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Mundell-Fleming Model: IS-LM in the Tropics
• Mundell-Fleming Model based on idea that capital flows must offset trade
deficits for stable international reserves.
1. Speed of capital flows depends on perceptions as captured by F.
2. The same differences in interest rate between two countries can cause
very different movement in international capital flows.
3. Without perfect capital mobility, there are unequal interest rates in
countries even without capital controls.
• IS Curve: combinations of income and the interest rate such that savings
equals investment.
• Algebraically, savings is equal to investment when
Y = C + I + G + E(r) − rM
where Y is GDP, I is investment, G is government expenditure, E(r) is
exports net of competitive imports, M is non-competitive imports and r
is the real exchange rate
∗
r = ePM
/P
∗
where e is the nominal exchange rate, PM
is the foreign price of imports
and P is the domestic price level. Note that G includes government wages,
but not transfers and C, I and G include competitive imports.
• The level of noncompetitive imports is given by M = rm(r) where m(r)
m� (r) < 0is the marginal propensity to import and is written as a function
of the real exchange rate, r, to allow for the possibility of expenditure
switching, increasing imports as the real exchange rate appreciates (a fall
in r).
• In other words, for a given level of income, what is the level of interest
that makes investment equal to the sum of savings?
• This is the locus of equilibria in the goods market.
• The definition of the LM curve is combinations of income and the interest
rate such that money demand equals money supply.
• In other words, for a given level of income what is the interest rate that
makes money demand, equal to money supply (Ms )
Ms = −h(i − i∗ ) + kY
where k is the transaction demand coefficient and h is the speculative demand coefficient and i* is the foreign interest rate. The domestic interest
rate is i
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• An approximation to the Baumol-Tobin model
• This is the locus of equilibria in the money market.
• BP or balance of payments curve (sometimes called the CM curve for
capital mobility)
E(r) − rM + F (i − i∗ ) + f¯ = ∆R = 0
where f¯ is the capital flow into or out of the country that is unrelated to the
interest rate.
• Along BP curve no change in reserves ( ∆R = 0)
1. F measures the relationship of the rest of the world to our country;
it is a catch all variable, reflecting traders, foreign investors, bankers
attitudes toward risk versus rate of return trade-offs for investments
in the country.
2. f¯ can be used for calibration to a SAM or to give a more realistic
value of the capital flow parameter F
3. current account E(r) − rM is equal to capital account F (i − i∗ ).
(a) The current account is in surplus when E(r) − rM > 0 (trade
surplus)
(b) The capital account is in surplus when F (i − i∗ ) > 0 (capital
inflow)
4. Graphically: above BP reserves are increasing, BP is in surplus.
5. Below BP reserves are falling, BP is in deficit
• If capital flows freely across borders the domestic interest rate and foreign
interest rate are the same:
i = i∗
• Defines perfect capital mobility, P CM ; but this is only relevant for developed countries and does not included a risk premium.
• In fixed exchange rates, the money supply becomes endogenous: LM curve
floats.
• Equilibrium in (i, Y ) space is determined by the IS and BP only.
1. The LM equation only determines the money supply.
• Inflow of capital under fixed exchange rates causes the money supply to
increase and outflow causes the reverse.
2
1. Exporters and foreign investors bring foreign currency to the central
bank and exchange it for domestic currency
2. Banking reserves rise and the money multiplier increases the total
money supply.
3. LM shift to the right
4. In fixed exchange rates the monetary authority is not able to choose
both the money supply and the exchange rate.
1.1
Equilibrium with Fixed Exchange Rates
• Short run equilibrium is determined by the IS curve and the BP curve
• Solve for IS and BP in standard slope-intercept form
• The IS curve is defined by the following
Y
C
Yd
I
= C + I + G + E(r) − rm(r)X
= c̄ + cY d
= (Y + Tr )(1 − t)
= I¯ − bi
where c is the marginal propensity to consume and c̄ is the level of autonomous consumption. The direct tax rate is t on disposable income Y d ,
which includes Tr , foreign and domestic transfers, if any.
• Substitute upward
Y = c̄ + cY − ctY + c(1 − t)Tr + I¯ − bi + G + E − rmY
and solve for i :
i = 1/c(c̄ + cY − ctY + −rmY − Y )
where A = c̄ + c(1 − t)Tr + I¯ + G is a constant introduced for convenience.
i = 1/b(A − rmY − Y + cY − tY )
i=
A + E(r) [1 − c(1 − t) + rm(r)]
−
Y
b
b
• The slope of the IS curve is
rise
di
∆i
[1 − c(1 − t) + rm(r)]
=
=
=−
<0
run
dY
∆Y
b
• The intercept of the IS curve is:
A + E(r)
b
3
(1)
• The BP curve is given by
E(r) − rm(r)Y + F (i − i∗ ) + f¯ = 0
rm(r)Y − E(r) − f¯
+ i∗ = i
F
i=
rm(r)
E(r) + f¯
Y −
+ i∗
F
F
(2)
where the slope is
rm(r)
F
and the intercept is
−
E(r) + f¯
+ i∗
F
• Any change in the parameters that causes
1. the slope to increase means the IS curve gets flatter.
2. the intercept to increase means that the IS curve shifts to the right
and vice-versa.
• Solving, set equation 1 and 2 equal and solve for Y
rm(r)
E(r)
A + E(r) [1 − c(1 − t) + rm(r)]
Y −
+ i∗ =
−
Y
F
F
b
b
Solution is:
Y =
rE(r) +
rm(r) +
F
b
F
b
�
�
A + E(r) + I¯ + F i∗
(1 + rm(r) − c (1 − t))
with i determined by either equation 1 or 2
• Put the LM curve into standard form:
Ms = −h(i − i∗ ) + kY
i=
k
Ms
Y −
+ i∗
h
h
• The slope of the LM curve is
rise
di
∆i
k
=
=
= >0
run
dY
∆Y
h
M
• The intercept of the LM curve is: − hP
+ i∗ < 0.Any change in the
parameters that causes
1. the slope to increase means the LM curve gets steeper.
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Table 1: The Base SAM
Firms
Firms
Value Added
Savings
Tax
Non-comp Imports
Total
125
C
I
G
E
Total
80
26
20
4
5
1
130
125
26
25
5
25
5
20
25
5
130
125
26
Source: Made up numbers
2. the intercept to decrease means that the LM curve shifts to the right
and vice-versa.
• Why the IS curve is downward sloping (verbal answer): an increase in
income causes savings to increase at the same level of the interest rate.
The only way investment can rise to meet the higher level of savings is
through a fall in the interest rate. Hence, the IS curve is downward
sloping.
• Why the LM curve is upward sloping (verbal answer): an increase in
income causes the demand for money to increase at the same level of the
interest rate. Because the supply of money is fixed, money demand must
come back down. This can only happen if there is a rise in the interest
rate. Hence, the LM curve is upward sloping.
1.2
Flexible Exchange Rates
• Solving the model with flexible exchange rates is difficult to do by hand
an so we resort to Excel.
• To do so we need a function for exports. Take E = Ē + νr where ν > 0 is
the marginal propensity to export.
The spreadsheet looks like
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Table 2: The parameters
k
h
int rate
F
fbar
i∗
Ibar
b
0.4
750
0.05
7
0.930
0.04
27
20
mpc
cbar
t
m
Ē
mpe
Ms
0.7
10
0.2
0.04
1
3
49.5
Source: Made up parameters
Table 3: Solving the MF model in Excel
Y
C
I
G
int rate
125.0
127.7
130.7
134.0
137.7
80
81
83
85
87
26.00
25.57
25.09
24.56
23.97
20.0
22.0
24.2
26.6
29.3
0.050
0.071
0.095
0.122
0.151
Source: The spreadsheet
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Table 4: Solving the MF model in Excel
CAS
KAS
∆R
r-fixed
r-flex
E
imports
-1.0000
-1.1886
-1.3907
-1.6083
-1.8437
1.00
1.15
1.32
1.50
1.71
0.00
-0.04
-0.07
-0.11
-0.13
1.0000
1.0387
1.0738
1.1057
1.1345
1.0000
1.0387
1.0738
1.1057
1.1345
4.00
4.12
4.22
4.32
4.40
5.0
5.3
5.6
5.9
6.2
Source: The spreadsheet
The level of income is = cbar + I + G + E − r ∗ impt while consumption
is = cbar + mpc ∗ (1 − t) ∗ Y . Investment is given by = Ibar − b ∗ int− rate
and government expenditure grows at an exogenous rate, here 10 percent. The
interest rate is = i− star + (k− ∗ Y − M s− )/h and the current account surplus
is = Ebar + mpe ∗ er − m ∗ er ∗ Y . The capital account surplus is = F ∗ (int −
i− star) + f bar, while the change in reservers ∆R is just the sum of the two.
For fixed exchange rates, the interest rate is determined by the BP curve.
For flexible exchange rates the interest rate is defined by the LM curve. The
flex rate is given by:
= −(F ∗ (int− rate − i− star) + f bar)/(E− + mpe − m ∗ Y ) and this completes
the model.
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