A Long-Run Exchange Rate Model Based on PPP
When combined with the framework of money demand and supply that we developed in
Chapter 15, the theory of PPP leads to a useful theory of how exchange rates and monetary
factors interact in the long run. Because factors that do not influence money supply or
money demand play no explicit role in this theory, it is known as the monetary approach
to the exchange rate. The monetary approach is this chapter’s first step in developing a
general long-run theory of exchange rates.
We think of the monetary approach as a long-run and not a short-run theory because it
does not allow for the price rigidities that seem important in explaining short-run macroeconomic
developments, in particular departures from full employment. Instead, the monetary
approach proceeds as if prices can adjust right away to maintain full employment as
well as PPP. Here, as in the previous chapter, when we refer to a variable’s “long-run”
value, we mean the variable’s equilibrium value in a hypothetical world of perfectly flexible
output and factor market prices.
There is actually considerable controversy among macroeconomists about the sources of
apparent price level stickiness, with some maintaining that prices and wages only appear
rigid and in reality adjust immediately to clear markets. To an economist of the aforementioned
school, this chapter’s models would describe the short-run behavior of an economy
in which the speed of price level adjustment is so great that no significant unemployment
ever occurs.
The Fundamental Equation of the Monetary Approach
To develop the monetary approach’s predictions for the dollar/euro exchange rate, we will
assume that in the long run, the foreign exchange market sets the rate so that PPP holds
(see equation (16-1)):
In other words, we assume the above equation would hold in a world where there are no
market rigidities to prevent the exchange rate and other prices from adjusting immediately
to levels consistent with full employment.
In the previous chapter, equation (15-5) showed how we can explain domestic price
levels in terms of domestic money demands and supplies. In the United States,
(16-3)
while in Europe,
(16-4) PE = ME s /L(R€,YE).
PUS = MUS
s /L(R$, YUS),
E$/€ = PUS/PE.
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 389
As before, we have used the symbol to stand for a country’s money supply and
to stand for its aggregate real money demand, which decreases when the interest rate rises
and increases when real output rises.2
Equations (16-3) and (16-4) show how the monetary approach to the exchange rate
comes by its name. According to the statement of PPP in equation (16-1), the dollar price
of a euro is simply the dollar price of U.S. output divided by the euro price of European
output. These two price levels, in turn, are determined completely by the supply and
demand for each currency area’s money: The United States’ price level is the U.S. money
supply divided by U.S. real money demand, as shown in (16-3), and Europe’s price level
similarly is the European money supply divided by European real money demand, as
shown in (16-4). The monetary approach therefore makes the general prediction that the
exchange rate, which is the relative price of American and European money, is fully determined
in the long run by the relative supplies of those monies and the relative real
demands for them. Shifts in interest rates and output levels affect the exchange rate only
through their influences on money demand.
In addition, the monetary approach makes a number of specific predictions about the
long-run effects on the exchange rate of changes in money supplies, interest rates, and
output levels:
1. Money supplies. Other things equal, a permanent rise in the U.S. money supply
causes a proportional increase in the long-run U.S. price level as equation (16-3)
shows. Because under PPP however, also rises in the long run in proportion
to the increase in the U.S. money supply. (For example, if rises by 10 percent,
and both eventually rise by 10 percent as well.) Thus, an increase in the U.S.
money supply causes a proportional long-run depreciation of the dollar against the euro.
Conversely, equation (16-4) shows that a permanent increase in the European money supply
causes a proportional increase in the long-run European price level. Under PPP, this
price level rise implies a proportional long-run appreciation of the dollar against the euro
(which is the same as a proportional depreciation of the euro against the dollar).
2. Interest rates. A rise in the interest rate on dollar-denominated assets lowers
real U.S. money demand By (16-3), the long-run U.S. price level rises, and
under PPP the dollar must depreciate against the euro in proportion to this U.S. price
level increase. A rise in the interest rate on euro-denominated assets has the reverse
long-run exchange rate effect. Because real European money demand falls,
Europe’s price level rises, by (16-4). Under PPP, the dollar must appreciate against the
euro in proportion to Europe’s price level increase.
3. Output levels. A rise in U.S. output raises real U.S. money demand
leading by (16-3) to a fall in the long-run U.S. price level. According to PPP, there is
an appreciation of the dollar against the euro. Symmetrically, a rise in European output
raises and, by (16-4), causes a fall in Europe’s long-run price level.
PPP predicts that this development will make the dollar depreciate against the euro.
To understand these predictions, remember that the monetary approach, like any longrun
theory, essentially assumes that price levels adjust as quickly as exchange rates do—
that is, right away. For example, a rise in real U.S. output raises the transactions demand
for real U.S. money balances. According to the monetary approach, the U.S. price level
drops immediately to bring about a market-clearing increase in the supply of real balances.
L(R€, YE)
L(R$, YUS),
L(R€, YE)
R€
L(R$, YUS).
R$
E$/€ PUS
MUS
s
E$/€ E$/€ = PUS/PE,
PUS,
MUS
s
Ms L(R,Y)
2To simplify the notation, we assume identical money demand functions for the United States and Europe.
390 PART THREE Exchange Rates and Open-Economy Macroeconomics
PPP implies that this instantaneous American price deflation is accompanied by an instantaneous
dollar appreciation on the foreign exchanges.
The monetary approach leads to a result familiar from Chapter 15, that the long-run
foreign exchange value of a country’s currency moves in proportion to its money supply
(prediction 1). The theory also raises what seems to be a paradox (prediction 2). In our
previous examples, we always found that a currency appreciates when the interest rate it
offers rises relative to foreign interest rates. How is it that we have now arrived at precisely
the opposite conclusion—that a rise in a country’s interest rate depreciates its currency by
lowering the real demand for its money?
At the end of Chapter 14, we warned that no account of how a change in interest rates
affects the exchange rate is complete until we specify exactly why interest rates have
changed. This point explains the apparent contradiction in our findings about interest and
exchange rates. To resolve the puzzle, however, we must first examine more closely how
monetary policies and interest rates are connected in the long run.
Ongoing Inflation, Interest Parity, and PPP
In the last chapter we saw that a permanent increase in the level of a country’s money
supply ultimately results in a proportional rise in its price level but has no effect on the
long-run values of the interest rate or real output. While the conceptual experiment of a
one-time, stepwise money supply change is useful for thinking about the long-run effects
of money, it is not very realistic as a description of actual monetary policies. More often,
the monetary authorities choose a growth rate for the money supply, say, 5, 10, or 50 percent
per year, and then allow money to grow gradually, through incremental but frequent
increases. What are the long-run effects of a policy that allows the money supply to grow
smoothly forever at a positive rate?
The reasoning in Chapter 15 suggests that continuing money supply growth will
require a continuing rise in the price level—a situation of ongoing inflation. As firms and
workers catch on to the fact that the money supply is growing steadily at, say, a 10 percent
annual rate, they will adjust by raising prices and wages by the same 10 percent every
year, thus keeping their real incomes constant. Full-employment output depends on supplies
of productive factors, but it is safe to assume that factor supplies, and thus output, are
unaffected over the long run by different choices of a constant growth rate for the money
supply. Other things equal, money supply growth at a constant rate eventually results in
ongoing price level inflation at the same rate, but changes in this long-run inflation rate do
not affect the full-employment output level or the long-run relative prices of goods and
services.
The interest rate, however, is definitely not independent of the money supply growth
rate in the long run. While the long-run interest rate does not depend on the absolute level
of the money supply, continuing growth in the money supply eventually will affect the
interest rate. The easiest way to see how a permanent increase in inflation affects the longrun
interest rate is by combining PPP with the interest rate parity condition on which our
previous analysis of exchange rate determination was built.
As in the preceding two chapters, the condition of interest parity between dollar and
euro assets is
(recall equation (14-2), page 338). Now let’s ask how this parity condition, which must
hold in the long run as well as in the short run, fits with the other parity condition we
are assuming in our long-run model, purchasing power parity. According to relative PPP,
the percentage change in the dollar/euro exchange rate over the next year, say, will equal
R$ = R€ + (E$/€
e - E$/€)/E$/€
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 391
the difference between the inflation rates of the United States and Europe over that year
(see equation (16-2)). Since people understand this relationship, however, it must also be
true that they expect the percentage exchange rate change to equal the U.S.–Europe inflation
difference. The interest parity condition written above now tells us the following:
If people expect relative PPP to hold, the difference between the interest rates offered by
dollar and euro deposits will equal the difference between the inflation rates expected,
over the relevant horizon, in the United States and in Europe.
Some additional notation is helpful in deriving this result more formally. If is the
price level expected in a country for a year from today, the expected inflation rate in that
country, is the expected percentage increase in the price level over the coming year,
If relative PPP holds, however, market participants will also expect relative PPP to hold,
which means that we can replace the actual depreciation and inflation rates in equation
(16-2) with the values the market expects to materialize:
By combining this “expected” version of relative PPP with the interest parity condition
and rearranging, we arrive at a formula that expresses the international interest rate difference
as the difference between expected national inflation rates:
(16-5)
If, as PPP predicts, currency depreciation is expected to offset the international inflation
difference (so that the expected dollar depreciation rate is ), the interest rate
difference must equal the expected inflation difference.
The Fisher Effect
Equation (16-5) gives us the long-run relationship between ongoing inflation and interest
rates that we need to explain the monetary approach’s predictions about how interest rates
affect exchange rates. The equation tells us that all else equal, a rise in a country’s
expected inflation rate will eventually cause an equal rise in the interest rate that deposits
of its currency offer. Similarly, a fall in the expected inflation rate will eventually cause a
fall in the interest rate.
This long-run relationship between inflation and interest rates is called the Fisher effect.
The Fisher effect implies, for example, that if U.S. inflation were to rise permanently from a
constant level of 5 percent per year to a constant level of 10 percent per year, dollar interest
rates would eventually catch up with the higher inflation, rising by 5 percentage points per
year from their initial level. These changes would leave the real rate of return on dollar
assets, measured in terms of U.S. goods and services, unchanged. The Fisher effect is therefore
another example of the general idea that in the long run, purely monetary developments
should have no effect on an economy’s relative prices.3
pUS
e - pE e
R$ - R€ = pUS
e - pE e .
R$ = R€ + (E$/€
e - E$/€)/E$/€
(E$/€
e - E$/€)/E$/€ = pUS
e - pE e .
pe = (Pe - P)/P.
pe,
Pe
3 The effect is named after Irving Fisher of Yale University, one of the great American economists of the early
20th century. The effect is discussed at length in his book The Theory of Interest (New York: Macmillan, 1930).
Fisher, incidentally, gave an early account of the interest parity condition on which our theory of foreign
exchange market equilibrium is based.
392 PART THREE Exchange Rates and Open-Economy Macroeconomics
The Fisher effect is behind the seemingly paradoxical monetary approach prediction that a
currency depreciates in the foreign exchange market when its interest rate rises relative to foreign
currency interest rates. In the long-run equilibrium assumed by the monetary approach, a
rise in the difference between home and foreign interest rates occurs only when expected
home inflation rises relative to expected foreign inflation. This is certainly not the case in the
short run, when the domestic price level is sticky. In the short run, as we saw in Chapter 15,
the interest rate can rise when the domestic money supply falls, because the sticky domestic
price level leads to an excess demand for real money balances at the initial interest rate. Under
the flexible-price monetary approach, however, the price level would fall right away, leaving
the real money supply unchanged and thus making the interest rate change unnecessary.
We can better understand how interest rates and exchange rates interact under the monetary
approach by thinking through an example. Our example illustrates why the monetary
approach associates sustained interest rate hikes with current as well as future currency
depreciation, and sustained interest rate declines with appreciation.
Imagine that at time , the Federal Reserve unexpectedly increases the growth rate of
the U.S. money supply from to the higher level Figure 16-1 illustrates how
this change affects the dollar/euro exchange rate, as well as other U.S. variables, under
the assumptions of the monetary approach. To simplify the graphs, we assume that in
Europe, the inflation rate remains constant at zero.
Figure 16-1a shows the sudden acceleration of U.S. money supply growth at time
(We have scaled the vertical axes of the graphs so that constant slopes represent constant
proportional growth rates of variables.) The policy change generates expectations of more
rapid currency depreciation in the future: Under PPP the dollar will now depreciate at the
rate rather than at the lower rate Interest parity therefore requires the dollar
interest rate to rise, as shown in Figure 16-1b, from its initial level to a new level that
reflects the extra expected dollar depreciation, (see equation (16-5)).
Notice that this adjustment leaves the euro interest rate unchanged; but since Europe’s
money supply and output haven’t changed, the original euro interest rate will still maintain
equilibrium in Europe’s money market.
You can see from Figure 16-1a that the level of the money supply does not actually
jump upward at —only the future growth rate changes. Since there is no immediate
increase in the money supply, but there is an interest rate rise that reduces money demand,
there would be an excess supply of real U.S. money balances at the price level prevailing
just prior to In the face of this potential excess supply, the U.S. price level does jump
upward at (see Figure 16-1c), reducing the real money supply so that it again equals real
money demand (see equation (16-3)). Consistently with the upward jump in at ,
Figure 16-1d shows the simultaneous proportional upward jump in implied by PPP.
How can we visualize the reaction of the foreign exchange market at time ? The dollar
interest rate rises not because of a change in current levels of money supply or demand, but
solely because people expect more rapid future money supply growth and dollar depreciation.
As investors respond by moving into foreign deposits, which momentarily offer higher
expected returns, the dollar depreciates sharply in the foreign exchange market, moving to a
new trend line along which depreciation is more rapid than it was up to time 4
Notice how different assumptions about the speed of price level adjustment lead to contrasting
predictions about how exchange and interest rates interact. In the example of a fall
in the money supply under sticky prices, an interest rate rise is needed to preserve money
t0.
t0
E$/€
PUS t0
t0
t0.
t0
R$
2 = R$
1 + ¢p
R$
1
p + ¢p p.
t0.
E$/€,
p p + ¢p.
t0
4In the general case in which Europe’s inflation rate is not zero, the dollar, rather than depreciating against
the euro at rate before and at rate afterward, depreciates at rate until and at rate
p + ¢p - pE thereafter.
p t0 p + ¢p p - pE t0
pE
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 393
+ Δπ
R$
1
(a) (b)
(c) (d)
U.S. money
supply, MUS
U.S. price
level, PUS
Dollar interest
rate, R$
Dollar/euro
exchange rate, E$/€
MUS,t0
Time
Slope = π
Slope = π + Δπ
Time
Time t0
Time
t0
t0 t0
Slope = π
Slope = π
Slope = π + Δπ
Slope = π + Δπ
R$
2 R$
= 1
Figure 16-1
Long-Run Time Paths of U.S. Economic Variables After a Permanent Increase in the Growth Rate
of the U.S. Money Supply
After the money supply growth rate increases at time in panel (a), the interest rate (in panel (b)),
price level (in panel (c)), and exchange rate (in panel (d)) move to new long-run equilibrium paths.
(The money supply, price level, and exchange rate are all measured on a natural logarithmic scale,
which makes variables that change at constant proportional rates appear as straight lines when they
are graphed against time. The slope of the line equals the variable’s proportional growth rate.)
t0
market equilibrium, given that the price level cannot do so by dropping immediately in
response to the money supply reduction. In that sticky-price case, an interest rate rise is
associated with lower expected inflation and a long-run currency appreciation, so the
currency appreciates immediately. In our monetary approach example of a rise in money
supply growth, however, an interest rate increase is associated with higher expected inflation
and a currency that will be weaker on all future dates. An immediate currency
depreciation is the result.5
5 National money supplies typically trend upward over time, as in Figure 16-1a. Such trends lead to corresponding
upward trends in price levels; if two countries’ price level trends differ, PPP implies a trend in their
exchange rate as well. From now on, when we refer to a change in the money supply, price level, or exchange
rate, we will mean by this a change in the level of the variable relative to its previously expected trend path—that
is, a parallel shift in the trend path. When instead we want to consider changes in the slopes of trend paths themselves,
we will say so explicitly.
394 PART THREE Exchange Rates and Open-Economy Macroeconomics
6 Some of the negative evidence on absolute PPP is discussed in the Case Study to follow. Regarding the law of
one price, see, for example, Peter Isard, “How Far Can We Push the Law of One Price?” American Economic
Review 67 (December 1977), pp. 942–948; Irving B. Kravis and Robert E. Lipsey, “Price Behavior in the Light of
Balance of Payments Theories,” Journal of International Economics 8 (May 1978), pp. 193–246; and the paper by
Goldberg and Knetter in Further Readings.
7 The price level measures in Figure 16-2 are index numbers, not dollar amounts. For example, the U.S. consumer
price index (CPI) was 100 in the base year 2000 and only about 50 in 1980, so the dollar price of a reference
commodity basket of typical U.S. consumption purchases doubled between 1980 and 2000. Base years for the
U.S. and Japanese price indexes were chosen so that their 1980 ratio would equal the 1980 exchange rate, but this
imposed equality does not mean that absolute PPP held in 1980. Although Figure 16-2 uses CPIs, other price
indexes lead to similar pictures.
8 See, for example, the paper by Taylor and Taylor in this chapter’s Further Readings.
These contrasting results of interest rate changes underlie our earlier warning that an
explanation of exchange rates based on interest rates must carefully account for the factors
that cause interest rates to move. These factors can simultaneously affect expected future
exchange rates and can therefore have a decisive impact on the foreign exchange market’s
response to the interest rate change. The appendix to this chapter shows in detail how
expectations change in the case we analyzed.
When combined with the framework of money demand and supply that we developed in
Chapter 15, the theory of PPP leads to a useful theory of how exchange rates and monetary
factors interact in the long run. Because factors that do not influence money supply or
money demand play no explicit role in this theory, it is known as the monetary approach
to the exchange rate. The monetary approach is this chapter’s first step in developing a
general long-run theory of exchange rates.
We think of the monetary approach as a long-run and not a short-run theory because it
does not allow for the price rigidities that seem important in explaining short-run macroeconomic
developments, in particular departures from full employment. Instead, the monetary
approach proceeds as if prices can adjust right away to maintain full employment as
well as PPP. Here, as in the previous chapter, when we refer to a variable’s “long-run”
value, we mean the variable’s equilibrium value in a hypothetical world of perfectly flexible
output and factor market prices.
There is actually considerable controversy among macroeconomists about the sources of
apparent price level stickiness, with some maintaining that prices and wages only appear
rigid and in reality adjust immediately to clear markets. To an economist of the aforementioned
school, this chapter’s models would describe the short-run behavior of an economy
in which the speed of price level adjustment is so great that no significant unemployment
ever occurs.
The Fundamental Equation of the Monetary Approach
To develop the monetary approach’s predictions for the dollar/euro exchange rate, we will
assume that in the long run, the foreign exchange market sets the rate so that PPP holds
(see equation (16-1)):
In other words, we assume the above equation would hold in a world where there are no
market rigidities to prevent the exchange rate and other prices from adjusting immediately
to levels consistent with full employment.
In the previous chapter, equation (15-5) showed how we can explain domestic price
levels in terms of domestic money demands and supplies. In the United States,
(16-3)
while in Europe,
(16-4) PE = ME s /L(R€,YE).
PUS = MUS
s /L(R$, YUS),
E$/€ = PUS/PE.
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 389
As before, we have used the symbol to stand for a country’s money supply and
to stand for its aggregate real money demand, which decreases when the interest rate rises
and increases when real output rises.2
Equations (16-3) and (16-4) show how the monetary approach to the exchange rate
comes by its name. According to the statement of PPP in equation (16-1), the dollar price
of a euro is simply the dollar price of U.S. output divided by the euro price of European
output. These two price levels, in turn, are determined completely by the supply and
demand for each currency area’s money: The United States’ price level is the U.S. money
supply divided by U.S. real money demand, as shown in (16-3), and Europe’s price level
similarly is the European money supply divided by European real money demand, as
shown in (16-4). The monetary approach therefore makes the general prediction that the
exchange rate, which is the relative price of American and European money, is fully determined
in the long run by the relative supplies of those monies and the relative real
demands for them. Shifts in interest rates and output levels affect the exchange rate only
through their influences on money demand.
In addition, the monetary approach makes a number of specific predictions about the
long-run effects on the exchange rate of changes in money supplies, interest rates, and
output levels:
1. Money supplies. Other things equal, a permanent rise in the U.S. money supply
causes a proportional increase in the long-run U.S. price level as equation (16-3)
shows. Because under PPP however, also rises in the long run in proportion
to the increase in the U.S. money supply. (For example, if rises by 10 percent,
and both eventually rise by 10 percent as well.) Thus, an increase in the U.S.
money supply causes a proportional long-run depreciation of the dollar against the euro.
Conversely, equation (16-4) shows that a permanent increase in the European money supply
causes a proportional increase in the long-run European price level. Under PPP, this
price level rise implies a proportional long-run appreciation of the dollar against the euro
(which is the same as a proportional depreciation of the euro against the dollar).
2. Interest rates. A rise in the interest rate on dollar-denominated assets lowers
real U.S. money demand By (16-3), the long-run U.S. price level rises, and
under PPP the dollar must depreciate against the euro in proportion to this U.S. price
level increase. A rise in the interest rate on euro-denominated assets has the reverse
long-run exchange rate effect. Because real European money demand falls,
Europe’s price level rises, by (16-4). Under PPP, the dollar must appreciate against the
euro in proportion to Europe’s price level increase.
3. Output levels. A rise in U.S. output raises real U.S. money demand
leading by (16-3) to a fall in the long-run U.S. price level. According to PPP, there is
an appreciation of the dollar against the euro. Symmetrically, a rise in European output
raises and, by (16-4), causes a fall in Europe’s long-run price level.
PPP predicts that this development will make the dollar depreciate against the euro.
To understand these predictions, remember that the monetary approach, like any longrun
theory, essentially assumes that price levels adjust as quickly as exchange rates do—
that is, right away. For example, a rise in real U.S. output raises the transactions demand
for real U.S. money balances. According to the monetary approach, the U.S. price level
drops immediately to bring about a market-clearing increase in the supply of real balances.
L(R€, YE)
L(R$, YUS),
L(R€, YE)
R€
L(R$, YUS).
R$
E$/€ PUS
MUS
s
E$/€ E$/€ = PUS/PE,
PUS,
MUS
s
Ms L(R,Y)
2To simplify the notation, we assume identical money demand functions for the United States and Europe.
390 PART THREE Exchange Rates and Open-Economy Macroeconomics
PPP implies that this instantaneous American price deflation is accompanied by an instantaneous
dollar appreciation on the foreign exchanges.
The monetary approach leads to a result familiar from Chapter 15, that the long-run
foreign exchange value of a country’s currency moves in proportion to its money supply
(prediction 1). The theory also raises what seems to be a paradox (prediction 2). In our
previous examples, we always found that a currency appreciates when the interest rate it
offers rises relative to foreign interest rates. How is it that we have now arrived at precisely
the opposite conclusion—that a rise in a country’s interest rate depreciates its currency by
lowering the real demand for its money?
At the end of Chapter 14, we warned that no account of how a change in interest rates
affects the exchange rate is complete until we specify exactly why interest rates have
changed. This point explains the apparent contradiction in our findings about interest and
exchange rates. To resolve the puzzle, however, we must first examine more closely how
monetary policies and interest rates are connected in the long run.
Ongoing Inflation, Interest Parity, and PPP
In the last chapter we saw that a permanent increase in the level of a country’s money
supply ultimately results in a proportional rise in its price level but has no effect on the
long-run values of the interest rate or real output. While the conceptual experiment of a
one-time, stepwise money supply change is useful for thinking about the long-run effects
of money, it is not very realistic as a description of actual monetary policies. More often,
the monetary authorities choose a growth rate for the money supply, say, 5, 10, or 50 percent
per year, and then allow money to grow gradually, through incremental but frequent
increases. What are the long-run effects of a policy that allows the money supply to grow
smoothly forever at a positive rate?
The reasoning in Chapter 15 suggests that continuing money supply growth will
require a continuing rise in the price level—a situation of ongoing inflation. As firms and
workers catch on to the fact that the money supply is growing steadily at, say, a 10 percent
annual rate, they will adjust by raising prices and wages by the same 10 percent every
year, thus keeping their real incomes constant. Full-employment output depends on supplies
of productive factors, but it is safe to assume that factor supplies, and thus output, are
unaffected over the long run by different choices of a constant growth rate for the money
supply. Other things equal, money supply growth at a constant rate eventually results in
ongoing price level inflation at the same rate, but changes in this long-run inflation rate do
not affect the full-employment output level or the long-run relative prices of goods and
services.
The interest rate, however, is definitely not independent of the money supply growth
rate in the long run. While the long-run interest rate does not depend on the absolute level
of the money supply, continuing growth in the money supply eventually will affect the
interest rate. The easiest way to see how a permanent increase in inflation affects the longrun
interest rate is by combining PPP with the interest rate parity condition on which our
previous analysis of exchange rate determination was built.
As in the preceding two chapters, the condition of interest parity between dollar and
euro assets is
(recall equation (14-2), page 338). Now let’s ask how this parity condition, which must
hold in the long run as well as in the short run, fits with the other parity condition we
are assuming in our long-run model, purchasing power parity. According to relative PPP,
the percentage change in the dollar/euro exchange rate over the next year, say, will equal
R$ = R€ + (E$/€
e - E$/€)/E$/€
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 391
the difference between the inflation rates of the United States and Europe over that year
(see equation (16-2)). Since people understand this relationship, however, it must also be
true that they expect the percentage exchange rate change to equal the U.S.–Europe inflation
difference. The interest parity condition written above now tells us the following:
If people expect relative PPP to hold, the difference between the interest rates offered by
dollar and euro deposits will equal the difference between the inflation rates expected,
over the relevant horizon, in the United States and in Europe.
Some additional notation is helpful in deriving this result more formally. If is the
price level expected in a country for a year from today, the expected inflation rate in that
country, is the expected percentage increase in the price level over the coming year,
If relative PPP holds, however, market participants will also expect relative PPP to hold,
which means that we can replace the actual depreciation and inflation rates in equation
(16-2) with the values the market expects to materialize:
By combining this “expected” version of relative PPP with the interest parity condition
and rearranging, we arrive at a formula that expresses the international interest rate difference
as the difference between expected national inflation rates:
(16-5)
If, as PPP predicts, currency depreciation is expected to offset the international inflation
difference (so that the expected dollar depreciation rate is ), the interest rate
difference must equal the expected inflation difference.
The Fisher Effect
Equation (16-5) gives us the long-run relationship between ongoing inflation and interest
rates that we need to explain the monetary approach’s predictions about how interest rates
affect exchange rates. The equation tells us that all else equal, a rise in a country’s
expected inflation rate will eventually cause an equal rise in the interest rate that deposits
of its currency offer. Similarly, a fall in the expected inflation rate will eventually cause a
fall in the interest rate.
This long-run relationship between inflation and interest rates is called the Fisher effect.
The Fisher effect implies, for example, that if U.S. inflation were to rise permanently from a
constant level of 5 percent per year to a constant level of 10 percent per year, dollar interest
rates would eventually catch up with the higher inflation, rising by 5 percentage points per
year from their initial level. These changes would leave the real rate of return on dollar
assets, measured in terms of U.S. goods and services, unchanged. The Fisher effect is therefore
another example of the general idea that in the long run, purely monetary developments
should have no effect on an economy’s relative prices.3
pUS
e - pE e
R$ - R€ = pUS
e - pE e .
R$ = R€ + (E$/€
e - E$/€)/E$/€
(E$/€
e - E$/€)/E$/€ = pUS
e - pE e .
pe = (Pe - P)/P.
pe,
Pe
3 The effect is named after Irving Fisher of Yale University, one of the great American economists of the early
20th century. The effect is discussed at length in his book The Theory of Interest (New York: Macmillan, 1930).
Fisher, incidentally, gave an early account of the interest parity condition on which our theory of foreign
exchange market equilibrium is based.
392 PART THREE Exchange Rates and Open-Economy Macroeconomics
The Fisher effect is behind the seemingly paradoxical monetary approach prediction that a
currency depreciates in the foreign exchange market when its interest rate rises relative to foreign
currency interest rates. In the long-run equilibrium assumed by the monetary approach, a
rise in the difference between home and foreign interest rates occurs only when expected
home inflation rises relative to expected foreign inflation. This is certainly not the case in the
short run, when the domestic price level is sticky. In the short run, as we saw in Chapter 15,
the interest rate can rise when the domestic money supply falls, because the sticky domestic
price level leads to an excess demand for real money balances at the initial interest rate. Under
the flexible-price monetary approach, however, the price level would fall right away, leaving
the real money supply unchanged and thus making the interest rate change unnecessary.
We can better understand how interest rates and exchange rates interact under the monetary
approach by thinking through an example. Our example illustrates why the monetary
approach associates sustained interest rate hikes with current as well as future currency
depreciation, and sustained interest rate declines with appreciation.
Imagine that at time , the Federal Reserve unexpectedly increases the growth rate of
the U.S. money supply from to the higher level Figure 16-1 illustrates how
this change affects the dollar/euro exchange rate, as well as other U.S. variables, under
the assumptions of the monetary approach. To simplify the graphs, we assume that in
Europe, the inflation rate remains constant at zero.
Figure 16-1a shows the sudden acceleration of U.S. money supply growth at time
(We have scaled the vertical axes of the graphs so that constant slopes represent constant
proportional growth rates of variables.) The policy change generates expectations of more
rapid currency depreciation in the future: Under PPP the dollar will now depreciate at the
rate rather than at the lower rate Interest parity therefore requires the dollar
interest rate to rise, as shown in Figure 16-1b, from its initial level to a new level that
reflects the extra expected dollar depreciation, (see equation (16-5)).
Notice that this adjustment leaves the euro interest rate unchanged; but since Europe’s
money supply and output haven’t changed, the original euro interest rate will still maintain
equilibrium in Europe’s money market.
You can see from Figure 16-1a that the level of the money supply does not actually
jump upward at —only the future growth rate changes. Since there is no immediate
increase in the money supply, but there is an interest rate rise that reduces money demand,
there would be an excess supply of real U.S. money balances at the price level prevailing
just prior to In the face of this potential excess supply, the U.S. price level does jump
upward at (see Figure 16-1c), reducing the real money supply so that it again equals real
money demand (see equation (16-3)). Consistently with the upward jump in at ,
Figure 16-1d shows the simultaneous proportional upward jump in implied by PPP.
How can we visualize the reaction of the foreign exchange market at time ? The dollar
interest rate rises not because of a change in current levels of money supply or demand, but
solely because people expect more rapid future money supply growth and dollar depreciation.
As investors respond by moving into foreign deposits, which momentarily offer higher
expected returns, the dollar depreciates sharply in the foreign exchange market, moving to a
new trend line along which depreciation is more rapid than it was up to time 4
Notice how different assumptions about the speed of price level adjustment lead to contrasting
predictions about how exchange and interest rates interact. In the example of a fall
in the money supply under sticky prices, an interest rate rise is needed to preserve money
t0.
t0
E$/€
PUS t0
t0
t0.
t0
R$
2 = R$
1 + ¢p
R$
1
p + ¢p p.
t0.
E$/€,
p p + ¢p.
t0
4In the general case in which Europe’s inflation rate is not zero, the dollar, rather than depreciating against
the euro at rate before and at rate afterward, depreciates at rate until and at rate
p + ¢p - pE thereafter.
p t0 p + ¢p p - pE t0
pE
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 393
+ Δπ
R$
1
(a) (b)
(c) (d)
U.S. money
supply, MUS
U.S. price
level, PUS
Dollar interest
rate, R$
Dollar/euro
exchange rate, E$/€
MUS,t0
Time
Slope = π
Slope = π + Δπ
Time
Time t0
Time
t0
t0 t0
Slope = π
Slope = π
Slope = π + Δπ
Slope = π + Δπ
R$
2 R$
= 1
Figure 16-1
Long-Run Time Paths of U.S. Economic Variables After a Permanent Increase in the Growth Rate
of the U.S. Money Supply
After the money supply growth rate increases at time in panel (a), the interest rate (in panel (b)),
price level (in panel (c)), and exchange rate (in panel (d)) move to new long-run equilibrium paths.
(The money supply, price level, and exchange rate are all measured on a natural logarithmic scale,
which makes variables that change at constant proportional rates appear as straight lines when they
are graphed against time. The slope of the line equals the variable’s proportional growth rate.)
t0
market equilibrium, given that the price level cannot do so by dropping immediately in
response to the money supply reduction. In that sticky-price case, an interest rate rise is
associated with lower expected inflation and a long-run currency appreciation, so the
currency appreciates immediately. In our monetary approach example of a rise in money
supply growth, however, an interest rate increase is associated with higher expected inflation
and a currency that will be weaker on all future dates. An immediate currency
depreciation is the result.5
5 National money supplies typically trend upward over time, as in Figure 16-1a. Such trends lead to corresponding
upward trends in price levels; if two countries’ price level trends differ, PPP implies a trend in their
exchange rate as well. From now on, when we refer to a change in the money supply, price level, or exchange
rate, we will mean by this a change in the level of the variable relative to its previously expected trend path—that
is, a parallel shift in the trend path. When instead we want to consider changes in the slopes of trend paths themselves,
we will say so explicitly.
394 PART THREE Exchange Rates and Open-Economy Macroeconomics
6 Some of the negative evidence on absolute PPP is discussed in the Case Study to follow. Regarding the law of
one price, see, for example, Peter Isard, “How Far Can We Push the Law of One Price?” American Economic
Review 67 (December 1977), pp. 942–948; Irving B. Kravis and Robert E. Lipsey, “Price Behavior in the Light of
Balance of Payments Theories,” Journal of International Economics 8 (May 1978), pp. 193–246; and the paper by
Goldberg and Knetter in Further Readings.
7 The price level measures in Figure 16-2 are index numbers, not dollar amounts. For example, the U.S. consumer
price index (CPI) was 100 in the base year 2000 and only about 50 in 1980, so the dollar price of a reference
commodity basket of typical U.S. consumption purchases doubled between 1980 and 2000. Base years for the
U.S. and Japanese price indexes were chosen so that their 1980 ratio would equal the 1980 exchange rate, but this
imposed equality does not mean that absolute PPP held in 1980. Although Figure 16-2 uses CPIs, other price
indexes lead to similar pictures.
8 See, for example, the paper by Taylor and Taylor in this chapter’s Further Readings.
These contrasting results of interest rate changes underlie our earlier warning that an
explanation of exchange rates based on interest rates must carefully account for the factors
that cause interest rates to move. These factors can simultaneously affect expected future
exchange rates and can therefore have a decisive impact on the foreign exchange market’s
response to the interest rate change. The appendix to this chapter shows in detail how
expectations change in the case we analyzed.
No comments:
Post a Comment