The principle of purchasing power parity is central to the theoretical underpinnings of the analysis of many trade issues, but up until recently, there was little evidence that PPP held in the long run. Current research has changed that. The key to finding the evidence was realizing how to test for a long-run effect given the fact that exchange rates adjust to their long-run levels in a nonlinear way.Purchasing power parity

Ben Craig

English

Research Papers in Economics

goods differ. Coffee differs in quality
and taste; wheat and corn come in differ-
ent varieties. Second, an item, even one
which is rigorously controlled to be the
same good, is still different once it is
sold in different places. Consider the dif-
ference between the same radio sold in
Hong Kong and Des Moines. The Chi-
nese radio is sold in a shop that pays
higher property fees, and it is sold by
salesmen who must, themselves, pay
higher rent in order to live. The act of
retailing a traded good ends up packag-
ing the tradable good with a nontraded
good, that is, the service of selling it.
Thus, even with many traded goods,
their prices reflect a combination of the
good and a nontraded service.
Third, even if the radio in Iowa were
exactly the same item as a radio sold in
Hong Kong, it might not make much
sense to buy cheap radios in Iowa and
ship them to China. It might cost too
much to find out the relatively expensive
prices, ship the cheaper radios to China,
set up distribution networks to sell them,
and so forth. These transactions costs
might mean that price differences
between goods that are the same can 
April 1, 2005
Federal Reserve Bank of Cleveland
The Growing Significance of Purchasing
Power Parity
by Ben Craig
ISSN 0428-1276
The principle of purchasing power
parity is central to the theoretical
underpinnings of the analysis of many
trade issues, but up until recently,
there was little evidence that PPP held
in the long run. Current research has
changed that. The key to finding the
evidence was realizing how to test for a
long-run effect given the fact that
exchange rates adjust to their long-
run levels in a nonlinear way.
Under the skin of any international
economist lies a deep-seated belief in
some variant of the PPP theory of the
exchange rate.
—Rudiger Dornbusch 
and Paul Krugman (1976)
Recently, trade diplomats from many
countries met in Ecuador to discuss
whether the Chinese currency was at
“the appropriate level.” The underlying
tool that was used in the debate was the
concept of purchasing power parity
(PPP), or the idea that the changes in
exchange rates should balance the price
of a basket of traded goods in a foreign
country so that it roughly equals the
price of the same basket in the United
States, once the foreign prices are con-
verted to American dollars at the
exchange rate. This concept constitutes a
major pillar of the economics of
exchange rates. 
Indeed, even the most naïve tourist,
when confronted with a cup of coffee
that costs the equivalent of $200 in some
(admittedly hypothetical) foreign coun-
try, would conclude one of three things:
either there is a scam, this is extremely
good coffee, or the foreign currency in
that country is overvalued. At some
point in the future the price of that cur-
rency in terms of dollars can be expected
to fall.
Faith in PPP is so strong that many
economists regard it as consistent with
long-term equilibrium in the exchange
market, claiming that the dollar is over-
valued or undervalued, as the case may
be, whenever the dollar deviates sub-
stantially from its PPP value. While
exchange rates do seem to revert to their
PPP values over long periods of time,
they need not remain there. Large devia-
tions from PPP are common and fully
consistent with equilibrium in the for-
eign exchange market. 
PPP is central to the theoretical under-
pinnings of our analysis of many trade
issues, but how empirically supportable
is it? Attempts to use PPP to predict
future exchange rates have not been suc-
cessful, suggesting that PPP might not
be empirically relevant. Up until 2000,
in fact, researchers could find scant
empirical support for PPP even in the
long run. Recent research has confirmed
that PPP is not so useful to forecasters
trying to predict short-term movements
in the exchange rate, but it has begun to
demonstrate that PPP is quite tenable to
use in economic models that analyze
medium- or long-range policies. 
■ The Law of One Price
The idea behind PPP evolved from the
law of one price, the idea that arbitrage
will ensure that the same good sold both
here and abroad will have the same price
when that price is expressed in a common
currency. If the same price were not to
hold, then someone could make a quick
profit by buying the good where it was
cheaper and selling it where it was more
expensive. The price of the good could be
expected to rise in the place where it was
cheaper and fall where it was more
expensive, and the foreign exchange rate
would also be expected to adjust to make
goods in the cheaper country relatively
more expensive. PPP is the mechanism
through which the exchange rate adjusts
to the aggregated changes in the prices of
tradable goods in two countries to reflect
the law of one price. 
Although the idea of the law of one price
seems reasonable enough, a quick look
at actual examples immediately points
up why a single price might not apply in
practice. First, even fairly homogeneousaverage (as is usually the case), this
identity will not hold, even when the law
of one price holds for all of the individ-
ual component prices. It is more com-
mon to see a relative form of PPP being
applied in practice, which holds that the
percentage change of the foreign price
index plus the percentage change in the
exchange rate should equal the percent-
age change in the domestic price index.
This will hold if all of the components
of the price index change by the same
percentage amount (as in a purely mone-
tary inflation). However, if the price
components change at differing rates,
then, once again, the relation does not
hold. The relative form of PPP is what
researchers actually test when they test
the validity of PPP. 
Another reason that PPP is tested using
its relative form is that some economists
base the principle of PPP on interest
rate differences rather than the law of
one price. Briefly, the idea is that inter-
est rates within a country are composed
of inflation plus a “real rate,” or the 
natural return that would accrue if the
prices of future goods did not reflect
inflation. Because of trade, the real 
rate in the long run is often assumed to
be the same for all countries, so that the
only difference in interest rates is the
expected inflation component. Arbi-
trage of international interest rates gives
a version of PPP that balances changes
in the relative price indexes with
changes in the exchange rate. 
Figures 1 and 2 show some patterns that
are relevant to PPP. These figures take
several price indexes from postwar
Britain, Canada, and Japan and convert
them to U.S. dollars at the contemporary
exchange rate. The corresponding U.S.
price index is also shown. If these
indexes measured the respective coun-
tries’underlying price levels accurately,
and if PPP held perfectly, these lines
would coincide. The first pattern to note
is that the producer price indexes (PPI),
when converted to dollar amounts, move
slightly more closely together than do
the consumer price indexes (CPI). 
Although the differences between the
consumer and producer price series are
admittedly slight, they may be due to the
fact that more of the components of the
PPI are tradable than those in the CPI.
CPI components such as housing are not
easily traded across countries, so it is
hard (if not impossible) to take advan-
tage of price differences in two different
FIGURE 1 CONSUMER PRICES IN U.S.DOLLARS
–1.0
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
U.S. Canada
Japan
1/70 1/75
UK
Log of the CPI expressed in U.s. dollars, index = 1987*
1/80 1/85 1/90 1/95 1/00
persist. This is true in the short run—
even when firms can find ways to
reduce the transactions costs with new
container ships, say—or in the longer
run, where they can reduce costs with
new distribution networks. Deviations
from the law of one price can be arbi-
traged away only as long as they are
larger than these transactions costs.
Studies of price differences of known
standard commodities show that the
differences tend to be larger with
greater distances between points of
sale. Given that transactions costs can
be expected to grow with distance (all
else equal), this is not surprising. What
is interesting about the results of this
research is that merely sending a good
across an international border results in
a large additional deviation from the
law of one price. Some researchers
interpret this as a strong preference for
domestically produced goods, a “home
bias,” although another interpretation
is that crossing a border imposes a
large additional transaction cost.
■ Purchasing Power Parity
(PPP)
It is a long way from the law of one
price to PPP, for the law of one price is
a statement about a single tradable
good, whereas PPP says that exchange
rates change to reflect the change in
prices of all tradable goods between
countries. How does one test the valid-
ity of PPP? Doing so requires first that
all prices within a country are aggregated
in such a way that they are consistent
with a statement of PPP. The aggregation
should capture the underlying price level
and not distort cross-country differences
in prices because of the way relative
price shocks of individual items are
included in the index. 
Typically, time series of price indexes in
two or more countries are used, along
with exchange rate data, to measure the
validity of PPP. Some of the measure-
ment problems that have been encoun-
tered when testing PPP center on the
use of these price indexes. Different
countries weight their goods differently
when measuring price changes, so that
even choosing a different base year will
yield different weights. It is fairly easy
to demonstrate several anomalies that
occur in the measurement of PPP sim-
ply because of cross-country differ-
ences in the weighting of the compo-
nent prices that constitute the price
indexes. 
In a perfectly measured world, PPP
could be applied to say that the average
price of a bundle of goods from some
foreign country, multiplied by the
exchange rate (that is, the amount of
domestic currency bought by one unit
of the foreign currency), should equal
the average domestic price of the same
bundle. However, when different
weights are used in constructing the
*Prices were calculated by converting each country’s CPI into U.S. dollars (dividing by the
exchange rate) and then taking the logarithm.
SOURCE: The International Monetary Fund.countries to make a profit. Further, the
consumer price indexes have services in
their baskets of goods, some of which
are tradable, some of which are hard to
trade. A rise in the relative price of 
nontradable to tradable components
will cause a failure of relative PPP. Pro-
ducer prices, on the other hand, have
more components that are likely to be
tradable, and thus provide more oppor-
tunities for profit if they deviate from 
a single price in the two countries.
However, the differences are small, and
in practice economists often test PPP
with differences in the relative CPIs. 
Another pattern to note is that both
price series do not move exactly the
same for all countries. There are
instances in the short term in which the
U.S. price index grows more quickly
than a foreign one, or vice versa. The
data in figures 1 and 2 provide a hint
that transactions costs are responsible
for this short-term failure of PPP. Recall
that transactions costs would explain
deviations from the law of one price
(and thus PPP) in the short run, while
allowing for the possibility that it might
hold in the long run. The hint is to be
found in the fact that the Canadian price
series move more closely to the Ameri-
can series than do the British and Japan-
ese series, a fact which is consistent
with the lower transactions costs inher-
ent in the smaller distance between the
two North American countries. How
strong is the statistical evidence that
PPP holds in the long run? And how
quickly do exchange rates return to the
PPP position once they are off the PPP
path? These questions have been the
subject of considerable controversy and
are just now being resolved.
■ Solving PPP Puzzles 
Research up until 2000 had found little
evidence that PPP held in the long run.
Most of the research also found that the
rate at which exchange rates returned to
the PPP position was very slow. Thus,
until about four years ago, the consen-
sus among researchers seemed to be that
PPP might exert a weak pull on
exchange rates, but the relationship
between exchange rates and PPP was so
statistically weak and took place over
such a long time, that it was empirically
irrelevant. These findings were obtained
even when the researchers were careful
to measure the prices of tradable goods.
It was puzzling that such seemingly
strong results should be found against
the existence of a single price, an idea
that has a great deal of intuitive appeal.
Many economic models relied on some
form of PPP—for which so little sup-
port could be found—as a foundation
for modeling the international sector,
yet these models were successful in
characterizing the behavior of this 
sector. What was going on? 
Resolution of these puzzles began
when researchers focused on one of the
assumptions that had always been
made when adjustment to PPP over
time was studied. The assumption con-
cerns the notion of a half-life. A half-
life represents the amount of time that
elapses before a discrepancy between
the PPP level and the current exchange
rate is half its current size. Thus, if the
exchange rate were one dollar above
the PPP value, and if the half-life were
three months, then, after one-quarter
year, the discrepancy would be 50
cents; after one year, it would be
slightly over 6 cents, and so forth. Cal-
culating the half-life is equivalent to
answering the question: How much of
the discrepancy will be left after one
year? In this example, only about 
6 percent of the discrepancy will
remain after one year—the exchange
rate has adjusted by 94 percent to its
PPP level. Further, if PPP did not hold
even in the extreme long run, then there
would be no adjustment after one year.
The half-life would be infinite.
Research into this question found a
half-life of between three and six years,
which suggested a very slow rate of
adjustment. In fact, there is only weak
evidence that the half-life is not infinite,
and in part, the process of testing
whether this number is infinite or not
leads to technical difficulties that make
the tests less convincing. Research that
attempts to account for these technical
difficulties suggests that the half-life
might be even larger and that exchange
rates adjust the difference between their
current position and the rate implied by
PPP at the speed of between ten percent
per year and nothing. 
Up until a few years ago, researchers
had always assumed that the half-life
stays the same, no matter what the dis-
tance is from PPP. But there is strong
reason to think that this would not be
true. Consider the transactions costs
that cause a persistent difference in
prices for the same good. If the differ-
ence in the price is small and largely
reflects the transactions costs, then
merchants might not be very motivated
to correct the difference by setting up
sales in the markets with the more
expensive good. However, if the differ-
ence is great, many merchants will be
motivated to take advantage of the
profit opportunity, and the price will
become the same much more quickly.
FIGURE 2 PRODUCER PRICES IN U.S. DOLLARS
–1.0
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
Log of the PPI expressed in U.S. dollars, index = 1987*
U.S.
Canada
Japan
UK
UK
1/70 1/75 1/80 1/90 1/85 1/95 1/00
*Prices were calculated by converting each country’s PPI into U.S. dollars (dividing by the
exchange rate) and then taking the logarithm.
SOURCE: The International Monetary Fund.Federal Reserve Bank of Cleveland
Research Department
P.O. Box 6387
Cleveland, OH 44101
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Ben Craig is an economic advisor at the
Federal Reserve Bank of Cleveland.
The views expressed here are those of the
author and not necessarily those of the Federal
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Governors of the Federal Reserve System, or
its staff. 
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What this suggests is that the half-life
period for adjustment may vary, depend-
ing on whether the difference between
the exchange rate and PPP is large or
small. Estimation techniques that are
based on this idea find a very different
set of results. First, there is strong evi-
dence that PPP holds in the long run.
Second, the half-life of the period of
adjustment is much smaller. For small
deviations from PPP, the half-life of the
difference is under three years. For larger
differences, it is even smaller, from less
than a year to 18 months. 
■ The Relegitimization of PPP
Current research suggests that PPP is
not only relevant in the long run, but
also that convergence to PPP happens
on average in a short time horizon that
it is both empirically and theoretically
relevant. It is just important to acknowl-
edge the role that the nonlinear nature
of the adjustment of exchange rates to
their long-run levels plays when testing
whether the long-run level is relevant,
and in estimating the speed at which the
adjustment occurs. 
As a predictive mechanism (where econ-
omists are trying to explain day-to-day
fluctuations in exchange rates, for exam-
ple), PPP is not a particularly useful pre-
dictive concept. This makes sense
because the arbitrage trading of goods
across borders, which enforces PPP,
takes some time to work. PPP evolves
slowly in many economic models
because information about the basics of
the model percolates into the decision
making slowly. In any case, the fact that
PPP is not instantaneously observed at
each point in time is completely consis-
tent with these economic models. 
■ Recommended Reading 
Alan M. Taylor, and Mark P. Taylor,
2004. “The Purchasing Power Parity
Debate.” National Bureau of Economic
Research, Working Paper no. 10607.
The opening quotation comes from
Rudiger Dornbusch, and Paul Krugman.
1976. “Flexible Exchange Rates in the
Short Run.” Brookings Papers on Eco-
nomic Activity 3, pp. 537–75.

The growing significance of purchasing power parity

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The growing significance of purchasing power parity

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