International Finance and MacroeconomicsLecture Notes Sectio.docx

International Finance and Macroeconomics
Lecture Notes Section 4
1 Some Preliminaries
We will now develop a model to analyze the impact of domestic
and external shocks on
output, interest rates, exchange rate and the trade balance. We
will start with a model
without capital flows and then later introduce capital flows. We
will analyze both fixed and
floating exchange rate systems.
First some comments about notation and simplifying
assumptions. I will assume that
NI = NL = U = 0 and that prices are set in the currency of the
exporter (PCP) with
P̄ = P̄ ∗ = 1. These assumptions imply that CA = TA and GNP =
GDP, which is also
disposable income. We will refer to Y as income or output.
Since P̄ = 1, it is both nominal
and real output. It is also equal to disposable income. Finally,
we now refer to X and M as
the dollar value of exports and imports. Previously we referred

to them as quantities. For
exports this makes no difference as P̄ = 1. Since M is the dollar
value of imports, it is equal
to EP̄ ∗ times the quantity of imports.
2 No Capital Flows; No Money
We will start with a simple model in which there is only a goods
market and foreign exchange
market. We abstract from the money market, which we
introduce later.
Goods market equilibrium is represented by
Y = C + I + G + X −M (1)
Output is equal to the sum of private consumption, investment,
government consumption,
exports, minus the part of these spending components that is
imports of foreign goods.
Assume that private consumption has a constant part C
̄ and a
part that is proportional
to income:
C = C
̄ + cY (2)
where c < 1 is the marginal propensity to consume. Assume that
imports takes the form
M = M
̄ (E) + mY (3)

1
Here M
̄ (E) is the part of imports that is a function of the
exchange rate E, capturing both
the price and quantity response to a change in the exchange
rate. Imports also rises with
income, which is reflected in the second part, mY . Here m is
the marginal propensity to
import. Exports is modeled analogously:
X = X
̄ (E) + m∗ Y ∗ (4)
We will assume that the Marshall Lerner condition is satisfied,
so that X
̄ (E)−M
̄ (E) depends
positively on E. Finally, we holdgovernment consumptionand
investment exogenously fixed:
G = Ḡ (5)
I = Ī (6)
Substituting the expressions for C, I, G, M and X into the goods
market equilibrium
equation (1), we have
Y =
1
s + m

(
C
̄ + Ī + Ḡ + X
̄ −M
̄ + m∗ Y ∗
)
(7)
Here s = 1 − c is the marginal propensity to save.
I will now start with a fixed exchange rate system. So far we
have described goods market
equilibrium. Under a fixed exchange rate system the central
bank will absorb any excess
demand or supply for foreign exchange. The foreign exchange
market equilibrium is then
simply described by E = Ē, which is the fixed exchange rate that
the central bank stands
ready to defend. Given that exchange rate, X
̄ and M
̄ are fixed as
well.
From (7) we have the following output effect of a change in
government consumption:
∆Y =
1
s + m
∆Ḡ (8)
Here 1/(s + m) is the multiplier. It is the same for changes in
other types of domestic
spending (C
̄ , Ī). In order to understand this multiplier, consider

the impact of a change
∆Ḡ in government consumption. The multiplier is the result of
many rounds of cumulative
spending effects. In the first round output rises by ∆Ḡ as firms
produce whatever demand
is at a given price P̄ . Income then rises by ∆Y = ∆Ḡ. In the
second round private
consumption rises in response to this change in income. It rises
by ∆C = c∆Y = c∆Ḡ.
But some of this is spent on imported goods: ∆M = m∆Y =
m∆Ḡ. Demand for domestic
2
goods then rises by ∆C − ∆M = (c−m)∆Ḡ = (1 −s−m)∆Ḡ. Output
rises by the same
amount: ∆Y = (1 −s−m)∆Ḡ. This then leads to a third round as
the increase in second
round income leads to a further increase in private consumption.
The third round leads
to an additional increase in demand for domestic goods, and
therefore domestic output, by
∆Y = (1 −s−m)2∆Ḡ. And so on. Adding up all these rounds of
spending effects we have
∆Y = ∆Ḡ + (1 −s−m)∆Ḡ + (1 −s−m)2∆Ḡ + ... =
1

s + m
∆Ḡ (9)
Notice that the multiplier is smaller the larger the marginal
propensity to import m. This is
the result of an import leak. The larger m, the more of an
additional increase in income is
spent on foreign rather than domestic goods. This reduces
demand for domestic goods and
therefore reduces the multiplier.
We can also compute the trade account. Substituting the
expression (7) for Y into the
expression for imports, we have
TA = X −M = −
m
s + m
(
C
̄ + Ḡ + Ī
)
+
s
s + m
(

X
̄ −M
̄ + m∗ Y ∗
)
(10)
We can also represent the equilibrium in an S−I, X−M diagram
as in Figure 1. Goods
market equilibrium Y = C + I + G + X −M can be rewritten as
(Y −C−G)−I = X −M
or S−I = X−M. This is represented as the intersection of the
X−M and S−I schedules
in Figure 1. We can then immediately see the equilibrium level
of output and trade account.
Using the S − I, X −M diagram, Figure 2 shows the impact of an
increase in govern-
ment consumption. It shifts the S − I schedule down by ∆Ḡ. The
increase in government
consumption reduces national saving. We go from equilibrium
point A to equilibrium B.
Output rises and the trade account goes down. From (10) we
have that the drop in the trade
account is
∆TA = −
m
s + m
∆Ḡ (11)
We can think about the trade deficit from both a trade and
saving-investment perspective.
From a trade perspective, the increase in income leads to an

increase in imports, which
leads to a trade deficit. From a saving-investment perspective
the increase in government
consumption reduces national saving, which is only partially
offset by the rise in saving due
to the higher income. We can also look at it from a capital flows
perspective, but in the
model so far there are only offi cial capital flows. The trade
deficit leads to an excess demand
for foreign exchange. The central bank therefore sells foreign
exchange, which means that
ORT > 0.
3
Figure 3 shows the impact of an increase in export demand ∆X
̄ .
It leads to an increase
in output and a trade surplus. From (7) the increase in output is
∆Y = ∆X
̄ /(s + m). From
(10) the increase in the trade account is
∆TA =
s
s + m
∆X
̄ (12)

We can again look at this surplus both from a trade and saving-
investment perspective.
From a trade perspective the exogenous increase in export
demand naturally leads to a
trade surplus. This is only partially dampened by the fact that
the higher income leads
to higher imports. From a saving-investment perspective the
higher income leads to higher
saving. The resulting trade surplus implies an excess supply of
foreign exchange. The central
banks then buys foreign exchange (ORT < 0).
So far we have considered a small open economy model as we
have taken foreign output
Y ∗ as given. We have assumed that domestic shocks have no
effect on Y ∗ . Now consider
an extension of the same model to two large countries. Still
consider a fixed exchange rate
regime. We will call the countries Home and Foreign. It is
useful to write again the Home
goods market equilibrium (7):
Y =
1
s + m

(
C
̄ + Ī + Ḡ + X
̄ −M
̄ + m∗ Y ∗
)
(13)
There is an exactly analogous Foreign goods market
equilibrium:
Y ∗ =
1
s∗ + m∗
(
C
̄ ∗ + Ī∗ + Ḡ∗ + M
̄ − X
̄ + mY
)
(14)
Here we have added a star superscript for Foreign variables and
coeffi cients. Note that since
Home imports is equal to Foreign exports and Home exports is
Foreign imports, we can
use X
̄ ∗ = M
̄ and M
̄ ∗ = X
̄ . Note also that m∗ Y ∗ in (13) is
replaced by mY in (14). An
increase in Foreign income raises Foreign imports, which raises
Home exports and therefore
Home output. Analogously, an increase in Home income raises
Home imports and therefore
Foreign exports, which raises Foreign output.

We can represent the schedules (13)-(14) in a diagram in (Y,Y
∗ ) space, as shown in
Figure 4. The Home schedule, which represents (13), has slope
m∗ /(s + m) as ∆Y =
[m∗ /(s + m)]∆Y ∗ . The Foreign schedule, which represents
(14), has slope (s∗ + m∗ )/m.
Note that ∆Y ∗ = [m/(s∗ + m∗ )]∆Y and therefore ∆Y = [(s∗ +
m∗ )/m]∆Y ∗ .
Figure 5 shows the impact of an increase in Home government
consumption. The Home
schedule shifts upward by ∆Ḡ/(s + m). This is the increase in
Home output for a given Y ∗ .
4
But now Y ∗ will endogenously change. We go to the new
equilibrium at point B. Both Home
and Foreign output rise and Home output rises by more than
∆Ḡ/(s + m). The intuition is
as follows. The rise in Home government consumption raises
Home output and income. This
raises Home imports, which implies a rise in Foreign exports.
This raises Foreign output
and income. This raises Foreign imports and therefore Home

exports. This implies a rise
in Home exports and a further rise in Home output. That is why
Home output now rises
more than in the small open economy model. The shock in the
Home country is transmitted
to the Foreign country through trade. Later on we will see that
capital flows are another
channel through which shocks can be transmitted across
countries.
We will now consider a floating exchange rate system. The
Foreign exchange market
equilibrium condition is then TA = X − M = 0. The reason is
that there are no private
capital flows (KA = 0) and no central bank intervention in the
foreign exchange market
(ORT = 0), so that from CA + KA + ORT = 0 it follows that CA
= 0, which here implies
TA = 0 (as we assumed U = NI = 0). The only sources of
demand and supply for foreign
exchange come from exports and imports, so that they have to
be equal in equilibrium. We
still also have the goods market equilibrium Y = C +I +G+X−M.
Using that X−M = 0,
this goods market equilibrium condition becomes Y = C + I + G,
the same as in a closed

economy. Substituting the expressions for C, I and G, we can
solve this as
Y =
1
s
(
C
̄ + Ḡ + Ī
)
(15)
Given the solution for Y , the exchange rate can be solved from
TA = 0.
Figure 6 shows the impact of an increase in government
consumption in the X − M,
S − I diagram. The increase in government consumption shifts
down the S − I schedule
by ∆Ḡ. We go from point A to point B. This is the equilibrium
in the fixed exchange rate
system. But it is not an equilibrium under a float. There is a
trade deficit and therefore
an excess demand for foreign exchange. The price of Foreign
exchange, the exchange rate
E, will then rise. This depreciation leads to an increase in net
exports, which shifts out the
X −M schedule until it crosses the new S − I schedule at TA = 0
(point C). The foreign
exchange market is then in equilibrium. Output rises more than

in the fixed exchange rate
system. This is because the depreciation leads to a rise in net
exports.
Figure 7 shows the impact of an increase in export demand X
̄ .
The X−M schedule shifts
out, bringing us to point B. This is the equilibrium in a fixed
exchange rate system. But it
is not an equilibrium under a float. There is a trade surplus and
therefore an excess supply
5
of foreign exchange. This leads to a drop in the price of foreign
exchange and therefore an
exchange rate appreciation. This lowers net exports, leading the
X − M schedule to shift
back. It shifts back all the way to its original position, where
TA = 0. Output therefore
does not change, consistent with (15). The country is insulated
from external shocks as the
trade account is always zero in equilibrium. We will see that
this result changes once we
introduce capital flows.
We can summarize the results so far by comparing the pros and
cons of both exchange

rate regimes. We can first consider what exchange rate system
is most desirable in terms
of having the least output volatility in response to internal
(domestic) and external shocks.
A float is most desirable when the economy is hit significantly
by external shocks as it
completely insulates domestic output from these shocks. A fixed
exchange rate system is
most desirable when the economy is hit significantly by
domestic demand shocks as output
fluctuates less in a fixed exchange rate system in response to
these shocks. We can also look
at it from a policy perspective. A float is then most desirable as
fiscal policy is more effective
in terms of changing output under a float.
3 Money Market
We now extend the model by introducing a money market. For
now we continue to assume
zero capital flows (KA = 0). We hold money supply M
̄ s
exogenously fixed. We will discuss
a little later what exactly determines the supply of money and
how it changes in response
to FX intervention. But for now we hold it fixed. Money
demand depends negatively on the

interest rate and positively on output:
Md = Md(i,Y ) (16)
A higher interest rate leads to a switch from money to bonds as
money earns no interest. A
higher output level implies more transactions in the economy,
raising the demand for money.
In equilibrium money demand equals money supply:
M
̄ s = Md(i,Y ) (17)
This is the LM schedule. There is money market equilibrium for
a positively sloped schedule
in (i,Y ) space. A combination of a higher interest rate and
higher output will leave money
demand unchanged, so that the money market continues to be in
equilibrium.
6
There is also a bonds market equilibrium, but due to Walras’law
we can ignore the bonds
market as it is automatically in equilibrium when the other 3
markets are in equilibrium
(goods market, FX market, money market). Generally, when
there are N markets and N−1

markets are in equilibrium, then the last market is in
equilibrium as well. While we do not
need to explicitly consider bonds market equilibrium, we will
mention the bonds market
when discussing the intuition regarding the response to shocks.
We now also assume that investment depends on the interest
rate:
I = Ī − bi (18)
Ahigher interest rate raises the cost of borrowing for firms,
which reduces investment. Goods
market equilibrium Y = C + I + G + X −M then implies
Y =
1
s + m
(
C
̄ + Ḡ + Ī − bi + X
̄ −M
̄ + m∗ Y ∗
)
(19)
This is the IS schedule. A rise in the interest rate lowers
investment demand, which lowers
output.
Diagramatically we can represent equilibrium in Figure 8. It has
two diagrams on top of

each other. The top diagram represents goods market
equilibrium (IS schedule) and money
market equilibrium (LM schedule). The X−M, S−I schedule
right below it also represents
goods market equilibrium as X − M = S − I follows from Y = C
+ I + G + X − M. It
therefore implies the same equilibrium level of output as in the
IS/LM diagram above. Using
these two diagrams on top of each other we can read offthe
equilibrium values of the interest
rate i, output Y and trade account TA.
For now we consider a fixed exchange rate system, so that E =
Ē is fixed and therefore X
̄
and M
̄ are fixed. The central bank absorbs any excess demand
or supply of foreign exchange.
Figure 9 shows the impact of an increase in government
consumption. In the IS/LM diagram
the IS curves shifts to the right by ∆Ḡ/(s + m). We go from A to
B, with a higher interest
rate and a higher output level. In the bottom diagram the S-I
schedule shifts twice. It first
shifts down by dḠ. It then shifts partially back up because the
higher interest rate lowers
investment (raising S − I). We end up at point B, with higher
output and a trade deficit.

To summarize, output rises, the interest rate rises and the trade
account goes down.
Intuitively, higher government spending raises demand for
goods, which raises output. This
raises money demand. For a given supply of money this
generates an excess demand for
money. People then sell bonds in exchange for money. This
lowers the price of bonds, which
7
raises the interest rate (the price today of a one year bond that
pays one dollar in one year is
1/(1 + i)). The higher interest rate lowers investment, which
reduces the increase in output.
This is called “crowding out”. It reduces the multiplier. The
increase in output also leads
to an increase in imports, which generates the trade deficit.
Figure 10 shows the impact of an increase in the money supply,
which shifts the LM
schedule to the right (if we raise output, money demand rises as
well, bringing us back
to money market equilibrium). We see that the interest rate falls
and output rises. In the

bottomdiagramtheS-I schedule shiftsdownbecause the lower
interest rate raises investment,
which lowers S−I. We see that the trade account goes down.
Intuitively, the higher money
supply leads to an excess supply of money. People then buy
bonds, which raises the price of
bonds and lowers the interest rate. This raises investment,
which raises output. The higher
output raises imports, which leads to a trade deficit.
Figure 11 shows the impact of an increase in export demand X
̄ .
This shifts out the
IS schedule. The interest rate rises and output rises. In the
bottom diagram the X − M
schedule shifts up by ∆X
̄ . At the same time the S − I schedule
shifts up a bit. This is
because the higher interest rate lowers investment, which raises
S − I. We have a trade
surplus. Intuitively, the higher export demand raises output.
This raises money demand.
There is an excess demand for money. People sell bonds,
lowering the price of bonds and
raising the interest rate. This lowers investment, leading to
some crowding out again. The
higher export demand leads to a trade surplus, which is only
slightly dampened by the higher
imports due to the higher income.

Now consider a floating exchange rate system. I will not do the
diagrams as there are
too many shifts of the schedules in this case. Foreign exchange
market equilibrium is now
TA = 0. The only sources of demand and supply of foreign
exchange are imports and
exports, which therefore have to be equal. The central bank
does not intervene in the
foreign exchange market. Since TA = 0, we also have Y = C + G
+ I. Substituting the
expressions for C, G and I, we can derive the IS schedule
Y =
1
s
(
C
̄ + Ḡ + Ī − bi
)
(20)
This is exactly the same as the closed economy IS schedule. The
reason is that TA = 0 in
equilibrium. The exchange rate will adjust such that TA = 0. If
we combine this IS schedule
with the LM schedule M
̄ s = Md(i,Y ), we can solve for the
interest rate and output. The

exchange rate is then solved from TA = 0.
8
As before, it remains the case that domestic shocks have a
larger impact under a floating
exchange rate system. Under a fixed exchange rate system both
an increase in government
spending and an increase in the money supply raise output and
lead to a trade deficit.
Under a float the trade deficit causes an excess demand for
foreign exchange, which leads to
an increase in the price of foreign exchange (exchange rate
depreciation). The depreciation
raises net exports, which raises output further. Also, it remains
the case as before that
external shocks have no impact under a float. It is immediate
that X
̄ does not enter the
IS and LM schedules and therefore does not affect the
equilibrium output and interest rate.
Under a fixed exchange rate system we saw that a rise in X
̄
leads to higher output and a
trade surplus. Under a float the trade surplus implies an excess
supply of foreign exchange,

which lowers the price of foreign exchange (exchange rate
appreciation). This lowers net
exports and output, bringing us back to TA = 0 and the same
level of output as before the
shock.
4 Endogenous Money Supply
So far we have assumed that the money supply is given. But as
we will soon see, under a
fixed exchange rate system the central bank may lose control
over the money supply. This
is especially the case with international capital flows, but even
without capital flows the
central bank has only limited control over the money supply. It
is hard to control two
nominal variables, the exchange rate and the money supply, at
the same time. To better
understand this, we first turn to a discussion of what determines
the money supply.
Figure 12 shows a simplified balance sheet of the central bank.
On the asset side there are
domestic securities like Treasury securities (called
DC=domestic credit) and international
reserves (mostly foreign exchange reserves). On the liability

side there is currency in circula-
tion C and commercial bank reserves R. The latter are currency
held by commercial banks
plus an account that commercial banks have at the central bank.
It used to be that the
interest on these reserves was zero, but during the Great
Recession the Fed started paying
interest on these reserves to better control the interest rate.
Banks lend these reserves to
each other (Federal funds market) at an interest rate called the
Federal Funds rate.
But getting back to the money supply, we can first define the
monetary base, which is also
called high powered money. It is equal to the sum of the
liabilities of the central bank. We
call it B. So B = C + R. The central bank imposes a required
reserve ratio on commercial
9
banks, which is the ratio of reserves to deposits, R/D. Call it rD.
As long as the banks
hold no more reserves than required we have R = rDD. Since the
Great Recession banks

hold large excess reserves, partially because they are now paid
interest on these reserves.
But that is an unusual situation that is only temporary.
Monetary policy right now is quite
unusual as we are near the zero lower bound (zero interest rate).
In what follows I will only
consider the more normal situation where reserves are equal to
required reserves (and banks
are not paid interest on these reserves). So R = rDD.
The money supply is equal to the sum of currency in circulation
C, which is currency held
by the general public, and deposits D held at commercial banks.
We assume that people
want to hold a certain ratio of currency relative to deposits C/D.
The money supply is
M
̄ s = C + D =
(
C
D
+ 1
)
D (21)
We also have

B = C + R =
(
C
D
+
R
D
)
D =
(
C
D
+ rD
)
D (22)
or
D =
B
C
D
+ rD
(23)
Substituting this into (21) we have

Ms =
C
D
+ 1
C
D
+ rD
B (24)
Since rD < 1, it follows that the money supply is a multiple of
the monetary base. This
multiple is called the money multiplier.
To see how the money multiplier works, consider the following
example: C/D = 0 and
rD = 0.1. Now assume that the central bank does an open market
operation. It buys
Treasury securities from commercial banks equal to $100. The
central bank pays for this by
crediting the reserves R of the commercial banks. The banks
then have excess reserves that
they want to lend out. They make $1000 in loans. When making
these loans they credit the
accounts of the borrowers by $1000. Now the increase in
reserves of $100 is equal to rD = 0.1
times the increase in deposits. The banks therefore satisfy the
required reserve ratio. In this

case the money supply has increased by $1000 (the increase in
deposits), which is 10 times
the increase in the monetary based (R increased by $100).
Notice that the money multiplier
is indeed 10 in this case (C/D = 0 and rD = 0.1).
10
Now consider what happens when there is a fixed exchange rate
system and the central
bank raises the money supply through such an open market
operation. We have already
considered the impact of an increase in the money supply in a
fixed exchange rate system.
Figure13repeats thecorresponding IS/LMandS-I/X-Mdiagrams.
Output rises, the interest
rate drops and the trade account goes into deficit. It is useful to
repeat the intuition. The
increase in the money supply leads to an excess supply of
money. People buy bonds, which
raises the price of bonds and lowers the interest rate. This raises
investment, which raises
output. The higher income raises imports, which leads to a trade
deficit. We go from point

A to point B.
But this is not necessarily the end. It is useful to again look at
the solution for the money
supply. It is equal to the money multiplier times high powered
money B. From the central
bank balance sheet its liabilities B are equal to its assets, DC +
Int.Reserves. So we have
M
̄ s =
C
D
+ 1
C
D
+ rD
(DC + Int.Reserves) (25)
As the central bank does the open market operation of buying
Treasury securities, domestic
credit DC rises and the money supply rises. But we also know
that there is a trade deficit
at point B, which leads to an excess demand for foreign
exchange. The central bank then
sells foreign exchange. The drop in international reserves
lowers the money supply, as can
be seen from (25). Intuitively, when the central bank sells

foreign exchange to commercial
banks, the banks have to pay for this through their reserves.
Banks will then have fewer
reserves and therefore can make fewer loans. This lowers the
money supply. As long as there
is a trade deficit this process will continue, which will
gradually shift the LM schedule back
to the left, until we eventually are back to its original position
and the long run equilibrium
is at point C, which is the same as the original equilibrium A.
Nothing has then changed in
the long run.
But suppose that the whole point of the open market operation
leading to increase in
the money supply is to stimulate the economy (raise output). So
the central bank wishes
to stay at point B. How can it do that? It can do so through
sterilized intervention in
the foreign exchange market. Sterilized intervention is FX
market intervention in a way
that keeps the money supply unchanged. We saw in the example
above that when the
central bank intervenes in the FX market by selling foreign
exchange in order to keep the

exchange rate fixed, it lowers the money supply. This is not
sterilized intervention. Under
sterilized intervention the central bank engages in offsetting
open market operations in order
11
to keep the money supply unchanged. So when it sells foreign
exchange, at the same time
it buys domestic securities in the same amount. The sum of DC
and Int.Reserves then
remains unchanged and we see from (25) that the money supply
remains unchanged. So the
central bank sterilizes the impact of its foreign exchange
intervention on the money supply
by engaging in offsetting open market operations at the same
time to keep the money supply
unchanged.
When the central bank does sterilized intervention it appears
that it can control both
the exchange rate and the money supply. In the example the
exchange rate remains fixed
while the central bank is able to increase the money supply and
keep it at the higher level.

We stay at point B. However, there is one problem with this. As
long as we are at point B
there is a trade deficit, resulting in an excess demand for
foreign exchange. The central bank
therefore has to continuously sell foreign exchange in order to
stay there. Eventually it will
run out of foreign exchange. At that point it can no longer
defend the fixed exchange rate.
So the bottom line is that in the short run the central bank can
control both the exchange
rate and the money supply, but not in the long run. In the long
run it either has to give up
control over the money supply or give up defending the fixed
exchange rate. If it wants to
continue to defend the fixed exchange rate the central bank
cannot continue to do sterilized
intervention. It will have to let the money supply go down, so
that we get back to point
A where TA=0 and there is no longer an excess demand for
foreign exchange. We will see
that when we introduce capital flows the central bank has even
less control over the money
supply.

5 Mundell Fleming Model
We will now introduce capital flows to the model. The resulting
model is known as the
Mundell Fleming model, which was developed in the late 1960s.
We will assume that capital
flows depend on the interest differential. More generally they
should depend on the expected
return differential
i− i∗ −
(
dE
E
)expected
which is the return i on domestic bonds minus the expected
dollar return i∗ + (dE/E)expected
on foreign bonds. For now we will assume that the expected
change in the exchange rate is
zero, so that the return differential is simply i−i∗ . In a fixed
exchange rate system dE/E = 0
12
anyway. Moreover, under a float this assumption is also close to
reality as changes in the

exchange rate are very hard to predict. Later on we will
consider a more dynamic exchange
rate model where we do not make this assumption and solve for
the expected change in the
exchange rate endogenously.
We model the capital account as follows:
KA = K
̄ A + k(i− i∗ ) (26)
A higher relative interest rate in the U.S. (higher i) leads to
larger capital inflows (KA
is bigger). The parameter k measures the sensitivity of capital
flows to the interest rate
differential. When k = 0 capital flows are not sensitive to the
interest differential at all. We
call this the case of no capital mobility. At the other extreme,
when k = ∞, capital flows
are infinitely sensitive to the interest differential and we have i
= i∗ . We call this perfect
capital mobility.
We define the balance of payments as BP = CA + KA. Using
that CA = TA in our
model, we have
BP = CA + KA = TA + KA = X
̄ −M
̄ + m∗Y ∗ −mY + K
̄ A +
k(i− i∗ ) (27)

In a floating exchange rate system foreign exchange market
equilibrium is represented by
BP = 0 as ORT = 0. There is now demand and supply for foreign
exchange associated
with both trade flows (in CA) and capital flows (in KA). Under
a fixed exchange rate system
BP may not be zero. When BP > 0 we have an excess supply of
foreign exchange. When
BP < 0 we have an excess demand for foreign exchange.
In what follows we will analyze the model with the IS/LM
diagram. But we add one
schedule, which is the BP = 0 line. Under a float we must
always be on this line, while
under a fixed exchange rate system we can see whether there is
an excess demand or supply
of foreign exchange by looking at whether we are to the right or
left of the BP = 0 schedule.
We can write the BP = 0 schedule algebraically by solving for i
as a linear function of
Y . We have
i = i∗ −
1
k

(
X
̄ −M
̄ + m∗Y ∗ + K
̄ A
)
+
m
k
Y (28)
The balance of payments schedule therefore is positively
sloped, as shown in Figure 14. To
the right of BP = 0 we have BP < 0. If we raise output, imports
will rise, the trade account
will go down and therefore BP drops below zero. Similarly, to
the left of BP = 0 we have
BP > 0.
13
The slope of the BP = 0 schedule is m/k. The higher the degree
of capital mobility the
higher the parameter k and therefore the lower the slope (the
flatter the BP = 0 schedule).
As shown in Figure 15, we will consider 4 cases. The case
where k = 0 is that of no capital
mobility. The BP = 0 schedule is then vertical:

Y =
1
m
(
X
̄ −M
̄ + m∗Y ∗ + K
̄ A
)
(29)
The case where k is positive but small is represented by chart B
of Figure 15. We refer to
this as low capital mobility. In that case the slope m/k is high.
In particular, we assume that
the BP = 0 line is steeper than the LM schedule. The case where
k is large is represented
by chart C of Figure 15. We refer to this as high capital
mobility. In that case the slope
m/k is low. In particular, we assume that the BP = 0 line is
flatter than the LM schedule.
The last case, where k = ∞, is the case of perfect capital
mobility, where the BP = 0 line
is horizontal. It is equal to i = i∗ .
5.1 Fixed Exchange Rate System
We first consider a fixed exchange rate system. Figure 16 shows
the impact of an increase in
government spending under the 4 different assumptions about

the degree of capital mobility.
The case of no capital mobility in chart A corresponds to the
one previously discussed. The
IS curve shifts to the right. We go from point A to point B.
Output rises and the interest rate
rises. Intuitively, the higher government consumption demand
raises output, which raises
money demand, which leads to an excess demand for money.
People sell bonds, leading to
a lower bond price and therefore higher interest rate. But in the
case of no capital mobility
the higher interest rate does not lead to higher capital inflows.
The only way that BP is
affected is through the trade account. Higher income leads to
higher imports, which leads
to a trade deficit. We therefore have a balance of payments
deficit at point B (we are to
the right of the BP = 0 line). This implies an excess demand for
foreign exchange. The
central bank sells foreign exchange. When it does this with
sterilization, we stay at point B.
But eventually the central bank will run out of foreign exchange
and can no longer sterilize.
Then the money supply will go down. We then eventually reach

point C where the balance
of payments is equal to zero again. Output will then be back at
its original level, but the
interest rate is higher. There will be full crowding out. The
higher government consumption
is offset by an equal drop in investment.
14
Chart B shows the case of low capital mobility. We again first
go to point B. The higher
interest rate now leads to capital inflows (KA > 0). But the
capital inflows are small.
Overall the BP is still negative TA + KA < 0, although less than
before because of the
capital inflows. There is now a small balance of payments
deficit, leading to a small excess
demand for foreign exchange. The central bank sells a small
amount of foreign exchange.
With sterilization we stay at point B. We can stay there a long
time as the central bank
will not run out of foreign exchange reserves quickly. But the
central bank cannot sterilize
forever, so that in the long run the money supply will go down.

The LM curve again shifts
to the left, until we reach point C, where BP = 0 and we no
longer have an excess demand
for foreign exchange. At that point we have TA < 0 and KA > 0,
while TA + KA = 0.
Output is now higher than before the shock as the higher
resulting imports now leads to a
trade deficit that is offset by an equal capital account surplus,
thus not creating an excess
demand for foreign exchange.
Chart C shows the case of high capital mobility. We again first
go to point B. The higher
interest rate now leads to large capital inflows (KA big). While
TA < 0 overall the BP is
now positive (TA + KA > 0). There is now a large balance of
payments surplus because of
the large capital inflows, leading to a large excess supply of
foreign exchange. The central
bank buys the foreign exchange. With sterilization we stay at
point B (there has to be an
offsetting sale of domestic securities to keep the money supply
fixed). But we will not stay
there a long time as there is a limit to the amount of foreign
exchange that the central bank

will buy. When the central bank stops sterilization, the money
supply will rise. The LM
curve shifts to the right and we go to point C where BP = 0. At
that point output is even
larger than in chart B. The trade deficit is then larger, but this is
offset by larger capital
inflows.
Finally, chart D shows the case of perfect capital mobility. At
that point capital inflows
are infinity at point B, leading to an infinite excess supply of
foreign exchange. Since the
central bank cannot buy an infinite amount of foreign exchange,
it has no choice but to raise
the money supply right away, bringing us to point C, where i =
i∗ again. The key takeaway
here is that the central bank completely loses control over the
money supply under perfect
capital mobility. It is unable to control both the exchange rate
and the money supply. This
was already impossible in the long run without capital mobility,
but with perfect capital
mobility it is impossible altogether. Even with a high degree of
capital mobility it is hard to

stay at point B for very long as the central bank can get quickly
overwhelmed by the capital
15
flows, making it hard to defend the fixed exchange rate. Note
that in chart D the level of
output has increased. We therefore have higher imports and a
trade deficit. This is offset
by equal net capital inflows.
Figure 17 shows the effect of an increase in the money supply
under all 4 assumptions
about the degree of capital mobility. Chart A is the familiar
case of no capital mobility. The
higher money supply leads to a rightward shift of the LM curve,
which leads to a rise in
output and a lower interest rate. Intuitively, it leads to an excess
supply of money, so that
people buy bonds. The price of bonds rises and the interest rate
falls. The lower interest
rate leads to higher investment and therefore higher output. The
higher income leads to
a trade deficit and therefore balance of payments deficit. There
is an excess demand for

foreign exchange. The central bank sells foreign exchange. As
long as the FX intervention
is sterilized we stay at point B. But eventually the central bank
will run out of foreign
exchange reserves and it will have to stop sterilizing and
therefore let the money supply go
down. The LM curve then shifts gradually back to its original
position and we end up back
at the original point A with output unchanged. The central bank
therefore only has control
over the money supply in the short run.
In chart B we introduce a low degree of capital mobility. The
lower interest rate then
leads to small capital outflows. This leads to an even larger
balance of payments deficit and
therefore a larger excess demand for foreign exchange. The
central bank needs to sell more
foreign exchange. Sterilized FX intervention is still possible,
but the central bank loses FX
reserves more quickly and therefore runs out of FX reserves
more quickly. At that point
it again needs to let the money supply go down and we go back
to the original point A.
The central bank loses control over the money supply more

quickly than under no capital
mobility.
Whenwegotoahighdegreeof capitalmobility, capital
outflowsarevery large in response
to the lower interest rate. This leads to a very large excess
demand for foreign exchange and
the central bank runs out of foreign exchange very quickly,
again being forced to lower the
money supply and go back to point A. So the message is that the
higher the degree of capital
mobility, the less control the central bank has over the money
supply under a fixed exchange
rate system. In the extreme case of perfect capital mobility
(chart D) the central bank has
no control over the money supply at all. If it raises the money
supply, the lower interest rate
would lead to infinite capital outflows and therefore an infinite
exchange demand for foreign
exchange. Since the central bank does not have an infinite
amount of foreign exchange, this
16
is simply not possible. The central bank has no control over the

money supply.
This brings us to the so-called “impossible trinity”. This means
that the following com-
bination is impossible:
1. fixed exchange rate system
2. control over money supply
3. perfect capital mobility
One of these needs to be given up. First consider giving up
number 1 (control over the
exchange rate). It is then possible to retain number 2 (control
over the money supply) and
number 3 (perfect capital mobility). To see this, consider Figure
18, where the central bank
raises the money supply under perfect capital mobility. We have
already seen that this is
impossible while holding the exchange rate fixed. Buy in Figure
18 we let the currency
devalue at the same time, so that net exports rise and the IS
curve shifts to the right. We
then end up at point C, where i = i∗ and therefore the infinite
capital outflows stop.
The second way out is to retain number 1 (fixed exchange rate)
and number 3 (perfect

capital mobility) but to give up control over the money supply.
This is very hard to do
though as countries like to have control over the money supply
as it is a very good policy
tool to affect output and inflation.
The last way out is to retain number 1 (fixed exchange rate) and
number 2 (control over
monetary policy) but give up number 3 (perfect capital
mobility). Indeed, we have seen that
under no capital mobility the central bank has much better
control over monetary policy.
This is the system that China has chosen to adopt. It is in fact
quite common for countries
with fixed exchange rate systems to impose capital controls in
order to maintain some control
over monetary policy.
In order to illustrate these points further I will now turn to a
discussion of the Bretton
Woods fixed exchange rate system. The Bretton Woods
exchange rate system is based on
an agreement about the post-war monetary system during a
conference in Bretton Woods,
New Hampshire, in July 1944 among the allies (44 countries

signed the agreement). Notice
that this was one month after the Normandy invasion and clearly
before the outcome of the
war was known. The agreed system had the following elements:
17
1. The price of gold was fixed at $35 per ounce. The United
States had the responsibility
of defending this gold-dollar exchange rate. Other central banks
could buy and sell to
the U.S. at this exchange rate (the U.S. had 60% of the world
gold reserves).
2. the other countries had the responsibility to defend their
currency against the dollar
with a 1% band around a central parity. The dollar therefore
automatically became
the principle reserve currency.
3. the IMF was established. Member countries had to deposit
gold and their own currency
at the IMF and received an IMF position in exchange. The IMF
could lend this
money to countries with short term balance of payments
problems, conditional on

these countries following policies advised by the IMF.
4. theexchangeratecouldonlybechanged if
thebalanceofpaymentswas in“fundamental
disequilibrium”(persistent BP deficit).
Most countries imposed significant capital controls (e.g. foreign
currency could only be
used for exports and imports, not to buy assets). As a result the
system worked quite well
for a while. There were not many revaluations and devaluations
until the late 1960s and
early 1970s. The system fell apart in March 1973. It is useful to
describe what lead to its
demise.
The story starts with the second part of the 1960s. Government
spending in the U.S. rose
significantly as a result of both the Vietnam war and the “Great
Society”programs under
President Johnson. The model tells us what happens when
government spending rises. The
model predicts a drop in the current account and a rise in the
capital account. Higher
government spending raises output, which raises imports, while
lowers the trade account.

At the same time the higher income raises money demand,
which lead to an excess demand
for money. People sell bonds, which leads to a lower price of
bonds and a higher interest
rate. This in turn leads to capital inflows and therefore a higher
capital account KA. This
is indeed what happened. Figure 19 shows the U.S. balance of
payments from 1964 to 1973.
From 1964 to 1969 we see that CA gradually drops while KA
gradually rises. Also notice
that KA rises more than CA falls. In the model this corresponds
to the case of a high degree
of capital mobility. Indeed, by the late 1960s the degree of
international capital mobility had
significantly increased.
18
By the end of the 1960s this fiscal policy had lead to a large
budget deficit, which lead
to a reduction in spending and a rise in taxes. This fiscal
contraction has the exact opposite
effect in the model as a fiscal expansion. The current account
rises and the capital account

falls. Indeed, this is what happened from 1969 to 1970. Notice
again that the change in
the capital account is much larger than the change in the current
account, an indication
of a very high degree of capital mobility. The large U.S.
balance of payments deficit as a
result of large capital outflows meant that there was an excess
supply of dollars. As a result,
European central banks and the Japanese central bank were
buying a lot of dollars.
Atthispoint it isuseful to introducetheconceptsof
internalbalanceandexternalbalance.
Internal balance means full employment, price stability.
External balance means BP = 0,
so that there is not an excess demand or supply of foreign
exchange that central banks need
to absorb. Under a fixed exchange rate system we cannot be
away from external balance
for a long time when there is a high degree of capital mobility.
External balance is needed
to keep the exchange rate fixed. Internal balance is needed to
make people happy. Without
internal balance for a sustained period of time, people become
angry and vote politicians

out of offi ce.
What should central banks have done in order to maintain
external balance? The central
banks of Europe and Japan should have lowered their interest
rates, while the U.S. should
have raised its interest rate. This would have stopped the U.S.
capital outflows and therefore
would have stopped the excess supply of dollars. The central
banks of Europe and Japan
then would no longer have to buy up all these dollars.
But in the end concerns about internal balance usually win out.
Central banks like to use
their monetary policy for domestic concerns about
unemployment and inflation. In Europe
there was concern that expansionary monetary policy (lowering
interest rates) would lead
to inflation. In the U.S. there was concern that contractionary
monetary policy (raising
interest rates) would lead to a recession. The economy was
already weak because of a fiscal
contraction. Moreover, there was a presidential election in
1972.
Central banks therefore did not follow the policies needed for

external balance. In fact,
monetary policy in the U.S. was expansionary for the internal
balance considerations dis-
cussed above. The model predicts that this lowers both the CA
and KA (trade deficit and
capital outflows due to lower interest rate). This is exactly what
we see from 1970 to 1971.
The resulting capital outflows were probably even much larger
than those reported in the
table of Figure 19 because of the very large negative statistical
discrepancy (see the last
19
column). To make matters worse, people started to anticipate a
dollar devaluation, which
lead to even larger capital outflows.
European central banks were buying very large amounts of
dollars. On May 5, 1971,
the Bundesbank purchased 1 bln. dollars in the first 40 minutes
of trading. The foreign
exchange market was closed and the DM and guilder were
allowed to float against the dollar.
In August 1971 the link between gold and dollars was severed

and more currencies went on
a float relative to the dollar: yen, Belgian Franc, Swiss Franc,
pound. But it was not the
end. In December of 1971 all the currencies went back to the
fixed exchange rate system in
what is known as the Smithsonian Agreement.
In 1972 Germany imposed further controls on capital inflows.
But overall 1972 was a
relatively tranquil year. The U.S. even experienced some net
capital inflows (see Figure 19)
as U.S. economic performance improved and confidence was
restored somewhat. But the
expansionary U.S. monetary policy continued, while German
policy became more contrac-
tionary by the end of 1972. This again lead to a drop in the
interest differential i−i∗ , leading
to U.S. capital outflows. This lead to a devaluation of the dollar
by 10% on February 12,
1973. But capital outflows continued (partially in response to a
further expected devalua-
tion). On March 1, 1973, European central banks purchased 3.6
bln. dollars. The foreign
exchange market was closed. On March 19 the foreign exchange
market was re-opened, all

currencies floating. This was intended as a temporary, but we
never returned to the Bretton
Woods fixed exchange rate system and the major currencies
(dollar, yen, Euro) continue to
float to this day.
This story illustrates the reluctance of central banks in
following policies consistent with
a fixed exchange rate system under a high degree of capital
mobility. That is why fixed
exchange rate systems tend not to last very long unless
significant controls on capital flows
are imposed (China).
5.2 Float
We next turn to discussing the impact of an increase in
government spending and money sup-
ply under a float. Figure 20 illustrates the impact of an increase
in government consumption
for different degrees of capital mobility.
First consider the case of no capital mobility, illustrated in
chart A. The increase in
government consumption shifts the IS curve to the right. We go
to point B (intersection of
20

IS and LM schedules). Without a change in the exchange rate
we then have a balance of
payments deficit (we are to the right of the BP = 0 line). This is
because the higher output
leads to more imports and therefore a trade deficit. The
resulting excess demand for foreign
exchange leads to a higher price of foreign exchange
(depreciation), which raises net exports.
This causes the IS curve to shift further to the right. It also
leads the BP = 0 schedule to
shift to the right. Recall that in the case of no capital mobility
(k = 0) the BP = 0 schedule
is
Y =
1
m
(
X
̄ −M
̄ + m∗Y ∗ + K
̄ A
)
(30)
It therefore shifts to the right (higher output) when net exports
rises due to a depreciation.

In the new equilibrium at point C the New BP schedule
intersects with the IS and LM
schedules. Under a float we must always have BP = 0 as this
represents foreign exchange
market equilibrium. The overall effect is a rise in output, and
more so than under a fixed
exchange rate system.
In chart B we consider a low degree of capital mobility. We still
have a balance of
payments deficit at point B because we are to the right of the
BP = 0 schedule. But the
balance of payments deficit will now be smaller as the higher
interest rate leads to capital
inflows. The resulting excess demand for foreign exchange is
smaller, leading to a smaller
depreciation. The IS curve again shifts further to the right due
to the depreciation, but less
than under no capital mobility. The BP = 0 schedule again shifts
to the right as well due to
the depreciation, intersecting with the IS and LM schedules.
Output rises less than in the
case of no capital mobility as the depreciation is smaller.
In chart C we consider a high degree of capital mobility. At

point B we now are to
the left of the BP = 0 schedule. This means that we have a
balance of payments surplus.
While there is still a trade deficit (higher income raises imports)
this is more than offset
by large capital inflows due to the higher interest rate. The
balance of payments surplus
implies an excess supply of foreign exchange, which leads to a
drop in the price of foreign
exchange (appreciation). This reduces net exports, leading the
IS curve to shift to the left.
The BP = 0 line shifts to the left as well due to the appreciation.
The new equilibrium
is at point C. The appreciation weakens the expansion that
results from the increase in
government spending.
Finally, chart D considers perfect capital mobility. In that case
we have infinite capital
inflows at point B and therefore an infinite excess supply of
foreign exchange. The resulting
appreciation leads to a drop in net exports that shifts the IS
curve to the left until it
21

comes back to its original position, where i = i∗ (otherwise
there would be infinite capital
flows). While output has not changed, there is a composition
shift, with more government
consumption and lower net exports.
The result that a fiscal expansion does not raise output under
perfect capital mobility is
not general. It does not hold under many extensions. First, we
will see in the next section
that a fiscal expansion under a float with perfect capital
mobility does raise output when
the domestic country is large (like the U.S.). Second, it does not
hold when we are in a
liquidity trap. In that case we are in the part of the LM schedule
that is flat at i = i∗ = 0.
A fiscal expansion then does not raise interest rates. It therefore
also does not generate an
appreciation. The interest rate will stay at zero. The increase in
output will be very large
as there will be no crowding out. Finally, even if we consider a
small country and we are not
in a liquidity trap, output will still rise in response to a fiscal
expansion if we consider a bit

more realistic monetary policy.
To see this last point, we need to take a little detour by
modeling monetary policy a bit
more carefully. So far we simply assumed that the central bank
holds the money supply fixed
at some level M
̄ s. In reality the central bank usually targets a
certain level of the interest
rate and will change the money supply accordingly. The interest
rate that the central bank
targets depends at least on two key variables: the output gap and
inflation. The output gap
is the deviation of output Y from full employment output.
Denoting the latter Ȳ , the output
gap is Y − Ȳ . The lower output relative to the full employment
level, the more the central
bank wishes to lower the interest rate in order to increase
output. At the same time the
central bank is also concerned with inflation. The higher
inflation, relative to some target,
the more the central bank wishes to raise the interest rate in
order to lower inflation. In our
model prices are fixed in the producer’s currency. The price of
domestic goods is fixed at
P̄ = 1. The price of foreign goods measured in dollars is EP̄ ∗ =

E. A depreciation will then
raise inflation.
This implies the following type of monetary policy:
i = constant + α(Y − Ȳ ) + λ(E − Ē) (31)
with α and λ both positive. Ē is the exchange rate during the
previous period. The larger
E − Ē, the larger the depreciation, the more inflation and
therefore the more the central
bank wishes to increase the interest rate. There are several other
reasons for the central bank
to respond to the exchange rate. A depreciation leads to a terms
of trade deterioration: the
22
price of domestic goods declines relative to foreign goods. This
reduces wealth. The central
bank can reverse this through a monetary contraction (raise the
interest rate), which will
lead to an appreciation (see below for the effect of monetary
policy under a float). The same
is the case when a country has a lot of foreign currency debt. In
that case a depreciation
raises the value of this debt measured in the domestic currency.

Again the central bank
may wish to avoid this by raising the interest rate, which leads
to capital inflows and an
appreciation.
For a given exchange rate this monetary rule implies a positive
relationship between the
interest rate i and output Y . It therefore delivers the same LM
curve that we already have.
But now the LM curve will shift when the exchange rate
changes. In particular, when the
exchange rate appreciates (E goes down) the interest rate will
fall and the LM curve shifts
down or to the right.
Now again consider a fiscal expansion under a float with perfect
capital mobility. Figure
21 shows what happens. At first we go to point B. The increase
in government spending
raises the interest rate as before. This leads to capital inflows
and an appreciation. The
LM curve therefore shifts to the right. The appreciation also
shifts the IS curve back (net
exports go down). We now reach a new equilibrium at point C.
The appreciation is now

smaller than before because of monetary policy. Output
increases and may even increase
substantially as there is no crowding out.
A fiscal expansion under a high degree of capital mobility can
lead to a twin deficit
problem: both a budget deficit and a current account deficit. In
our model the current
account deficit is a result of the appreciation. In the early 1980s
the U.S. engaged in a
combinationof
expansionaryfiscalpolicyunderReagan(lowertaxes,
moremilitaryspending)
and a monetary contraction. The model implies that a fiscal
expansion leads to a dollar
appreciation and a current account deficit (assuming high or
perfect capital mobility). A
monetary contraction also leads to an appreciation. We will
discuss monetary policy in a
moment.
There was indeed a twin deficit problem. The budget deficit
increased from 1.2% of GDP
in 1980 to 3.2% of GDP in 1985. The current account changed
from +0.3% to -2.7% over
the same period. The dollar appreciated by 28%. The real

interest rate increased a bit (from
0 to 2.5%) but that is because the U.S. is a large economy and
we cannot take i∗ as given.
We will consider transmission with two large economies in the
next section.
Figure 22 considers an increase in the money supply. First again
consider the case of no
23
capital mobility in chart A. The LM curve shifts to the right and
we go to point B. The
interest rate falls, investment rises and output increases. The
higher income raises imports,
causing a trade deficit (we are to the right of the BP = 0
schedule). The resulting excess
demand for foreign exchange leads to a depreciation, which
raises net exports. Both the IS
and BP = 0 schedules shift to the right and we reach the new
equilibrium at point C.
Once we introduce capital flows the balance of payments deficit
at point B is even bigger.
This is because the lower interest rate leads to capital outflows.
The larger excess demand

of foreign exchange that follows leads to an even bigger
depreciation, a bigger outward shift
of the IS and BP = 0 schedules and therefore a bigger increase
in net exports and output
(all of this is hard to see in Figure 22). In the extreme case of
perfect capital mobility the IS
curve shifts out so much that in equilibrium the interest rate
does not change at all (i = i∗ ).
While a monetary expansion leads to a depreciation, a monetary
contraction leads to
an appreciation. As mentioned above, the U.S. had a large
monetary contraction in the
early 1980s, which was meant to get rid of double digit
inflation. This indeed lead to a
large dollar appreciation. By contrast, during the second half of
the 1970s there was a large
dollar depreciation as expansionary monetary policy was used in
response to the first oil
price shock, which weakened the economy. The large dollar
depreciation during 2002-2008
has been partly attributed to expansionary monetary policy as
well.
6 Transmission under Perfect Capital Mobility
We saw that without capital mobility the domestic economy was

insulated from external
shocks under a float. This is no longer the case with capital
mobility. We will now consider
transmission of shocks across countries for the case of a two-
country world, where both
countries are large, and perfect capital mobility. We first
consider a float and then a fixed
exchange rate system.
Without capital mobility and a float, foreign exchange market
equilibrium is CA = TA =
0, so that shocks cannot be transmitted through net exports. But
with capital mobility we
have CA + KA = 0. Net exports can then be different from zero.
For example, a trade
deficit can be financed through capital inflows and the FX
market is in equilibrium.
In what follows the domestic country is the U.S. and the foreign
country is Europe.
Figure 23 shows what happens when there is a fiscal expansion
in the United States. The
IS curve shifts to the right, raising the interest rate. This leads
to infinite capital flows to
24

the U.S. and therefore an infinite excess demand for dollars.
The dollar will appreciate and
the Euro will depreciate. U.S. net exports fall and European net
exports rise. This means
that the IS curve shifts back to the left in the U.S. and shifts to
the right in Europe. Part
of the rightward shift in the European IS schedule is also the
result of increase demand
for European goods as U.S. income rises. We go to the new
equilibrium at point C where
both U.S. and European output are higher. The positive
transmission to Europe operates
through net exports and is the result of both the depreciation of
the Euro, improving the
competitiveness of European firms, and the increased demand
for European goods because
of the expansion in the United States.
Figure 24 considers the impact of a U.S. monetary expansion.
The LM curve shifts to
the right and the interest rate falls. This results in infinite
capital flows from the U.S. to
Europe. The dollar then depreciates and the Euro appreciates.
This causes the U.S. IS curve

to shift to the right (net exports rises) and the European IS
curve to shift to the left (net
exports falls). The new equilibrium is at point C, where U.S.
output is higher and European
output is lower. This is also known as beggar-thy-neighbor
policy. The expansion in the
U.S. comes at the cost of a contraction in Europe. Transmission
again operates through net
exports, but is now negative.
A small technical comment regarding Figure 24 is in order. One
might argue that it could
be possible that the European IS curve shifts to the right
because of higher net exports as
the U.S. has higher income and will import more from Europe.
While this does happen,
it is more than offset by the appreciation of the Euro, which
lowers European net exports
and shifts the European IS schedule to the left. If the European
IS schedule had shifted to
the right, the world interest rate would have increased. But this
cannot be. There would
then be a European trade surplus and therefore a U.S. trade
deficit, while at the same time

S − I would have increased in the U.S. (higher output raises
saving, higher interest rate
lowers investment). This is inconsistent with S − I = X − M. So
the bottom line is that
the European IS schedule shifts to the left due to the Euro
appreciation and transmission is
negative.
Next consider transmission under a fixed exchange rate system
and perfect capital mo-
bility. We first again consider a fiscal expansion in the United
States. We now need to be
careful to consider two separate cases as the outcome depends
on which country’s central
bank has responsibility to keep the exchange rate fixed. We first
assume that this is the
responsibility of the U.S. central bank. This case is illustrated
in Figure 25. The IS curve
25
shifts out in the U.S. due to the increase in government
spending. This leads to a higher
interest rate and therefore infinite capital flows to the United
States. It causes an infinite
excess demand for dollars and excess supply of Euros. The U.S.
central bank needs to buy

all these Euros to keep the exchange rate fixed. It cannot buy an
infinite amount of Euros, so
it is forced to lower the U.S. interest rate through a monetary
expansion. The LM schedule
shifts to the right. At the same time the U.S. expansion leads to
an increase in demand for
European goods, which raises European net exports and shifts
out the European IS schedule.
We then have a new equilibrium at point B with a higher world
interest rate. Transmission
to Europe is positive and occurs through net exports.
Figure 26 shows what happens when instead the European
central bank has responsibility
for keeping the exchange rate fixed. The increase in government
spending in the U.S. again
leads to an outward shift of the U.S. IS schedule and a rise in
the interest rate. There is again
an infinite excess demand for dollars. But the European central
bank cannot sell an infinite
amount of dollars. It will therefore raise its interest rate through
a monetary contraction
(European LM schedule shifts to left). This stops the capital
flows to the U.S. and the excess

demand for dollars. At the same time the U.S. expansion raises
import demand for European
goods, which shifts out the European IS schedule. Overall it is
ambiguous whether output
rises or falls in Europe. The U.S. fiscal expansion causes a rise
in the world interest rate,
which is contractionary for Europe. At the same time European
exports to the U.S. will
increase, which is expansionary.
Finally consider monetary policy under a fixed exchange rate
system. It is impossible for
the U.S. to raise the money supply if the U.S. has responsibility
for keeping the exchange
rate fixed. A higher U.S. money supply would lead to a lower
interest rate and therefore
infinite capital flows to Europe and an infinite excess demand
for Euros. The U.S. central
bank cannot sell an infinite amount of Euros, so this is not
feasible. The U.S. central bank
cannot raise the money supply in the first place. If it agrees to
be responsible for external
balance (fixed exchange rate) it cannot at the same time have
control over the money supply
for internal balance considerations.

Figure 27 considers what happens if the U.S. raises the money
supply, but the European
central bank has the responsibility for keeping the exchange rate
fixed (external balance).
The U.S. LM curve shifts out, leading to a lower interest rate.
This leads again to infinite
capital flows to Europe. There is an infinite excess demand for
Euros and excess supply of
dollars. The European central bank cannot buy an infinite
amount of dollars and is therefore
26
forced to stop the capital inflows by lowering the interest rate.
It raises the money supply
and the European LM schedule shifts out until i = i∗ . The world
interest rate falls. In this
case Europe is a follower. The U.S. can follow any monetary
policy it wishes and Europe
needs to follow if it wants to maintain the fixed exchange rate
system. Of course in practice
this does not work very well as the Bretton Woods system has
illustrated. It would only
work if Europe completely gives up on internal balance and

dedicates its entire monetary
policy to external balance. Not many countries are willing to do
that.
7 Exchange Rate Determination in Dynamic Model
The Mundell-Fleming model is a static model. It is a one period
model. We will now
analyze what determines the exchange rate when instead we
adopt a dynamic model. We
will also deviate from the Mundell-Fleming model in that we no
longer assume that the
expected change in the exchange rate is zero. In the dynamic
model we need to solve for the
equilibrium exchange rate each period and it is not necessarily
the case that the expected
change in the exchange rate is zero. We only consider perfect
capital mobility. It is now
represented by
it = i
∗
t + Et
St+1 −St
St
(32)

Here St is the exchange rate, which is dollars per unit of foreign
currency. We no longer call
it Et, which now denotes the expectation at time t. So the dollar
interest rate is equal to
the foreign interest rate plus the expected depreciation of the
dollar over the next period.
This is the uncovered interest rate parity condition. It holds
when people only care about
expected returns. With risk-averse investors we would need to
add a risk premium as well,
but I will abstract from that here.
In the models that we will discuss a key message is that the
exchange rate is like an
asset price. It is forward looking. A stock price depends on the
present discounted value
of the dividends or profits of the firm. Similarly, the exchange
rate depends on the present
discounted value of future macro fundamentals, such as output
and the money supply. It is
not just the current money supply but also the expected future
money supply that affects
the exchange rate today.
We will consider two types of models. The first one is a simple
flexible price, full em-

ployment model. The second one has sticky prices in the short
run, but flexible prices in the
27
long run (it takes times for prices to adjust). This second model
is known as the Dornbusch
overshooting model.
First consider the flexible price model. Apart from (32) we need
only three more equa-
tions. First, we assume that the level of output is equal to its
full employment level:
Yt = Ȳt Y
∗
t = Ȳ
∗
t (33)
Here Ȳt is the full employment output level in the U.S. and Ȳ
∗ t is the foreign full employment
output level.
Second, assume that there is just one good and that the law of
one price holds:
Pt = StP
∗

t (34)
Here P∗ t is the price of the good in the foreign currency in the
foreign country and Pt is the
price in the U.S. in dollars. We also refer to this as the PPP
condition.
Finally, real money demand, which is equal to Y e−αi in the
U.S. and Y ∗ e−αi
∗
in the
foreign country, must equal the real money supply:
M
̄ t
Pt
= Ȳte
−αit M
̄
∗
t
P∗ t
= Ȳ ∗ t e
−αi∗ t (35)
where M
̄ t and M
̄ ∗ t are the U.S. and foreign money supply.
We can solve the exchange rate as follows. From (34) we have
St =
Pt
P∗ t

(36)
From money market equilibrium we have
Pt =
M
̄ t
Ȳt
eαit (37)
P∗ t =
M
̄ ∗ t
Ȳ ∗ t
eαi
∗
t (38)
Substsituting these two expressions into (36) gives
St =
M
̄ t
M
̄ ∗ t
Ȳ ∗ t
Ȳt
eα(it−i
∗
t) (39)
Finally, using (32) for the interest differential in the last term,
we have
St =
M
̄ t

M
̄ ∗ t
Ȳ ∗ t
Ȳt
e
αEt
St+1−St
St (40)
28
The last equation is a first-order difference equation in the
exchange rate. I will quickly
solve it here, but since you are not expected to know how to
solve first-order difference
equations I will not test you on this. Apply logs to the last
equation and approximate
(St+1−St)/St with the change in the log exchange rate, which is
st+1−st. Lower case letters
will denote logs. (40) then becomes
st = ft + αEt(st+1 −st) (41)
where
ft = (m
̄ t − m
̄ ∗t ) − (ȳt − ȳ
∗
t ) (42)
is the exogenous relative fundamental of the two countries

(relative log money supply minus
relative log output).
It follows that
(1 + α)st = ft + αEtst+1 (43)
so that
st =
1
1 + α
ft +
α
1 + α
Etst+1 (44)
Therefore (replace t with t + 1)
st+1 =
1
1 + α
ft+1 +
α
1 + α
Et+1st+2 (45)
Substitute this last expression into (44). This gives

st =
1
1 + α
ft +
α
1 + α
1
1 + α
Etft+1 +
(
α
1 + α
)2
Etst+2 (46)
We can keep integrating forward like this (the next step
substitutes the time t + 2 version
of (44) into the last equation). This leads to
st =
1
1 + α
(
ft +

α
1 + α
Etft+1 +
(
α
1 + α
)2
Etft+2 +
(
α
1 + α
)3
Etft+3 + ...
)
(47)
The equilibrium exchange rate is therefore equal to the present
discounted value of the
expected fundamental, with α/(1 + α) being the discount rate. A
key message is that the
exchange rate today depends not just on the current
fundamentals (e.g. the current money
supply) but also on the expected future fundamentals.
29

Again, you do not need to know how to solve algebraically for
st. I will therefore take the
following approach below. I will consider two different types of
shocks to the money supply
(an unanticipated permanent increase in money supply M
̄ and an
anticipated increase in
future money supply). I will then show the response over time
of the exchange rate, price
level and interest rate and I will argue that this solution is
consistent with the equations of
the model. I will also provide an intuitive explanation for the
solution.
Figure 28 shows the impact of an unanticipated permanent
increase in the money supply
M
̄ . Let us say that the money supply rises permanently by 10%.
Then the exchange rate
and price level immediately jump up by 10% as well (10%
depreciation) and then remain
flat (just like the money supply). The interest rate does not
change at all and remains equal
to i∗ . The Foreign price level and interest rate, not shown in
Figure 28, remain the same.

It is immediate that these results are consistent with the
equations of the model. The
interest parity still holds as the expected change in the exchange
rate remains zero (it jumps
and then is expected to remain constant) and we continue to
have i = i∗ . The PPP equation
(34) holds as well since S and P both jump by 10% (same as
money supply), while P∗ does
not change. The U.S. money market equilibrium equation holds.
As both the money supply
and price level jump up by the same 10% the real money supply
remains unchanged. Money
demand also does not change since the interest rate does not
change.
Figure 29 shows the impact of an anticipated increase in the
future money supply. Again
assume that the increase is 10%, but now this is anticipated to
start at a future date. The
exchange rate and price level then immediately jump up today,
but by less than 10%. They
then continue to rise until they have increased a full 10% by the
time the money supply
jumps up. The interest rate first jumps up, then rises more and
then drops back to i∗ by the

time the money supply jumps up. As before, P∗ and i∗ do not
change.
This solution is consistent with the interest parity condition.
After the initial jump the
exchange rate is expected to depreciate further. The interest rate
rate must then by larger
than i∗ . Starting at the future date when the money supply
jumps up the exchange rate
will be constant. The expected change in the exchange rate will
therefore be zero, so that
the interest rate drops back to i∗ . By construction the PPP
equation holds as the exchange
rate and price level move together. Money market equilibrium
holds as well. The initial
jump in the price level lowers the real money supply. The
higher interest rate immediately
lowers money demand as well. As the price level rises further
over time, real money supply
declines further. Real money demand declines further as well as
the nominal interest rate
30
rises. Then, when the money supply jumps up, money demand
jumps up as well through a

discrete downward jump of the interest rate.
The key message here is that, consistent with (46), the exchange
rate already changes
today in response to an anticipated increase in the money supply
in the future. One can
think about this intuitively as follows. Assume that the
exchange rate does not change
today. Then the price level does not change either (PPP
equation). Since the real money
supply does not change, the interest rate does not change either
(money demand also does
not change). But we know that the money supply will rise in the
future, so we expect the
exchange rate to depreciate in the future. Therefore
it < i
∗
t + Et
St+1 −St
St
(48)
This causes infinite capital outflows. The resulting excess
demand for foreign exchange leads
to a depreciation today. The depreciation restores the interest

rate parity condition in two
ways. First, the resulting higher price level Pt reduces the real
money supply, which leads to
a rise in the nominal interest rate. Second, the expected future
depreciation is smaller when
the exchange rate depreciates today.
Next I will consider a model where the price level is sticky in
the short run but flexible in
the long run. When demand is larger than full employment
supply, the price will gradually
rise. When demand is lower than supply, the price will
gradually fall. For simplicity (this
is not important) I will assume that the actual output level is
equal to its full employment
level Ȳ . The interest parity and money market equilibrium
equations are the same as before:
it = i
∗
t + Et
St+1 −St
St
(49)
M
̄ t
Pt

= Ȳte
−αit (50)
We now simply take i∗ and P∗ as given (small open economy).
Demand for goods is equal
to C + G + I + X −M, which is equal to
Y dt = C
̄ + Ḡ + Ī − bit + (c−m)Ȳt + m
∗Ȳ ∗t + [X
̄ −M
̄ ](StP
∗
t /Pt) (51)
Here we have written X
̄ −M
̄ as a function of the relative price
SP∗ /P. Exports and imports
depend on the relative price of foreign goods to U.S. goods,
which is SP∗ /P. In the Mundell-
Fleming model we held P and P∗ fixed. In the current model P
is also fixed in the short
31
run, but can adjust over time. Pt gradually rises over time when
demand is larger than full
employment output and drops when it is lower:
Pt+1 −Pt
Pt
= ψ(Y dt − Ȳt) (52)

Figure 30 shows the impact of an unanticipated permanent
increase in the money supply.
In this case the exchange rate and price level are not tied to
each other through the PPP
equation. The price level cannot jump in the immediate response
to the shock (it is sticky in
the short run); it can only adjust gradually. By contrast, the
exchange rate can immediately
jump to a new level. The surprising finding is that when we
introduce the short run price
stickyness the exchange rate now jumps up even more than the
money supply. If the money
supply rises permanently by 10%, we saw in the flexible price
model that the exchange rate
depreciates immediately by 10%. In the current model it
remains the case that the exchange
rate will depreciate by 10% in the long run (prices are flexible
in the long run), but in the
immediate response to the shock the exchange rate will
depreciate more than 10%. It will
therefore “overshoot”its new long run equilibrium. After that
the exchange rate gradually
appreciates, so that in the long-run it is 10% higher than its
level before the shock.

This overshooting result is a result of the assumption of short
run price stickyness. If
we assumed that prices are perfectly flexible and equilibrate
demand and full employment
supply at all times, the exchange rate would have depreciated by
10% in the immediate
response to the shock. The overshooting result is nice as
exchange rates are much more
volatile than macro fundamentals like the money supply.
What gives rise to this overshooting result? Since the price
level is sticky in the short
run, the 10% increase in the nominal money supply leads to a
10% increase in the real money
supply. There is then an excess supply of money. People buy
bonds. The price of bonds
rises and the interest rate goes down. This establishes money
market equilibrium. If the
exchange rate does not change at all (and is not expected to
change), the lower U.S. interest
rate leads to capital outflows. This leads to an excess demand
for foreign exchange and
causes a depreciation today.
But why does the exchange rate depreciate by more than 10%?

There are two ways
to develop the intuition. The first way goes as follows. Assume
that the exchange rate
goes up by 10% and then stays there. It reaches its long-run
level right away as in the
flexible price model. Then the expected change in the exchange
rate is zero. Since the
interest rate it falls, it follows that it < i∗ t + Et(St+1 − St)/St.
This causes infinite capital
32
outflows, an excess demand for foreign exchange and therefore
a further depreciation today.
The exchange rate therefore depreciates more than 10% today.
An alternative way to look
at it is as follows. Assume that the interest rate parity condition
always holds. Since we
have already established that the nominal interest rate will fall,
it must be the case that
Et(St+1−St)/St falls and therefore becomes negative. This
means that there is an expected
future appreciation. This can only happen if the exchange rate
overshoots (rises more than
10% today) and then appreciates downwards to its long-run

level, which is 10% above its
pre-shock value.
8 Disconnect between Exchange Rate and Macro Fun-
damentals
We will now turn to empirical evidence on exchange rates. I
will consider two very different
types of evidence, which both point in the same direction: it is
hard to explain exchange
rate fluctuations with movements in observed macro
fundamentals. This implies a significant
shortcoming of our models of exchange rate determination.
The first piece of evidence is known as the Meese-
Rogoffpuzzle. Meese and Rogoffwrote
2 papers in the early 1980s that had a very big impact on the
profession. They documented
a puzzle that has turned out to be very persistent as new data
became available. Of course
their original papers were based on exchange rate models of that
time. But their conclusions
have turned out to be robust to many extensions that followed.
To understand what they did, consider the flexible price model.
Taking the log of (39)

gives
st = (mt −m∗ t ) − (yt −y
∗
t ) + α(it − i
∗
t ) (53)
If you use the Dornbusch overshooting model it is possible to
show that the inflation differ-
ential is added to the right hand side as well. The general point
is that we can write the
exchange rate as a function of various observed macro
fundamentals.
MeeseandRogoffconsider3models: theflexiblepricemodel,
theDornbuschovershooting
model (adding the inflation differential) and a third where the
exchange rate also depends
on the difference in the trade balance across countries. They
then take these models to
the data, using monthly data for three currencies (dollar/DM,
dollar/yen and dollar/pound)
from March 1973 to June 1981. They first estimate the
relationship between the exchange
33

rate and the right hand side variables based on data from March
1973 to November 1976.
They then use the estimated coeffi cients to produce exchange
rate forecasts at 1, 3, 6, and
12 month horizons. Then one month is added to the data, the
parameters are re-estimated
and new forecasts are produced. They keep doing this until they
reach the last data point.
They do these rolling regressions because the parameters might
change over time. Note that
while in (53) the parameters on relative money and relative
output are respectively 1 and
-1, a more general setup will have different coeffi cients. Meese
and Rogofftherefore estimate
all parameters associated with the fundamentals on the right
hand side.
It is important to point out that the forecasts are not true
forecasts. They use the actual
future values of the right hand side variables, which are not
known at the time that the
forecast is made. The method therefore tells us more about the
explanatory power of the
macro fundamentals in the model for the exchange rate than the
ability to forecast future

exchange rates (which also requires forecasting future values of
the macro variables on the
right hand side).
The primary measure of out of sample forecast errors is the root
mean squared error:
RMSE =
√√√√ 1
T
T∑
t=1
(Ft −St)2 (54)
where T is the number of forecasts, St is the actual nominal
exchange rate and Ft is the
forecast based on estimated parameters over a sample prior to
date t, but using the actual
macro variables at date t and earlier.
The results are reported in Figure 30 (Table 1). Of interest to us
is the first column, which
says “random walk”and the last three columns. The random
walk column shows results
when instead of a forecast based on the model as described
above we use the random walk

forecast. The random walk forecast today of the exchange rate 3
months from now is equal
to the exchange rate today because expected changes in the
exchange rate are zero. The
RMSE based on the random walk is then compared to that based
on the model. The Frenkel
Bilson model is the flexible price model. The Dornbusch-
Frankel model is the Dornbusch
overshooting model. The Hooper Morton model also adds the
relative trade balance as a
right hand side variable.
Comparing the RMSE of the random walk to that for the model
we see that with the
exception of the dollar/DM 1-month forecast, the random walk
always performs better than
the model, for all currencies, horizons and models. The RMSE
is lower for the random walk
34
than the model. This tells us that the macro model performs
even more poorly than using
no macro variables at all (the random walk forecast).
More recently people have applied the Meese Rogoffmethod to

changes in the exchange
rate rather than the level. The model then takes the form
∆st = β∆ft + ut (55)
where ∆ft is a vector of variables and ut an error term. After
estimating β with rolling
regressions (of constant sample length), we then use the actual
fundamentals (which are
often also in first differences) to “forecast”∆st. Figure 32 shows
the MSE (mean squared
error– same as RMSE but without taking the root) of the model
relative to the MSE for
the random walk based on a much longer sample of data from
September 1975 to September
2008 for 6 currencies. It shows results as a function of the
sample length L used to estimate
the parameters of the model. When the sample length goes up,
estimates of the parameters
improve and the relative performance of the model improves
(MSE of the model relative
to the random walk drops). But still, only with the exception for
very long samples for
the Canadian dollar, the random walk outperforms the model.
The macro variables used

here are the relative money supply growth, relative industrial
production growth, relative
unemployment rate, growth in the oil price and the relative
interest rate differential.
There are two reasons then why the model does not outperform
the random walk. The
first is estimation error of the parameters, which is especially a
problem for small samples.
But this alone cannot explain it. Figure 32 shows that even
when the sample length is as long
as 200 months, which is more than 16 years, the model still
does not outperform the random
walk. The only explanation for this is the weak explanatory
power of the fundamentals.
Studies that do find that the model outperforms the random walk
find the outperformance
to be usually very small. Moreover, it tends not to be robust and
only hold only over certain
periods for certain currencies. The conclusion we can draw from
all this then is that macro
variables have very little explanatory power. This conclusion
has turned out to be robust to
sample periods, currencies and sets of macro fundamentals.
For a very different look at the limited explanatory power of

macro fundamentals, I turn
next to a 2003 paper in the American Economic Review by
Andersen, Bollerslev, Diebold
and Labys. This paper looks at micro level exchange rate data.
Their data consist of 5
different currencies and contains data from January 3, 1992 to
December 30, 1998. There
are 2189 days in the sample and the data are at 5 minute
intervals during the day. There
35
are 288 such 5 minute intervals, which gives a total of 630,432
data points.
They regress exchange rate changes over the 5 minute intervals
on lags of itself as well
as current values and lags of macro announcements. For
example, Figure 33 reports results
related to macroeconomic announcements for payroll
employment, durable goods orders, the
trade balance and initial claims. It reports the change in the
exchange rate in response to
a 1 standard deviation increase in the announcement variable (a
favorable announcement).

The pictures show the change in the exchange rate during the
interval of the announcement
as well as additional changes in the exchange rate over the next
two 5 minute intervals. Most
of the exchange rate changes take place instantaneously at the
time of the announcement.
Moreover, they go in the direction that theory would predict.
For example, a positive U.S.
payroll announcement increases the DM/dollar exchange rate,
which means an appreciation
of the dollar. Our models indeed have the implication that an
increase in output leads to an
appreciation. Similarly, the dollar appreciates after a favorable
trade balance announcement.
This implies a dollar depreciation when the trade deficit gets
bigger. This makes sense as
the depreciation is needed to lower the relative price of US
goods, which improves US net
exports.
Figure 34 reports regression results when only the news
announcement intervals are used
and only the instantaneous exchange rate response is
considered. It should first of all be
noted that only 0.2% of the 5 minute intervals in the sample are

intervals in which there
are macro announcements. This usually happens in the morning
around 8:30am. The
coeffi cients again make sense. For example, look at variable
24: the target federal funds
rate. When the federal funds rate goes up, the Fed tightens
monetary policy, which leads
to a dollar appreciation as expected (a positive coeffi cient
means appreciation here since
the exchange rates are expressed here as foreign currency per
dollar rather than dollars per
foreign currency).
But while the theory does a good job in explaining the direction
of the exchange rate
when there is a macro announcement, such macro news
announcements have very little
explanatory power for the exchange rate. First, as already
mentioned, only 0.2% of the
intervals contain macroeconomic news announcements. Second,
the R2 numbers reported in
Figure 34 tend to be small, perhaps 0.1 on average. This means
that 90% of the variance of
the exchange rate during the 5 minute interval that there is a
news announcement is caused

by factors that have nothing to do with the news
announcements. Clearly other things than
macroeconomic news are dominating exchange rate fluctuations.
36
9 Possible Explanations for the Disconnect between
Exchange Rates and Macro Fundamentals
In this section I will discuss 3 possible explanations for the lack
of explanatory power of
observed macro fundamentals for the exchange rate:
1. speculative bubbles
2. bandwagon expectations, technical analysis
3. information heterogeneity
First consider speculative bubbles. To understand how a
speculative bubble can arise,
consider again the flexible price model. Assume that the
fundamentals are constant. Now
consider what happens when suddenly, without a change in
fundamentals, the exchange rate
increases (depreciates). The rise in St implies a rise in Pt, which
implies a drop in the real

money supply. The nominal interest rate will then need to rise
to clear the money market.
But interest rate parity implies that a higher interest rate implies
an expected depreciation.
So the exchange rate will depreciate more in the future, causing
the price to rise more, the
real money supply to fall more and therefore the interest rate to
rise more.
This process can continue forever. You can have this jump in
the exchange rate, followed
by continued depreciation over time, which is consistent with
all equations of the model and
occurs without a change in fundamentals. This is called a
bubble. There are also stochastic
bursting bubbles, where there is some probability that the
bubble bursts (and therefore the
exchange rate is determined by fundamentals again). In that
case the bubble will not go on
forever. It is not clear though that such bubbles are actually
important in reality. In all
cases where we see a sustained large depreciation of the
exchange rate it is the result of a
high growth rate of the money supply, which is also
accompanied by very high inflation.

The second explanation is bandwagon expectations and the
related “technical analysis”.
Bandwagon expectations are a type of exchange rate
expectations where investors expect a
further depreciation when the exchange rate depreciates and
expect a further appreciation
when the exchange rate appreciates. They jump on the
bandwagon. Such expectations
are destabilizing and can lead to large deviations from
fundamentals. This is related to
“technical analysis”, where traders try to predict future
exchange rates by trying to identify
certain patters in observed exchange rate data. Such technical
analysis is indeed widely
37
used by traders. Also related are so-called stop-loss orders,
where you automatically sell a
currency when the exchange rate depreciates to a certain level,
with the goal to limit your
losses. Such trading has nothing to do with the actual
fundamentals.
Finally, the exchange rate can become disconnected from

observed fundamentals because
of information heterogeneity. I will devote more space to this
explanation as I believe that it
is particularly important. Becauseof suchheterogeneity investors
maytrade basedonprivate
information rather than public information. This is consistent
with the close relationship
between exchange rates and order flow that we have seen
before. Order flow is a result of
private information. As we discussed, when the information is
public, the exchange rate will
immediately jump to its new level without any need for order
flow. When all traders can see
the same information and all agree what it means, there is no
actual need to trade in order
to reach the new price. But in reality order flow is very large is
the main driver of exchange
rates. And we know that order flow aggregates trades based on
private information.
There are different types of information heterogeneity:
1. investors have different views about future macro
fundamentals (e.g. future monetary
policy)

2. investors may have different beliefs about what the model is;
Henry Blodget, a past
Merrill Lynch analyst, has been quoted as saying “we all have
the same information,
and we’re just making different conclusions about what the
future may hold”
3. there are lots of idiosyncratic types of private information:
heterogeneous liquidity
needs, heterogeneous hedging needs, heterogeneous access to
private investment op-
portunities; heterogeneous rates of risk aversion; in these cases
you do not know about
others what you know about yourself (e.g. you only know your
own liquidity needs)
It is obvious that when investors trade based on private
information, it disconnects the
exchange rate from observed public information. But it can even
be worse than that. Differ-
ent types of private information can interact in a way that
amplifies the resulting disconnect
of the exchange rate from observed fundamentals. Assume that
investors have private in-
formation about the future state of the economy. Then the
exchange rate itself becomes a

useful source of information. The reason is that people trade
based on their private informa-
tion and these trades affect the exchange rate, so that the
exchange rate tells you something
about the information than others have about the future state of
the economy.
38
Now add to this a second type of private information that falls
in the category 3 above:
private information about your own liquidity needs. Assume
that as a result of liquidity
trades theexchange ratedepreciates. But since these
tradesarebasedonprivate information,
investors cannot observe this. All they see is that the exchange
rate depreciates and they
conclude that this may have two causes: either others are
trading based on liquidity needs
or others have new private information about the future state of
the economy. They will at
least give some weight to the latter even if in reality the
depreciation was a result of liquidity
trades.

This leads to an amplification effect. First the liquidity trades
cause a direct depreciation.
Then the depreciation itself causes people to change their
expectation of fundamentals (e.g.
more expansionary monetary policy), which leads to a further
depreciation. Everyone may
start to believe that everyone else has private information that
the fundamentals will be
weaker and that this has caused the exchange rate to depreciate,
even if in reality the
depreciation was caused by liquidity trades. This rational
confusion therefore amplifies the
impact of the liquidity trades on the exchange rate, increasing
the disconnect between the
exchange rate and observed fundamentals.
As an illustration of such amplification effects, consider the
stock market (the same story
holds for the stocks market as for the FX market). On October
19, 1987 the U.S. stock
market dropped by over 20% in one day. This is known as Black
Friday. The peculiar thing
is that there was no particular “news”that day. What happened
is that there was about $6
bln. in sales associated with portfolio insurance. This is like a

stop-loss order where investors
sell when the price drops below a certain level. These orders are
private and are therefore
another type of private information. The $6 bln. in sales may
sound like a lot, but it was
only 0.2% of the entire stock market, which was about $3.5
trillion. Normally this would
not lead to a very large decline in the price. But it has been
estimated that because of the
rational confusion discussed above the amplification factor was
250. Uninformed investors
thought that more informed investors had some new information
that caused the price to
go down. When they saw the price go down, they therefore
changed their own view of the
fundamentals, leading to a further selloff. As prices kept going
down this process build on
itself. It lead to a downward spiral that was caused by a
relatively small initial selloff but
was enormously amplified because of rational confusion.
The week following Black Friday the market quickly recovered
as investors realized that
in fact there was no real news that day. But rational confusion
can also be very persistent.

39
Imagine that investors in the stock market have private
information about long term tech-
nology growth of the U.S. economy. If informed investors have
favorable news, this will be
hard to confirm or deny as the long-term is far away from today.
It can lead to persistent
rational confusion. In the mid 1990s the stock market started to
rise. This might initially
have been a result of liquidity trades, hedge trades or noise
trades (expectational errors),
which are all types of idiosyncratic private information. But
when the stock market started
going up, investors did not know whether it was for example
noise trades (which Greenspan
referred to as “irrational exuberance”) or whether instead others
(perhaps more informed
traders) had information that we had entered a “new
economy”or “information age”with
permanently higher technology growth. Investors gave at least
some weight to this, which
increased everyone’s expectations about future growth and

caused further stock purchases
that drove the price up further. Since the hypothesis of higher
long-run growth rates is hard
to confirm or deny, such rational confusion can last a long time.
This may explain why the
stock price kept rising all the way until 2000, when there was a
significant correction.
10 Forward Discount Puzzle
Other than the exchange rate disconnect puzzle (the disconnect
of exchange rates from ob-
served fundamentals), the other main exchange rate puzzle is
known as the forward discount
puzzle. I will describe what the puzzle is and consider some
possible explanations.
I will start by making two assumptions:
1. investors are risk-neutal
2. investors have rational expectations
Thefirstassumptionmeans that
investorsonlycareaboutexpectedreturnsandnotabout
risk. The second assumption means that expectational errors
about the future exchange
rate are not predictable based on information available today. If
you can predict your own

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