A Note on the Empirical Relation Between Oil Prices and the

Value of the Dollar1

Jaime Marquez and Silvia Merler

Johns Hopkins School of Advanced International Studies

April 26, 2017

1The calculations are carried out with OxMetrics; see Doornik and Henry (2013). We have not received fundingfrom any source to conduct this project.

Abstract

We offer an empirical characterization of the association between the real price of oil and various measures of

the external value of the dollar: effective versus bilateral rates. Most of the literature uses effective exchange

rates and this practice has conceptual limitations. First, they suffer from an identification problem: is the

relation between price of oil and exchange rates or between the price of oil and time-varying aggregation

weights? Second, effective exchange rates are mental constructs for which there is no financial market.

These limitations are avoided by the use of bilateral exchange rate. We consider models with effective

exchange rates and with bilateral exchange rates. We find that models using effective exchange rates lack

the statistical reliability that is central for practical applications. The model using bilateral exchange rates

satisfies the statistical reliability criteria.

Contents

1 Introduction 2

2 Data 3

3 Analysis 63.1 Econometric Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2 Time-series Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3 Cointegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 Reliability 104.1 Deviations from Long Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.2 Predictive Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.3 Parameter Constancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.4 Dynamic Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.5 Residuals’Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5 Conclusions 16

A Appendices 17A.1 Evolution of the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

A.2 Data Sources and Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

A.3 Augmented Dickey-Fuller Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1

1 Introduction

Knowing the relation between the price of oil and the external value of the dollar is relevant for practitioners

in the field of international finance: oil and currencies are financial assets and knowing their relation might

be helpful in exploiting profit opportunities.1 Yet, thirty years of empirical work on this relationship yields

contradictory and unreliable results.2 Indeed, as table 1 shows, there is no agreement on how to measure

the value of the dollar, on the sample period used for estimation, and on the nature of the relation:

Table 1: Attributes of Selected Studies on the Relation Between the Price of Oil and the Value of the Dollar

Study Price of Oil (P ) Measure of Dollar (D) Sample Causality Relation

Reboredo et al (2014) WTI bilateral currencies 2000-2012 P −→ D Inverse

Fratzscher et al. (2013) WTI NEER 2001-2012 P ↔ D Inverse

Grisse (2010) WTI NEER major currencies 2003-2010 P −→ D Inverse

Breitenfeller et al. (2008) WTI Dollar against euro 1983-2006 P ↔ D Inverse

Cheng (2008) Average, nominal NEER & REER 2000-2007 D −→ P Inverse

Yousefi et al (2005) Exporter specific REER major currencies 1989-1999 D −→ P Inverse

Benassy-Quere et al. (2005) WTI/CPIus REER & Dollar/euro 2002-2004 P −→ D Direct

Amano et al. (1998) WTI/CPIus REER major currencies 1972-1993 P −→ D Direct

This study WTI/CPIus REER, major & other 2000-2016 P ↔ D Inverse

bilateral currencies 2000-2016 P ↔ D Direct

Memo. WTI: West Texas Intermediate; REER: real effective exch. rate; NEER: nominal effective exch. rate

For measuring the dollar, the literature uses either effective or bilateral exchange rates. As documented

below, the difference is consequential. For estimation, the literature devotes a fair amount of effort to

determining whether movements in oil prices "cause" movements in the value of the dollar or the other way

around3 . The results from this effort are not, however, invariant to the choice of sample-periods. Indeed,

the oil market has witnessed a tangible decline in OPEC’s ability to set prices, which means that treating

the price of oil as an exogenous variable is of questionable usefulness.4 Further, the importance of emerging

economies for both oil and international financial markets has been consequential: China is the largest

economy in the world and the yuan is now included in the IMF’s Special Drawing Rights (SDR) basket.

Yet studies routinely neglect the currencies of emerging markets.5 In terms of statistical reliability, evidence

on the properties of the residuals, forecast accuracy, and parameter constancy are generally not reported.6

Finally, given that we are dealing with time series, how do we know that existing results are not reflecting

a spurious relation?

We offer an empirically reliable relation between the real price of oil and the external value of the dollar,

both in real terms, since 2000. To this end, we use a vector-error correction modeling strategy in which both

oil prices and exchange rates are endogenous. We use three models that differ in how to measure the external

1For example, one could combine futures and options contracts. The futures contract would be for a given price of oil; theoption contract would have strike prices determined by a long-run relation between the price of oil and the dollar.

2The increased in attention is fairly recent: (see appendix). For early theoretical work, see Golub (1983) and Krugman(1980); Breitenfellner, A. and J. Crespo Cuaresma (2008) offer more recent work on the origins of this relation.

3See Amano et al. (1998) for example.4As evidence of this loss of power, the multiplcity of exchange-rate crises during the 1990s and the large-scale offi cial

intervention in foreign exchange markets had little effect on movements on oil prices because of oil producers did not have thepricing power to offset losses in purchasing power from adverse currency movements.

5An important exception is Bnassy-Qur, Mignon and Penot (2005).6An important exception is Amano and Norden (1998).

2

value of the dollar: effective versus bilateral real exchange rates. Our results replicate the literature’s most

common finding: an inverse association between the price of oil and effective exchange rate. But this finding

suffers from conceptual and empirical limitations. Conceptually, the finding assumes that there is a market

in which "the" effective dollar is internationally traded. This mental construct would be useful if all bilateral

currencies moved in tandem or if the aggregation weights were fixed, but these two conditions are not met

in practice. Further, because movements in the effective value of the dollar owe to changes in both exchange

rates and weights one cannot identify whether the relation is between oil prices and trade weights or between

oil prices and exchange rates.

Ignoring these considerations amounts to ignoring the loss of information associated with aggregation of

bilateral exchange rates. Thus we apply our empirical strategy to the bilateral exchange rates included in

the SDR. The results contradict those based on effective exchange rates: A real appreciation of the dollar

is associated with an increase in the real price of oil. To the extent that this relation is relevant to hedging

strategies, we argue that reliance on effective exchange rates needs to be replaced with reliance on bilateral

rates. From a statistical standpoint, reliance on bilateral exchange rates yields a statistically reliable model

whereas using effective exchange rates does not. Further, from an economic standpoint, reliance on bilateral

rates avoids having to assume the existence of a fictitious financial market for the dollar and solves the

identification problem of not knowing whether the relation is between price of oil and exchange rates and

price of oil and weights.

2 Data

For the real effective exchange rates, we use the Federal Reserve Board’s three measures.7 The first measure,

known as the broad, is for the 26 currencies that are associated with bulk of U.S. trade; this measure is using

chained aggregation:Dt

Dt−1=

26∏i=1

(r i$,t

r i$,t−1

)wit,∑

wit = 1

where

r i$,t =

(CPIus,tCPIi,t

)·

D i$,t

D i$,t0

,

D i$,t is the nominal price of the U.S. dollar in terms of the ith currency, CPIj is the consumer price index

for the jth country, and wit is the "total" trade share (Leahy 1998). By convention, Dt=base is set equal to

100 in a given base period and the level of the index for all other periods is defined recursively. As a result,

the value of Dt represents the average growth rate of the aggregate relative to the base period.

Notice that movements inDt owe to changes in both exchange rates and weights. Thus one cannot identify

whether the relation is between oil prices and trade weights or between oil prices and exchange rates. Further,

the literature neglects the role that currencies of emerging markets might have on the relation between oil

prices and the value of the dollar. This neglect is not inconsequential: Since 2005 currencies of the emerging

economies are the most important in D (figure 1):

7Section A.2 contains all the data sources and transformations used in this paper.

3

EmergingWeightMajorWeight

1975 1980 1985 1990 1995 2000 2005 2010 2015 2020

30

40

50

60

70

Emerg in g Weig h t = M ex ico _ wg h t+ Ch in a_ wg h t+ Ko rea_ wg h t+ In d ia_ wg h t+ S in g ap o re_ wg h t+ Ho n g _ Ko n g _ wg h t+ M alay sia_ wg h t+ Brazil_ wg h t+ Th ailan d _ wg h t+ P h ilip p in es_ wg h t+ In d o n esia_ wg h t+ Israel_ wg h t+ S au d i_ Arab ia_ wg h t+ Ru ssia_ wg h t+ Ven ezu ela_ wg h t+ Ch ile_ wg h t+ Co lo mb ia_ wg h t ;M ajo rWeig h t = To talWeig h t ­ Emerg in g Weig h t;

EmergingWeightMajorWeight

Figure 1: Shares of Major and Other Currencies in D —in percent

This observation raises the question of whether sole reliance on D is helpful for characterizing its relation

to the real price of oil. Thus we also use the other two Federal Reserve’s real effective exchange rates: one

for the Major Currencies, Dmt, and one for the currencies of Other Important Trading Partners, Dot; these

measures use the same formula as that of D but differ in the choice of currencies and weights. Figure 2

shows the evolution of all three measures of the real effective exchange rates since 2000:

2000 2005 2010 2015

­0.20

­0.15

­0.10

­0.05

0.00

0.05

0.10

0.15

Majo r

Majo r

O th er Imp o rtan t Par tn ers

Bro ad

Figure 2: Real Effective Exchange Rates for the US Dollar displayed in logs

Though the three measures exhibit similar secular swings, their short-term movements are far from synchro-

nized: knowing movements in one measure do not translate into knowledge of the other measure.

We measure the real price of oil as the West-Texas Intermediate price divided by the U.S. Consumer

Price Index since 2000 (figure 3):

2000 2005 2010 2015

­0.25

0.00

0.25

0.50

0.75

1.00

1.25

1.50

U S CPI

CPI U S

N o min al W TI

N o min al W TI

Real W TI

Figure 3: US CPI and the Price of Oil: Nominal and Real - displayed in logs

4

After more than doubling in 12 years since 2000, the real price of oil has declined substantially since 2014;

movements between 2000 and 2016 exhibit substantial volatility.

Figure 4 shows scatter plots between the real price of oil and the three measures of the real effective

exchange value of the dollar:

­0.4 ­0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

­0.1

0.1

price of oil

Bro

ad

­0.4 ­0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

­0.2

0.0

0.2

price of oil

Maj

or

p

­0.4 ­0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

­0.1

00.

1

price of oil

Oth

er Im

porta

nt P

artn

ers

Figure 4: Unconditional Correlations Between the Real Price of Oil (x-axis) and alternative measures of

the Real Effective Value of the Dollar (y-axis)

Inspection of the evidence reveals what previous work has found: an inverse associations between these

real effective exchange rates and the real price of oil. But these results are not without limitations. First,

because changes in the D′s owe to changes in both exchange rates and weights, one cannot identify whether

are we detecting a relation between oil prices and trade weights or a relation between oil prices and exchange

rates. Second, even if the weights were fixed, it is not possible to rule out these results being an artifact

of aggregation of bilateral currencies. Third, given that the only information embodied in the D′s is the

average growth rate relative to the base period, what is the meaning of a relation between an average growth

rate and the level of the price of oil? Finally, these correlations assume that the notion of "the" effective

dollar is meaningful —that is, that there is a market where this dollar is internationally traded. This mental

construct is useful if the various bilateral currencies move in tandem or if the weights are fixed but as figures

5 and 6, these conditions are not met in practice:

Eu ro _ area_ wg h tJap an _ wg h tCh in a_ wg h tKo rea_ wg h tHo n g _ Ko n g _ wg h tBrazil_ wg h tTh ailan d _ wg h tAu stralia_ wg h tIn d ia_ wg h tSau d i_ Arab ia_ wg h tSwed en _ wg h tVen ezu ela_ wg h tCo lo mb ia_ wg h t

Can ad a_ wg h tM ex ico _ wg h tUn ited _ Kin g d o m_ wg h tS in g ap o re_ wg h tM alay sia_ wg h tSwitzerlan d _ wg h tPh ilip p in es_ wg h tIn d o n esia_ wg h tIsrael_ wg h tRu ssia_ wg h tArg en tin a_ wg h tCh ile_ wg h t

1980 1985 1990 1995 2000 2005 2010 2015

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

Eu ro _ area_ wg h tJap an _ wg h tCh in a_ wg h tKo rea_ wg h tHo n g _ Ko n g _ wg h tBrazil_ wg h tTh ailan d _ wg h tAu stralia_ wg h tIn d ia_ wg h tSau d i_ Arab ia_ wg h tSwed en _ wg h tVen ezu ela_ wg h tCo lo mb ia_ wg h t

Can ad a_ wg h tM ex ico _ wg h tUn ited _ Kin g d o m_ wg h tS in g ap o re_ wg h tM alay sia_ wg h tSwitzerlan d _ wg h tPh ilip p in es_ wg h tIn d o n esia_ wg h tIsrael_ wg h tRu ssia_ wg h tArg en tin a_ wg h tCh ile_ wg h t

Figure 5: Evolution of Bilateral Trade Weights - in percent

5

2000 2005 2010 2015

5.2

5.3

5.4

5.5

5.6

5.7 y en / d o llar

2000 2005 2010 2015

0.1

0.2

0.3

0.4

0.5Po u n d / d o llar

2000 2005 2010 2015

2.7

2.8

2.9

3.0rmb /d o llar

2000 2005 2010 2015

0.6

0.8

1.0

eu ro / d o llar

Figure 6: Evolution of real bilateral rates for yen, pound,RMB, and euro - displayed in logs

To emphasize the pitfalls of aggregation, figure 7 shows the unconditional correlations between the price

of oil and the bilateral exchange rates included in the SDR:

yen × p

­0.25 0.00 0.25 0.50 0.75 1.00 1.25

5.2

5.3

5.4

5.5

5.6

5.7 yen × ppound × p

­0.25 0.00 0.25 0.50 0.75 1.00 1.25

0.1

0.2

0.3

0.4

0.5 pound × p

rmb × p

­0.25 0.00 0.25 0.50 0.75 1.00 1.25

2.7

2.8

2.9

3.0

rmb × p euro × p

­0.25 0.00 0.25 0.50 0.75 1.00 1.25

0.6

0.8

1.0euro × p

Figure 7: Unconditional Correlations Between the Real Price of Oil (x-axis) and Bilateral Real Exchange

Rates (y-axis)

The associated unconditional correlations reveal that this identification problem is not just academic curios-

ity: There is a negative relation but only the relation with the euro appears meaningful.

3 Analysis

3.1 Econometric Framework

The unconditional correlations of figures 4 and 7, though informative, do not offer an unambiguous interpre-

tation of the regression lines: Should these be interpreted as causal relations from one variable to another

or as long-run equilibrium relations? If so, what is then the profile of dynamic adjustments?

To address these questions, we use a vector error correction model treating both oil prices and exchange

rates as endogenous. Specifically, this model explains the growth rates of the real price of oil p, real exchange

rates in terms of past growth rates and on the levels of this variables:

∆yt = Γ(L) ·∆yt−1 + Π · yt−1 + ut, ut˜IN(0,Ω) (1)

where Γ(L) = ‖λij(L)‖ and λij(L) is a polynomial of order 12 in the lag operator L, and Π is a matrix of

unknown coeffi cients; the specification includes seasonal dummies. This approach has several advantages: it

6

addresses the spurious regression critique, it treats both variables as jointly determined, and differentiates

between responses to short-run shocks and adjustments to the long-run relation.

To examine the potential loss of information from using effective exchange rates, we use three models

that differ in their measurement of the external value of the dollar:

Model 1 : Effective Broad yt = (pt dt)′

Model 2 : Effective, Major and Other Trading Partners yt = (pt dmt dot)′

Model 3 : Bilateral rates yt =(pt r yen

$t r euro$ t r pound

$t r rmb

$t

)′where p is the real price of oil; d is the broad measure of the dollar, dm is the measure of the dollar for the

major currencies, do is the measure for other important trading partners. Variables in lower case denote

logarithms. As an example, the analytical expression for model 2 is ∆pt

∆dmt

∆dot

= Γ(L) ·

∆pt

∆dmt

∆dot

+ Π ·

pt−1

dm,t−1

do,t−1

+

upt

udm,t

udo,t

(2)

Analytically, extracting the long run relation implied by equation (1) involves setting ∆yt = 0 in equation

(1):

0 = Γ(L) · 0 + Π · y + 0 ∴ Π · y = 0 (3)

Empirically, the existence of a long-run relation depends on the rank of Π. If the rank equals one, then

Π = α · β′ where β characterizes the long-run association among the components of y and α characterizes

responsiveness of y to deviations from the long-run association. For model 2, this condition is

Π =

αp

αdm

αdo

[ 1 βm β0

](4)

and substituting it into (2) yields ∆pt

∆dmt

∆dot

= Γ(L) ·

∆pt

∆dmt

∆dot

︸ ︷︷ ︸

short-run

+

αp

αdm

αdo

[ 1 βm β0

]·

pt−1

dm,t−1

do,t−1

︸ ︷︷ ︸

long-run

+

upt

udm,t

udo,t

(5)

Equation (5) explains the growth rate of the variables as responding to two forces: lagged effects from

previous shocks and the adjustment to deviations from long-run equilibrium (lre) measured as

lre =[

1 βm β0

]·

p

dm

do

= p+ βm · dm + βo · do = 0

This equation can be re-written as

p = −βm · dm − βo · do (6)

7

To be sure, this equation is an analytical construct based on the assumption that the rank of Π is one;

we have not shown yet empirical support for this assumption. Further, there is nothing causal about this

equation: it is not determining p in terms of d′s or the other way around. Rather, this equation is the

long-run equilibrium relation between p and the d′s. Further, as shown below in section 4.4, shocks induce

deviations from long-run equilibrium generate dynamically stable responses in all the endogenous variables.

3.2 Time-series Properties

The time-series properties of the variables examined here are crucial to characterizing the long-run relation.

Intuitively, the long run condition Π · y = 0 can only be met if y is non-stationary. To assess whether this

condition is met, we use monthly observations from January 2000 to December 2015 to estimate the series’

autocorrelation functions. Figures 8 and 9 report the results:

0 5 10 15 20

0.5

1.0 Broad

0 5 10 15 20

0.5

1.0 Major

0 5 10 15 20

0.5

1.0 Other Important Trading Partners

0 5 10 15 20

0.5

1.0 Price of Oil

0 5 10 15 20

0

1Broad

0 5 10 15 20

0

1 Major

0 5 10 15 20

0

1Other Important Trading Partners

0 5 10 15 20

0

1Price of Oil

Figure 8: Autocorrelation Function for d, dm, do, and p. The horizonal axis is in months.

8

0 5 10 15 20

0.5

1.0 Yen

0 5 10 15 20

0.5

1.0 Pound

0 5 10 15 20

0.5

1.0 RMB

0 5 10 15 20

0.5

1.0 Euro

0 5 10 15 20

0

1Yen

0 5 10 15 20

0

1 Pound

0 5 10 15 20

0

1 RMB

0 5 10 15 20

0

1 Euro

Figure 9: Autocorrelation Function for yen, pound,RMB, and euro. The horizonal axis is in months.

The series exhibit significant autocorrelation that does not disappear after 20 months; this persistence is

evidence of non-stationarity. The figures also report the autocorrelation function for ∆y which show no

persistence. These two results suggest that the variables are I(1). These results are confirmed by the

augmented Dickey-Fuller tests reported in the appendix A.3.

3.3 Cointegration

Having established that the series are integrated of order one, we now estimate the parameters of the models

to determine the rank of Π. Following Amano et al. (1998), we use Johansen’s Trace and Max tests.8 The

results are shown in table 2:8This method begins by testing whether the rank of Π is zero. If this hypothesis is not rejected, then there is no long-run

relation between p and d. If this hypothesis rejected, then it tests whether the rank of Π is one. If this hypothesis cannot berejected, then the rank Π is one and that there is linear combination of the levels of p and d that is stationary. Finding that therank of Π is two, then there would be two long-run relations that would not be possible to interpret as an arbitrage condition.

9

Table 2: p-values for Johansen’s Rank Tests: 2000-2015

Rank of Π Trace Max

Test Test

Model 1 0 0.032 0.054

1 0.100 0.100

Model 2 0 0.012 0.079

1 0.060 0.232

2 0.024 0.024

Model 3 0 0.000 0.002

1 0.065 0.235

2 0.18 0.579

3 0.121 0.197

4 0.110 0.110

Only for model 3 we cannot reject the hypothesis that the rank of Π equals one. For models 1 and 2, we

cannot reject the hypothesis that the rank of Π is one with the Trace test only.

The associated long-run equilibrium relations are shown in table 3

Table 3: Long-run Equilibrium Relations—FIML Estimation: January 2000 to December 2015

Model 1 p = −4.00 · d(se) (0.44)

Model 2 p = −2.56 · dm −0.81 · do(se) (0.55) (0.58)

Model 3 p = 1.46 · r yen$

+2.95 · r pound$

+0.44 · r rmb$−2.55 · r euro

$

(se) (0.44) (0.90) (0.43) (0.49)

At the risk of stating the obvious, the differences in both magnitude and signs across models are not

trivial: a one percent real appreciation in the dollar is associated with decline in the real price of oil ranging

from four percent decline usingD to 2.6 percent when usingDm.9 In contrast, a one percent real appreciation

of all the dollar using the SDR currencies is associated with an increase in the real price of oil of 2.3 percent.

These differences are not due to differences in sample periods or estimation methods. Instead, they are due

to ignoring that pitfalls of aggregation: the relations for models 1 and 2 are between the level of real oil

prices and the growth rate of a mental construct.

4 Reliability

The absence of strong priors about parameter values injects an ambiguity as to what measure of the dollar to

use. To address this ambiguity, we apply criteria to these models to examine whether they are statistically9The coeffi cient for do is statistically insginificant.

10

reliable. If they are not, then that model’s relevance is undermined.

4.1 Deviations from Long Run

For a long-run equilibrium relation to be meaningful, deviations from it should be transitory. The alternative

is being in disequilibrium for extended periods which undermines the very notion of equilibrium. So the

question is whether the time series of β′· yt−1 shows frequent oscillations around zero. Figure 10 shows

β′· yt−1 for the three models:

2000 2005 2010 2015

­0.25

0.00

0.25model 1

2000 2005 2010 2015

­0.25

0.00

0.25 model 2

2000 2005 2010 2015

­0.25

0.00

0.25

0.50 model 3

Figure 10: Deviations of the Long-Run Equilibrium Relation - Alternative Models

Deviations from the long-run relation are short-lived only for model 3. For the other models, such deviations

last years and are not consistent with the notion of equilibrium given the lack of support for cointegration

for models 1 and 2 (table 2 above).

4.2 Predictive Accuracy

To judge the predictive accuracy of the models, we compare the one-step ahead forecasts from January 2016

to December 2016; table 4 shows the root mean squared forecast errors (RMSFE) in percent for the three

models and for the random walk model:

11

Table 4: 1-step ahead RMSFE for Alternative Models

January 2016-December 2016

Random

Model 1 Model 2 Model 3 Walk

p 11.4 12.6 11.9 10.7

d 1.3 1.5

dm 1.9 1.7

do 1.5 1.5

r pound$

4.5 3.3

r euro$

2.3 1.8

r rmb$

1.6 1.5

r yen$

4.1 3.3

Inspection of the results reveals three conclusions: First, the RMSFE for the real oil prices are comparable

across models and a somewhat higher than the one from the random walk model. Second, the RMSFE

for real exchange rates from all three models are generally higher than the one from the random walk; the

exception is for D. Third, predictive accuracy is comparable across models and thus forecast errors do not

help discriminate among these models.

But models do not live by forecasts alone: though random walk formulations offer a slight increase in

accuracy, they cannot give any information on whether there is a relation between the price of oil and the

dollar.

4.3 Parameter Constancy

Following Amano and Norden (1998), we test the stability of the parameter estimates. This consideration

is important because our sample includes the financial crisis of 2008 and the abrupt decline in the price of

oil in 2014. In other words, is there evidence that the parameters are invariant to those disruptions? To

this end, we estimate the β′s recursively. We begin with a sample of 70 observations and then proceed to

increase the sample size one observation at a time. Figures 11-13 show the recursive 95 percent confidence

intervals for the estimated β′s:

12

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 20162.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5Co in tegration Coefficient fo r Bro ad Effective ER

Figure 11: Recursive 95% bands for Model 1

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

2.5

5.0

7.5 Co in tegration Coefficient fo r Majo r Effective ER

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

­5.0

­2.5

0.0

2.5

Co in tegration Coefficient fo r Oth er Imp ortan t Partners Effective ER

Figure 12: Recursive 95% bands for Model 2

13

2010 2015

­10

­5

0

5Co in tegratio n Coefficient fo r y en /d ollar

2010 2015

­10

0

10Co in tegratio n Coefficient fo r p oun d/do llar

2010 2015

­5

0

5Co in tegration Coefficient fo r RMB/dollar Co in tegration Coefficient fo r euro/do llar

2010 2015­5

0

5

10

Figure 13: Recursive 95% bands for Model 3

All of the parameters estimates are consistent with their assumed constancy. Thus, unless one has strong

priors about the parameter values, recursive estimation does not help discriminate among these models. To

this end, we examine the properties of the residuals.

4.4 Dynamic Stability

So far, we have focused on characterizing the long-run equilibrium relation. Little, however, has been shown

on how the system adjusts to such relation after a shock takes place. Is the response gradual or oscillatory?

Is it quick or does it show prolonged persistence? To assess the dynamic stability of the responses of p and

d to shocks, we implement a one-time unit shock to the equations’residuals.10 For model 2, the system of

equations providing those responses is

∆pt = λ11(L)∆pt+ λ12(L)∆dmt+ λ13(L)∆dot +αp · lret−1 + upt

∆dmt = λ21(L)∆pt+ λ22(L)∆dmt+ λ23(L)∆dot +αdm · lret−1 + udmt

∆dot = λ31(L)∆pt+ λ32(L)∆dmt+ λ33(L)∆dot +αdo · lret−1 + udot

lret = pt+ βm · dmt + βo · dot

A shock to upt, for example, produces a response in pt which induces a deviation in the long-run equilibrium

relation that affects, in turn, all the endogenous variables. These these responses continue until the long-run

relation is re-stored (lret = 0). Figures 14-16 show the responses:

10The alternative of using the Cholesky decomposition of the residuals’ variance-covariance matrix gave virtually identicalresults and did not change the profile of the responses.

14

0 20 40 60 80 100 120 140 160 180 200

­0.075

­0.050

­0.025

0.000Response of Broad Effective to an Oil­Price Shock

0 20 40 60 80 100 120 140 160 180 200­7.5

­5.0

­2.5

0.0

Response of Price of Oil to a shock to Broad Effective

Figure 14: Impulse Responses for Model 1. The horizonal axis is expressed in months.

0 50 100 150 200

­0.05

0.00

0.05

Response of Major Effective to an Oil­Price Shock

0 50 100 150 200

­0.03

­0.02

­0.01

0.00

0.01

Response of Other Trading Effective to an Oil­Price Shock

0 50 100 150 200

­4

­2

0

Response of Price of Oil to Major Effective Shock

0 50 100 150 200­4

­2

0

2

Response of Price of Oil to Other Trading Effective Shock

Figure 15: Impulse Responses for Model 2. The horizonal axis is expressed in months.

15

0 50 100 150 2000.0

0.1

0.20.3 Yen response to an oil price shock

0 50 100 150 200

0.0

0.1

0.2 Pound response to an oil price shock

0 50 100 150 200­0.03

­0.02

­0.010.00 RMB response to an oil price shock

0 50 100 150 200

0.0

0.1

0.2 Euro response to an oil price shock

0 50 100 150 200

0.0

0.5

1.0 Oil price repsonse to a shock in the yen

0 50 100 150 200

0

2Oil price repsonse to a shock in the pound

0 50 100 150 200

­5

0Oil price repsonse to a shock in the RMB

0 50 100 150 200

­2

­1

0Oil price repsonse to a shock in the euro

Figure 16: Impulse Responses for Model 3. The horizonal axis is expressed in months.

The results show that the systems are dynamically stable: the responses do not exhibit oscillations of

increasing magnitude but rather converge after eight years to their long-run values; the half-life of the

responses is four years. The results also indicate that for the model using bilateral exchange rates, there is

an inverse association between p and r′s initially. After ten months, however, there is a direct association

as predicted by the cointegration results (table 3 above). Again, unless one has strong priors about these

impulse responses, they do not help discriminate among these models. To this end, we examine whether the

joint distribution of the residuals are consistent with the maintained assumptions used for estimation.

4.5 Residuals’Properties

A necessary condition for using the above results to carry out statistical inferences is for the residuals to

be consistent with the maintained assumptions used in estimation: serial independence, normality, and

homoskedasticity. The results of these tests are shown in table 5:

Table 5: Properties of Residuals’Joint Distributions

Null Hypothesis Model 1 Model 2 Model 3

Serial Independence 0.944 0.849 0.166

Normality 0.001 0.016 0.569

Homoskedasticity 0.031 0.412 0.131

For model 3, one cannot reject the hypothesis that the joint empirical distributions of the residuals satisfy

serial independence, normality, and homoskedasticity only for model 3; for models 1 and 2, these assumptions

are rejected by the data. Thus inferences based on models 1 and 2 are not statistically reliable.

5 Conclusions

Our work has several limitations. First, the number of observations is not large which means that both

statistical estimates and forecast evaluation will benefit from expanding the sample. Second, using monthly

16

observations limits the applicability of the findings to address high-frequency financial decisions. Until

these, and other, limitations are addressed, the findings have an undeniable tentative character and need to

be treated as preliminary.

We offer an empirical characterization of the long-run association between the real price of oil and

alternative measures of the external value of the dollar. From a statistical standpoint, the evidence gives the

model using bilateral exchange rates an edge. Reliance on this model generates a direct association between

the price of oil and the value of the dollar whereas reliance on effective exchange rates embodies an inverse

association. Given the similarity in forecast performance, the obvious question to ask is what measure to

use. We argue that the current reliance on effective exchanges rates needs to be replaced with reliance on

bilateral rates for three reasons. First, using bilateral exchange rates avoids the identification problem of

effective exchange rates — that is, not knowing whether the relation is between price of oil and exchange

rates and price of oil and weights. Second, using effective exchange rates requires a fictional financial market

in which the effective exchange rate is international traded. Third, the statistical evidence using effective

exchange rates is not consistent with a long-run relation or with the properties of the residuals.

A Appendices

A.1 Evolution of the Literature

0

10

20

30

40

50

60

1980198719901992199319941996199719981999200020012002200320042005200620072008200920102011201220132014201520162017

Number of Papers from Web Science with Oil Price and the Dollar

A.2 Data Sources and Transformations

• All the data come from The St. Louis Federal Reserve database Fred: https://fred.stlouisfed.org/

Variables in upper case represent the mnemonics used in the Fred data base. Numerical entries represent

the values of these variables in January 2000.

• Data for the weights are from https://www.federalreserve.gov/releases/h10/weights/default.htm

d = log(TWEXBPA/99.84)

dm = log(TWEXMPA/98.189)

do = log(TWEXOPA/110.784)

p = po - pus

17

po = log(MCOILWTICO/27.26)

pus = log(CPIAUCNS/168.8)

r yen$= log(EXJPUS*CPIAUCNS/JPNCPIALLMINMEI)

r pound$

= log((1/EXUSUK)*CPIAUCNS/GBRCPIALLMINMEI)

r rmb$= log(EXCHUS*CPIAUCNS/CHNCPIALLMINMEI)

r euro$= log((1/EXUSEU)*CPIAUCNS/CP0000EZ19M086NEST)

A.3 Augmented Dickey-Fuller Test Results

The Augmented Dickey Fullet tests are implemented as

∆yt =

12∑j=1

ρj ·∆yt−j + β · yt−1

where y is the variable of interest. Using the tests’s critical values developed by Dickey and Fuller, one

cannot reject the hypothesis that log-levels of the variables are integrated of order one:

18

19

20

References

[1] Amano, R. A. and S. Norden (1998) - "Oil Prices and the Rise and Fall of the US Real Exchange Rate",

Journal of International Money and Finance 17, 299-316

[2] Backus, D. K. and M. J. Crucini (2000) - "Oil prices and the terms of trade", Journal of International

Economics 50 (2000) 185?213

[3] Bnassy-Qur, A., V. Mignon and A. Penot (2005) - "China and the Relationship between the Oil Price

and the Dollar", CEPII Working Paper

[4] Breitenfellner, A. and J. Crespo Cuaresma (2008) - "Crude Oil Prices and the USD/EUR Exchange

Rate", Monetary Policy and the Economy

[5] Cheng, K. C. (2008) - "Dollar Depreciation and Commodity Prices", in: IMF (ed.). 2008. World Eco-

nomic Outlook

[6] Courdet, V., Couharde, C. and V. Mignon (2013) - "On the impact of oil price volatility on the real

exchange rate - terms of trade nexus: Revisiting commodity currencies", CEPII Working Paper, De-

cember

[7] Doornik, J. and D. Hendry, 2013, Empirical Econometric Modeling Vols. I and II, Timberlake Consul-

tants, London

[8] Fratzscher, M., Schneider, D. and I. van Robays (2014) - "Oil prices, exchange rates and asset prices",

ECB Working Paper 1689, July

[9] Golub, S.S. (1983) - "Oil Prices and Exchange Rates", Economic Journal, 1983, vol. 93, issue 371, pages

576-93

[10] Grisse, C. (2010) - "What Drives the Oil-Dollar Correlation?" Federal Reserve Bank of New York.

[11] Krichene, N. (2005) - "A Simultaneous Equations Model for World Crude Oil and Natural Gas Markets",

IMF Working Paper

[12] Krugman, P. R. (1980) - "Oil and the Dollar", NBER Working Paper

[13] Leahy, M. P. (1998) - "New Summary Measures of the Foreign Exchange Value of the Dollar", Federal

Reserve Bulletin

[14] Razgallah, B. and K. Smimou (2011) - "Oil prices and the greenback: it takes two to tango", Applied

Financial Economics, January

[15] Reboredo, J.C., M. Rivera-Castro, and G. Zebende (2014) - "Oil and US dollar exchange-rate depen-

dence: A detrended cross-correlation approach" Energy Economics. 42, 132-139.

[16] Yousefi, A. and T.S. Wirjanto (2005) - "A Stylized Exchange Rate Pass-through Model of Crude Oil

Price Formation", OPEC Review 29. 177-187

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