Asset Market Equilibrium in the Short Run:
The AA Schedule
We have now derived the first element in our account of short-run exchange rate and
income determination, the relation between the exchange rate and output that is consistent
with the equality of aggregate demand and supply. That relation is summarized by the DD
schedule, which shows all exchange rate and output levels at which the output market is in
short-run equilibrium. As we noted at the beginning of the preceding section, however,
equilibrium in the economy as a whole requires equilibrium in the asset markets as well as
in the output market, and there is no reason in general why points on the DD schedule
should lead to asset market equilibrium.
To complete the story of short-run equilibrium, we therefore introduce a second element
to ensure that the exchange rate and output level consistent with output market equilibrium
are also consistent with asset market equilibrium. The schedule of exchange rate and output
combinations that are consistent with equilibrium in the domestic money market and the
foreign exchange market is called the AA schedule.
Output, the Exchange Rate, and Asset Market Equilibrium
In Chapter 14 we studied the interest parity condition, which states that the foreign exchange
market is in equilibrium only when the expected rates of return on domestic and foreign
currency deposits are equal. In Chapter 15 we learned how the interest rates that enter the
interest parity relationship are determined by the equality of real money supply and real
money demand in national money markets. Now we combine these asset market equilibrium
conditions to see how the exchange rate and output must be related when all asset markets
simultaneously clear. Because the focus for now is on the domestic economy, the foreign
interest rate is taken as given.
For a given expected future exchange rate, , the interest parity condition describing
foreign exchange market equilibrium is equation (14-2),
where is the interest rate on domestic currency deposits and is the interest rate on foreign
currency deposits. In Chapter 15 we saw that the domestic interest rate satisfying the
R R*
R = R* + (Ee - E)/E,
Ee
CHAPTER 17 Output and the Exchange Rate in the Short Run 433
interest parity condition must also equate the real domestic money supply, , to aggregate
real money demand (see equation (15-4)):
You will recall that aggregate real money demand, ( ), rises when the interest rate falls
because a fall in makes interest-bearing nonmoney assets less attractive to hold. (Conversely,
a rise in the interest rate lowers real money demand.) A rise in real output, , increases real
money demand by raising the volume of monetary transactions people must carry out (and a
fall in real output reduces real money demand by reducing people’s transactions needs).
We now use the diagrammatic tools developed in Chapter 15 to study the changes in
the exchange rate that must accompany output changes so that asset markets remain in
equilibrium. Figure 17-6 shows the equilibrium domestic interest rate and exchange rate
Y
R
L R, Y
Ms/P = L(R, Y).
Ms/P
Ms
P
Exchange
rate, E
1 2
L(R, Y 1)
1'
2'
0
R1 R2
Real money supply
Real domestic
money holdings
Domestic interest
rate, R
Domestic-currency
return on foreigncurrency
deposits
E1
E2
L(R, Y 2)
Foreign
exchange
market
Money
market Output rises
Money demand curves
Figure 17-6
Output and the Exchange Rate in Asset Market Equilibrium
For the asset (foreign exchange and money) markets to remain in equilibrium, a rise in
output must be accompanied by an appreciation of the currency, all else equal.
434 PART THREE Exchange Rates and Open-Economy Macroeconomics
associated with the output level for a given nominal money supply, ; a given domestic
price level, ; a given foreign interest rate, ; and a given value of the expected
future exchange rate, . In the lower part of the figure, we see that with real output at
and the real money supply at , the interest rate clears the home money market
(point 1), while the exchange rate clears the foreign exchange market (point ). The
exchange rate clears the foreign exchange market because it equates the expected rate
of return on foreign deposits, measured in terms of domestic currency, to .
A rise in output from to raises aggregate real money demand from to
, shifting out the entire money demand schedule in the lower part of Figure 17-6.
This shift, in turn, raises the equilibrium domestic interest rate to (point 2). With
and fixed, the domestic currency must appreciate from to to bring the foreign exchange
market back into equilibrium at point . The domestic currency appreciates by
just enough that the increase in the rate at which it is expected to depreciate in the future
offsets the increased interest rate advantage of home currency deposits. For asset markets
to remain in equilibrium, a rise in domestic output must be accompanied by an appreciation
of the domestic currency, all else equal, and a fall in domestic output must be accompanied
by a depreciation.
Deriving the AA Schedule
While the DD schedule plots exchange rates and output levels at which the output market
is in equilibrium, the AA schedule relates exchange rates and output levels that keep the
money and foreign exchange markets in equilibrium. Figure 17-7 shows the AA schedule.
From Figure 17-6 we see that for any output level , there is a unique exchange rate
satisfying the interest parity condition (given the real money supply, the foreign interest
rate, and the expected future exchange rate). Our previous reasoning tells us that other
things equal, a rise in to will produce an appreciation of the domestic currency, that
is, a fall in the exchange rate from to . The AA schedule therefore has a negative
slope, as shown in Figure 17-7.
Factors That Shift the AA Schedule
Five factors cause the AA schedule to shift: changes in the domestic money supply, ;
changes in the domestic price level, ; changes in the expected future exchange rate, ;
changes in the foreign interest rate, ; and shifts in the aggregate real money demand
schedule.
1. A change in . For a fixed level of output, an increase in causes the domestic
currency to depreciate in the foreign exchange market, all else equal (that is, rises).
Since for each level of output the exchange rate, , is higher after the rise in ,
the rise in causes AA to shift upward. Similarly, a fall in causes AA to shift
downward.
2. A change in P. An increase in reduces the real money supply and drives the interest
rate upward. Other things (including ) equal, this rise in the interest rate causes to
fall. The effect of a rise in is therefore a downward shift of AA. A fall in results in
an upward shift of AA.
3. A change in . Suppose participants in the foreign exchange market suddenly revise
their expectations about the exchange rate’s future value so that rises. Such a
change shifts the curve in the top part of Figure 17-6 (which measures the expected
domestic currency return on foreign currency deposits) to the right. The rise in
therefore causes the domestic currency to depreciate, other things equal. Because the
exchange rate producing equilibrium in the foreign exchange market is higher after a
Ee
Ee
Ee
P P
Y E
P
Ms Ms
E Ms
E
Ms Ms
R*
P Ee
Ms
E1 E2
Y1 Y2
Y E
2oe
R* E1 E2
R2 Ee
L(R, Y2)
Y1 Y2 L(R, Y1)
R1
E1
E1 1oe
Ms/P R1
Ee Y1
P R*
Y1 Ms
CHAPTER 17 Output and the Exchange Rate in the Short Run 435
Exchange
rate, E
Output, Y
1
2
E1
E 2
Y1 Y 2
AA
Figure 17-7
The AA Schedule
The asset market equilibrium
schedule (AA) slopes downward
because a rise in output from Y1
to Y2, all else equal, causes a rise
in the home interest rate and a
domestic currency appreciation
from E1 to E2.
rise in , given output, AA shifts upward when a rise in the expected future exchange
rate occurs. It shifts downward when the expected future exchange rate falls.
4. A change in . A rise in raises the expected return on foreign currency deposits
and therefore shifts the downward-sloping schedule at the top of Figure 17-6 to the
right. Given output, the domestic currency must depreciate to restore interest parity.
A rise in therefore has the same effect on AA as a rise in : It causes an upward
shift. A fall in results in a downward shift of AA.
5. A change in real money demand. Suppose domestic residents decide they would prefer
to hold lower real money balances at each output level and interest rate. (Such a
change in asset-holding preferences is a reduction in money demand.) A reduction in
money demand implies an inward shift of the aggregate real money demand function
( ) for any fixed level of , and it thus results in a lower interest rate and a rise in .
A reduction in money demand therefore has the same effect as an increase in the
money supply, in that it shifts AA upward. The opposite disturbance of an increase in
money demand would shift AA downward.
The AA Schedule
We have now derived the first element in our account of short-run exchange rate and
income determination, the relation between the exchange rate and output that is consistent
with the equality of aggregate demand and supply. That relation is summarized by the DD
schedule, which shows all exchange rate and output levels at which the output market is in
short-run equilibrium. As we noted at the beginning of the preceding section, however,
equilibrium in the economy as a whole requires equilibrium in the asset markets as well as
in the output market, and there is no reason in general why points on the DD schedule
should lead to asset market equilibrium.
To complete the story of short-run equilibrium, we therefore introduce a second element
to ensure that the exchange rate and output level consistent with output market equilibrium
are also consistent with asset market equilibrium. The schedule of exchange rate and output
combinations that are consistent with equilibrium in the domestic money market and the
foreign exchange market is called the AA schedule.
Output, the Exchange Rate, and Asset Market Equilibrium
In Chapter 14 we studied the interest parity condition, which states that the foreign exchange
market is in equilibrium only when the expected rates of return on domestic and foreign
currency deposits are equal. In Chapter 15 we learned how the interest rates that enter the
interest parity relationship are determined by the equality of real money supply and real
money demand in national money markets. Now we combine these asset market equilibrium
conditions to see how the exchange rate and output must be related when all asset markets
simultaneously clear. Because the focus for now is on the domestic economy, the foreign
interest rate is taken as given.
For a given expected future exchange rate, , the interest parity condition describing
foreign exchange market equilibrium is equation (14-2),
where is the interest rate on domestic currency deposits and is the interest rate on foreign
currency deposits. In Chapter 15 we saw that the domestic interest rate satisfying the
R R*
R = R* + (Ee - E)/E,
Ee
CHAPTER 17 Output and the Exchange Rate in the Short Run 433
interest parity condition must also equate the real domestic money supply, , to aggregate
real money demand (see equation (15-4)):
You will recall that aggregate real money demand, ( ), rises when the interest rate falls
because a fall in makes interest-bearing nonmoney assets less attractive to hold. (Conversely,
a rise in the interest rate lowers real money demand.) A rise in real output, , increases real
money demand by raising the volume of monetary transactions people must carry out (and a
fall in real output reduces real money demand by reducing people’s transactions needs).
We now use the diagrammatic tools developed in Chapter 15 to study the changes in
the exchange rate that must accompany output changes so that asset markets remain in
equilibrium. Figure 17-6 shows the equilibrium domestic interest rate and exchange rate
Y
R
L R, Y
Ms/P = L(R, Y).
Ms/P
Ms
P
Exchange
rate, E
1 2
L(R, Y 1)
1'
2'
0
R1 R2
Real money supply
Real domestic
money holdings
Domestic interest
rate, R
Domestic-currency
return on foreigncurrency
deposits
E1
E2
L(R, Y 2)
Foreign
exchange
market
Money
market Output rises
Money demand curves
Figure 17-6
Output and the Exchange Rate in Asset Market Equilibrium
For the asset (foreign exchange and money) markets to remain in equilibrium, a rise in
output must be accompanied by an appreciation of the currency, all else equal.
434 PART THREE Exchange Rates and Open-Economy Macroeconomics
associated with the output level for a given nominal money supply, ; a given domestic
price level, ; a given foreign interest rate, ; and a given value of the expected
future exchange rate, . In the lower part of the figure, we see that with real output at
and the real money supply at , the interest rate clears the home money market
(point 1), while the exchange rate clears the foreign exchange market (point ). The
exchange rate clears the foreign exchange market because it equates the expected rate
of return on foreign deposits, measured in terms of domestic currency, to .
A rise in output from to raises aggregate real money demand from to
, shifting out the entire money demand schedule in the lower part of Figure 17-6.
This shift, in turn, raises the equilibrium domestic interest rate to (point 2). With
and fixed, the domestic currency must appreciate from to to bring the foreign exchange
market back into equilibrium at point . The domestic currency appreciates by
just enough that the increase in the rate at which it is expected to depreciate in the future
offsets the increased interest rate advantage of home currency deposits. For asset markets
to remain in equilibrium, a rise in domestic output must be accompanied by an appreciation
of the domestic currency, all else equal, and a fall in domestic output must be accompanied
by a depreciation.
Deriving the AA Schedule
While the DD schedule plots exchange rates and output levels at which the output market
is in equilibrium, the AA schedule relates exchange rates and output levels that keep the
money and foreign exchange markets in equilibrium. Figure 17-7 shows the AA schedule.
From Figure 17-6 we see that for any output level , there is a unique exchange rate
satisfying the interest parity condition (given the real money supply, the foreign interest
rate, and the expected future exchange rate). Our previous reasoning tells us that other
things equal, a rise in to will produce an appreciation of the domestic currency, that
is, a fall in the exchange rate from to . The AA schedule therefore has a negative
slope, as shown in Figure 17-7.
Factors That Shift the AA Schedule
Five factors cause the AA schedule to shift: changes in the domestic money supply, ;
changes in the domestic price level, ; changes in the expected future exchange rate, ;
changes in the foreign interest rate, ; and shifts in the aggregate real money demand
schedule.
1. A change in . For a fixed level of output, an increase in causes the domestic
currency to depreciate in the foreign exchange market, all else equal (that is, rises).
Since for each level of output the exchange rate, , is higher after the rise in ,
the rise in causes AA to shift upward. Similarly, a fall in causes AA to shift
downward.
2. A change in P. An increase in reduces the real money supply and drives the interest
rate upward. Other things (including ) equal, this rise in the interest rate causes to
fall. The effect of a rise in is therefore a downward shift of AA. A fall in results in
an upward shift of AA.
3. A change in . Suppose participants in the foreign exchange market suddenly revise
their expectations about the exchange rate’s future value so that rises. Such a
change shifts the curve in the top part of Figure 17-6 (which measures the expected
domestic currency return on foreign currency deposits) to the right. The rise in
therefore causes the domestic currency to depreciate, other things equal. Because the
exchange rate producing equilibrium in the foreign exchange market is higher after a
Ee
Ee
Ee
P P
Y E
P
Ms Ms
E Ms
E
Ms Ms
R*
P Ee
Ms
E1 E2
Y1 Y2
Y E
2oe
R* E1 E2
R2 Ee
L(R, Y2)
Y1 Y2 L(R, Y1)
R1
E1
E1 1oe
Ms/P R1
Ee Y1
P R*
Y1 Ms
CHAPTER 17 Output and the Exchange Rate in the Short Run 435
Exchange
rate, E
Output, Y
1
2
E1
E 2
Y1 Y 2
AA
Figure 17-7
The AA Schedule
The asset market equilibrium
schedule (AA) slopes downward
because a rise in output from Y1
to Y2, all else equal, causes a rise
in the home interest rate and a
domestic currency appreciation
from E1 to E2.
rise in , given output, AA shifts upward when a rise in the expected future exchange
rate occurs. It shifts downward when the expected future exchange rate falls.
4. A change in . A rise in raises the expected return on foreign currency deposits
and therefore shifts the downward-sloping schedule at the top of Figure 17-6 to the
right. Given output, the domestic currency must depreciate to restore interest parity.
A rise in therefore has the same effect on AA as a rise in : It causes an upward
shift. A fall in results in a downward shift of AA.
5. A change in real money demand. Suppose domestic residents decide they would prefer
to hold lower real money balances at each output level and interest rate. (Such a
change in asset-holding preferences is a reduction in money demand.) A reduction in
money demand implies an inward shift of the aggregate real money demand function
( ) for any fixed level of , and it thus results in a lower interest rate and a rise in .
A reduction in money demand therefore has the same effect as an increase in the
money supply, in that it shifts AA upward. The opposite disturbance of an increase in
money demand would shift AA downward.
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