Purchasing Power Parity
The theory of purchasing power parity states that the exchange rate between two countries’
currencies equals the ratio of the countries’ price levels. Recall from Chapter 15 that
the domestic purchasing power of a country’s currency is reflected in the country’s price
level, the money price of a reference basket of goods and services. The PPP theory therefore
predicts that a fall in a currency’s domestic purchasing power (as indicated by an
increase in the domestic price level) will be associated with a proportional currency depreciation
in the foreign exchange market. Symmetrically, PPP predicts that an increase in the
currency’s domestic purchasing power will be associated with a proportional currency
appreciation.
The basic idea of PPP was put forth in the writings of 19th-century British economists,
among them David Ricardo (the originator of the theory of comparative advantage).
Gustav Cassel, a Swedish economist writing in the early 20th century, popularized PPP by
making it the centerpiece of a theory of exchange rates. While there has been much controversy
about the general validity of PPP, the theory does highlight important factors
behind exchange rate movements.
To express the PPP theory in symbols, let be the dollar price of a reference commodity
basket sold in the United States and the euro price of the same basket in Europe.
(Assume for now that a single basket accurately measures money’s purchasing power in
both countries.) Then PPP predicts a dollar/euro exchange rate of
(16-1)
If, for example, the reference commodity basket costs in the United States
and in Europe, PPP predicts a dollar/euro exchange rate of
. If the U.S. price level were to triple (to per basket), so
would the dollar price of a euro. PPP would imply an exchange rate of per euro
By rearranging equation (16-1) to read
we get an alternative interpretation of PPP. The left side of this equation is the dollar price
of the reference commodity basket in the United States; the right side is the dollar price of
the reference basket when purchased in Europe (that is, its euro price multiplied by the
dollar price of a euro). These two prices are the same if PPP holds. PPP thus asserts that all
countries’ price levels are equal when measured in terms of the same currency.
Equivalently, the right side of the last equation measures the purchasing power of a
dollar when exchanged for euros and spent in Europe. PPP therefore holds when, at going
exchange rates, every currency’s domestic purchasing power is always the same as its
foreign purchasing power.
The Relationship Between PPP and the Law of One Price
Superficially, the statement of PPP given by equation (16-1) looks like the law of one price,
which says that for any commodity . There is a difference between PPP
and the law of one price, however: The law of one price applies to individual commodities
E$/€ = Pi i
US/Pi
E
PUS = (E$/€) * (PE),
(= $600 per basket/ €160 per basket).
$3.75
basket/€160 per basket) $600
€160 $1.25 per euro ($200 per
$200
E$/€ = PUS/PE.
PE
PUS
E$/€ = PUS
i /PE i .
i
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 387
(such as commodity ), while PPP applies to the general price level, which is a composite of
the prices of all the commodities that enter into the reference basket.
If the law of one price holds true for every commodity, of course, PPP must hold
automatically as long as the reference baskets used to reckon different countries’ price levels
are the same. Proponents of the PPP theory argue, however, that its validity (in particular,
its validity as a long-run theory) does not require the law of one price to hold exactly.
Even when the law of one price fails to hold for each individual commodity, the argument
goes, prices and exchange rates should not stray too far from the relation predicted
by PPP. When goods and services become temporarily more expensive in one country than
in others, the demands for its currency and its products fall, pushing the exchange rate and
domestic prices back in line with PPP. The opposite situation of relatively cheap domestic
products leads, analogously, to currency appreciation and price level inflation. PPP thus
asserts that even when the law of one price is not literally true, the economic forces behind
it will help eventually to equalize a currency’s purchasing power in all countries.
Absolute PPP and Relative PPP
The statement that exchange rates equal relative price levels (equation (16-1)) is sometimes
referred to as absolute PPP. Absolute PPP implies a proposition known as relative
PPP, which states that the percentage change in the exchange rate between two currencies
over any period equals the difference between the percentage changes in national price
levels. Relative PPP thus translates absolute PPP from a statement about price and
exchange rate levels into one about price and exchange rate changes. It asserts that prices
and exchange rates change in a way that preserves the ratio of each currency’s domestic
and foreign purchasing powers.
If the U.S. price level rises by 10 percent over a year while Europe’s rises by only
5 percent, for example, relative PPP predicts a 5 percent depreciation of the dollar against
the euro. The dollar’s 5 percent depreciation against the euro just cancels the 5 percent
by which U.S. inflation exceeds European inflation, leaving the relative domestic and
foreign purchasing powers of both currencies unchanged.
More formally, relative PPP between the United States and Europe would be written as
(16-2)
where denotes an inflation rate (that is, the percentage change in a
price level between dates and ).1 Unlike absolute PPP, relative PPP can be defined
only with respect to the time interval over which price levels and the exchange rate change.
In practice, national governments do not take pains to compute the price level indexes they
publish using an internationally standardized basket of commodities. Absolute PPP makes no
sense, however, unless the two baskets whose prices are compared in equation (16-1) are the
t t - 1
pt pt = (Pt - Pt-1)/Pt-1,
(E$/€, t - E$/€, t-1)/E$/€, t-1 = pUS, t - pE, t
i
1To be precise, equation (16-1) implies a good approximation to equation (16-2) when rates of change are not
too large. The exact relationship is
After subtracting 1 from both sides, we write the preceding exact equation as
But if and are small, the term in the last equality is negligibly small,
implying a very good approximation to (16-2).
pUS, t pE, t -pE, t(pUS, t - pE, t)/(1 + pE, t)
= (pUS, t - pE, t) - pE, t(pUS, t - pE, t)/(1 + pE, t).
= (pUS, t - pE, t)/(1 + pE, t)
(E$/€, t - E$/€, t-1)/E$/€, t-1 = (pUS, t +1) (PE, t-1/PE, t) - (PE, t /PE, t)
E$/€, t /E$/€, t-1 = (PUS, t /PUS, t-1)/(PE, t /PE, t-1).
388 PART THREE Exchange Rates and Open-Economy Macroeconomics
same. (There is no reason to expect different commodity baskets to sell for the same price!)
The notion of relative PPP therefore comes in handy when we have to rely on government
price level statistics to evaluate PPP. It makes logical sense to compare percentage exchange
rate changes to inflation differences, as above, even when countries base their price level estimates
on product baskets that differ in coverage and composition.
Relative PPP is important also because it may be valid even when absolute PPP is not.
Provided the factors causing deviations from absolute PPP are more or less stable over
time, percentage changes in relative price levels can still approximate percentage changes
in exchange rates.
The theory of purchasing power parity states that the exchange rate between two countries’
currencies equals the ratio of the countries’ price levels. Recall from Chapter 15 that
the domestic purchasing power of a country’s currency is reflected in the country’s price
level, the money price of a reference basket of goods and services. The PPP theory therefore
predicts that a fall in a currency’s domestic purchasing power (as indicated by an
increase in the domestic price level) will be associated with a proportional currency depreciation
in the foreign exchange market. Symmetrically, PPP predicts that an increase in the
currency’s domestic purchasing power will be associated with a proportional currency
appreciation.
The basic idea of PPP was put forth in the writings of 19th-century British economists,
among them David Ricardo (the originator of the theory of comparative advantage).
Gustav Cassel, a Swedish economist writing in the early 20th century, popularized PPP by
making it the centerpiece of a theory of exchange rates. While there has been much controversy
about the general validity of PPP, the theory does highlight important factors
behind exchange rate movements.
To express the PPP theory in symbols, let be the dollar price of a reference commodity
basket sold in the United States and the euro price of the same basket in Europe.
(Assume for now that a single basket accurately measures money’s purchasing power in
both countries.) Then PPP predicts a dollar/euro exchange rate of
(16-1)
If, for example, the reference commodity basket costs in the United States
and in Europe, PPP predicts a dollar/euro exchange rate of
. If the U.S. price level were to triple (to per basket), so
would the dollar price of a euro. PPP would imply an exchange rate of per euro
By rearranging equation (16-1) to read
we get an alternative interpretation of PPP. The left side of this equation is the dollar price
of the reference commodity basket in the United States; the right side is the dollar price of
the reference basket when purchased in Europe (that is, its euro price multiplied by the
dollar price of a euro). These two prices are the same if PPP holds. PPP thus asserts that all
countries’ price levels are equal when measured in terms of the same currency.
Equivalently, the right side of the last equation measures the purchasing power of a
dollar when exchanged for euros and spent in Europe. PPP therefore holds when, at going
exchange rates, every currency’s domestic purchasing power is always the same as its
foreign purchasing power.
The Relationship Between PPP and the Law of One Price
Superficially, the statement of PPP given by equation (16-1) looks like the law of one price,
which says that for any commodity . There is a difference between PPP
and the law of one price, however: The law of one price applies to individual commodities
E$/€ = Pi i
US/Pi
E
PUS = (E$/€) * (PE),
(= $600 per basket/ €160 per basket).
$3.75
basket/€160 per basket) $600
€160 $1.25 per euro ($200 per
$200
E$/€ = PUS/PE.
PE
PUS
E$/€ = PUS
i /PE i .
i
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 387
(such as commodity ), while PPP applies to the general price level, which is a composite of
the prices of all the commodities that enter into the reference basket.
If the law of one price holds true for every commodity, of course, PPP must hold
automatically as long as the reference baskets used to reckon different countries’ price levels
are the same. Proponents of the PPP theory argue, however, that its validity (in particular,
its validity as a long-run theory) does not require the law of one price to hold exactly.
Even when the law of one price fails to hold for each individual commodity, the argument
goes, prices and exchange rates should not stray too far from the relation predicted
by PPP. When goods and services become temporarily more expensive in one country than
in others, the demands for its currency and its products fall, pushing the exchange rate and
domestic prices back in line with PPP. The opposite situation of relatively cheap domestic
products leads, analogously, to currency appreciation and price level inflation. PPP thus
asserts that even when the law of one price is not literally true, the economic forces behind
it will help eventually to equalize a currency’s purchasing power in all countries.
Absolute PPP and Relative PPP
The statement that exchange rates equal relative price levels (equation (16-1)) is sometimes
referred to as absolute PPP. Absolute PPP implies a proposition known as relative
PPP, which states that the percentage change in the exchange rate between two currencies
over any period equals the difference between the percentage changes in national price
levels. Relative PPP thus translates absolute PPP from a statement about price and
exchange rate levels into one about price and exchange rate changes. It asserts that prices
and exchange rates change in a way that preserves the ratio of each currency’s domestic
and foreign purchasing powers.
If the U.S. price level rises by 10 percent over a year while Europe’s rises by only
5 percent, for example, relative PPP predicts a 5 percent depreciation of the dollar against
the euro. The dollar’s 5 percent depreciation against the euro just cancels the 5 percent
by which U.S. inflation exceeds European inflation, leaving the relative domestic and
foreign purchasing powers of both currencies unchanged.
More formally, relative PPP between the United States and Europe would be written as
(16-2)
where denotes an inflation rate (that is, the percentage change in a
price level between dates and ).1 Unlike absolute PPP, relative PPP can be defined
only with respect to the time interval over which price levels and the exchange rate change.
In practice, national governments do not take pains to compute the price level indexes they
publish using an internationally standardized basket of commodities. Absolute PPP makes no
sense, however, unless the two baskets whose prices are compared in equation (16-1) are the
t t - 1
pt pt = (Pt - Pt-1)/Pt-1,
(E$/€, t - E$/€, t-1)/E$/€, t-1 = pUS, t - pE, t
i
1To be precise, equation (16-1) implies a good approximation to equation (16-2) when rates of change are not
too large. The exact relationship is
After subtracting 1 from both sides, we write the preceding exact equation as
But if and are small, the term in the last equality is negligibly small,
implying a very good approximation to (16-2).
pUS, t pE, t -pE, t(pUS, t - pE, t)/(1 + pE, t)
= (pUS, t - pE, t) - pE, t(pUS, t - pE, t)/(1 + pE, t).
= (pUS, t - pE, t)/(1 + pE, t)
(E$/€, t - E$/€, t-1)/E$/€, t-1 = (pUS, t +1) (PE, t-1/PE, t) - (PE, t /PE, t)
E$/€, t /E$/€, t-1 = (PUS, t /PUS, t-1)/(PE, t /PE, t-1).
388 PART THREE Exchange Rates and Open-Economy Macroeconomics
same. (There is no reason to expect different commodity baskets to sell for the same price!)
The notion of relative PPP therefore comes in handy when we have to rely on government
price level statistics to evaluate PPP. It makes logical sense to compare percentage exchange
rate changes to inflation differences, as above, even when countries base their price level estimates
on product baskets that differ in coverage and composition.
Relative PPP is important also because it may be valid even when absolute PPP is not.
Provided the factors causing deviations from absolute PPP are more or less stable over
time, percentage changes in relative price levels can still approximate percentage changes
in exchange rates.
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