Real Interest Parity
Economics makes an important distinction between nominal interest rates, which are rates
of return measured in monetary terms, and real interest rates, which are rates of return measured
in real terms, that is, in terms of a country’s output. Because real rates of return often are
uncertain, we usually will refer to expected real interest rates. The interest rates we discussed
in connection with the interest parity condition and the determinants of money demand were
nominal rates, for example, the dollar return on dollar deposits. But for many other purposes,
economists need to analyze behavior in terms of real rates of return. No one who is thinking
of investing money, for example, could make a decision knowing only that the nominal interest
rate is 15 percent. The investment would be quite attractive at zero inflation, but disastrously
unattractive if inflation were bounding along at 100 percent per year!21
We conclude this chapter by showing that when the nominal interest parity condition
equates nominal interest rate differences between currencies to expected changes in
nominal exchange rates, a real interest parity condition equates expected real interest rate
differences to expected changes in real exchange rates. Only when relative PPP is
expected to hold (meaning no real exchange rate change is anticipated) are expected real
interest rates in all countries identical.
The expected real interest rate, denoted , is defined as the nominal interest rate,
, less the expected inflation rate,
In other words, the expected real interest rate in a country is just the real rate of return a
domestic resident expects to earn on a loan of his or her currency. The definition of the
expected real interest rate clarifies the generality of the forces behind the Fisher effect:
Any increase in the expected inflation rate that does not alter the expected real interest rate
must be reflected, one for one, in the nominal interest rate.
A useful consequence of the preceding definition is a formula for the difference in
expected real interest rates between two currency areas such as the United States and Europe:
If we rearrange equation (16-9) and combine it with the equation above, we get the
desired real interest parity condition:
r US (16-10)
e - rE e = (q$/€
e - q$/€)/q$/€.
r US
e - rE e = (R$ - pUS
e ) - (R€ - pE e ).
r e = R - pe.
R pe:
r e
21We could get away with examining nominal return differences in the foreign exchange market because (as
Chapter 14 showed) nominal return differences equal real return differences for any given investor. In the context
of the demand for money, the nominal interest rate is the real rate of return you sacrifice by holding interest-barren
currency.
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 413
Equation (16-10) looks much like the nominal interest parity condition from which it is
derived, but it explains differences in expected real interest rates between the United
States and Europe by expected movements in the dollar/euro real exchange rate.
Expected real interest rates are the same in different countries when relative PPP is
expected to hold (in which case (16-10) implies that ). More generally, however,
expected real interest rates in different countries need not be equal, even in the long run, if
continuing change in output markets is expected.22 Suppose, for example, that productivity
in the South Korean tradables sector is expected to rise during the next two decades,
while productivity stagnates in South Korean nontradables and in all U.S. industries. If the
Balassa-Samuelson hypothesis is valid, people should expect the U.S. dollar to depreciate
in real terms against South Korea’s currency, the won, as the prices of South Korea’s nontradables
trend upward. Equation (16-10) thus implies that the expected real interest rate
should be higher in the United States than in South Korea.
Do such real interest differences imply unnoticed profit opportunities for international
investors? Not necessarily. A cross-border real interest difference does imply that residents
of two countries perceive different real rates of return on wealth. Nominal interest
parity tells us, however, that any given investor expects the same real return on domestic
and foreign currency assets. Two investors residing in different countries need not calculate
this single real rate of return in the same way if relative PPP does not link the prices of
their consumption baskets, but there is no way either can profit from their disagreement by
shifting funds between currencies.
SUMMARY
1. The purchasing power parity theory, in its absolute form, asserts that the exchange rate
between countries’ currencies equals the ratio of their price levels, as measured by the
money prices of a reference commodity basket. An equivalent statement of PPP is that
the purchasing power of any currency is the same in any country. Absolute PPP
implies a second version of the PPP theory, relative PPP, which predicts that percentage
changes in exchange rates equal differences in national inflation rates.
2. A building block of the PPP theory is the law of one price, which states that under free
competition and in the absence of trade impediments, a good must sell for a single
price regardless of where in the world it is sold. Proponents of the PPP theory often
argue, however, that its validity does not require the law of one price to hold for every
commodity.
3. The monetary approach to the exchange rate uses PPP to explain long-term exchange
rate behavior exclusively in terms of money supply and demand. In that theory, longrun
international interest differentials result from different national rates of ongoing
inflation, as the Fisher effect predicts. Sustained international differences in monetary
growth rates are, in turn, behind different long-term rates of continuing inflation. The
monetary approach thus finds that a rise in a country’s interest rate will be associated
with a depreciation of its currency. Relative PPP implies that international interest
differences, which equal the expected percentage change in the exchange rate, also
equal the international expected inflation gap.
4. The empirical support for PPP and the law of one price is weak in recent data. The failure
of these propositions in the real world is related to trade barriers and departures from
r US
e = rE e
22The two-period analysis of international borrowing and lending in Chapter 6 assumed that all countries face a
single worldwide real interest rate. Relative PPP must hold in that analysis, however, because there is only one
consumption good in each period.
414 PART THREE Exchange Rates and Open-Economy Macroeconomics
free competition, factors that can result in pricing to market by exporters. In addition,
different definitions of price levels in different countries bedevil attempts to test PPP
using the price indices governments publish. For some products, including many services,
international transport costs are so steep that these products become nontradable.
5. Deviations from relative PPP can be viewed as changes in a country’s real exchange
rate, the price of a typical foreign expenditure basket in terms of the typical domestic
expenditure basket. All else equal, a country’s currency undergoes a long-run real
appreciation against foreign currencies when the world relative demand for its output
rises. In this case, the country’s real exchange rate, as just defined, falls. The home currency
undergoes a long-run real depreciation against foreign currencies when home
output expands relative to foreign output. In this case, the real exchange rate rises.
6. The long-run determination of nominal exchange rates can be analyzed by combining
two theories: the theory of the long-run real exchange rate and the theory of how
domestic monetary factors determine long-run price levels. A stepwise increase in a
country’s money stock ultimately leads to a proportional increase in its price level and
a proportional fall in its currency’s foreign exchange value, just as relative PPP predicts.
Changes in monetary growth rates also have long-run effects consistent with
PPP. Supply or demand changes in output markets, however, result in exchange rate
movements that do not conform to PPP.
7. The interest parity condition equates international differences in nominal interest
rates to the expected percentage change in the nominal exchange rate. If interest parity
holds in this sense, a real interest parity condition equates international differences
in expected real interest rates to the expected change in the real exchange rate. Real
interest parity also implies that international differences in nominal interest rates
equal the difference in expected inflation plus the expected percentage change in the
real exchange rate.
Economics makes an important distinction between nominal interest rates, which are rates
of return measured in monetary terms, and real interest rates, which are rates of return measured
in real terms, that is, in terms of a country’s output. Because real rates of return often are
uncertain, we usually will refer to expected real interest rates. The interest rates we discussed
in connection with the interest parity condition and the determinants of money demand were
nominal rates, for example, the dollar return on dollar deposits. But for many other purposes,
economists need to analyze behavior in terms of real rates of return. No one who is thinking
of investing money, for example, could make a decision knowing only that the nominal interest
rate is 15 percent. The investment would be quite attractive at zero inflation, but disastrously
unattractive if inflation were bounding along at 100 percent per year!21
We conclude this chapter by showing that when the nominal interest parity condition
equates nominal interest rate differences between currencies to expected changes in
nominal exchange rates, a real interest parity condition equates expected real interest rate
differences to expected changes in real exchange rates. Only when relative PPP is
expected to hold (meaning no real exchange rate change is anticipated) are expected real
interest rates in all countries identical.
The expected real interest rate, denoted , is defined as the nominal interest rate,
, less the expected inflation rate,
In other words, the expected real interest rate in a country is just the real rate of return a
domestic resident expects to earn on a loan of his or her currency. The definition of the
expected real interest rate clarifies the generality of the forces behind the Fisher effect:
Any increase in the expected inflation rate that does not alter the expected real interest rate
must be reflected, one for one, in the nominal interest rate.
A useful consequence of the preceding definition is a formula for the difference in
expected real interest rates between two currency areas such as the United States and Europe:
If we rearrange equation (16-9) and combine it with the equation above, we get the
desired real interest parity condition:
r US (16-10)
e - rE e = (q$/€
e - q$/€)/q$/€.
r US
e - rE e = (R$ - pUS
e ) - (R€ - pE e ).
r e = R - pe.
R pe:
r e
21We could get away with examining nominal return differences in the foreign exchange market because (as
Chapter 14 showed) nominal return differences equal real return differences for any given investor. In the context
of the demand for money, the nominal interest rate is the real rate of return you sacrifice by holding interest-barren
currency.
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 413
Equation (16-10) looks much like the nominal interest parity condition from which it is
derived, but it explains differences in expected real interest rates between the United
States and Europe by expected movements in the dollar/euro real exchange rate.
Expected real interest rates are the same in different countries when relative PPP is
expected to hold (in which case (16-10) implies that ). More generally, however,
expected real interest rates in different countries need not be equal, even in the long run, if
continuing change in output markets is expected.22 Suppose, for example, that productivity
in the South Korean tradables sector is expected to rise during the next two decades,
while productivity stagnates in South Korean nontradables and in all U.S. industries. If the
Balassa-Samuelson hypothesis is valid, people should expect the U.S. dollar to depreciate
in real terms against South Korea’s currency, the won, as the prices of South Korea’s nontradables
trend upward. Equation (16-10) thus implies that the expected real interest rate
should be higher in the United States than in South Korea.
Do such real interest differences imply unnoticed profit opportunities for international
investors? Not necessarily. A cross-border real interest difference does imply that residents
of two countries perceive different real rates of return on wealth. Nominal interest
parity tells us, however, that any given investor expects the same real return on domestic
and foreign currency assets. Two investors residing in different countries need not calculate
this single real rate of return in the same way if relative PPP does not link the prices of
their consumption baskets, but there is no way either can profit from their disagreement by
shifting funds between currencies.
SUMMARY
1. The purchasing power parity theory, in its absolute form, asserts that the exchange rate
between countries’ currencies equals the ratio of their price levels, as measured by the
money prices of a reference commodity basket. An equivalent statement of PPP is that
the purchasing power of any currency is the same in any country. Absolute PPP
implies a second version of the PPP theory, relative PPP, which predicts that percentage
changes in exchange rates equal differences in national inflation rates.
2. A building block of the PPP theory is the law of one price, which states that under free
competition and in the absence of trade impediments, a good must sell for a single
price regardless of where in the world it is sold. Proponents of the PPP theory often
argue, however, that its validity does not require the law of one price to hold for every
commodity.
3. The monetary approach to the exchange rate uses PPP to explain long-term exchange
rate behavior exclusively in terms of money supply and demand. In that theory, longrun
international interest differentials result from different national rates of ongoing
inflation, as the Fisher effect predicts. Sustained international differences in monetary
growth rates are, in turn, behind different long-term rates of continuing inflation. The
monetary approach thus finds that a rise in a country’s interest rate will be associated
with a depreciation of its currency. Relative PPP implies that international interest
differences, which equal the expected percentage change in the exchange rate, also
equal the international expected inflation gap.
4. The empirical support for PPP and the law of one price is weak in recent data. The failure
of these propositions in the real world is related to trade barriers and departures from
r US
e = rE e
22The two-period analysis of international borrowing and lending in Chapter 6 assumed that all countries face a
single worldwide real interest rate. Relative PPP must hold in that analysis, however, because there is only one
consumption good in each period.
414 PART THREE Exchange Rates and Open-Economy Macroeconomics
free competition, factors that can result in pricing to market by exporters. In addition,
different definitions of price levels in different countries bedevil attempts to test PPP
using the price indices governments publish. For some products, including many services,
international transport costs are so steep that these products become nontradable.
5. Deviations from relative PPP can be viewed as changes in a country’s real exchange
rate, the price of a typical foreign expenditure basket in terms of the typical domestic
expenditure basket. All else equal, a country’s currency undergoes a long-run real
appreciation against foreign currencies when the world relative demand for its output
rises. In this case, the country’s real exchange rate, as just defined, falls. The home currency
undergoes a long-run real depreciation against foreign currencies when home
output expands relative to foreign output. In this case, the real exchange rate rises.
6. The long-run determination of nominal exchange rates can be analyzed by combining
two theories: the theory of the long-run real exchange rate and the theory of how
domestic monetary factors determine long-run price levels. A stepwise increase in a
country’s money stock ultimately leads to a proportional increase in its price level and
a proportional fall in its currency’s foreign exchange value, just as relative PPP predicts.
Changes in monetary growth rates also have long-run effects consistent with
PPP. Supply or demand changes in output markets, however, result in exchange rate
movements that do not conform to PPP.
7. The interest parity condition equates international differences in nominal interest
rates to the expected percentage change in the nominal exchange rate. If interest parity
holds in this sense, a real interest parity condition equates international differences
in expected real interest rates to the expected change in the real exchange rate. Real
interest parity also implies that international differences in nominal interest rates
equal the difference in expected inflation plus the expected percentage change in the
real exchange rate.
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