Macroeconomics
Chamberlin and Yueh
Chapter 12
Lecture slides
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The IS-LM-BP Model
• Constructing the IS-LM-BP Model
•
The Open Economy IS Curve (The ISXM
Schedule)
•
The BP curve
•
The Open Economy LM Curve
•
Exchange Rate Regimes
•
Equilibrium in the IS-LM-BP Model
• Comparative Statics
• The Mundell-Fleming Model
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Learning objectives
• Extend the traditional IS-LM model to incorporate open
economy considerations
• Understand the open economy version of this model, the ISLM-BP model. The BP schedule reflects equilibrium in the
balance of payments.
• Analyse the various applications of this model.
• Evaluate a particular version of the IS-LM-BP model,
known as the Mundell-Fleming model.
• Understand the impact of different exchange rate regimes
on the IS-LM-BP model.
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The IS-LM-BP Model
• The open economy version of the IS-LM model is the ISLM-BP model.
• This adds a new line: the BP schedule which reflects
equilibrium in the balance of payments. Overall
equilibrium will now exist where the economy is in real,
monetary and external equilibrium.
• There are many different variants of the IS-LM-BP model.
Different versions make different assumptions about the
degree of capital mobility and the exchange rate regime.
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The IS-LM-BP Model
• A particular version of the IS-LM-BP model which
definitely deserves attention is known as the MundellFleming model. This is just the basic IS-LM-BP model
with perfect capital mobility.
• The second way in which different versions of the model
may arise is through the type of exchange rate regime that is
assumed. Under a floating regime, the exchange rate is
market determined and can fluctuate accordingly. A fixed
regime is where the policy maker acts to maintain the
exchange rate at a particular level. It will be seen that the
effects of different policies is not independent of the
exchange rate regime in place.
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Constructing the IS-LM-BP Model
• Extending the basic IS-LM to the open economy requires
two additions.
• Firstly, the closed economy IS and LM curves need to be
adapted to take into account the foreign influences on the
domestic goods and money markets, respectively.
• Secondly, the BP schedule represents the combination of
income and interest rates where the balance of payments (or
the external part of the economy) is in equilibrium.
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The open economy IS curve (The
ISXM Schedule)
• Extending the IS curve to the open economy simply
requires the addition of the current account or net exports.
• Demand will therefore equal supply when this national
income identity holds:
(12.1)
Y CI G X  M
• C represents domestic consumption, which is represented
by a typical Keynesian consumption function consisting of
disposable income:
C  a  c Y  T

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The ISXM Schedule
• Investment is a negative function of the interest rate and
also a set of exogenous factors:
I
I  I r ,  
r
 0
• Government spending is exogenously set: G  Gˆ
• In the previous chapter, a simple function form for the real
value of net exports or the trade balance was given as
follows:

X

M

x
Y
  m Y  Y
(12.2)
Y
*
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The ISXM Schedule
• There are several parameters and factors here which
determine the size of net exports.
• The first is the real exchange rate. Providing the MarshallLerner condition holds, a depreciation in the real exchange
rate will lead to an improvement in net exports, as
consumers substitute away from foreign produced goods to
domestic produced goods.
• Exports are determined by the level of overseas income and
the parameter x   , which is the proportion of foreign
income spent on domestic goods. If foreign income rises,
or foreigners develop a higher preference for domestic
goods, then each of these and net exports will rise.
Y

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The ISXM Schedule
• The total level of imports is the product of
domestic income Y and the marginal propensity to
import. As income rises, consumers will tend to
spend more – a proportion of which will be on
foreign goods and services. Alternatively, if the
preferences of domestic consumers were to switch
towards foreign goods, then and total imports will
rise.
• Hence, substituting this into (12.1) gives:
(12.3) Y  a  c Y  T   I r ,    Gˆ  x Y  Y    m Y  Y

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The ISXM Schedule
• Rearranging this, we can derive the equilibrium level of income as a
function of all the parameters and variables:
(12.4)
Y 

a  cT  I  r ,    Gˆ  x Y   Y
1  c   m Y  
• This is the open economy version of the IS curve. To differentiate this
from the closed economy version, we can entitle it as the ISXM
schedule.
• The ISXM curve also slopes downwards, as a rise in interest rates will
lead to a fall in investment, and then a multiplied fall in income.
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IS vs. ISXM Curves
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The ISXM Schedule
• However, the slope of the ISXM curve will be steeper than
that of the standard IS curve. This is because the multiplier
is now smaller, following the addition of the marginal
propensity to import.
• In the closed economy, the multiplier was 1/(1-c). This can
be written as 1/s, where s is the marginal propensity to save.
• In the open economy, the multiplier is: 1 1  c   m Y  

or 1 s   m Y   .

• As long as the marginal propensity to import is positive, the
multiplier will be smaller.
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The ISXM Schedule
• Imports are a leakage from the circular flow of income. As
the marginal propensity of import increases, a higher
proportion of any additional income will be spent overseas
rather than on domestically produced goods and services.
Consequently, the multiplier will be lower.
• Other than this, the ISXM schedule will behave in exactly
the same way as the closed economy version.
• A change in anything other than the level of income or the
interest rate will lead to a shift in the ISXM curve.
Specifically, if exports rise because foreign income or the
proportion dedicated to domestic goods and services
increase; or imports fall due to a decline in the marginal
propensity to import, then equilibrium output will rise and
the ISXM curve will shift outwards.
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The ISXM Schedule
• An important feature of the ISXM curve is that it will be
expected to shift if there is a change in the real exchange
rate.
• Providing that the Marshall-Lerner condition holds, a real
appreciation reduces the competitiveness of domestic goods
and services. Exports will fall, and imports will rise and the
ISXM curve will shift inwards.
• If there’s a real depreciation, then the opposite holds true.
The improved competitiveness of output produced at home
will lead to a fall in imports and a rise in exports, and the
ISXM curve will shift outwards.
• Strictly speaking, the ISXM curve should also pivot as the
multiplier will change due to the exchange rate effect on the
marginal propensity to import.
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Shifting the ISXM Schedule
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The BP curve
• This represents equilibrium in the balance of payments.
• The BP schedule plots the combinations of income (Y) and
interest rates (r) where total inflows and outflows to and
from overseas are equal.
• The balance of payments consists of two main parts: the
current and capital accounts.
• The current account is mainly determined by the trade
balance or the value of net exports (X-M).
• The capital account is largely driven by financial flows,
where international investors move funds around the world
in search of the highest returns.
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Versions of the IS-LM-BP Model
• Different versions of the IS-LM-BP model make varying
assumptions about the degree of capital mobility.
• If there is no capital mobility, then finance cannot flow
across borders and the capital account doesn’t exist. The
entire balance of payments position is set by the trade
balance.
• Where there is perfect capital mobility, capital can flow
freely with no restrictions. Given that capital flows are
large in comparison to trade (exports and imports), the
capital account will then tend to dominate the balance of
payments position.
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Versions of the IS-LM-BP Model
• In constructing the BP curve, we allow for
three different levels of capital mobility.
– no or zero capital mobility
– Perfect capital mobility
– capital mobility is neither zero nor perfect
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No capital mobility
• The balance of payments is represented by only the trade
balance or the value of net exports. The BP schedule
(equilibrium in the balance of payments) can therefore be
substituted by a BT schedule (equilibrium in the balance of
trade).
• The BT curve is plotted as the combinations of income and
interest rates where the trade balance is in equilibrium,
BT=0 =X-M.
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Export function: Depreciation in the real
exchange rate
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No capital mobility
• The import function relates the domestic level of income to
the total amount of imports. Assuming a positive and
constant marginal propensity to import, the import function
will be an upward sloping function against the domestic
level of income.
• A real depreciation in the exchange rate will lead to a
downward pivot in the import function. As domestic goods
become more competitive, consumers will switch their
consumption towards them and away from foreign goods;
so, the marginal propensity to import will fall.
• The import function will pivot, and the total fall in imports
will of course depend on the level of income.
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Import function: Depreciation in the real
exchange rate
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No capital mobility
• Overall equilibrium in the balance of trade
will arise where the export and import
functions coincide. This will then determine
the BT schedule:
0  x Y   Y
x Y   Y
(12.6)
Y TB 


  m Y  Y
  m Y  Y
x Y   Y

 m Y  
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BT Schedule: Zero Capital Mobility
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No capital mobility
• A position to the right of the BT schedule indicates a deficit
in the balance of trade. Here, imports exceed exports.
Likewise, a position to the left of the BT schedule
represents a deficit, exports exceed imports.
• We have already seen that a change in the real exchange
rate leads to a shift in the export function and a pivot in the
import function.
• Following a real depreciation, domestic goods become more
competitive vis-à-vis those produced abroad. As a result,
the export function will shift upwards and the import
function will pivot downwards. This means that the level of
income where the balance of trade is in equilibrium will
increase.
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Depreciation in the real exchange
rate
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Perfect Capital Mobility
• Under conditions of perfect capital mobility, if r is the
domestic interest rate and r* is the foreign rate, then the
following holds true:
• If the domestic interest rate exceeds the foreign interest rate,
then capital will flow into the country and the balance of
payments will move into surplus.
• If the domestic interest rate is less than the foreign interest
rate, then capital will flow out of the country and the
balance of payments will move into deficit.
• Therefore, balance of payments equilibrium will be where
r=r*. As only a miniscule deviation from the overseas
interest rate is required to generate large capital flows, the
BP schedule will hence be flat at the overseas interest rate.
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BP Schedule: Perfect Capital
Mobility
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Perfect Capital Mobility
• Changes in the exchange rate will not have any
impact on this curve.
• As the BP schedule is horizontal, a horizontal shift
in itself will have no discernable effect.
• The other reason is due to the fact that the trade
balance is only a small part of the balance of
payments. Therefore, changes in exports and
imports have a very small effect on the balance of
payments relative to the scale of capital flows.
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Intermediate Capital Mobility
• BP curve is upward sloping.
• As income rises, imports and the balance of trade deficit
become greater. In turn, larger capital account surpluses
will be required to offset this deficit. These capital account
surpluses can be achieved by offering higher interest rates.
• If a country borrows heavily, however, the increased
perception of default is likely to increase the risk premium.
• As a result, higher and higher interest rates would be
required in order to attract the required capital inflows to
maintain the balance of payments.
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BP Schedule: Intermediate Capital
Mobility
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Depreciation in the real exchange
rate
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What Shifts the Furthest: The IS or
BP Schedules?
• Following a change in the real exchange rate, and assuming
that the Marshall-Lerner condition holds, both the IS and
BP schedules will shift horizontally and in the same
direction.
• The answer to the question as to which one shifts the
furthest can be answered by looking at the equations that
describe the ISXM and the BT schedules.
• As we are only interested in what happens following a
change in the exchange rate, we can make some simplifying
assumptions to the ISXM equation. These are
a T  I G  0
as none of these variables depend on the real exchange rate.
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What Shifts the Furthest: The IS or
BP Schedules?
• The new ISXM schedule is now written as:
Y 
x Y   Y

1  c   m Y 

• Suppose there was a real depreciation in the currency.
Exports will rise and produce a multiplier effect on the level
of income where the goods market and the trade balance are
in equilibrium.
• The only difference between the multipliers is the term 1-c
in the IS schedule. As long as this is greater than zero, the
multiplier attached to the ISXM schedule will be smaller.
Given that it is almost certainly the case that 1-c>0, the
ISXM schedule will shift by a smaller amount than the BT
schedule.
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Real depreciation
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The Open Economy LM Curve
• The LM curve in an open economy is exactly the same as
its closed economy counterpart. It defines the combinations
of income and interest rates where the demand and supply
of money are equal to each other.
• As we have seen in chapter 7, this is an upward sloping
function.
• As income rises, the demand for money increases due to the
transactions motive.
• By increasing interest rates, the excess demand for money is
countered, as higher bond yields encourage people to hold
less cash and move into bonds.
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The Open Economy LM Curve
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The Open Economy LM Curve
• The open economy, though, can exert a powerful effect on
the money market. The conventional closed economy LM
curve is derived under the assumption that the money
supply is fixed. In a closed economy, the government or the
monetary authority is assumed to have complete control
over the money supply.
• In an open economy, in contrast, this proposition is less
likely. As we will see, there is a direct relationship between
the money supply and the balance of payments position.
• The position of the LM curve is therefore linked to that of
the BP schedule.
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The Open Economy LM Curve
• The factors determining the supply of money are covered in
some detail in chapter 5. In brief, the money supply is
equal to a multiple of the high powered money stock (H),
also known as the monetary base. The money supply,
including the demand deposits, will be a multiple of the
monetary base. This multiple willS be determined by the size
M  mH
of the money multiplier:
• In the closed economy, the change in the monetary base is
equal to the public sector deficit (PSD) less government
sales of bonds. This is essentially the government deficit
that is paid for by cash (by printing money) rather than
through bond sales:
 H  PSD  bond _ sales
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The Open Economy LM Curve
• In an open economy, there will a further determinant to the
stock of high powered money. This is the net purchase of
foreign reserves (R) by the central bank:
 H  PSD  bond _ sales   R
• Assuming that the public deficit is entirely financed by
bond sales, then in the open economy, the money supply is
driven by central bank changes in reserves (foreign assets).
The change in reserves now represents the official financing
of the balance of payments.
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The Open Economy LM Curve
• For the sake of simplicity assume that there is no capital
mobility, so that the balance of payments position and thus
the size of official financing or the change in foreign
reserves is determined by the trade balance .
• In this case, the high powered money stock can be
described as follows:
H  R  X  M
• Any discrepancy between exports and imports will see the
domestic monetary base rising or falling in line with
movements in the foreign exchange reserves of the central
bank. The change in the money supply is:
M
S
 m  R   m  X  M

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The Open Economy LM Curve
• We are now in a
position to describe
how the LM and BP
(money markets and
the balance of
payments) interact.
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The Open Economy LM Curve
• The interaction between the balance of payments
and the money supply implies that the central bank,
government, or other monetary authority will find
it impossible to exert control over the money
supply in an open economy. This, though, is not
entirely true.
• In the above figure, points a and c are not
sustainable because adjustments in the money
supply will push the economy to a position where
the balance of payments is equilibrated.
• In an open economy, the money supply can be
expressed as follows:
S
M
 m  PSD   B   R 
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The Open Economy LM Curve
• In the above, we simply assumed that the public sector debt
was funded entirely by bond sales, leaving the money
supply to be driven by the change in foreign reserves.
• Bond sales in this case are just sufficient to stop any public
sector surplus or deficit from affecting the money supply.
However, in the same way, it is possible for bond sales to be
used to prevent trade imbalances from affecting the
domestic money supply.
• In this case, bond sales are set so that: PSD   B   R  0
• This process of selling or purchasing excess bonds is known
as sterilization.
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The Open Economy LM Curve
• The balance of payments consists of not only the trade
balance (current account) but also the capital account: BP =
X – M + net capital inflows.
• The change in reserves (R) is determined by the official
financing required to achieve BoP equilibrium.
• When there is perfect capital mobility, any domestic interest
rate above the foreign rate would produce large-scale
capital inflows and lead to an increase in the money supply
as foreign reserves accumulate (c to d).
• Conversely, when the equilibrium in the money market
produces an interest below the foreign rate, large capital
flows lead to a deficit on the balance of payments. The
process of official financing will lead to falling foreign
reserves and a fall in the money supply, shifting the LM
curve upwards – a movement from a to b.
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Domestic interest rate exceeds
foreign interest rate
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The Open Economy LM Curve
• An important issue which certainly requires some
discussion is the ability of the monetary authorities
to control the domestic money supply (the position
of the LM schedule) in an open economy.
• Previously, we mentioned that the monetary policy
can do this by sterilizing the impact of official
financing on the money supply. This was in the
case of there being low capital mobility.
• Does the result carry over to the case of perfect
capital mobility? The conventional wisdom would
argue that the answer to this question is no.
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The Open Economy LM Curve
• Where there is no capital mobility, sterilization is only
required to offset the effects of the trade balance. However,
under perfect capital mobility, only very small differences
in home and foreign interest rates are required in order to
produce very large flows of capital.
• It, therefore, comes down to a question of scale.
• Sterilization is more realistic when dealing with relatively
smaller levels of official financing. For this reason, it has
become a well-established phenomenon that policy makers
cannot hope to have high capital mobility and also the
power to control the money supply (set the position of the
LM curve).
• Where capital is perfectly mobile, the LM curve effectively
disappears, and the money supply is automatically
determined so that r*=r.
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Equilibrium in the IS-LM-BP Model
• The point where the three schedules intersect
represents the combination of income and interest
rates where the goods market, the money market
and the balance of payments are all in equilibrium.
• Having established this model, it can now be
applied in a number of ways. Fiscal policy will
shift the IS schedule, monetary policy the LM
schedule, and exchange rate policy the BP
schedule.
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Equilibrium in the IS-LM-BP Model
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The Mundell-Fleming Model
• The Mundell-Fleming model is just the IS-LM-BP model under the
conditions of perfect capital mobility.
• The IS-LM-BP model is a fixed price model; there is nothing that
explains or accounts for price changes. It is assumed that prices are
determined implicitly in this model. Extending the model to account for
prices:
• There is a full employment/natural level of output such that:

P   Y  Yˆ

• Prices will change in the same direction as the deviation of output from
its natural level, and  determines the speed at which prices change in
this case.
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Equilibrium in the Mundell-Fleming
model
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Monetary and Fiscal Policy under
Floating Exchange Rates
• An expansionary
monetary policy
implies path a-b-c-a,
whereas expansionary
fiscal policy implies
path a-d-a.
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Monetary and Fiscal Policy under
Fixed Exchange Rates
• An expansionary
monetary policy will
imply path a-b-a,
whereas an
expansionary fiscal
policy will move the
economy along the
path a-d-c-a.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• The IS-LM-BP has been constructed and analysed in all its
variety. This is a very useful model that can be widely
applied in the analysis of an open economy and the impact
of shocks and policies.
• We worked through the general equilibrium of the IS-LMBP model, which includes a new BP schedule that reflects
equilibrium in the balance of payments. Overall
equilibrium will now show where the economy is in real,
monetary and external equilibrium.
• We saw that the IS-LM-BP model has many applications,
including taking into account the actions or reactions from
overseas.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• We covered many different variants of the IS-LM-BP
model, which make different assumptions about the degree
of capital mobility and the exchange rate regime.
• We spent time on the Mundell-Fleming model, which is the
basic IS-LM-BP model with perfect capital mobility.
• Finally, we saw that the effects of different policies are not
independent of the exchange rate regime in place in the ISLM-BP model.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning