N
2 = Q
N
2 .
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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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ECON7520
The Dynamics of A Sudden Stop
24 / 36
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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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.
26 / 36
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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Dynamis of a Sudden Stop
SUW Figure 10.4.
28 / 36
Dynamics of A Sudden Stop
SUW Figure 10.4.
29 / 36
Dynamics of A Sudden Stop
We derived that the real exchange rate equals
e1 =
φ (1,1)
φ (1,p1)
.
Given φ(·, ·) is an increasing function of each argument, e1
increases as p1 decreases.
Thus, the real exchange rate depreciates towards the
home country.
30 / 36
Dynamics of A Sudden Stop
SUW Figure 10.4.
31 / 36
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.
32 / 36
Dynamics of A Sudden Stop
SUW Figure 10.4.
33 / 36
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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Intuition Behind the Dynamics
Thus, a sudden stop involves
1 An improvementin 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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Summary and Conclusion
Today, we studied:
1 A theory of sudden stops.
A sharp increase in the interest rate for borrowing.
2 Effects of a sudden stop are
A change in the current account balance toward the surplus.
A real exchange rate depreciation.
A reduction in GDP.
Next week, we will study sudden stops and
unemployment.