Exchange Rates and Prices
Charles M. Engel*
* Engel is a Research Associate in the NBER's International Finance and Macroeconomics
Program and a Professor of Economics at the University of Washington. His "Profile" appears
later in this issue.
In the early 1970s, when the industrialized countries abandoned the fixed
exchange rates of the Bretton Woods system, many economists were surprised by the high
volatility of exchange rates under the new regime of more flexible rates. Dornbusch provided a
new paradigm, based on the Mundell-Fleming model of the 1960s, but granting a prominent role
to expectations in the determination of exchange rates.(1) His model assumed that nominal goods
prices adjusted sluggishly, but that exchange rates resembled asset prices more closely. In that
model, expectations generated the short-run "overshooting" of exchange rates in response to
monetary and other demand shocks.
The Dornbusch model dominated academic discussions of exchange rates for at least a
decade, but gradually began to lose favor. There were two reasons for the decline of the
overshooting model. First was evidence that the model was not very useful in forecasting
exchange rates. Meese and Rogoff showed that forecasts of the exchange rate based on the
Dornbusch model could not beat the simplest forecast of no-change-in-the-exchange-rate.(2) Still,
not all of the empirical evidence on the Dornbusch model was negative. For example, Frankel
and I used the Dornbusch model to explain the famous money supply announcements puzzle of
the early 1980s.(3) The model was successful in explaining the simultaneous jump in short-term
interest rates and appreciation of the dollar at the moment the Federal Reserve announced money
supply totals that were greater than anticipated by markets. However, many of the movements of
exchange rates appeared to be completely unrelated to the economic fundamentals - money
supplies and government budgets - stressed by Dornbusch. Even after dozens of variants of the
model were introduced, nobody was able to tweak the model to produce consistently successful
forecasts of exchange rates.
The second cause for the decline in popularity of the Dornbusch model was the
movement in macroeconomics in the 1980s toward models based explicitly on utility
maximization. Dornbusch developed a rational expectations version of the Mundell-Fleming
model, which was based on descriptive equations for asset markets and goods markets. Although
the new Keynesian theory of the 1980s established a formal basis for slow adjustment of prices
by optimizing firms, the new international macroeconomics of the 1980s was based primarily on
neoclassical models with flexible prices. One assumption that characterized all of these models
was the law of one price: that any traded good would sell for the same price (corrected for
currency of denomination) in every country.
Law of One Price
The data clearly show that there are large fluctuations in real exchange rates (that is, the price of
a consumption basket in one country relative to another). Since the neoclassical models did not
allow for the failure of the law of one price, there had to be some other mechanism for explaining
these movements in real exchange rates. Probably the most popular type of model assumed that
there was a group of goods that were not traded, so that the law of one price did not need to hold
for these goods. Fluctuations in the prices of nontraded goods relative to traded goods explained
the movements in real exchange rates. For example, services generally were nontraded. A
country experiencing rapid inflation in services relative to traded manufactured goods would
experience a greater increase in its price level than a country without inflation in services prices.
Another class of models assumed that countries weighted goods differently in their consumption
bundles. For example, wine might receive a high weight in the French consumption bundle and
beer a high weight in the U.S. consumption bundle. Even though Frenchmen and Americans pay
the same prices for each good, an increase in the price of wine relative to beer would drive the
overall French price index up relative to the U.S. index.
Both of these neoclassical models assume that there will be large, very visible changes in
relative prices within each country. In the first model, prices of services move relative to prices
of manufactured goods. In the second model, there will be large changes in the price of wine
relative to beer. Any model must make certain assumptions about the world. My 1993 paper(4)
asks whether the general pattern assumed by the neoclassical models - that failures of the law of
one price across countries are relatively small, and that there are significant relative price changes
within countries - is true in the data. For that paper, I examined two datasets. The first collected
price indexes for disaggregated categories of goods - such as energy, food, and rent - for several
large OECD (Organization for Economic Cooperation and Development) countries. The second
collected price indexes on even more disaggregated goods - such as bananas, televisions, and
automobile tires - for the United States and Canada. For each dataset, I calculated the variance of
changes in all relative prices within each country: bananas to televisions, televisions to tires, tires
to bananas, and so on. I also calculated the variance of changes in prices of the same goods
across countries: bananas in Canada compared to bananas in the United States, televisions in
Canada relative to televisions in the United States, and so on.
My results strongly contradict the underlying presumption of the neoclassical models.
Failures of the law of one price, as measured by the variance of prices of the same good across
countries, tended to be much larger than the variance of prices of different goods within
countries. Indeed, the median volatility of prices of similar goods across borders was nearly an
order of magnitude larger than the median volatility of prices of goods within each country. The
evidence runs exactly counter to the underlying assumption of the neoclassical models of the
1980s. Modeling failures of the law of one price appear to be much more important for our
understanding of real exchange rate movements than the channels examined in the neoclassical
One of my recent papers presents a more complete examination of similar issues.(5) I
decompose real exchange rates into two components: the price of traded goods in one country
relative to their price in another country, and the relative price of nontraded goods to traded
goods. Variation in the first term represents deviations from the law of one price, and variation in
the second term comes from movements in the relative price of nontraded goods. I use five
different measures of traded goods and nontraded goods for the United States. For some
measures, there are data for up to 20 countries, although for others there are data available for
only six or seven countries. In each case, I calculate the variance of changes in each of the two
components at every horizon - from one month, in some cases, out to 30 years. Then, I compare
the variance of these two components to ask which accounts for most of the variance of real
exchange rates at each horizon.
The results are startling: at almost every horizon for almost every measure and every
country relative to the United States (generally with the exception of Canada), the failure of the
law of one price accounts for over 90 percent of real exchange rate variation. In many cases it
accounts for 98 to 99 percent of the variation.
The case of the real U.S.-Japan exchange rate is worth special mention. It is often claimed
that the real value of the yen has risen precisely because of the increase in prices of nontraded
goods in Japan. However, the evidence does not support this view. There has been a large
increase in the relative price of nontraded to traded goods in Japan over the past 30 years, but it
has been matched by the size of the relative price increase in the United States. Moreover, the
U.S.-Japan real exchange rate has been marked by a high degree of short-run and medium-run
volatility, but that sort of volatility is not apparent in the data on the relative price of nontraded to
Purchasing Power Parity
I have argued recently that variation in the price of nontraded to traded goods could
actually explain very long-run movements in the real exchange rate.(6) Tests of purchasing power
parity (PPP) with very long datasets (100 years and more) appear to rule out permanent changes
in relative prices of nontraded to traded goods between the United States and other countries,
because their results suggest that PPP holds in the long run. (Long-run PPP is the proposition that
in the long run the real exchange rate converges to a constant mean.) I argue that those tests have
a serious size bias; they are too likely to reject the null hypothesis that there are important
long-run relative price movements between countries. This paper appears to contradict my earlier
work, which downplays the importance of relative price changes, but the arguments are actually
closely related. My point in the more recent paper is simply: The relative price movements are
very small in the short run compared to movements in real exchange rates arising from failures of
the law of one price. In tests of PPP, even with long datasets, the short-run variation from the law
of one price dominates the data. The failure of the law of one price is transitory, so it appears that
deviations from PPP are transitory. That is, the movements in the first component of my
decomposition are so dominant that they swamp the movements in the second component which
may be important for the long run.
My paper with Chang-Jin Kim can be read as a resolution of these issues.(7) We estimate a
model for the U.S.-U.K. real exchange rate using more than 100 years of data. With Kalman
filter techniques, we decompose the real exchange rate into two components: one that has
permanent shocks (and, thus, a unit root), and one in which all shocks are transitory. We note that
the volatility of the real exchange rates has changed from time to time over the decades. So we
allow the variance of each component to follow a Markov-switching process. It turns out that a
single variance is sufficient for the permanent component, but that the transitory component
switches among three variance states. The transitory component is generally much more volatile
than the permanent component. The switches among states of low, medium, and high volatility
all are associated with monetary events. Generally when nominal exchange rates are floating, the
transitory component of the real exchange rate is highly volatile; when the exchange rate is fixed,
the transitory component is very quiescent. Other significant monetary events affect the volatility
of the transitory component. Based on this evidence, we note that the behavior of the transitory
component is consistent with a model of real exchange rates in which consumer prices in each
country adjust sluggishly, so that the nominal exchange rate dominates movements in real
exchange rates. The permanent component, although not very important in short-run movements
of the real exchange rates, appears to be related to fundamentals that drive relative prices as in
the neoclassical literature.
Pricing to Market
My research with John H. Rogers(8) aims to explain why the law of one price fails. We use
data on disaggregated price indexes for U.S. and Canadian cities.(9) We ask what is responsible
for variations in prices of similar goods across cities. For example, what leads to variance in the
price of men's clothing in New York compared to Los Angeles or Toronto? One hypothesis is
that more distant city pairs should witness greater variation, because transportation and other
costs effectively segment the markets and keep economic forces from equalizing prices. Another
view is that nominal prices are sticky. Under this view, there should not be too much variation of
prices between pairs of U.S. cities or pairs of Canadian cities. However, there should be large
fluctuations between Canadian-U.S. pairs, because in each country prices are set in their
respective currencies and the nominal exchange rate has been highly volatile.
In fact, the evidence in all the papers lends some support to both views. Distance does
play a role in explaining deviations from the law of one price, but the "border" effect is much
larger. Interestingly, further investigation(10) finds that sticky nominal prices can explain only a
bit more than half of the failure of the law of one price across borders. An alternative way of
comparing prices is to take the price of individual goods in each city relative to the overall price
index in that city. When that ratio is compared to the similar ratio in another city, no exchange
rate is involved. For example, we calculate the price of men's clothing in Toronto relative to
overall prices in that city, and compare it to the same ratio in New York. As we are comparing
one relative price to another, we do not need to convert any prices using nominal exchange rates.
Even using this method, though, there appear to be extremely large failures of the law of one
price between Canadian and U.S. cities. This suggests that other types of market segmentation
may be important for explaining international price movements. We focus on formal trade
barriers, but find that the implementation of the U.S.-Canada Free Trade Agreement had little
effect on the price behavior among North American cities. It is more likely that informal trade
barriers - marketing, transportation, and distribution services that are organized on a national
basis - account for the segmentation that prevents price convergence between U.S. and Canadian
Devereux and I have recently investigated the implications of this empirical evidence for
the choice of fixed versus floating exchange rates.(11) We follow the approach of the neoclassical
literature by modeling optimizing agents with long horizons facing uncertainty about the
economic environment. However, we augment that literature by allowing for price stickiness. We
pay special attention to the source of price stickiness: Do producers set prices in their own
currencies or do they set different prices in different national markets? The empirical evidence
seems to support the latter view. From a welfare standpoint, if prices are set in the producer's
currency, then there is some ambiguity about whether fixed or floating exchange rates are better.
Floating exchange rates tend to insulate the economy more from foreign monetary shocks, but the
average level of consumption is actually higher under fixed rates. However, if it is true that
producers "price to market," then (as we show) floating rates are unambiguously better than fixed
exchange rates in terms of maximizing welfare of consumers. If this is the proper description of
price setting, then floating exchange rates provide a tremendous advantage over fixed exchange
rates in terms of insulation from foreign monetary shocks. (I have investigated some of the same
issues in a traditional Mundell-Fleming framework, also providing some new empirical evidence
on the significance of failures of the law of one price for real exchange rate movements among
This line of research certainly undercuts the empirical foundations of the new neoclassical
models of exchange rates, but it leaves open this question: Do we have a successful empirical
model of nominal exchange rates? I believe the answer to that is still negative, at least for the
short-run behavior of exchange rates. Furthermore, I believe it is unlikely that we will develop a
model that can identify fundamental economic causes of short-run exchange rate movements,
because I believe that many short-run exchange rate movements are driven by herding behavior
This is a difficult position to defend, because it is a large leap from the statement that we
do not have a model of the fundamental determinants of short-run exchange rate movements to
the statement that those movements are not driven by fundamentals. One of the seminal pieces of
evidence to support this latter view is from Flood and Rose, who find that there is virtually no
difference in the behavior of economic fundamentals between fixed and floating exchange rate
periods.(13) One would think that if fundamentals were driving the exchange rate, they would
behave very differently when exchange rates were fixed compared to when they were floating.
My suspicions about speculative herd behavior arise from my study of the uncovered
interest parity puzzle. That parity relation says, for example, that when the short-term U.S.
interest rate exceeds the short-term German interest rate, investors should expect a depreciation
of the dollar. Unless one of the two assets is considered to be a riskier investment, the expected
return on the assets would be equalized. Investors must require a higher interest rate in one
country to compensate for the expected depreciation of the currency of that country.
The puzzle is that in the data (over an extremely wide variety of time periods and
countries(14)) the currency of the country with the higher interest rate actually tends to appreciate
rather than depreciate! There is a neoclassical literature that attempts to explain the puzzle by
attributing it to a time-varying risk premium. But I have argued that those models are not capable
of explaining the interest parity puzzle.(15) I have surveyed dozens of studies that attempt to
explain the puzzle with various models of rational risk-averse behavior.(16) None of those models
come close to explaining the perverse relationship between interest differentials and
Instead, I think the most convincing explanation comes from Frankel and Froot's model
with a group of "chartist" speculators who do not evaluate investment opportunities rationally,
but instead chase trends.(17) The idea is quite simple. Suppose that the Federal Reserve Board
were to raise short-term interest rates. In the Dornbusch model, the dollar would appreciate, but
then would immediately begin to depreciate in a gradual way. So, the higher interest rate would
be associated with an instantaneous appreciation, but also with expectations of a depreciation.
Frankel and Froot suggest that after that initial appreciation, there is herding behavior by
speculators. The speculators see that the dollar has appreciated, and they follow the trend and
plunge into dollars. There will be a further appreciation of the dollar, so that the interest rate
increase is associated with an expectation of future appreciation of the dollar. Investors'
sentiment is swayed by recent trends: when the interest rate rises, investors come to believe that
U.S. assets are good investments. They reinforce the interest rate advantage of U.S. assets by
bidding up the value of dollars. An analysis by Eichenbaum and Evans(18) lends support for
Frankel and Froot's theory of interest rate and exchange rate dynamics. Also, the
Markov-switching model estimated in my work with Hamilton fits the Frankel-Froot theory
precisely.(19) There are long swings in the value of the dollar. Once the dollar starts appreciating
(or depreciating), it continues in that direction for a long period. Furthermore, interest rates do
not rationally reflect those long-term exchange rate movements.
From the modern (1990s) perspective, the shortcoming of the Frankel-Froot model is that
it allows irrational herding behavior by economic agents. Additional serious research is needed to
understand whether nonfundamental speculation can really drive short-run behavior of exchange
1. R. Dornbusch, "Expectations and Exchange Rate Dynamics," Journal of Political Economy, 84
(1976), pp. 1161-1176.
2. R. Meese and K. Rogoff, "Empirical Exchange Rate Models of the Seventies," Journal of
International Economics, 14 (1993), pp. 3-24.
3. C. Engel and J. Frankel, "Why Interest Rates React to Money Announcements: An Answer
From the Foreign Exchange Market," Journal of Monetary Economics, 13 (1984), pp. 31-39.
4. C. Engel, "Real Exchange Rates and Relative Prices," Journal of Monetary Economics, 32
(1993), pp. 35-50.
5. ---, "Accounting for U.S. Real Exchange Rate Changes," Journal of Political Economy (1999,
6. ---, "Long Run PPP May Not Hold After All," Journal of International Economics (1999,
7. C. Engel and C.-J. Kim, "The Long-Run U.S./U.K. Real Exchange Rate," Journal of Money,
Credit and Banking (1999, forthcoming).
8. C. Engel and J.H. Rogers, "How Wide Is the Border?," American Economic Review, 86
(1996), 1112-1125; "Regional Patterns in the Law of One Price: The Roles of Geography and
Currency," in The Regionalization of the World Economy, J.A. Frankel, ed. Chicago: University
of Chicago Press, 1998; "Relative Price Volatility: What Role Does the Border Play?," Working
paper, 1998, available at http://www.econ.washington.edu; and C. Engel, M.K. Hendrickson, and
J.H. Rogers, "Intranational, Intracontinental, and Intraplanetary PPP," NBER Working Paper No.
6069, June 1997, also published in Journal of the Japanese and International Economies, 11
(1997), pp. 480-501.
9. C. Engel and J.H. Rogers, "How Wide Is the Border?," American Economic Review, 86
10. ---, "Relative Price Volatility: What Role Does the Border Play?," Working paper, 1998,
available at http://www.econ.washington.edu.
11. M.B. Devereux and C. Engel, "Fixed vs. Floating Exchange Rates: How Price Setting Affects
the Optimal Choice of Exchange-Rate Regime," Working paper, 1998, available at
http://www.econ.washington.edu; and "The Optimal Choice of Exchange-Rate Regime:
Price-Setting Rules and Internationalized Production," Working paper, 1998, available at
12. C. Engel, "A Retrial in the Case Against the EMU," Working paper, 1998, available at
13. R. Flood and A. Rose, "Fixing Exchange Rates: A Virtual Quest for Fundamentals," Journal
of Monetary Economics, 36 (1995), pp. 3-37.
14. C. Engel, "The Forward Discount Anomaly and the Risk Premium: A Survey of Recent
Evidence," Journal of Empirical Finance, 3 (1996), pp. 123-192.
15. ---, "On the Foreign Exchange Risk Premium in a General Equilibrium Model," Journal of
International Economics, 32 (1992), pp. 305-319; C. Engel, "The Risk Premium and the
Liquidity Premium in Foreign Exchange Markets," International Economic Review, 33 (1992),
16. ---, "The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence,"
Journal of Empirical Finance, 3 (1996), pp. 123-192.
17. J. Frankel and K. Froot, "Chartists, Fundamentalists and the Demand for Dollars," in Private
Behavior and Government Policy in Interdependent Economies, A. Courakis and M. Taylor, eds.
Oxford: Clarendon Press, 1990.
18. M. Eichenbaum and C. Evans, "Some Empirical Evidence on the Effects of Shocks to
Monetary Policy on Exchange Rates," Quarterly Journal of Economics, 110 (1995), pp.
19. C. Engel and J.D. Hamilton, "Long Swings in the Dollar: Are They in the Data and Do
Markets Know It?," American Economic Review, 80 (1990), pp. 689-713; C. Engel, "Can the
Markov-Switching Model Forecast Exchange Rates?," Journal of International Economics, 36
(1994), pp. 151-165.