Beyond Purchasing Power Parity:
A General Model of Long-Run Exchange Rates
Why devote so much discussion to the purchasing power parity theory when it is fraught
with exceptions and apparently contradicted by the data? We examined the implications of
PPP so closely because its basic idea of relating long-run exchange rates to long-run
national price levels is a very useful starting point. The monetary approach presented
above, which assumed PPP, is too simple to give accurate predictions about the real world,
but we can generalize it by taking account of some of the reasons why PPP predicts badly
in practice. In this section we do just that.
The long-run analysis below continues to ignore short-run complications caused by
sticky prices. An understanding of how exchange rates behave in the long run is, as mentioned
earlier, a prerequisite for the more complicated short-run analysis that we undertake
in the next chapter.
14See Kravis and Lipsey, Toward an Explanation of National Price Levels, Princeton Studies in International
Finance 52 (International Finance Section, Department of Economics, Princeton University,
November 1983); and Bhagwati, “Why Are Services Cheaper in the Poor Countries?” Economic Journal 94
(June 1984), pp. 279–286.
15This argument assumes that factor endowment differences between rich and poor countries are sufficiently great
that factor-price equalization cannot hold.
16You may wonder about the group of countries in Figure 16-3 that have higher per capita incomes than the U.S.
but significantly lower price levels. These are countries such as Saudi Arabia, where wealth is the result of
resource endowments rather than high manufacturing productivity or abundant capital. Excluding these countries
from the sample would make the regression line in Figure 16-3 steeper, at the same time improving its fit.
404 PART THREE Exchange Rates and Open-Economy Macroeconomics
17A similar presumption was made in our discussion of the transfer problem in Chapter 6. Nontradables are one
important factor behind the relative preference for home products.
The Real Exchange Rate
As the first step in extending the PPP theory, we define the concept of a real exchange
rate. The real exchange rate between two countries’ currencies is a broad summary measure
of the prices of one country’s goods and services relative to the other country’s. It is
natural to introduce the real exchange rate concept at this point because the major prediction
of PPP is that real exchange rates never change, at least not permanently. To extend
our model so that it describes the world more accurately, we need to examine systematically
the forces that can cause dramatic and permanent changes in real exchange rates.
As we will see, real exchange rates are important not only for quantifying deviations
from PPP but also for analyzing macroeconomic demand and supply conditions in open
economies. When we wish to differentiate a real exchange rate—which is the relative
price of two output baskets—from a relative price of two currencies, we will refer to the
latter as a nominal exchange rate. But when there is no risk of confusion, we will
continue to use the shorter term, exchange rate, to refer to nominal exchange rates.
Real exchange rates are defined in terms of nominal exchange rates and price levels.
Before we can give a more precise definition of real exchange rates, however, we need to
clarify the price level measure we will be using. Let , as usual, be the price level in the
United States, and the price level in Europe. Since we will not be assuming absolute
PPP (as we did in our discussion of the monetary approach), we no longer assume that the
price level can be measured by the same basket of commodities in the United States as in
Europe. Because we will soon want to link our analysis to monetary factors, we require
instead that each country’s price index give a good representation of the purchases that
motivate its residents to demand its money supply.
No measure of the price level does this perfectly, but we must settle on some definition
before we can formally define the real exchange rate. To be concrete, you can think of
as the dollar price of an unchanging basket containing the typical weekly purchases of
U.S. households and firms; , similarly, is based on an unchanging basket reflecting the
typical weekly purchases of European households and firms. The point to remember is that
the U.S. price level will place a relatively heavy weight on commodities produced and consumed
in America, and the European price level a relatively heavy weight on commodities
produced and consumed in Europe.17
Having described the reference commodity baskets used to measure price levels, we
can now formally define the real dollar/euro exchange rate, denoted as the dollar
price of the European basket relative to that of the American basket. We can express the
real exchange rate as the dollar value of Europe’s price level divided by the U.S. price
level or, in symbols, as
(16-6)
A numerical example will clarify the concept of the real exchange rate. Imagine that the
European reference commodity basket costs 100 (so that basket),
that the U.S. basket costs (so that ), and that the nominal
exchange rate is The real dollar/euro exchange rate would then be
= 1 U.S. basket per European basket.
= 1$120 per European basket2/1$120 per U.S. basket2
q$/€ =
1$1.20 per euro2 * 1€100 per European basket2
1$120 per U.S. basket2
E$/€ = $1.20 per euro.
$120 PUS = $120 per U.S. basket
€ PE = €100 per European
q$/€ = (E$/€ * PE)/PUS.
q$/:,
PE
PUS
PE
PUS
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 405
A rise in the real dollar/euro exchange rate (which we call a real depreciation of
the dollar against the euro) can be thought of in several equivalent ways. Most obviously,
(16-6) shows this change to be a fall in the purchasing power of a dollar within Europe’s
borders relative to its purchasing power within the United States. This change in relative
purchasing power occurs because the dollar prices of European goods rise
relative to those of U.S. goods .
In terms of our numerical example, a 10 percent nominal dollar depreciation, to
causes to rise to 1.1 U.S. baskets per European basket, a real
dollar depreciation of 10 percent against the euro. (The same change in could result
from a 10 percent rise in or a 10 percent fall in .) The real depreciation means that
the dollar’s purchasing power over European goods and services falls by 10 percent relative
to its purchasing power over U.S. goods and services.
Alternatively, even though many of the items entering national price levels are nontraded,
it is useful to think of the real exchange rate as the relative price of European products in
general in terms of American products, that is, the price at which hypothetical trades of
American for European commodity baskets would occur if trades at domestic prices were
possible. The dollar is considered to depreciate in real terms against the euro when rises
because the hypothetical purchasing power of America’s products in general over Europe’s
declines. America’s goods and services thus become cheaper relative to Europe’s.
A real appreciation of the dollar against the euro is a fall in . This fall indicates a
decrease in the relative price of products purchased in Europe, or a rise in the dollar’s
European purchasing power compared with that in the United States.18
Our convention for describing real depreciations and appreciations of the dollar against
the euro is the same one we use for nominal exchange rates (that is, up is a dollar
depreciation, down is an appreciation). Equation (16-6) shows that at unchanged output
prices, nominal depreciation (appreciation) implies real depreciation (appreciation). Our discussion
of real exchange rate changes thus includes, as a special case, an observation we
made in Chapter 14: With the domestic money prices of goods held constant, a nominal
dollar depreciation makes U.S. goods cheaper compared with foreign goods, while a nominal
dollar appreciation makes them more expensive.
Equation (16-6) makes it easy to see why the real exchange rate can never change when
relative PPP holds. Under relative PPP, a 10 percent rise in , for instance, would always
be exactly offset by a 10 percent fall in the price level ratio , leaving unchanged.
Demand, Supply, and the Long-Run Real Exchange Rate
It should come as no surprise that in a world where PPP does not hold, the long-run values
of real exchange rates, just like other relative prices that clear markets, depend on demand
and supply conditions. Since a real exchange rate tracks changes in the relative price of
two countries’ expenditure baskets, however, conditions in both countries matter. Changes
in countries’ output markets can be complex, and we do not want to digress into an
exhaustive (and exhausting) catalogue of the possibilities. We focus instead on two specific
cases that are both easy to grasp and important in practice for explaining why the
long-run values of real exchange rates can change.
1. A change in world relative demand for American products. Imagine that total world
spending on American goods and services rises relative to total world spending on
q$/€ PE/PUS
E$/€
E$/€
E$/€
q$/€
q$/€
q$/€
PE PUS
q$/€
q$/€ E$/€ = $1.32 per euro,
(PUS)
(E$/€ * PE)
q$/€,
18This is true because implying that a real depreciation of the dollar against the euro is the same
as a real appreciation of the euro against the dollar (that is, a rise in the purchasing power of the euro within the
United States relative to its purchasing power within Europe, or a fall in the relative price of American products
in terms of European products).
E€/$ = 1/E$/€,
406 PART THREE Exchange Rates and Open-Economy Macroeconomics
Sticky nominal prices and wages are central to macroeconomic
theories, but just why might it be difficult
for money prices to change from day to day as market
conditions change? One reason is based on the idea of
“menu costs.” Menu costs could arise from several
factors, such as the actual costs of printing new price
lists and catalogs. In addition, firms may perceive a
different type of menu cost due to their customers’
imperfect information about competitors’ prices.
When a firm raises its price, some customers will shop
around elsewhere and find it convenient to remain
with a competing seller even if all sellers have raised
their prices. In the presence of these various types of
menu costs, sellers will often hold prices constant
after a change in market conditions until they are certain
the change is permanent enough to make incurring
the costs of price changes worthwhile.*
If there were truly no barriers between two markets
with goods priced in different currencies, sticky
prices would be unable to survive in the face of an
exchange rate change. All buyers would simply
flock to the market where a good had become
cheapest. But when some trade impediments exist,
deviations from the law of one price do not induce
unlimited arbitrage, so it is feasible for sellers to
hold prices constant despite exchange rate changes.
In the real world, trade barriers appear to be significant,
widespread, and often subtle in nature.
Apparently, arbitrage between two markets may
be limited even when the physical distance between
them is zero, as a surprising study of pricing behavior
in Scandinavian duty-free outlets shows.
Swedish economists Marcus Asplund and Richard
Friberg studied pricing behavior in the duty-free
stores of two Scandinavian ferry lines whose catalogs
quote the prices of each good in several currencies
for the convenience of customers from different
countries.† Since it is costly to print the catalogs,
they are reissued with revised prices only from time
to time. In the interim, however, fluctuations in
exchange rates induce multiple, changing prices for
the same good. For example, on the Birka Line of
Sticky Prices and the Law of One Price: Evidence from Scandinavian
Duty-Free Shops
*It is when economic conditions are very volatile that prices seem to become most flexible. For example, restaurant menus
will typically price their catch of the day at “market” so that the price charged (and the fish offered) can reflect the high
variability in fishing outcomes.
†“The Law of One Price in Scandinavian Duty-Free Stores,” American Economic Review 91 (September 2001), pp. 1072–1083.
European goods and services. Such a change could arise from several sources—for example,
a shift in private U.S. demand away from European goods and toward American goods; a
similar shift in private foreign demand toward American goods; or an increase in U.S.
government demand falling primarily on U.S. output. Any increase in relative world
demand for U.S. products causes an excess demand for them at the previous real
exchange rate. To restore equilibrium, the relative price of American output in terms of
European output will therefore have to rise: The relative prices of U.S. nontradables will
rise, and the prices of tradables produced in the United States, and consumed intensively
there, will rise relative to the prices of tradables made in Europe. These changes all work
to reduce , the relative price of Europe’s reference expenditure basket in terms of the
United States’. We conclude that an increase in world relative demand for U.S. output
causes a long-run real appreciation of the dollar against the euro (a fall in ).
Similarly, a decrease in world relative demand for U.S. output causes a long-run real
depreciation of the dollar against the euro (a rise in ).
2. A change in relative output supply. Suppose that the productive efficiency of U.S.
labor and capital rises. Since Americans spend part of their increased income on foreign
goods, the supplies of all types of U.S. goods and services increase relative to the
demand for them, the result being an excess relative supply of American output at the
q$/€
q$/€
q$/€
19Our discussion of the Balassa-Samuelson effect in the Case Study on pages 401–403 would lead you to expect
that a productivity increase concentrated in the U.S. tradables sector might cause the dollar to appreciate, rather
than depreciate, in real terms against the euro. In the last paragraph, however, we have in mind a balanced productivity
increase that benefits the traded and nontraded sectors in equal proportion, thus resulting in a real dollar
depreciation by causing a drop in the prices of nontraded goods and in those of traded goods that are more
important in America’s consumer price index than in Europe’s.
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 407
previous real exchange rate. A fall in the relative price of American products—both nontradables
and tradables—shifts demand toward them and eliminates the excess supply.
This price change is a real depreciation of the dollar against the euro, that is, an increase
in . A relative expansion of U.S. output causes a long-run real depreciation of the
dollar against the euro ( rises). A relative expansion of European output causes a
long-run real appreciation of the dollar against the euro ( falls).19
A useful diagram summarizes our discussion of demand, supply, and the long-run real
exchange rate. In Figure 16-4, the supply of U.S. output relative to European output,
, is plotted along the horizontal axis while the real dollar/euro exchange rate, , is
plotted along the vertical axis.
The equilibrium real exchange rate is determined by the intersection of two schedules.
The upward-sloping schedule RD shows that the relative demand for U.S. products in general,
relative to the demand for European products, rises as rises, that is, as American
products become relatively cheaper. This “demand” curve for U.S. relative to European
goods has a positive slope because we are measuring a fall in the relative price of U.S.
goods by a move upward along the vertical axis. What about relative supply? In the long
run, relative national output levels are determined by factor supplies and productivity, with
q$/€
q$/€ YUS/YE
q$/€
q$/€
q$/€
ferries between Sweden and Finland, prices were
listed in both Finnish markka and Swedish kronor
between 1975 and 1998, implying that a relative
depreciation of the markka would make it cheaper
to buy cigarettes or vodka by paying markka rather
than kronor.
Despite such price discrepancies, Birka Line
was always able to do business in both currencies—
passengers did not rush to buy at the lowest price.
Swedish passengers, who held relatively large
quantities of their own national currency, tended to
buy at the kronor prices, whereas Finnish customers
tended to buy at the markka prices.
Often, Birka Line would take advantage of
publishing a new catalog to reduce deviations
from the law of one price. The average deviation
from the law of one price in the month just before
such a price adjustment was 7.21 percent, but only
2.22 percent in the month of the price adjustment.
One big impediment to taking advantage of the
arbitrage opportunities was the cost of changing
currencies at the onboard foreign exchange
booth—roughly 7.5 percent. That transaction cost,
given different passengers’ currency preferences
at the time of embarkation, acted as an effective
trade barrier.‡
Surprisingly, Birka Line did not completely eliminate
law of one price deviations when it changed
catalog prices. Instead, Birka Line practiced a kind
of pricing to market on its ferries. Usually, exporters
who price to market discriminate among
different consumers based on their different locations,
but Birka was able to discriminate based on
different nationality and currency preferences, even
with all potential consumers located on the same
ferry boat.
‡Customers could pay in the currency of their choice not only with cash, but also with credit cards, which involve lower foreign
exchange conversion fees but convert at an exchange rate prevailing a few days after the purchase of the goods. Asplund and
Friberg suggest that for such small purchases, uncertainty and the costs of calculating relative prices (in addition to the creditcard
exchange fees) might have been a sufficient deterrent to transacting in a relatively unfamiliar currency.
408 PART THREE Exchange Rates and Open-Economy Macroeconomics
Real exchange
rate, q$/€
q$/€
Ratio of U.S. to
European real
output (YUS/YE)
1
(YUS/YE)1
RS RD
1
Figure 16-4
Determination of the
Long-Run Real Exchange
Rate
The long-run equilibrium
real exchange rate equates
world relative demand to
the full-employment level
of relative supply.
20Notice that these RD and RS schedules differ from the ones used in Chapter 6. The earlier ones referred to relative
world demand for and supply of two products that could be produced in either of two countries. In contrast,
the RD and RS curves in this chapter refer to the relative world demand for and supply of one country’s overall
output (its GDP) relative to another’s.
little, if any, effect on the real exchange rate. The relative supply curve, RS, therefore is
vertical at the long-run (that is, full-employment) relative output ratio, . The equilibrium
long-run real exchange rate is the one that sets relative demand equal to long-run
relative supply (point 1).20
The diagram easily illustrates how changes in world markets affect the real exchange
rate. Suppose world gasoline prices fall, making American sport-utility vehicles more
desirable for people everywhere. This change would be a rise in world relative demand for
American goods and would shift RD to the right, causing to fall (a real dollar appreciation
against the euro). Suppose the United States improves its health-care system, reducing
illness throughout the American work force. If workers are able to produce more
goods and services in an hour as a result, the rise in U.S. productivity shifts RS to the right,
causing to rise (a real dollar depreciation against the euro).
Nominal and Real Exchange Rates in Long-Run Equilibrium
We now pull together what we have learned in this chapter and the last one to show how
long-run nominal exchange rates are determined. One central conclusion is that changes in
national money supplies and demands give rise to the proportional long-run movements
in nominal exchange rates and international price level ratios predicted by the relative
purchasing power parity theory. Demand and supply shifts in national output markets,
however, cause nominal exchange rate movements that do not conform to PPP.
q$/€
q$/€
(YUS/YE)1
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 409
Recall our definition of the real dollar/euro exchange rate as
(See equation (16-6).) If we now solve this equation for the nominal exchange rate, we get
an equation that gives us the nominal dollar/euro exchange rate as the real dollar/euro
exchange rate times the U.S.–Europe price level ratio:
(16-7)
Formally speaking, the only difference between (16-7) and equation (16-1), on which we
based our exposition of the monetary approach to the exchange rate, is that (16-7)
accounts for possible deviations from PPP by adding the real exchange rate as an additional
determinant of the nominal exchange rate. The equation implies that for a given real
dollar/euro exchange rate, changes in money demand or supply in Europe or the United
States affect the long-run nominal dollar/euro exchange rate as in the monetary approach.
Changes in the long-run real exchange rate, however, also affect the long-run nominal
exchange rate. The long-run theory of exchange rate determination implied by equation
(16-7) thus includes the valid elements of the monetary approach, but in addition it corrects
the monetary approach by allowing for nonmonetary factors that can cause sustained
deviations from purchasing power parity.
Assuming that all variables start out at their long-run levels, we can now understand the
most important determinants of long-run swings in nominal exchange rates:
1. A shift in relative money supply levels. Suppose the Fed wishes to stimulate the
economy and therefore carries out an increase in the level of the U.S. money supply.
As you will remember from Chapter 15, a permanent, one-time increase in a country’s
money supply has no effect on the long-run levels of output, the interest rate, or any
relative price (including the real exchange rate). Thus, (16-3) implies once again that
rises in proportion to , while (16-7) shows that the U.S. price level is the sole
variable changing in the long run along with the nominal exchange rate . Because
the real exchange rate does not change, the nominal exchange rate change is consistent
with relative PPP: The only long-run effect of the U.S. money supply increase
is to raise all dollar prices, including the dollar price of the euro, in proportion to the
increase in the money supply. It should be no surprise that this result is the same as the
one we found using the monetary approach, since that approach is designed to account
for the long-run effects of monetary changes.
2. A shift in relative money supply growth rates. Suppose the Fed concludes, to its
dismay, that over the next few years the U.S. price level will fall. (A falling price level is
called deflation.) A permanent increase in the growth rate of the U.S. money supply
raises the long-run U.S. inflation rate and, through the Fisher effect, raises the dollar
interest rate relative to the euro interest rate. Because relative U.S. real money demand
therefore declines, equation (16-3) implies that rises (as shown in Figure 16-1).
Because the change bringing this outcome about is purely monetary, however, it is neutral
in its long-run effects; specifically, it does not alter the long-run real dollar/euro
exchange rate. According to (16-7), then, rises in proportion to the increase in
(a depreciation of the dollar against the euro). Once again, a purely monetary change
brings about a long-run nominal exchange rate shift in line with relative PPP, just as the
monetary approach predicted.
3. A change in relative output demand. This type of change is not covered by the
monetary approach, so now the more general perspective we’ve developed, in which the
real exchange rate can change, is essential. Since a change in relative output demand
E$/€ PUS
PUS
q$/€
E$/€
PUS MUS
E$/€ = q$/€ * (PUS/PE).
q$/€ = (E$/€ * PE)/PUS.
410 PART THREE Exchange Rates and Open-Economy Macroeconomics
does not affect long-run national price levels—these depend solely on the factors appearing
in equations (16-3) and (16-4)—the long-run nominal exchange rate in (16-7) will
change only insofar as the real exchange rate changes. Consider an increase in world
relative demand for U.S. products. Earlier in this section, we saw that a rise in demand
for U.S. products causes a long-run real appreciation of the dollar against the euro (a fall
in ); this change is simply a rise in the relative price of U.S. output. Given that longrun
national price levels are unchanged, however, (16-7) tells us that a long-run nominal
appreciation of the dollar against the euro (a fall in ) must also occur. This prediction
highlights the important fact that even though exchange rates are nominal prices, they
respond to nonmonetary as well as monetary events, even over long horizons.
4. A change in relative output supply. As we saw earlier in this section, an increase
in relative U.S. output supply causes the dollar to depreciate in real terms against
the euro, lowering the relative price of U.S. output. This rise in is not, however,
the only change in equation (16-7) implied by a relative rise in U.S. output. In addition,
the U.S. output increase raises the transaction demand for real U.S. money balances,
raising aggregate U.S. real money demand and, by (16-3), pushing the long-run
U.S. price level down. Referring back to equation (16-7), you will see that since
rises while falls, the output and money market effects of a change in output supply
work in opposite directions, thus making the net effect on is ambiguous. Our
analysis of an output-supply change illustrates that even when a disturbance originates
in a single market (in this case, the output market), its influence on exchange rates may
depend on repercussion effects that are channeled through other markets.
We conclude that when all disturbances are monetary in nature, exchange rates obey
relative PPP in the long run. In the long run, a monetary disturbance affects only the general
purchasing power of a currency, and this change in purchasing power changes
equally the currency’s value in terms of domestic and foreign goods. When disturbances
occur in output markets, the exchange rate is unlikely to obey relative PPP, even in the
long run. Table 16-1 summarizes these conclusions regarding the effects of monetary and
output market changes on long-run nominal exchange rates.
In the chapters that follow, we will appeal to this section’s general long-run exchange
rate model even when we are discussing short-run macroeconomic events. Long-run
factors are important in the short run because of the central role that expectations about the
future play in the day-to-day determination of exchange rates. That is why news about the
current account, for example, can have a big impact on the exchange rate. The long-run
exchange rate model of this section will provide the anchor for market expectations, that is,
the framework market participants use to forecast future exchange rates on the basis of
information at hand today.
A General Model of Long-Run Exchange Rates
Why devote so much discussion to the purchasing power parity theory when it is fraught
with exceptions and apparently contradicted by the data? We examined the implications of
PPP so closely because its basic idea of relating long-run exchange rates to long-run
national price levels is a very useful starting point. The monetary approach presented
above, which assumed PPP, is too simple to give accurate predictions about the real world,
but we can generalize it by taking account of some of the reasons why PPP predicts badly
in practice. In this section we do just that.
The long-run analysis below continues to ignore short-run complications caused by
sticky prices. An understanding of how exchange rates behave in the long run is, as mentioned
earlier, a prerequisite for the more complicated short-run analysis that we undertake
in the next chapter.
14See Kravis and Lipsey, Toward an Explanation of National Price Levels, Princeton Studies in International
Finance 52 (International Finance Section, Department of Economics, Princeton University,
November 1983); and Bhagwati, “Why Are Services Cheaper in the Poor Countries?” Economic Journal 94
(June 1984), pp. 279–286.
15This argument assumes that factor endowment differences between rich and poor countries are sufficiently great
that factor-price equalization cannot hold.
16You may wonder about the group of countries in Figure 16-3 that have higher per capita incomes than the U.S.
but significantly lower price levels. These are countries such as Saudi Arabia, where wealth is the result of
resource endowments rather than high manufacturing productivity or abundant capital. Excluding these countries
from the sample would make the regression line in Figure 16-3 steeper, at the same time improving its fit.
404 PART THREE Exchange Rates and Open-Economy Macroeconomics
17A similar presumption was made in our discussion of the transfer problem in Chapter 6. Nontradables are one
important factor behind the relative preference for home products.
The Real Exchange Rate
As the first step in extending the PPP theory, we define the concept of a real exchange
rate. The real exchange rate between two countries’ currencies is a broad summary measure
of the prices of one country’s goods and services relative to the other country’s. It is
natural to introduce the real exchange rate concept at this point because the major prediction
of PPP is that real exchange rates never change, at least not permanently. To extend
our model so that it describes the world more accurately, we need to examine systematically
the forces that can cause dramatic and permanent changes in real exchange rates.
As we will see, real exchange rates are important not only for quantifying deviations
from PPP but also for analyzing macroeconomic demand and supply conditions in open
economies. When we wish to differentiate a real exchange rate—which is the relative
price of two output baskets—from a relative price of two currencies, we will refer to the
latter as a nominal exchange rate. But when there is no risk of confusion, we will
continue to use the shorter term, exchange rate, to refer to nominal exchange rates.
Real exchange rates are defined in terms of nominal exchange rates and price levels.
Before we can give a more precise definition of real exchange rates, however, we need to
clarify the price level measure we will be using. Let , as usual, be the price level in the
United States, and the price level in Europe. Since we will not be assuming absolute
PPP (as we did in our discussion of the monetary approach), we no longer assume that the
price level can be measured by the same basket of commodities in the United States as in
Europe. Because we will soon want to link our analysis to monetary factors, we require
instead that each country’s price index give a good representation of the purchases that
motivate its residents to demand its money supply.
No measure of the price level does this perfectly, but we must settle on some definition
before we can formally define the real exchange rate. To be concrete, you can think of
as the dollar price of an unchanging basket containing the typical weekly purchases of
U.S. households and firms; , similarly, is based on an unchanging basket reflecting the
typical weekly purchases of European households and firms. The point to remember is that
the U.S. price level will place a relatively heavy weight on commodities produced and consumed
in America, and the European price level a relatively heavy weight on commodities
produced and consumed in Europe.17
Having described the reference commodity baskets used to measure price levels, we
can now formally define the real dollar/euro exchange rate, denoted as the dollar
price of the European basket relative to that of the American basket. We can express the
real exchange rate as the dollar value of Europe’s price level divided by the U.S. price
level or, in symbols, as
(16-6)
A numerical example will clarify the concept of the real exchange rate. Imagine that the
European reference commodity basket costs 100 (so that basket),
that the U.S. basket costs (so that ), and that the nominal
exchange rate is The real dollar/euro exchange rate would then be
= 1 U.S. basket per European basket.
= 1$120 per European basket2/1$120 per U.S. basket2
q$/€ =
1$1.20 per euro2 * 1€100 per European basket2
1$120 per U.S. basket2
E$/€ = $1.20 per euro.
$120 PUS = $120 per U.S. basket
€ PE = €100 per European
q$/€ = (E$/€ * PE)/PUS.
q$/:,
PE
PUS
PE
PUS
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 405
A rise in the real dollar/euro exchange rate (which we call a real depreciation of
the dollar against the euro) can be thought of in several equivalent ways. Most obviously,
(16-6) shows this change to be a fall in the purchasing power of a dollar within Europe’s
borders relative to its purchasing power within the United States. This change in relative
purchasing power occurs because the dollar prices of European goods rise
relative to those of U.S. goods .
In terms of our numerical example, a 10 percent nominal dollar depreciation, to
causes to rise to 1.1 U.S. baskets per European basket, a real
dollar depreciation of 10 percent against the euro. (The same change in could result
from a 10 percent rise in or a 10 percent fall in .) The real depreciation means that
the dollar’s purchasing power over European goods and services falls by 10 percent relative
to its purchasing power over U.S. goods and services.
Alternatively, even though many of the items entering national price levels are nontraded,
it is useful to think of the real exchange rate as the relative price of European products in
general in terms of American products, that is, the price at which hypothetical trades of
American for European commodity baskets would occur if trades at domestic prices were
possible. The dollar is considered to depreciate in real terms against the euro when rises
because the hypothetical purchasing power of America’s products in general over Europe’s
declines. America’s goods and services thus become cheaper relative to Europe’s.
A real appreciation of the dollar against the euro is a fall in . This fall indicates a
decrease in the relative price of products purchased in Europe, or a rise in the dollar’s
European purchasing power compared with that in the United States.18
Our convention for describing real depreciations and appreciations of the dollar against
the euro is the same one we use for nominal exchange rates (that is, up is a dollar
depreciation, down is an appreciation). Equation (16-6) shows that at unchanged output
prices, nominal depreciation (appreciation) implies real depreciation (appreciation). Our discussion
of real exchange rate changes thus includes, as a special case, an observation we
made in Chapter 14: With the domestic money prices of goods held constant, a nominal
dollar depreciation makes U.S. goods cheaper compared with foreign goods, while a nominal
dollar appreciation makes them more expensive.
Equation (16-6) makes it easy to see why the real exchange rate can never change when
relative PPP holds. Under relative PPP, a 10 percent rise in , for instance, would always
be exactly offset by a 10 percent fall in the price level ratio , leaving unchanged.
Demand, Supply, and the Long-Run Real Exchange Rate
It should come as no surprise that in a world where PPP does not hold, the long-run values
of real exchange rates, just like other relative prices that clear markets, depend on demand
and supply conditions. Since a real exchange rate tracks changes in the relative price of
two countries’ expenditure baskets, however, conditions in both countries matter. Changes
in countries’ output markets can be complex, and we do not want to digress into an
exhaustive (and exhausting) catalogue of the possibilities. We focus instead on two specific
cases that are both easy to grasp and important in practice for explaining why the
long-run values of real exchange rates can change.
1. A change in world relative demand for American products. Imagine that total world
spending on American goods and services rises relative to total world spending on
q$/€ PE/PUS
E$/€
E$/€
E$/€
q$/€
q$/€
q$/€
PE PUS
q$/€
q$/€ E$/€ = $1.32 per euro,
(PUS)
(E$/€ * PE)
q$/€,
18This is true because implying that a real depreciation of the dollar against the euro is the same
as a real appreciation of the euro against the dollar (that is, a rise in the purchasing power of the euro within the
United States relative to its purchasing power within Europe, or a fall in the relative price of American products
in terms of European products).
E€/$ = 1/E$/€,
406 PART THREE Exchange Rates and Open-Economy Macroeconomics
Sticky nominal prices and wages are central to macroeconomic
theories, but just why might it be difficult
for money prices to change from day to day as market
conditions change? One reason is based on the idea of
“menu costs.” Menu costs could arise from several
factors, such as the actual costs of printing new price
lists and catalogs. In addition, firms may perceive a
different type of menu cost due to their customers’
imperfect information about competitors’ prices.
When a firm raises its price, some customers will shop
around elsewhere and find it convenient to remain
with a competing seller even if all sellers have raised
their prices. In the presence of these various types of
menu costs, sellers will often hold prices constant
after a change in market conditions until they are certain
the change is permanent enough to make incurring
the costs of price changes worthwhile.*
If there were truly no barriers between two markets
with goods priced in different currencies, sticky
prices would be unable to survive in the face of an
exchange rate change. All buyers would simply
flock to the market where a good had become
cheapest. But when some trade impediments exist,
deviations from the law of one price do not induce
unlimited arbitrage, so it is feasible for sellers to
hold prices constant despite exchange rate changes.
In the real world, trade barriers appear to be significant,
widespread, and often subtle in nature.
Apparently, arbitrage between two markets may
be limited even when the physical distance between
them is zero, as a surprising study of pricing behavior
in Scandinavian duty-free outlets shows.
Swedish economists Marcus Asplund and Richard
Friberg studied pricing behavior in the duty-free
stores of two Scandinavian ferry lines whose catalogs
quote the prices of each good in several currencies
for the convenience of customers from different
countries.† Since it is costly to print the catalogs,
they are reissued with revised prices only from time
to time. In the interim, however, fluctuations in
exchange rates induce multiple, changing prices for
the same good. For example, on the Birka Line of
Sticky Prices and the Law of One Price: Evidence from Scandinavian
Duty-Free Shops
*It is when economic conditions are very volatile that prices seem to become most flexible. For example, restaurant menus
will typically price their catch of the day at “market” so that the price charged (and the fish offered) can reflect the high
variability in fishing outcomes.
†“The Law of One Price in Scandinavian Duty-Free Stores,” American Economic Review 91 (September 2001), pp. 1072–1083.
European goods and services. Such a change could arise from several sources—for example,
a shift in private U.S. demand away from European goods and toward American goods; a
similar shift in private foreign demand toward American goods; or an increase in U.S.
government demand falling primarily on U.S. output. Any increase in relative world
demand for U.S. products causes an excess demand for them at the previous real
exchange rate. To restore equilibrium, the relative price of American output in terms of
European output will therefore have to rise: The relative prices of U.S. nontradables will
rise, and the prices of tradables produced in the United States, and consumed intensively
there, will rise relative to the prices of tradables made in Europe. These changes all work
to reduce , the relative price of Europe’s reference expenditure basket in terms of the
United States’. We conclude that an increase in world relative demand for U.S. output
causes a long-run real appreciation of the dollar against the euro (a fall in ).
Similarly, a decrease in world relative demand for U.S. output causes a long-run real
depreciation of the dollar against the euro (a rise in ).
2. A change in relative output supply. Suppose that the productive efficiency of U.S.
labor and capital rises. Since Americans spend part of their increased income on foreign
goods, the supplies of all types of U.S. goods and services increase relative to the
demand for them, the result being an excess relative supply of American output at the
q$/€
q$/€
q$/€
19Our discussion of the Balassa-Samuelson effect in the Case Study on pages 401–403 would lead you to expect
that a productivity increase concentrated in the U.S. tradables sector might cause the dollar to appreciate, rather
than depreciate, in real terms against the euro. In the last paragraph, however, we have in mind a balanced productivity
increase that benefits the traded and nontraded sectors in equal proportion, thus resulting in a real dollar
depreciation by causing a drop in the prices of nontraded goods and in those of traded goods that are more
important in America’s consumer price index than in Europe’s.
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 407
previous real exchange rate. A fall in the relative price of American products—both nontradables
and tradables—shifts demand toward them and eliminates the excess supply.
This price change is a real depreciation of the dollar against the euro, that is, an increase
in . A relative expansion of U.S. output causes a long-run real depreciation of the
dollar against the euro ( rises). A relative expansion of European output causes a
long-run real appreciation of the dollar against the euro ( falls).19
A useful diagram summarizes our discussion of demand, supply, and the long-run real
exchange rate. In Figure 16-4, the supply of U.S. output relative to European output,
, is plotted along the horizontal axis while the real dollar/euro exchange rate, , is
plotted along the vertical axis.
The equilibrium real exchange rate is determined by the intersection of two schedules.
The upward-sloping schedule RD shows that the relative demand for U.S. products in general,
relative to the demand for European products, rises as rises, that is, as American
products become relatively cheaper. This “demand” curve for U.S. relative to European
goods has a positive slope because we are measuring a fall in the relative price of U.S.
goods by a move upward along the vertical axis. What about relative supply? In the long
run, relative national output levels are determined by factor supplies and productivity, with
q$/€
q$/€ YUS/YE
q$/€
q$/€
q$/€
ferries between Sweden and Finland, prices were
listed in both Finnish markka and Swedish kronor
between 1975 and 1998, implying that a relative
depreciation of the markka would make it cheaper
to buy cigarettes or vodka by paying markka rather
than kronor.
Despite such price discrepancies, Birka Line
was always able to do business in both currencies—
passengers did not rush to buy at the lowest price.
Swedish passengers, who held relatively large
quantities of their own national currency, tended to
buy at the kronor prices, whereas Finnish customers
tended to buy at the markka prices.
Often, Birka Line would take advantage of
publishing a new catalog to reduce deviations
from the law of one price. The average deviation
from the law of one price in the month just before
such a price adjustment was 7.21 percent, but only
2.22 percent in the month of the price adjustment.
One big impediment to taking advantage of the
arbitrage opportunities was the cost of changing
currencies at the onboard foreign exchange
booth—roughly 7.5 percent. That transaction cost,
given different passengers’ currency preferences
at the time of embarkation, acted as an effective
trade barrier.‡
Surprisingly, Birka Line did not completely eliminate
law of one price deviations when it changed
catalog prices. Instead, Birka Line practiced a kind
of pricing to market on its ferries. Usually, exporters
who price to market discriminate among
different consumers based on their different locations,
but Birka was able to discriminate based on
different nationality and currency preferences, even
with all potential consumers located on the same
ferry boat.
‡Customers could pay in the currency of their choice not only with cash, but also with credit cards, which involve lower foreign
exchange conversion fees but convert at an exchange rate prevailing a few days after the purchase of the goods. Asplund and
Friberg suggest that for such small purchases, uncertainty and the costs of calculating relative prices (in addition to the creditcard
exchange fees) might have been a sufficient deterrent to transacting in a relatively unfamiliar currency.
408 PART THREE Exchange Rates and Open-Economy Macroeconomics
Real exchange
rate, q$/€
q$/€
Ratio of U.S. to
European real
output (YUS/YE)
1
(YUS/YE)1
RS RD
1
Figure 16-4
Determination of the
Long-Run Real Exchange
Rate
The long-run equilibrium
real exchange rate equates
world relative demand to
the full-employment level
of relative supply.
20Notice that these RD and RS schedules differ from the ones used in Chapter 6. The earlier ones referred to relative
world demand for and supply of two products that could be produced in either of two countries. In contrast,
the RD and RS curves in this chapter refer to the relative world demand for and supply of one country’s overall
output (its GDP) relative to another’s.
little, if any, effect on the real exchange rate. The relative supply curve, RS, therefore is
vertical at the long-run (that is, full-employment) relative output ratio, . The equilibrium
long-run real exchange rate is the one that sets relative demand equal to long-run
relative supply (point 1).20
The diagram easily illustrates how changes in world markets affect the real exchange
rate. Suppose world gasoline prices fall, making American sport-utility vehicles more
desirable for people everywhere. This change would be a rise in world relative demand for
American goods and would shift RD to the right, causing to fall (a real dollar appreciation
against the euro). Suppose the United States improves its health-care system, reducing
illness throughout the American work force. If workers are able to produce more
goods and services in an hour as a result, the rise in U.S. productivity shifts RS to the right,
causing to rise (a real dollar depreciation against the euro).
Nominal and Real Exchange Rates in Long-Run Equilibrium
We now pull together what we have learned in this chapter and the last one to show how
long-run nominal exchange rates are determined. One central conclusion is that changes in
national money supplies and demands give rise to the proportional long-run movements
in nominal exchange rates and international price level ratios predicted by the relative
purchasing power parity theory. Demand and supply shifts in national output markets,
however, cause nominal exchange rate movements that do not conform to PPP.
q$/€
q$/€
(YUS/YE)1
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 409
Recall our definition of the real dollar/euro exchange rate as
(See equation (16-6).) If we now solve this equation for the nominal exchange rate, we get
an equation that gives us the nominal dollar/euro exchange rate as the real dollar/euro
exchange rate times the U.S.–Europe price level ratio:
(16-7)
Formally speaking, the only difference between (16-7) and equation (16-1), on which we
based our exposition of the monetary approach to the exchange rate, is that (16-7)
accounts for possible deviations from PPP by adding the real exchange rate as an additional
determinant of the nominal exchange rate. The equation implies that for a given real
dollar/euro exchange rate, changes in money demand or supply in Europe or the United
States affect the long-run nominal dollar/euro exchange rate as in the monetary approach.
Changes in the long-run real exchange rate, however, also affect the long-run nominal
exchange rate. The long-run theory of exchange rate determination implied by equation
(16-7) thus includes the valid elements of the monetary approach, but in addition it corrects
the monetary approach by allowing for nonmonetary factors that can cause sustained
deviations from purchasing power parity.
Assuming that all variables start out at their long-run levels, we can now understand the
most important determinants of long-run swings in nominal exchange rates:
1. A shift in relative money supply levels. Suppose the Fed wishes to stimulate the
economy and therefore carries out an increase in the level of the U.S. money supply.
As you will remember from Chapter 15, a permanent, one-time increase in a country’s
money supply has no effect on the long-run levels of output, the interest rate, or any
relative price (including the real exchange rate). Thus, (16-3) implies once again that
rises in proportion to , while (16-7) shows that the U.S. price level is the sole
variable changing in the long run along with the nominal exchange rate . Because
the real exchange rate does not change, the nominal exchange rate change is consistent
with relative PPP: The only long-run effect of the U.S. money supply increase
is to raise all dollar prices, including the dollar price of the euro, in proportion to the
increase in the money supply. It should be no surprise that this result is the same as the
one we found using the monetary approach, since that approach is designed to account
for the long-run effects of monetary changes.
2. A shift in relative money supply growth rates. Suppose the Fed concludes, to its
dismay, that over the next few years the U.S. price level will fall. (A falling price level is
called deflation.) A permanent increase in the growth rate of the U.S. money supply
raises the long-run U.S. inflation rate and, through the Fisher effect, raises the dollar
interest rate relative to the euro interest rate. Because relative U.S. real money demand
therefore declines, equation (16-3) implies that rises (as shown in Figure 16-1).
Because the change bringing this outcome about is purely monetary, however, it is neutral
in its long-run effects; specifically, it does not alter the long-run real dollar/euro
exchange rate. According to (16-7), then, rises in proportion to the increase in
(a depreciation of the dollar against the euro). Once again, a purely monetary change
brings about a long-run nominal exchange rate shift in line with relative PPP, just as the
monetary approach predicted.
3. A change in relative output demand. This type of change is not covered by the
monetary approach, so now the more general perspective we’ve developed, in which the
real exchange rate can change, is essential. Since a change in relative output demand
E$/€ PUS
PUS
q$/€
E$/€
PUS MUS
E$/€ = q$/€ * (PUS/PE).
q$/€ = (E$/€ * PE)/PUS.
410 PART THREE Exchange Rates and Open-Economy Macroeconomics
does not affect long-run national price levels—these depend solely on the factors appearing
in equations (16-3) and (16-4)—the long-run nominal exchange rate in (16-7) will
change only insofar as the real exchange rate changes. Consider an increase in world
relative demand for U.S. products. Earlier in this section, we saw that a rise in demand
for U.S. products causes a long-run real appreciation of the dollar against the euro (a fall
in ); this change is simply a rise in the relative price of U.S. output. Given that longrun
national price levels are unchanged, however, (16-7) tells us that a long-run nominal
appreciation of the dollar against the euro (a fall in ) must also occur. This prediction
highlights the important fact that even though exchange rates are nominal prices, they
respond to nonmonetary as well as monetary events, even over long horizons.
4. A change in relative output supply. As we saw earlier in this section, an increase
in relative U.S. output supply causes the dollar to depreciate in real terms against
the euro, lowering the relative price of U.S. output. This rise in is not, however,
the only change in equation (16-7) implied by a relative rise in U.S. output. In addition,
the U.S. output increase raises the transaction demand for real U.S. money balances,
raising aggregate U.S. real money demand and, by (16-3), pushing the long-run
U.S. price level down. Referring back to equation (16-7), you will see that since
rises while falls, the output and money market effects of a change in output supply
work in opposite directions, thus making the net effect on is ambiguous. Our
analysis of an output-supply change illustrates that even when a disturbance originates
in a single market (in this case, the output market), its influence on exchange rates may
depend on repercussion effects that are channeled through other markets.
We conclude that when all disturbances are monetary in nature, exchange rates obey
relative PPP in the long run. In the long run, a monetary disturbance affects only the general
purchasing power of a currency, and this change in purchasing power changes
equally the currency’s value in terms of domestic and foreign goods. When disturbances
occur in output markets, the exchange rate is unlikely to obey relative PPP, even in the
long run. Table 16-1 summarizes these conclusions regarding the effects of monetary and
output market changes on long-run nominal exchange rates.
In the chapters that follow, we will appeal to this section’s general long-run exchange
rate model even when we are discussing short-run macroeconomic events. Long-run
factors are important in the short run because of the central role that expectations about the
future play in the day-to-day determination of exchange rates. That is why news about the
current account, for example, can have a big impact on the exchange rate. The long-run
exchange rate model of this section will provide the anchor for market expectations, that is,
the framework market participants use to forecast future exchange rates on the basis of
information at hand today.
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