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International Macro
Real Exchange Rate and Net
Exports


S  PF
s
P
Are net exports a
decreasing function of
the real exchange
rate?
imq
Assume real imports
imq
are a (positive)
s
s
constant elasticity
function of real
exchange rate and
exports are a
(negative) constant
elasticity function
xq 
X
Q
imq 
IM
Q
  IM
xq
xq
s
s
 X
Marshall-Lerner Conditions

Real Net Exports
PX  S  P F  IM X
IM
nxy 
 s
 xq  s  imq
P Q
Q
Q

Effect of a Change in Real Exchange Rate
nxy   xq  s  imq  xq
imq
nxy
xq
s  imq


s
 imq 
 X
 ( IM  1)
s
s
s
s
s
s
s

Near trade balance rnx=0
nxy
xq
s  imq
 X
 ( IM  1)
  X   IM   1 imq
s
s
s
nxy
  X   IM   1  s  imq
s
s
Marshall-Lerner Conditions


Marshall-Lerner Condition: An increase in
the relative price of foreign goods
increases real net exports if
Two effects:


 X   IM   1  0
Expenditure Switching: A rise in the relative
price of domestic goods will cause people to
purchase more imports and reduce exports.
A rise in the price of domestic goods
increases the value of those goods in trade.
Long Run Elasticities



Elasticities are % change in variable
caused by a % change in another
variable.
A variable may have different effect at
different horizons depending on
adjustment costs and inertia.
Allow for dynamics in an equation
describing the effects.
Does Marshall-Lerner
Condition Hold

In the short run, No. In the long run yes.
ln X t   X ln st   X ln X t 1
ln IM t   IM ln st   IM ln IM t 1
 X  IM  1
X

 IM  1
1   X 1   IM
In 1984, Finance ministers of major economies
met in Plaza Hotel in NY to conspire to weaken
US dollar. US Current Account initially fell.
USA
.012
.011
.010
.00
.009
-.01
.008
-.02
.007
-.03
-.04
82
83
84
85
86
87
88
89
Trade Balance (% of GDP)
90
91
S
92
J-Curve
nxy
s
time
Real Exchange Rate
s
S-I
NX
Intuition


S – I is the (net) number of domestic
currency units trying to buy foreign
currency to buy foreign assets. Demand
for foreign currency.
NX is the (net) number of foreign currency
units trying to buy domestic currency to
buy domestic goods. Supply of foreign
currency.
Increase in Capital Outflows
NX
S-I
s
S-I
s
Increase in Competitiveness of
NX
Goods
S-I
s
s
NX
Back of the Envelope


If U.S shifts to sustainable nxy, what is
the % effect on real exchange rate
Assumptions



Imports about 15% share of US GDP
Unit import and export elasticities.
Trade balance must increase by 5%
nxy
nxy
nxy .05 1
  X   IM   1  s  imq  s 



s      1  s  imq s  imq .15
3
s
X
IM


s
Forward and Spot Rates

Spot Exchange Rate: Rate at which
exchange is traded for immediate
settlement.


S: # DCU/FCU if delivered today.
Forward Exchange Rate: Rate at which
exchange is traded for settlement at
some future date.

FW: #DCU/FCU if delivered in 1 period.
Bilateral Exchange Rates vs.
Effective Exchange Rates


No country has a single exchange rate
since they trade with countries with many
currencies.
To measure the value of the domestic
currency against a broader set of
currency units, economists sometimes
construct “effective” exchange rates or
“trade” weighted exchange rates.
Assume trading partners indexed n = 1
.. N with exchange rates St,1, St,2, ….,
St,N and calculate the growth rates of
the exchange rates.

gtS1  ln(

g
STW
t
St ,1
St ,1
), gtS2  ln(
St ,2
St ,2
),...., gtSN  ln(
St , N
St , N
)
Using weights, that add up to 1, w1 +
w2 + …wN = 1, calculated a weighted
average of exchange rates.
 w g  w2 g  ....  wN g
S1
1 t
S2
t
SN
t
 STW ,t  STW ,t 1 e
gtSTW
Ja
n9
M 9
ay
-9
Se 9
p99
Ja
n0
M 0
ay
-0
Se 0
p00
Ja
n0
M 1
ay
-0
1
Se
p01
Ja
n0
M 2
ay
-0
Se 2
p02
Ja
n0
M 3
ay
-0
Se 3
p03
Ja
n0
M 4
ay
-0
4
Se
p04
Trade Weighted Exchange
Rate
US Exchange Rate
140
120
100
80
60
40
20
0
TW
Euro
Euro Deposits

Banks offer deposits in foreign
currency.



Domestic interest rate 1+i
Foreign interest rate 1+iF
The bank also offers forward contracts
for foreign currency.
Two Strategies


Deposit $1 in
domestic currency
bank account.
Pay-off: After 1
period, collect $1+i


Buy 1/S FCU’s.
Deposit 1/S in foreign
currency account. Sell
(1+iF)1/S in forward
market.
Pay-off: After 1 period,
collect
F FW
Arbitrage would suggest “Covered Interest Parity”
FW
1  i  (1  i )
S
F
(1  i )
S
Covered Interest Parity


Beyond freedom to invest in either
type of asset and competitive markets,
no assumptions needed to get covered
interest parity since pay-off is known
with certainty.
Covered interest parity holds true and
is often used to price forward contracts.
Two Strategies


Deposit $1 in
domestic currency
bank account.
Pay-off: After 1
period, collect $1+i

Buy 1/St FCU’s.
Deposit 1/St in foreign
currency account. After
1 period, collect
(1+iF)/St. Sell in spot
market at St+1
St 1
(1  i )
St
F
Arbitrage and perfect knowledge or risk-neutrality would suggest “Covered
Interest Parity”
S
1  i  (1  i F )
t 1
St
Real Interest Parity
St 1
 UIP 1  i  (1  i )
St
F

Divide and multiply by inflation
Pt F1
Pt F
1 i
(1  i F ) St 1
 F


Pt 1
Pt 1
St Pt 1
Pt
Pt F
Pt
1 r  1 r 
St 1  Pt F1
Pt 1
F
St  Pt F
Pt
st 1
 1 r 
 1 r *
st
F
Domestic Real Interest Rate equals
Foreign Real Interest Rate ∙Real
Depreciation Rate

Implication


For developed economies, we should see
equal real interest rates in the long-run.
For high growth economies with open capital
markets, we should see low real interest rates
in the long run due to real appreciation of the
exchange rate.
Uncovered Interest Parity


Is uncovered interest parity true? No. It relies on
assumptions that aren’t true. Empirically, forward
exchange rates are not a good predictor of future
spot exchange rates because there are large,
unpredictable shocks to exchange rates.
Sometimes forward rates reflect attitude of risk
toward these shocks.
Uncovered Interest Parity does seem to work
roughly in the long-run. Long run averages of
interest rate differentials do seem to coincide with
rates of exchange rate depreciation.
Testing Uncovered Interest Parity

If uncovered interest parity were true then
ln St 1  ln St  ln FWt  ln St

Estimating the regression equation
ln St 1  ln St  0  1  ln FWt  ln St    t

UIP implies
0  0, 1  1
Capital Flow Curve




How do capital flows respond to real interest
differentials?
Under real interest parity, capital flows (i.e. NFI)
will flow to the high interest rate country.
Portfolio Balance Approach: Investors seem to
prefer assets from their own economy. NFI
(investment into the domestic economy) is an
increasing function of the
The stronger the Portfolio Balance motivation
the steeper the NFI curve.
Portolio Balance Approach
Capital
Controls
r*
Real
Interest
Capital
Parity
Outflow
CF(r-r*)=
(S-I)
NFI
0
Planned Expenditure in Open
Economy



Capital expenditure CF(r-r*) = NX(s)
PE = C + I +G +CF
Inclusion of international sector makes
planned expenditure more sensitive to
the real interest rate.

If real interest rate goes up, outward
capital flows decrease, real exchange
rate decreases, net exports decline.
Planned Expenditure
r
r(π1)
MP
r(π0)
ISRP
ISPB
r(π2)
ISCC
Q
Planned Expenditure
r
r(π1)
MP
r(π0)
r(π2)
ISPB
ISCC
Q1 ’
Q
Q1
Q0
Q2
Q2
AD Curve
π
AD’
AD’
Q
Implications



Expenditure in the open economy
becomes much more sensitive to
changes in monetary policy
Since expenditure is more sensitive to
monetary policy, AD curve is flatter.
Output will be less sensitive to
changes in fiscal policy or other forms
of demand changes.
AD Curve
π
SRAS
ADPB’
ADPB
ADcc
ADcc’
Q
Fixed Exchange Rate



An alternative monetary policy is to
maintain a fixed exchange rate.
From UIP, we can interpret this as
maintaining an interest rate that is
fixed at the level of foreign rates r*.
Output will be more sensitive to shocks
to planned expenditure.
Foreign Interest Rate Shocks


Floating exchange rates. A rise in foreign interest
rates will lead to a capital outflow (which
depreciates the exchange rates and leads to
greater NX). The higher demand leads to higher
inflation and higher interest rates which reduces
consumption and investment.
Fixed Exchange rates. A rise in the foreign
interest rates will lead directly 1-for-1 increase
interest rates which will lead to less demand
without depreciating the exchange rate and
stimulating interest rates.
Equilibrium Exchange Rate
S
S*
1+i
1 iF
R
St 1
St
Exchange Rates


Uncovered interest parity is a
complicated dynamic equation but we
can use it to identify the effects of
temporary shocks to interest rates.
Assume a change in interest rates is
strictly temporary so it has no effect on
future exchange rate.
Rise in Domestic Interest Rate
S
S*
1+i
1 iF
S**
R
St 1
St
Rise in Foreign Interest Rates
S
1+i
S**
S*
1 iF
R
St 1
St
ECB Rates
Fed Funds
Sep-04
May-04
Jan-04
Sep-03
May-03
Jan-03
Sep-02
May-02
Jan-02
Sep-01
May-01
Jan-01
Sep-00
May-00
Jan-00
Sep-99
May-99
Jan-99
Sep-98
May-98
Jan-98
Sep-97
May-97
Jan-97
Interest Rate Policy
7
6
5
4
3
2
1
0
UIRP & Exchange Rate
Volatility


1  itF
St 
St 1 ,
Using UIRP we can write the 1  it
1  itF1
St 1 
St  2
1  it 1
exchange rate as a function
of the future series of
1  itF 2
exchange rate differentials.
St  2 
St 3 ,...
1  it  2
Since forecasts of future
variables may be volatile
1  itF 1  itF1 1  itF 2 1  itF3
and subject to optimism andSt  1  it  1  it 1  1  it 2  1  it 3  .....StLR ,
pessimism, this may explain
a large degree of exchange
rate volatility.