Review of International Economics, 6(4), 683–694, 1998
Exchange Rates and Oil Prices
Robert A. Amano and Simon van Norden*
Abstract
The paper documents a robust and interesting relationship between the real domestic price of oil and real
effective exchange rates for Germany, Japan and the United States. It also offers an explanation of why the
real oil price captures exogenous terms-of-trade shocks, and why such shocks could be the most important
factor determining real exchange rates in the long run.
1. Introduction
The exchange rate is arguably the most difficult macroeconomic variable to model
empirically. Surveys of exchange rate models, such as Meese (1990) and Mussa (1990),
tend to agree on only one point: existing models are unsatisfactory. Monetary models
that appeared to fit the data for the 1970s are rejected when the sample period is
extended to the 1980s (Meese and Rogoff, 1983). Later work on the monetary
approach, such as Meese and Rogoff (1988), find that even quite general predictions
about the co-movements of real exchange rates and real interest rates are rejected by
the data. In short, there are several reasons to doubt the ability of traditional exchange
rate models to explain exchange rate movements.
Quite recently, however, we have begun to see more positive (but still controversial)
results emerging in three areas. First, work by researchers such as MacDonald and
Taylor (1994) has shown that a long-run relationship exists among the variables in the
monetary model of exchange rates, and that such models perform better than a random
walk in out-of-sample forecasting. The data, however, reject most of the parameter
restrictions imposed by the monetary approach, so it is uncertain whether these results
are really evidence in favor of the monetary model.1 Moreover, this positive evidence
of a long-run monetary model contrasts with the findings of other researchers such as
Cushman et al. (1996).
The second line of research has evolved around the idea of purchasing power parity
(PPP). As noted by Froot and Rogoff (1994), researchers have found significant evidence in favor of PPP when they use sufficiently long spans of data. This is a particularly confusing result, since it is precisely over such long periods that we would expect
gradual shifts in industrial structure, relative productivity growth and other factors to
alter real equilibrium exchange rates.2
Third, structural time-series work on the determinants of real exchange rate fluctuations indicate that real shocks or permanent components play a major and significant
role in explaining real exchange rate fluctuations. Univariate and multivariate
Beveridge and Nelson (1981) decompositions by Huizinga (1987) and Baxter (1994)
* Amano: Bank of Canada, Ottawa, Ontario, Canada, K1A 0G9. Fax: (613) 782-7163; E-mail: bamano@bankbanque-canada.ca. van Norden: Service de l’enseignement de la finance, Ecole des Haute Etudes Commerciales, Montreal, Quebec, H3T 2A7, Canada. Fax: (514) 340-5632; E-mail: svn@alum.mit.edu. We thank
seminar participants at the Bank of Canada and the Federal Reserve Bank of Kansas City for their suggestions. Preliminary versions of this paper were written while the authors were with the International
Department of the Bank of Canada. This paper represents the views of the authors and does not necessarily reflect those of the Bank of Canada or its staff. Any errors or omissions are ours.
© Blackwell Publishers Ltd 1998, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA.
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Robert A. Amano and Simon van Norden
find that, even though real exchange rates may not follow a random walk, most of their
movements are due to changes in the permanent components. Evans and Lothian
(1993) use the Blanchard and Quah (1989) decomposition, and find that much of the
variance of both real and nominal exchange rates from a number of countries over
both short and long horizons is due to real shocks. The conclusions from the structural
time-series literature therefore seem to be robust to both decomposition method and
currencies. This has led some to suggest that an unidentified real factor may be causing
persistent shifts in real equilibrium exchange rates.3
In this paper, we try to identify this real factor by examining the ability of real
domestic oil prices to account for permanent movements in the real effective exchange
rate of Germany, Japan, and the United States over the post-Bretton Woods period.
The potential importance of oil prices for exchange rate movements has been noted
by, inter alios, Krugman (1983) and Rogoff (1991). Although these models are intuitively appealing, the empirical work in this area has several important gaps. First, while
there are several studies on the link between oil prices and US macroeconomic aggregates, exchange rates are not included (Hamilton, 1983; Dotsey and Reid, 1992).
Second, there is also some analysis with calibrated macromodels (Yoshikawa, 1990)
which suggests that oil price fluctuations play an important role in exchange rate movements. These studies, however, tend to lack econometric rigor and consider a data
sample limited either in length or number of currencies. Third, some recent papers such
as Throop (1993) find evidence of a long-run relationship between exchange rates and
a number of macroeconomic factors, including oil prices. The tests used in these papers,
however, tend to produce false evidence of cointegration when several variables are
included in the system.4 In addition, they do not examine the causal relationship
between these variables, so it is not clear whether these are models of exchange rate
determination or whether they simply capture the influence of exchange rates on a
variety of other macroeconomic variables.
We do not argue that oil prices play a unique role in exchange rate determination.
Instead, we rationalize its explanatory power by noting that, for the three currencies
and for the time period we consider (roughly the post-Bretton Woods period), oil
prices have been the dominant source of persistent changes in the terms of trade. This
follows from the fact that oil has been an important share of these nations’ imports,
and that its price was extremely volatile in the 1970s and 80s as a result of three distinct and highly persistent oil price shocks.5 In other work (not reported here), we show
that oil prices alone cannot explain the exchange rate movements for industrial nations
like Canada or the United Kingdom whose international trade in oil is much more
nearly balanced than that of the oil importers we consider in this paper.6
Of course, it would be a mistake to assume that terms of trade is an exogenous variable and to interpret its explanatory power for exchange rates as a causal relationship.
We have, however, good reason to treat oil prices as an exogenous variable. If we
examine the behavior of oil prices over the most recent floating exchange rate period,
we see that the series is dominated by major persistent shocks around 1973–74,
1979–80, and 1985–86, with another large but transitory shock in 1990–91. The historical record offers us a very plausible explanation for these shocks; they were supplyside shocks that were themselves the result of political conflicts specific to events in
the Middle East and therefore exogenous in a macroeconomic sense. Note that we are
not arguing that oil prices (or even the stability of price cartels) are immune to the
laws of supply and demand, or that they cannot be affected by shifts in the growth
rates of the industrialized world. Instead, we feel that there is ample reason to believe
that such demand-side factors have been small relative to the supply-side shocks expe© Blackwell Publishers Ltd 1998
EXCHANGE RATES AND OIL PRICES
685
rienced over the last 20 years, and that the supply shocks have been exogenous in the
sense of most macroeconomic models.7 Furthermore, comparing domestic real oil
prices with terms-of-trade series for each of the United States, Japan and Germany in
Figure 1 shows that oil prices shocks, indeed, appear to account for most of the major
movements in the terms of trade.8 In fact, the point correlation between the terms of
trade and the one-period lagged price of oil is −0.57, −0.78 and −0.92 for the United
States, Japan and Germany, respectively.
In the empirical work we present in subsequent sections, we use the real price of oil
as a proxy for exogenous changes in the terms of trade. While we do not claim that oil
prices would be a useful proxy for all nations, we feel that the price of oil is a good
approximation for some industrialized nations, such as the United States, Japan and
Figure 1. Terms of Trade and the Price of Oil
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Robert A. Amano and Simon van Norden
Germany. It should be noted that we also examined the relationship using terms-oftrade data rather than real oil prices. These results, available from the authors, are
broadly similar to the results which we present below using oil price data. As the case
for exogeneity of the terms of trade is less convincing than that for the real price of
oil, we will henceforth consider oil prices rather than the terms of trade. We are,
however, comforted by the fact that broadly similar results are found using aggregate
terms-of-trade data.
2. Unit-Root and Cointegration Results
In this section, we present evidence of a stable long-run relationship between real
exchange rates and real oil prices. The data we use are the Morgan Guaranty 15country real effective exchange rate series of Germany (mark), Japan (yen), and the
United States (dollar), and the domestic price of oil, defined as the US price of West
Texas intermediate crude oil converted to the domestic currency and then deflated by
the domestic consumer price index. The data are observed monthly and cover the
period 1973:01 to 1993:06.9 Figure 2 plots each country’s real exchange rate with its
respective real price of oil. From the figure, it is readily apparent that the real exchange
rate and the price of oil for each country are related over the sample period. In the
remainder of this section we examine these relationships in some detail.
Our first step is to examine the time-series properties of each variable using the augmented Dickey and Fuller (1979) and Phillips and Perron (1988) tests. The results,
available from the authors upon request, suggest that the data are well-characterized
as nonstationary processes.10,11
Our approach to testing for a long-run relationship between the real effective
exchange rate and the price of oil is to look for evidence of cointegration between the
two variables. This allows us to gauge the adequacy of specifying the real exchange
rate simply as a function of the price of oil. If the long-run real exchange rate is determined by nonstationary factors other than those associated with the price of oil, then
their omission should prevent us from finding significant evidence of cointegration (see
Engle and Granger, 1987). Evidence of cointegration, on the other hand, suggests that
asymptotically, the price of oil can adequately capture all the permanent innovations
in the real effective exchange rate.
We test for cointegration between exchange rates and oil prices using a cointegration test developed by Johansen and Juselius (1990). These results are reported in Table
1. The Johansen–Juselius (JJ) tests find evidence consistent with cointegration for all
three currencies, suggesting that the price of oil captures the permanent innovations
in the real exchange rate for Germany, Japan and the United States. Table 2 presents
the parameter estimates using the JJ methodology as well as that using Phillips and
Hansen’s (1990) fully modified least-squares (FMLS) estimator (we apply the latter
method since it allows us to apply Hansen’s (1992) tests for parameter stability).
According to the results, a 10% rise in oil prices causes a depreciation of the mark of
0.9%, a 1.7% depreciation of the yen, and an appreciation of the dollar of about 2.6%.
While the United States is a major importer of crude oil, our results imply that higher
oil prices lead to an appreciation of the US dollar in the long run.12 This “reverse”
effect is not entirely counterintuitive; in fact it is consistent with explanations offered
by various sources. For instance, one often-mentioned hypothesis is the relative termsof-trade effect. This effect posits that while the United States is a significant energy
importer, it is less dependent on imports than most of its major trading partners (apart
from Canada and Mexico).Therefore while the US dollar should depreciate in absolute
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Figure 2. Effective Exchange Rates and the Price of Oil
Table 1. Johansen and Juselius Tests for Cointegration
λ max statistic
Trace statistic
Equation
Mark
Yen
Dollar
Lags
r≤0
r≤1
r≤0
r≤1
5
4
4
19.81*
20.60*
21.89*
3.84
2.61
4.76
15.98*
17.99*
15.123*
3.84
2.61
4.76
Note: We performed the tests under the assumption that the cointegrating vector annihilates any drift terms in the exchange rate or price of oil.
Tests of this restriction are available from the authors. The critical values
are taken from Johansen and Juselius (1990). Lag lengths are determined
using standard likelihood ratio tests. We begin with 13 lags and use a 5%
critical value. r denotes the number of cointegrating vectors.
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Robert A. Amano and Simon van Norden
Table 2. The Estimated Effect of Oil Prices on Exchange Rates
Estimation
method
JJ
FMLS
Mark
Yen
Dollar
−0.087 (0.012)
−0.086 (0.011)
−0.183 (0.032)
−0.170 (0.029)
0.245 (0.073)
0.276 (0.089)
Note: Standard errors are in parentheses. The FMLS estimates are based
on a VAR(2) prewhitening procedure of Andrews and Monahan (1992)
as this gave us serially uncorrelated residuals. The JJ estimates are based
on the lag structure of Table 1.
Table 3. Hansen Stability Tests of the Cointegrating Vector
Equation
Mark
Yen
Dollar
Lc
MeanF
SupF
0.380 (> 0.09)
0.111 (> 0.20)
0.260 (> 0.19)
2.493 (> 0.20)
1.334 (> 0.20)
2.421 (> 0.20)
4.447 (> 0.20)
3.087 (> 0.20)
5.451 (> 0.20)
Note: We use the FMLS estimates from Table 2 to calculate these test
statistics. The reported values in parentheses are p-values.
terms, it should be expected to depreciate less than the currencies of its major trading
partners. Put another way, proponents of this view would argue that although higher
oil prices lower the US absolute terms of trade, higher oil prices will raise the US terms
of trade relative to its industrialized trading partners. Since our measure of the effective exchange rate takes only those countries into consideration, it is not surprising
that higher oil prices lead to an appreciation of the US dollar.
To interpret these elasticities it is important that the long-run parameter estimates
be structurally stable over the sample period. To test for structural stability of the parameter estimates we use a series of parameter constancy tests for I(1) processes recently
proposed by Hansen (1992)—the Lc, MeanF and SupF tests. All three tests have the
same null hypothesis of parameter stability, but differ in their alternative hypothesis.
Specifically, the SupF is useful if we are interested in testing whether there is a sharp
shift in regime, while the Lc and MeanF tests are useful for determining whether or
not the specified model captures a stable relationship. The results presented in Table
3 suggest that we are unable to reject the null hypothesis for any of the tests even at
the 20% level. We note that Hansen (1992) suggests that these tests may also be viewed
as tests for the null of cointegration against the alternative of no cointegration. Thus,
these test results also corroborate our previous conclusion of cointegration among the
variables under study.
Another way to assess the stability of these cointegrating relationships is to evaluate their performance in forecasting exchange rate movements out-of-sample. This
allows us to compare our results with those of Meese and Rogoff (1983), who reported
that structural exchange rate models failed to forecast consistently better out-ofsample than a random walk. Accordingly, we updated our data sample to March 1995
(April in the case of the United States) and used Meese and Rogoff’s methodology to
assess the forecast performance of the oil-price/exchange-rate relationship.13 The forecasting equation simply fits the log exchange rate to lagged values of itself and of the
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Table 4. Theil’s U-Statistics for Real Exchange Rate Forecasts
One lag
Four lags (five for Germany)
Starting
period
Horizon
(months)
USA
Germany
Japan
USA
Germany
Japan
1985:01
1
2
3
6
12
18
24
0.9703
0.9647
0.9574
0.9243
0.8251
0.7204
0.6499
1.0162
0.9980
0.9570
0.8096
0.6274
0.5539
0.5827
0.9736
0.9485
0.9264
0.8388
0.6907
0.5956
0.5633
0.8773
0.9357
0.9572
0.9740
0.8948
0.7627
0.6630
0.9622
0.9812
0.9778
0.9054
0.6658
0.5624
0.5737
0.8541
0.8680
0.8463
0.7599
0.5947
0.5127
0.4606
1989:01
1
2
3
6
12
18
24
1.0331
1.0449
1.0546
1.0630
1.1093
1.3258
1.5338
1.0548
1.0527
1.0246
0.8743
0.7293
0.7631
1.2056
1.0396
1.0365
1.0322
0.9421
0.8371
0.7200
0.5864
0.9158
0.9701
0.9889
1.0188
1.0222
1.1876
1.2771
0.9330
0.9431
0.9682
0.9149
0.7315
0.7274
1.1646
0.9090
0.9461
0.9418
0.8596
0.7353
0.6319
0.5269
Note: The U-statistic is the ratio of the RMSE of a linear forecasting equation to the RMSE of a random
walk forecast. The forecast equation contains the indicated number of lags of the real exchange rate and the
real price of oil in domestic currency. The equation is estimated recursively by least squares and forecasts
use ex post information on real oil prices only.
log of the real oil price. Two alternative lag lengths were used. In constructing the cointegration tests we saw that four lags (five in the case of Germany) were required to
correct for serial correlation in the residuals of the vector error-correction model. We
also examine the behaviour of a system with only one lag in order to isolate the forecasting ability of the long-run error-correction mechanism from any associated shortrun dynamics.
Table 4 reports Theil’s U-statistic (which is the ratio of the root-mean-squared error
(RMSE) of the model’s forecast to the RMSE of a random-walk forecast) for a variety
of forecast periods and forecast horizons. Values less than 1.0 indicate that the oil-price
relationship forecasts better than a random walk over the period examined, while
values greater than 1.0 imply the opposite.
For the forecast period beginning in 1985, we see that the forecasts based on oil
prices perform better than a random walk for nearly every currency, forecast horizon
and lag length considered. The improvement tends to increase with the forecast
horizon, with the oil price model showing little advantage at the shortest horizons, but
at horizons of 12–24 months its forecast has a RMSE that is roughly one-third less than
that of the random walk. The results for the four- and five-lag models are usually quite
similar to those for the one-lag model, implying that most of the forecasting power is
coming from the cointegrating relationship as opposed to any additional short-run
dynamics.
For the forecast period beginning in 1989, the forecasting equation does noticeably
worse. Roughly half the U-statistics are now greater than 1.0, there is no clear tendency
for them to improve as the forecast horizon lengthens (except for Japan), and the equation with several lags now tends to forecast better than the single-lag equation. The
reasons for this deterioration in forecast performance can be easily understood if we
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Robert A. Amano and Simon van Norden
consider the behaviour of real oil prices over this period (see Figure 1 or 2). Oil prices
experienced a major persistent drop at the end of 1985 and, with the exception of a
sharp and very short-lived rise during the Gulf War in 1990–91, have been relatively
stable thereafter. Obviously, in the absence of large persistent movements in oil prices,
a forecasting equation based on long-run movements in oil prices will have difficulty
forecasting better than a random walk. This is precisely what we find in Table 4.
Some may argue that because our measure of domestic oil prices uses the bilateral
exchange rate with the United States to convert US dollar oil prices into a domestic
price, any evidence of cointegration is simply a result of a common trend between the
effective and bilateral exchange rates. However, this is unlikely to be the case. Specifically, we investigated this possibility by using the bilateral rate as the explanatory variable in the place of the real domestic price of oil. With this change, we find no evidence
of cointegration even at the 10% significance level. Moreover, such an explanation
cannot explain the evidence of cointegration found between real US dollar oil prices
and the US real exchange rate. Finally, if we are simply capturing a relationship
between bilateral and effective exchange rates we should not find unidirectional
causality in our systems. We address this point in the next section.
3. Causality and Exogeneity
From Engle and Granger (1987) we know that cointegration in a two-variable system
implies that at least one of the variables must Granger-cause the other. However, the
results presented above do not indicate whether the long-run relationship we have
found reflects the endogeneity of the domestic price of oil, or the determination of the
exchange rate, or both. While understanding the causal links between these variables
may be interesting in its own right, we note that causality from the price of oil to the
exchange rate would also imply that exchange rate changes are forecastable, and therefore implies a rejection of semi-strong market efficiency.
Our first step in testing for causality is to test for “long-run causality”, or more accurately, whether any of our variables are weakly exogeneous in the sense of Engle
et al. (1983). This can be tested using the likelihood-ratio test described in Johansen
and Juselius (1990). The results shown in Table 5 imply that the price of oil is weakly
exogeneous, while the real exchange rates are not. This implies that deviations from
the long-run relationship between oil prices and exchange rates significantly influence
exchange rates, but do not significantly affect domestic oil prices.
Next we test for more general Granger-causality using standard tests on the vector
autoregression level representation of our system. As demonstrated in Sims et al.
(1990), standard inference procedures are valid in this case under the maintained
Table 5. Johansen Weak Exogeneity Tests
Equation
Mark
Yen
Dollar
Lags
H0: Price of oil is
weakly exogeneous
H0: Exchange rate is
weakly exogeneous
5
4
4
0.414
0.158
0.901
< 0.000
< 0.000
0.001
Note: Reported numbers are p-values (the lowest significance level at
which we can reject the null hypothesis).
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hypothesis of one cointegrating vector and provided that we test the exclusion restrictions on one variable at a time. These results are reported in Table 6.14 They indicate
strong evidence that the price of oil Granger-causes the real exchange rate, whereas
there is no evidence of the reverse.
If we accept the conclusion that exchange rates do not Granger-cause oil prices as
our empirical evidence suggests, what other interpretation can we offer for the apparent long-run relationship between these two variables? An important possibility to
consider is that oil prices and exchange rates are jointly determined by some third
(omitted) macroeconomic variable. This would imply that we have a reduced-form
relationship, but not one that should be thought of as a structural or causal link.
Without a specific alternative, this is not a criticism that we can test. Nonetheless we
feel that this is unlikely to be the case. As we argued in the introduction, the behavior
of oil prices over our sample period is dominated by major persistent supply shocks
that have been exogenous in the sense of most macroeconomic models. Accordingly,
few macroeconomic insights are likely to be gained from a search for a codeterminant
of exchange rates and oil prices.
Previous formal analysis of this question for the United States would seem to
support our view. In particular, Hamilton’s (1983) claim that major oil price increases
preceded almost all post World War II recessions in the United States is accompanied
by an extensive search for variables that were Granger-causally-prior to domestic US
oil prices. After exploring a wide range of variables including aggregate prices, wages,
real output, monetary aggregates, bond yields, and a stock-price index, Hamilton finds
that almost none seemed to cause oil prices and none could explain its effect on
output.15 As for the monetary and fiscal variables that have been the mainstay of
modern exchange rate modeling, we have already cited studies which show that the
explanatory power of these variables for exchange rates is limited. Furthermore, even
supposedly “exogenous” measures of monetary policy such as that recently proposed
by Romer and Romer (1989) for the United States may capture a considerable amount
of endogenous policy reaction to exogenous external oil prices. Indeed, Dotsey and
Reid (1992) show that Romer and Romer’s measure of monetary policy is coincident
with several major oil price shocks, and that its explanatory power for output variables
vanishes when oil prices are included in the system. We therefore think it is unlikely
that oil prices are simply acting as a proxy for some other macroeconomic determinant
of long-run exchange rates.
4. Concluding Remarks
We have documented what we think is a robust and interesting relationship between
the real domestic price of oil and real effective exchange rates for Germany, Japan and
Table 6. Granger-Causality Tests
Equation
Mark
Yen
Dollar
Lags
H0: Price of oil does not cause
exchange rates
H0: Exchange rates do not cause
oil prices
5
4
4
0.002
0.012
0.017
0.239
0.422
0.857
Note: Reported numbers are p-values.
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Robert A. Amano and Simon van Norden
the United States. We have also explained why we think the real oil price captures
exogenous terms-of-trade shocks, and why such shocks could be the most important
factor determining real exchange rates in the long run. Given the ongoing debate over
the determination of exchange rates and the other work we have cited examining relationships between exchange rates and the term of trade for other industrialized countries, we think that this is an area that deserves further research.
This research could be usefully extended in several directions. Obviously, more evidence could be gathered, perhaps for additional currencies, for additional measures of
the terms of trade, or from additional testing methods. More structural work on the
relationship between oil prices and exchange rates would also be useful. There are
several terms-of-trade models that predict oil prices will have important effects on
industrialized-country exchange rates. As such, more detailed testing and comparison
of these competing models may be warranted.
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Notes
1. Recent Monte Carlo studies (Godbout and van Norden, 1997) have found that the systems
approach to cointegration, an approach often used in this literature, will tend to find evidence
of cointegration where none exists in systems with many variables (as is the case with the monetary model of exchange rate determination).
2. For example, see the discussion on Balassa–Samuelson effects in Froot and Rogoff (1994).
3. Those investigating the failure of real interest rate parity relationships have already tried to
identify this factor, without much success (Meese and Rogoff, 1988; Baxter, 1994). Their research
has focused on the explanatory power of fiscal policy and external indebtedness. Other studies
have used a broader range of explanatory variables.
4. For reference, see note 1.
5. The macroeconomic importance of oil prices may also in part be due to the fact that other
important forms of energy (coal, gas, and to a lesser extent electricity) are substitutes for oil, so
that their prices tend to reflect variations in oil prices.
6. Amano and van Norden (1995) document the Canadian evidence.
7. See Adelman (1995) for a full discussion of the determination of oil prices over this period.
8. The terms-of-trade variables are calculated as the ratio between the unit value of exports and
the unit value of imports. These data are taken from the International Financial Statistics (International Monetary Fund).
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Robert A. Amano and Simon van Norden
9. Although other measures of the real exchange rate are available, we chose the Morgan Guaranty 15-country measure simply because it gave us the longest span of data. We should note that
the results appear robust to different price deflators and measures of the real effective exchange
rate. The latter is not surprising as the different measures are very highly correlated (> 0.98).
10. In additional work not reported here, we also found that real interest rate differentials alone
cannot explain the failure of PPP, and structural decompositions suggest that real shocks are an
important source of persistent real exchange rate movements. These results are available from
the authors.
11. We emphasize that the nonstationarity assumption is not crucial to our conclusions concerning the stability, causality or out-of-sample forecasting ability of the relationship we uncover
between the price of oil and real exchange rates.
12. We note that the United States is not the only nation for which there is evidence of such a
“reverse” effect. Amano and van Norden (1995) present evidence of a similar effect for Canada,
where higher energy prices lead to a weaker Canadian dollar despite the fact that Canada is a
substantial exporter of energy.
13. Specifically, we used least-squares to estimate the level of the exchange rate as a linear function of past exchange rates and oil prices, and then forecast the exchange rate a number of
periods ahead using ex post realizations of oil prices and (if needed) previously calculated forecasts of the exchange rate at shorter horizons. The least-squares estimates were updated each
period while ensuring that no data from the forecast sample were used to estimate the forecasting equation. No attempt was made to optimize the number of lags used, this being fixed at
the length used for the cointegration tests. See Meese and Rogoff (1983) for further details.
14. Since all results are based on asymptotic approximations, we use the limiting chi-squared
critical values instead of their more common F-distributed counterparts.
15. Apparently, causally-prior variables were import prices (weak evidence that is sensitive to
the lag-length used), coal prices, and the ratio of person-days idle due to strike to total employment. The first two variables could simply reflect the same external energy supply shocks, but
might respond to these shocks more quickly than domestic energy prices. The latter variable
may simply reflect the influence of strikes by US coal miners on domestic energy prices in the
1950s.
© Blackwell Publishers Ltd 1998