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NEW EVIDENCE ON THE RELATIONSHIP BETWEEN CRUDE
OIL AND PETROLEUM PRODUCT PRICES
Mario Denni Geoffrey Frewer
Working Paper n° 61, 2006
UNIVERSITÀ DEGLI STUDI ROMA TRE
DIPARTIMENTO DI ECONOMIA
UNIVERSITÀ DEGLI STUDI ROMA TRE
DIPARTIMENTO DI ECONOMIA
Working Paper n° 61, 2006
Comitato Scientifico
C. Conigliani
G. M. Rey
S. Terzi
- I “Working Papers” del Dipartimento di Economia svolgono la funzione di divulgare
tempestivamente, in forma definitiva o provvisoria, i risultati di ricerche scientifiche
originali. La loro pubblicazione è soggetta all’approvazione del Comitato Scientifico.
-Per ciascuna pubblicazione vengono soddisfatti gli obblighi previsti dall’art. 1 del D.L.L.
31.8.1945, n. 660 e successive modifiche.
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REDAZIONE:
Dipartimento di Economia
Università degli Studi Roma Tre
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Tel. 0039-6-57374003 fax 0039-6-57374093
E-mail: dip_eco@uniroma3.it
UNIVERSITÀ DEGLI STUDI ROMA TRE
DIPARTIMENTO DI ECONOMIA
NEW EVIDENCE ON THE RELATIONSHIP BETWEEN CRUDE
OIL AND PETROLEUM PRODUCT PRICES
Mario Denni Geoffrey Frewer
Abstract 5
1. Introduction 6
2. Literature Review 8
3. The Data 14
3.1 Descriptive Statistics and Correlations 14
4. Econometric Results 16
4.1 Stationary 16
4.2 Cointegrating Vectors 17
4.3 Brent Weak Exogeneity 18
4.4 Long-Run Elasticities and Error-Correction Model 19
5. The Asymmetric Refining Margin Effects 23
6. Concluding Remarks 28
Appendix A: Data Description 40
Appendix B: the Refining Margin Computation 42
Bibliography 44
New Evidence on the Relationship Between Crude
Oil and Petroleum Product Prices
Mario Denni∗Geoffrey Frewer∗∗
November 2005
Abstract
The present study aims at providing new evidence on the price re-
lationships between crude oil and petroleum products. We employ
single-equation error correction models (ECM) in which both changes
in crude oil price and deviations from the long-run equilibrium are used
to explain product price dynamics. A GARCH structure is applied to
models’ residuals to account for the time-varying volatility. Our key
piece of innovation is the introduction of refining margin effects to the
analysis of the asymmetric products price movements. Results suggest
that the overall balance in the refinery sector plays an important part
in the adjustment to crude price shocks.
JEL classification: E32; C22; D40; Q40
Keywords: Oil prices; Market integration; Cointegration; Error correction models;
GARCH models; Asymmetric adjustment.
∗Dipartimento di Economia, Universit`a degli Studi Roma Tre. Correspondence Ad-
dress: Dipartimento di Economia, Via Ostiense 139, 00154, Roma, Italia. E-mail Address:
denni@uniroma3.it
∗∗European Investment Bank. Correspondence Address: 100, Bd. K. Adenauer L-2950
Luxembourg. E-mail Address: frewer@eib.org. The views expressed are personal and
need not necessarily reflect those of the EIB.
1 Introduction
Significant price volatility in global energy markets is of interest to investors
and policy-makers, given the impact that unanticipated movements in en-
ergy prices can have on project profitability and macroeconomic perfor-
mance. Despite recent attempts by oil-producing nations to introduce some
stability into crude oil price, there continues to be difficulty in anticipat-
ing its movements and the implications for economic activity and inflation.
Moreover, different scenarios for crude oil price are likely to be character-
ized by different levels of and ratios among refined product prices, given that
crude is the major input in the refining process. In many activities these
product price differentials turn out to have more relevance than the general
level of energy prices in assessing the potential profitability of a project. For
example, this is primarily the case for integrated companies operating in
the oil industry, which both extract and refine crude oil. In such situations,
changes in the overall level of energy prices may not contain useful infor-
mation for project risk management since oil price relationships are the key
determinant of profit.
Relative demand for petroleum products varies over time. So do rel-
ative prices. Nevertheless, some market integration leads to the existence
of stable long-lasting relationship among oil product prices. This is due to
the possibility for refiners to choose the optimal output mix in response to
variations in the economic situation by changing the relative amounts of
different products that can be distillate from a barrel of crude, that is their
relative supply. And where, especially in the short-term, physical and tech-
nological constraints would reduce this output flexibility, stock adjustments
can re-establish refiners’ ability of meeting relative demand changes leaving
2
relative prices almost unchanged. As a result, there are reasons to believe
that a fairly stable equilibrium holds between crude and petroleum product
prices, and consequently, among product prices.
The present study aims at exploring the existence and the behaviour of
such price relationships. We adopt a single-equation framework based on
the assumption of weak exogeneity of crude oil price. The presence of coin-
tegration between crude and oil product prices suggests the use of an error
correction model (ECM thereafter) in order to account for both variations in
crude oil price and deviations from long-run equilibrium in predicting prod-
uct price dynamics. Moreover both visual inspection and statistical tests
provide evidence that oil product price series exhibit variance persistence
and are characterized by many extreme values. Then we employ a GARCH
structure over the error terms. As to the short-run dynamics of the series
we divide our exercise in two steps. Firstly, we explore the two conventional,
widely tested, sources of asymmetry: the one in the adjustment to long-run
disequilibria and that relative to the direction of the Brent price change.
Secondly, the usual asymmetric error correction model will be modified to
introduce refining margin effects to the analysis. Since refining adds value
to crude oil, this plays a central role in the oil business. Our intuition is
that the composition of refinery throughput and the relative product prices
respond to changes in crude oil price in different ways depending on the last
period performance (in terms of the refining margin) of the refining sector.
We will adjust our error correction model in order to be able to distinguish
between two types of asymmetries: the first refers to the direction of crude
price changes, the second one instead is related to the sign of last period’s
refining margin. Should this setting hold, the result would be twofold. First,
it would confirm the existence of an asymmetric response of all product’s
3
prices to crude price changes. Second, it would suggest that taking into ac-
count recent path of the refining margin may be of some help in our attempt
to understand and predict product price movements and best direct eco-
nomic policy tools. Our findings show that every coefficient is statistically
significant and interestingly a substantial, economic meaningful difference
between all them is in fact found. Such an outcome leads us to conclude for
the presence of a double asymmetry driving the price patterns of petroleum
products. Statistical tests performed to establish whether the divergences
among coefficients are statistically significant attest the robustness of the
outcome.
The rest of the paper is organized as follows. Next section 2 provides a
review of the recent literature on these topics followed by a description of the
price series used (section 3). A first investigation of these data and of their
possible co-movements through some descriptive statistics and a correlation
analysis comes after in section 3.1. Section 4 contains the analysis of the
econometric aspects of the model. Section 4.4 shows and discusses first
results and tests their robustness. The role of the refining margin effects in
explaining the asymmetric dynamics is investigated in section 5. Section 6
concludes.
2 Literature Review
Surprisingly, just a couple of papers deal with the price relationship between
crude and refinery products and the patterns of oil product price differen-
tials. Indeed the majority of the related literature pay much more attention
to the gasoline market. Gjlberg and Johnsen (1999) analyses co-movements
between monthly prices (observed on the Northwest European market) of
4
crude oil (Brent) and six oil products (Gasoline, Naphtha, Jet Fuel, Gas Oil,
Light Fuel Oil 1%, and Heavy Fuel Oil 3.5%) for the period 1992 −1998.
They follow a pairwise approach taking crude price as the exogenous vari-
able and using co-integration and error correction techniques. Technically,
they specify and estimate a short-run dynamics and then calculate the long-
run solution of the process resulting from the estimated short-run model.
Authors put some emphasis on the lack of sensitivity of heavier products
(1% and 3.5% fuel oils) to crude changes. They also state that the error
correction mechanism is faster in gasoline and naphtha (in two-month time)
than in jet fuel and gasoil (it takes two more months). Finally, they examine
the price spreads finding again that the correction process works faster for
the lighter products.
A multivariate framework is used by Asche et al. (2003). Their analysis
is restricted to the relationship between monthly prices of Brent and four
oil products (Naphtha, Gas Oil, Jet Fuel and Heavy Fuel Oil) traded on
the Rotterdam market in the period 1992 −2000. Their results indicate
that heavy fuel oil 3.5% is not cointegrated with any of the other prices,
suggesting that the price for this product is independent of crude oil price,
whereas all other prices appear to be cointegrated with crude oil price. In
addition, with the exception of naphtha and kerosene, product prices seem
to be also cointegrated with each other, implying that products markets
are integrated and their price series share the same stochastic trend. As
pointed out by the same authors, this link provides evidence of the output
mix adjustments made by refiners to respond to changes in the relative
product demand. Finally, they state, completely in line with our results,
that “weak exogeneity cannot be rejected for crude oil, while it is clearly
rejected for the other three products. These results suggest that crude oil is
5
the driving factor in the price generating process and that it is crude oil that
binds the price series together in the long-run. Furthermore, it indicates that
the relationships between crude oil and the refined products can be modeled
in single equation specifications.” (p.298)
As far as asymmetric price movements are concerned, despite the enor-
mous effort, the specific literature is yet far to reach a generally accepted
conclusion.1First of all, it should be noted that the empirical studies dealing
with this topic greatly differ in data frequency, sample period, choice of the
input price and of the model specification, which may account for the dif-
ferent conclusions on price asymmetry they reach. However, some common
features can be pointed out. The price setting behaviour in the U.S. and
U.K. gasoline market in a period usually spanning from early 80s to late 90s
is explored. The frequency of the data is typically either weekly or monthly,
although sometimes biweekly data are also employed. As a rule, a single
stage analysis relating directly the price of crude oil to the pump price is
set up. Sometimes, the oil industry is instead broken down into two stages:
the production and the distribution chain. The former framework involves
crude price and spot gasoline price, whereas the latter wholesale and retail
gasoline prices. Differences can be also found about the econometric tool
employed. While most research has been carried out by using the usual, but
unappropriate with cointegrated series, Vector Autoregression (VAR) anal-
1Asymmetric price movement is cause of concern not only in the oil industry. Many
studies investigate price asymmetries in various markets (including bank deposits and
agricultural products). Above all, Peltzman (2000) uses large samples of diverse products:
77 consumer and 165 producer goods. He concludes for the pervasiveness of prices rising
faster than they fall. On average, the immediate effect on prices of an increase in input
costs was at least twice as large as the effect of a decline in input costs. Moreover, the
differential was sustained for at least five to eight months.
6
ysis, just few papers make use of the unit-root and cointegration technique,
modeling asymmetric price effects both in the short-run and long-run. As
said, the resulting general picture is confused.
In regard to the U.K. gasoline market, Bacon (1991) and Manning (1991)
report partially conflicting results. Using semi-monthly data from 1982 to
1989 and a quadratic quantity adjustment function, Bacon reports evidence
of a faster and more concentrated response of the retail price to spot price
increases. The latter instead exploiting monthly data on crude oil prices
and retail prices from an even earlier period (1973 −1988), concludes that
price asymmetry, though present, is relatively short-lived, being any asym-
metry virtually absent after four months. Reilly and Witt (1998) revisit the
evidence of these authors with monthly data for 1982−1995 and emphasize
the role of the dollar-pound exchange rate and the potential asymmetries
associated with it, in addition to those of crude oil prices. A restricted ECM
is estimated which allows only for short-run asymmetry. The hypothesis of
a symmetric response by petrol retailers to crude price rises and falls is
rejected by the data, and so is for changes in the exchange rate.
Shifting attention to the U.S., even less uniformity appears. Boren-
stein and Shepard (1996) estimate an asymmetric partial adjustment model
and a VAR model on weekly observations at 188 terminals for the period
1986 −1992 finding that terminal prices respond asymmetrically to changes
in crude oil price. Borenstein et al. (1997) estimate a VAR model for the
gasoline market using semi-monthly data over the period 1986−1990. Their
results also indicate that retail prices adjust more quickly to crude oil price
increases than to decreases. In the next stage, there appears to be no asym-
metry between spot and wholesale prices. Finally, retail prices show asym-
metry in responding to wholesale price changes, possibly indicating short
7
run market power among retailers. In sharp contrast, opposite conclusions
can be drawn from the very first works by Karrenbrock (1991) and Shin
(1994). Karrembrock employs 1983 −1990 monthly data to study the em-
pirical relationship between wholesale and (after tax) retail gasoline prices.
The author uses a distributed lags model to find that the length of time in
which a wholesale price increase is fully reflected in the retail gasoline price
is the same as that of a wholesale price decrease for premium and unleaded
regular gasoline. The author concludes, contrary to the popular belief that
consumers do not benefit from wholesale gasoline price decreases, these are
eventually passed along to consumers as fully as are wholesale gasoline price
increases. Similarly in his investigation of the U.S. market, Shin (1994) re-
lates the average wholesale price of oil products to the price of oil. He uses
monthly data for the period 1986 −1992 and regresses average wholesale
price changes on positive and negative oil price changes and shows no ev-
idence of short-run asymmetric effects. In line with them is also a more
recent paper by Balke et al. (1998) who extend the work of Borenstein et
al. (1997) by using two different model specifications with weekly data from
1987 through 1997. In particular the authors use a distributed lags model
in price levels with asymmetric effects and an ECM representation which
allows for both long-run and short-run asymmetries. The authors do not
obtain unambiguous evidence concerning asymmetry, which is found to be
weak in the specification in levels and moderate and persistent in the ECM.
Lastly, Godby et al. (2000) apply a threshold error correction model to test
for asymmetric pricing in the Canadian (both premium and regular) gaso-
line market since they state that the asymmetric ECM specifications used
in previous studies are misspecified if price asymmetries are triggered by a
minimum absolute increase in crude cost. The analysis is based on weekly
8
data for thirteen cities between 1990 and 1996. On this basis the authors
fail to find evidence of asymmetric pricing behavior.
Finally, three recent papers look at the experience of other countries.
Asplund et al. (2000) use monthly data during 1980 −1996 to explore the
Swedish gasoline market. They find support for the hypothesis that re-
tail prices are stickier downwards than upwards in response to cost shocks.
Kirchg¨assner and K¨ubler (1992) look at West Germany for the period 1972−
1989 using monthly data. The authors consider the response of both con-
sumer and producer leaded gasoline prices to the spot price on the Rotter-
dam market; they distinguish two periods, before and after January 1980.
By adopting a very rigorous methodology (tests for unit roots, Granger
causality, cointegration, and structural breaks are performed and when coin-
tegration can not be rejected, both symmetric and asymmetric ECMs are
fitted) they show that, while long-run reactions are not significantly differ-
ent for the 1970s and the 1980s, there is considerable asymmetry in the
former period but not in the latter in the short-run adjustment processes.
In particular, reductions in the Rotterdam prices are transferred faster to
German markets than increases. Finally, Galeotti et al. (2002) carry out
an international comparison of gasoline market. They examine the issue of
asymmetries in the transmission of shocks to crude oil prices into the re-
tail price of gasoline in five major European countries (Italy, Spain, France,
Germany and the U.K.). The data are monthly and in general range from
1985 and 2000 and are used in the estimation of an ECM specification which
allows for asymmetries both in the long-run and short-run components. The
authors adopt a two-stage modeling (refinery and distribution stages) and
find that widespread differences in the adjustment speeds and in the short-
run elasticities characterize both stages.
9
3 The Data
Our analysis is based on weekly price series of crude oil and six oil products
in the period from January 1990 to September 2005. The focus is on the
Northwest European market. The crude oil price is dated Brent and product
prices are those set in the Rotterdam market (the name used to indicate the
large refining and storage complex in the area between Antwerp, Rotterdam,
and Amsterdam) for naphtha, gasoline premium, gasoil, kerosene, light fuel
oil (1%), and heavy fuel oil (3.5%). Rotterdam prices are generally regarded
as the “base” level to price oil products in trade and in internal company
transfer throughout Northern Europe. All product prices are in U.S.$ per
metric ton, whilst Brent price is in U.S.$ per barrel. All data are either
provided by Platt’s, an energy industry information and service agency or
taken from the Oil Market Report of the International Energy Agency.2
3.1 Descriptive Statistics and Correlations
Table 1 shows some descriptive statistics of the series over the period covered
by our analysis (1990 −2005). Gasoline premium and kerosene are yielding
the highest prices, whereas as expected heavier products show the lowest
values. Although mean prices differ widely, the coefficients of variations
(a measure of the deviation of a variable from its mean) are pretty similar
one another. The price level variability is around 40% of the corresponding
mean. Visual inspection of graphs in figure 1 highlights changes over time
in the variability of the series, as well as in their means. Apart from the
exceptionally high value in the early 90’s (due to the first Gulf war), all
price series show relatively smooth dynamics, with uniformly low levels and
2For more information about the data used in this study see Appendix A.
10
volatilities till 1997. Since 1998 instead the series have had markedly higher
average levels and risen together with considerable variation. This may be
due to many different events that have occurred during the last eight years,
the most relevant being the Asian Crisis,3which reduced the demand for
oil immediately by more than half a million barrels a day and cumulatively
by more than a million barrel a day, leading to the collapse of oil prices in
1998, the attack to the American Twin Towers in September 11th and the
second Gulf war (in 2003).4
In tables 2 and 3 we report the simple partial correlation of price levels
and percent price changes respectively. As already noted in Gjolberg and
Johnsen (1999), the most striking result is not the strong co-movements
between crude and oil product price levels as well as across the different
products, but instead the relatively high figures of percent price change
correlations. As usual, the strongest tie is found between products coming
from the same part of the crude barrel, like gasoil and kerosene, since an
increase in the output of one product can not be obtained without decreasing
the amount of the other. Again not surprisingly, this link becomes less
evident as heavier product are concerned. However, with respect to the
previous studies, our results indicate a tight market integration also for the
“bottom end” oil products. This can be consider as a first signal, to be
confirmed later on, that in contrast with the choice made in Gjolberg and
3For an analysis of the impact of the Asian crisis on the behaviour of US and interna-
tional petroleum prices, see Hammoudeh and Li (2004).
4Even if we do not report the values, it is interesting to note that these facts have
affected all the prices’ distributions as shown by the post-1998 values of kurtosis and skew-
ness that are much lower than they were before 1998. This corresponds to distributions
less peaked and with much less flat right tails.
11
Johnsen (1999) and Asche et al. (2003),5fuel oil dynamics are now to be
considered jointly with those of crude and the other oil products.
4 Econometric Results
In the following sections we implement the cointegration technique. We fol-
low the procedure indicated by Engle and Granger (1987), that is made up
of different steps. In the first step we pretest all variables for their order of
integration. Then we determine the number, if any, of the cointegrating re-
lations in the Brent-oil product price bivariate models. Finally, we estimate
the long-run relationship and the error-correction model.
4.1 Stationarity
Cointegration necessitates the series to be integrated of the same order. We
use the augmented Dickey-Fuller and the Philip-Perron tests for prices in
log-levels to determine the number of unit roots in each series. Standard
augmented Dickey-Fuller unit root test has great difficulty in distinguishing
between integrated processes (I(1)) and stationary processes (I(0)) incorpo-
rating a jump, shift or break of some kind. As descriptive statistics in table
1 show it could be the case. This issue is the motivation for the use of the
Philip-Perron unit root test. Table 4 reports the results of both tests. The
null that the series has a unit root is accepted for all the prices in levels,
whilst it is always rejected for their first differences. This implies that all
5An economic explanation offered in Asche et al. (2003) for this low correlation be-
tween fuel oil and the remaining oil products is that the high degree of possible substitution
to other fuels in its main use (power generation) would represent an upper bound beyond
which substitution would reduce price again (p.293).
12
price series are integrated of order one. In all cases, the tests are performed
including a drift (constant) but not a time trend.6The lag length is chosen
according to the Schwarz Info Criterion.
4.2 Cointegrating Vectors
To determine the number of cointegrating vectors, that is of stationary lin-
ear combinations between integrated series, in a multivariate framework we
follow the usual Johansen procedure. It aims at finding out the rank of the
matrix associated to the lagged levels of the series (it includes the adjustment
coefficients and the long-run elasticities). This amounts at testing the num-
ber of the characteristic roots that are different from zero. The statistical
problem is to derive a test procedure to discriminate between the eigenval-
ues which are large enough to correspond stationary eigenvectors and those
which are small enough to correspond to non-stationary eigenvectors. Ac-
tually the Johansen likelihood-ratio technique uses two test statistics. The
first, called the trace statistics, tests the null hypothesis that the number
of distinct cointegrating vectors is less than or equal to ragainst a general
alternative. The second, known as the max-eigenvalue statistics, tests the
null that the number of cointegrating vectors is ragainst the alternative of
r + 1. In a bivariate framework as the one employed here we should able to
discriminate between the following alternatives: no, one, or two cointegrat-
ing vectors. The first case would correspond to prices being integrated of
order one, I(1), but with no stationary cointegrating relation between them.
In the second case there is one stationary combiantion whereas in the last
case the series are stationary. We compute these statistics to our Brent-oil
6None of the results is sensitive to the inclusion of a time trend.
13
product price bivariate models. The results are in table 5. For all products
both rank tests indicate one cointegrating equation at the 5% level of sig-
nificance. This result suggests that in each bivariate system there must be
one stochastic trend (that is, the two series share the same stochastic trend)
and that at most one weakly exogenous variable that can be found for each
price relationship.
4.3 Brent Weak Exogeneity
When investigating the relationship between prices economic theory does
provide little guidance with respect to which variable should be chosen as
exogenous. It is equally possible to argue that it is the demand for refinery
products that is driving the crude oil price or that the relationship goes in
both directions. In our single-equation framework we choose the Brent price
as the right-hand side weakly exogenous variable. It means that this price is
not ”equilibrium adjusting”. In other words, it does not move to compensate
for deviations from the long-run equilibrium.7Although it seems unlikely
that regional changes in product demand would affect the price of crude oil
(which would be determined in a world market) it is not a priori obvious
that this assumption always holds.8For such a reason, in this section we test
the appropriateness of the weak exogeneity assumption of crude oil price.
We estimate a bivariate vector error correction model for all the pos-
sible Brent-product price combinations and tested the hypothesis that the
7Note that long-run weak exogeneity does not imply short-run exogeneity. Hence, it
does not exclude the possibility that the weak exogenous Brent price is reacting in the
short run to changes in the product prices in the model. Then changes in product prices
may feed back to crude oil prices but these effect vanish in the long period.
8See Adrangi et al., 2001, for a comprehensive test of the causal relationship flowing
from product prices to crude oil price.
14
adjustment coefficient (to the long-run relationship) in the Brent equation is
null. In such a case, the Brent price can be considered as exogenous for the
estimation of coefficients in the single-equation models. The results in table
6 show that we can always accept the null hypothesis of a binding restriction
with a high level of significance. Solely in the case of gasoline premium the
Wald χ2-statistics is quite high. However this test also is not significant at
a 5% level. Then, the direction of causality (the flow of information) in the
long-run is from the Brent price (the leader) to the other product prices (the
followers).
4.4 Long-Run Elasticities and Error-Correction Model
In a first stage of our analysis, the ECM is estimated in two rounds following
Engle and Granger (1987). The initial step is the estimation of the long-run
equation using OLS:
pt=β0+β1bt+²t(1)
This determines the response of each oil product price to changes in the
Brent price in the long-run when the entire adjustment process is completed.
Then we capture the short run dynamics allowing for asymmetry both in
the adjustment path to long-run disequilibria and in the response to crude
price changes:
∆pt=α+
pˆet−1+α−
pˆet−1+
n
X
i=0
γ+
i∆bt−i+
n
X
i=0
γ−
i∆bt−i+
m
X
j=1
ωj∆pt−j+νt(2)
where pand bstand for oil product and Brent prices, ˆet−1are the estimated
residuals from equation 1, ∆pt−iand ∆bt−ilagged changes of the variables,
and νtis the disturbance term. The coefficient superscripts refer to the
direction of the associated series (that is whether the long-run equilibrium
shock has been positive or negative and the crude price rising or falling).
15
Table 7 show the entire set of result. The estimates of the long-run elas-
ticities, β1, are all near unity indicating in no case a complete, one-to-one
pass-through rate from input price growth to output price growth. This
implies that in the long run a 10% increase in the price of Brent results on
average in a 9% increase in the spot price of oil products. It is also rele-
vant to stress that these preliminary results provide some further evidence
of the fuel oil sensitivity relative to Brent price changes. Although lower
than those of lighter products, the long-run parameters associated to light
and heavy fuel oil are very significant. Regarding the short-run dynamics,
the results vary across products. Last week’s deviation from the long-run
equilibrium has significant explanatory power for current price change in all
products. Except for few cases, all the adjustment speeds range between
0.07 and 0.12 implying roughly from 6 to 10 weeks to close half of the gap
between actual and long-run price levels.9Hardly is there any evidence of
asymmetric behaviour of the series either in the long-run adjustment or in
the brent price change response. We should perform the Wald test to con-
firm our impression. Yet the diagnostic tests at the bottom of table 7 deserve
attention. The AR(7) is a test of residual autocorrelation of order 1 to 7.
The null of autocorrelation is rejected in three out of six cases. Moreover,
the last two lines show that also the assumptions of residuals normality and
homoskedasticity are strongly rejected. The ARCH (7) is a test of autore-
9To compute the mean lag adjustment period we use the formula
t=ln(1 −x)
α,
where the numerator is the log of the proportional gap closed and the denominator the
speed of adjustment coefficient estimated in the ECM equations. This formula tells us
how many weeks it takes for oil product prices to revert to their equilibrium levels once a
shock has caused them to diverge upward or downward.
16
gressive residual heteroskedasticity of order 7 whereas N ormality denotes
the usual Jarque-Bera statistics to test the residual normality. Thus, it is
clear from visual inspection of figure 2 and the results of these statistics
that the standard assumption underlying the regression model are clearly
violated. Even though residuals fluctuate around zero and do not show high
serial correlation of the first order, they exhibit serial correlation of the sec-
ond order (a non-linear form of dependence), their fluctuations seem to be
clustered in time (that is, there is volatility clustering or conditional het-
eroskedasticity), and finally there are many extreme values (distributions are
leptokurtic). Assuming as is done in OLS regressions that the residuals are
independently and identically distributed through periods results in loss of
statistical efficiency. An appropriate extension to the above ECM model is
therefore required to simultaneously accommodate for such evidence. Then
we employ a GARCH structure over the residuals of the models.
The simplest GARCH(1,1) model reveals to be in most cases sufficient
to provide the desired result. In few cases a richer model is instead needed.
Diagnostic tests in table 8 say that heteroskedasticity is no longer a problem.
There are however several outliers in the data. Then dummies are used to
account for the effects of extraordinary events (i.e. wars, the Asian crisis) on
the oil products prices in this period that violate the normality assumption.
Actually, we have to understand what type of dummy we need. The main
difference concerns the length of the “impulse”. A shift in the level of the
variables corresponds to a permanent impulse in their differences, whereas
an impulse effect in the levels corresponds to a transitory impulse in the
differences. For example, a war can cause either a permanent or a transitory
shift in the level of product prices. In the latter case, we would see an initial
rise in the product price followed later on by a return to the previous price
17
level. Here, we used three types of dummies. Firstly, a step dummy, being
zero up to t=Tand unity after that. Secondly, a “pure” impulse dummy,
that is unity for t=Tand zero otherwise. Lastly, a “transitory” impulse
dummy, taking the value of unity for t=T,−1 for t=T+1, and 0 otherwise.
As to the presence of dummies in the variance equations, there we put only
some step dummies. The meaning of that we think is quite clear. In some
periods (the first Gulf War for instance) or from that moment on (the Asian
crises in 98) the volatility of the prices series has been much higher. A
good way to account for this phenomenon in the analysis is to include in the
part of the model governing the conditional variance a dichotomic variable
being zero up to that period and unity hereafter. The Jarque-Bera tests
for normality in table 8 show that indeed the use of dummies solves the
non-normality problem. Some concern still remains for the heavier products
models solely.
Now we can conduct robust inference on the existence of asymmetries.
The picture that emerges (the results are in table 9) is at least ambiguous.
Surely there is no adjustment asymmetry. Hence product prices restore last
period’s long-run disequilibria at the same pace regardless the sign of such
deviations. Only the heavy fuel oil seems to follow an asymmetric path
since it does not respond to negative long-run imbalance. This might be
due to the fact that it is used as an alternative to other non-oil products
whose prices represent a lower bound for the heavy fuel oil price. There
is more evidence of the timing or pattern asymmetry (the one relative to
the direction of crude price changes). However only the result of gasoil
confirms the common feelings of prices being sticky. In this case indeed
upward movements of the product price are significantly (but only at a 10%
level) faster than downward adjustments. In the other two cases where the
18
coefficients equality is rejected product prices seem to respond more quickly
to Brent price drops.
5 The Asymmetric Refining Margin Effects
The ambiguous results we found are in line with the weak consensus reached
by the recent literature on the asymmetry issue. Indeed economists have
tried to provide some competing economic explanations for the asymme-
try. Comprehensive studies by Borenstein et al. (1997) and Brown and
Y¨ucel (2000) argue that price asymmetries might have different sources at
different stages in the oil industry. Potential explanations include market
power, search costs, consumer response to changing prices, inventory man-
agement, accounting practices, and refinery adjustment costs. However, to
our knowledge the role of the refining margin has never directly been ac-
count for. Consequently, this last section constitutes an attempt to “fill the
gap” and shed some more light on the reasons behind the asymmetry.
On theoretical grounds our intuition is broadly linked to one hypothesis
(namely, Hypothesis 1 ) put forward in Borenstein et al. (1997). They state
that “a significant positive crude price shock would trigger retail price in-
creases, otherwise, retail margins would become negative. Retail prices need
not respond immediately to a negative crude price shock” (p.325). This is
based on the assumption that each firm chooses its selling price with im-
perfect information about the prices charged by the others. Therefore, in
response to a negative cost shock, firms might keep prices at the same level
as before the shock until demand conditions force a change (for example,
a firm should interpret a drop in sales as a good signal of price cutting by
its competitors). A similar restraint would not be present in the case of a
19
positive cost shock, so explaining the asymmetric product price behaviour.10
With respect to such a framework, we take a step forward by modeling a
double asymmetry. Besides the usual one related to the sign of the current
crude price change, we include in our error correction model a new variable
whose value reflects last period’s sign of the refining margin (a proxy for the
trend of the profitability rate in the refining sector11). This would reflect the
idea that oil companies optimise their operations and have some flexibility
in adjusting refinery throughput’s levels and inventories, and therefore the
overall balance in the sector plays a part in the adjustment to crude price
shocks.
To implement and test our thesis the error-correction equation 2 takes
now the following form:
∆pt=c+αp(pt−1−β0−β1bt−1) + γ1DbDm∆bt+γ2Db(1 −Dm)∆bt+
+γ3(1 −Db)Dm∆bt+γ4(1 −Db)(1 −Dm)∆bt+
m
X
i=1
θi∆bt−i+
+
n
X
j=1
ωj∆pt−j+νt(3)
where Dband Dmare the two dummies. Dbis 1 if the current change
in Brent price is positive and 0 otherwise. Similarly, Dmis the dummy
variable associated to last period’s sign of the refining margin, 1 when this
10It is fair to note that according the authors, this hypothesis would have a drawback
related to the lack of mechanism for firms to coordinate on a particular equilibrium among
the existing ones.
11Because of the existence of many other factors affecting refinery throughput levels,
we are well aware that our approach might be questioned for taking the refining margin as
an indicator of the opportunity to make profit in this industry. However, in our opinion
it is the trend of the margin that matters much more than its absolute level in evaluating
the economics of the sector.
20
quantity is positive and 0 when the opposite holds.12 As such, with respect
the framework generally employed we have four (not only two) possible
scenarios:
1. Db= 1 and Dm= 1, a rise in crude price in a period of positive
refining margin (γ1);
2. Db= 1 and Dm= 0, a margin-depressing increase in input price when
refining margin is already negative (γ2);
3. Db= 0 and Dm= 1, a drop in Brent price that ceteris paribus further
raises refining margin (γ3);
4. Db= 0 and Dm= 0, a decrease in Brent price that if not fully passed
12We construct the refining margin series by using crude and product price series at our
disposal. The assumptions we use to compute the refining margin are taken from the Users’
Guide of the International Energy Agency and a detailed description of them is presented
in Appendix B. Since the refining margin is here meant to represent the monetary gain or
loss associated with processing a marginal or incremental barrel of crude oil that a refiner
might choose to process, it should be assessed which refinery configuration is the marginal
one. Regressing the gross product worth on crude price, Bacon et al. (1990) concludes for
the semi-complex (a configuration whose characteristics are similar to those of cracking in
Appendix B) as the marginal technique because this shows a “dollar-for-dollar passing-on”
(p.208). Using the same approach, we found hydroskimming to be the marginal refining
process. A possible explanation for such a difference might be the fact that in the mid
80s (the period covered by Bacon et al.’s study) the refining industry had substantial
uneconomic spare capacity that has then been shut down. As a result, capacity utilization
has been increasing since then. Following the same ascending arrangement with respect
to the yielded amount of gross product worth to order the different refining technologies
proposed by the authors, the higher degree of capacity utilization started from the early
90s would have caused the shift from a semi-complex to a simple configuration as the
marginal process.
21
through output prices contributes to restore a positive refining margin
(γ4).
Since the focus is on the new potential source of asymmetric price path we
use a one-step econometric technique instead of the two-step previously em-
ployed.13 Generally the one-equation estimation is preferred to the two-step
one for two orders of reasons. First, it provides more efficient econometric
estimates (since only one equation is actually estimated and not two) and
the estimated long-run effects tend to be less prone to bias. Second, the
two-step technique has the drawback of imposing a common dynamic factor
on the regression model.14 As a result, our preferred procedure should al-
ways be the one-step one. However, to test the long-run asymmetry we need
the estimated residuals from the first-step equation in the two-step proce-
dure. Hence our initial choice to set up a two-step ECM estimation model
to test the traditional sources of asymmetry. Yet leaving aside the long-run
asymmetry story we do not need anymore the estimated residuals. Then our
mean equation will take the form of equation 3 and the conditional variance
part the GARCH structure we used above.15
Final results are reported in table 10. They suggest several remarks.
Firstly, all coefficients of the refining margin effects are statistically signifi-
cant at the 1% level. According to Granger and Lee (1989), the significance
13The one-step estimation of an ECM is also used in Borenstein et al., 1997, and
Gjolberg and Johnsen, 1999
14Empirical evidence has not produced much support for such common factors, ren-
dering the two-step method non-optimal. See Campos, Ericsson, and Hendry, 1996, for a
discussion of this drawback.
15As shown in Kremers, Ericsson, and Dolado, 1992, in the one-step procedure the
existence of a stationary cointegrating relation between the two series can be proved by
testing that the adjustment coefficient estimate is non-null (αpin equation 3).
22
of individual coefficients is a necessary condition for testing for asymmetric
effects. Secondly, the comparison between the four scenarios reveals that
when different coefficients estimates confirm our intuition. That is the re-
action of refiners to cost shocks is bigger, the worse the past trend of the
economic performance of their business. The pass-through of a drop in crude
price into product prices is indeed lower when the refining margin is neg-
ative so that the spread between output and input prices increases and so
does the marginal profit. In the case of positive past refining margin levels,
instead, a negative cost shock is rapidly reflected into lower product prices
keeping fixed both the current demand and the existing, positive profit rate.
This results in γ3greater than γ4. A similar mechanism works when a rise in
crude price occurs. Brent price increases are likely to be quickly passed into
higher product prices when the profitability rate of the industry is negative
so to prevent further loss in the refinery activity return. Then γ2exceeds
γ1.
As above we now proceed to test statistically such differences between
coefficients estimates. Conventional Wald tests of the null hypothesis of
symmetric short-run responses have been performed and results reported in
table 11. The general picture is encouraging.16 The symmetry of the four
16Indeed it is important to stress that a few recent papers (Cook, Holly and Turner,
1998, 1999; Cook, 1999) have questioned the reliability of conventional tests of symmetry
in the above and similar contexts. In particular, these contributions note that there is
a tendency to over-reject the null hypothesis of symmetry (a biasness of this statistics
in falling in the acceptance area) which can be traced to the low power of standard F-
statistics. In order to overcome this unreliability of standard Wald tests of symmetry
Galeotti et al. (2002) have bootstrapped the F statistics and have calculated rejection
frequencies at the 5% significance level on the basis of 1000 replications. Reinterpreting
the previous results in the light of the new findings leads the authors to draw different
23
coefficients is always rejected but for gasoline. It implies that the overall
balance in the refinery sector does play an important part in the adjustment
to crude price shocks. Moreover, gasoline, kerosene, gasoil, light fuel oil, and
heavy fuel oil respond to rises in the brent price when last period’s refining
margin is negative. Finally, this variable seems to govern also the reaction
of product prices to input shocks. Naphtha, light, and heavy fuel oil react
faster to a declining Brent cost when the refinery profitability has a positive
trend.
6 Concluding Remarks
In the present study, we focus our attention to the long-run spot price rela-
tionship between Brent and oil products. The econometric evidence strongly
supports the hypothesis that crude and product prices are co-integrated.
As a result, we have investigated how deviations from a long-run equilib-
rium may be used in predicting short-term product price dynamics. We
conclude that past deviations from long-term equilibrium are significant in
an error correction specification of short-term product price changes. The
results represent valuable information for assessing project profitability, par-
ticularly in integrated oil companies for which risk management is mainly
related to price differentials. To sum up, the long-run elasticities are lower
as heavier products are considered. Differently from previous findings in the
literature, we infer that also light and heavy fuel oils have stable relation-
ships with Brent. The adjustment period which is necessary for a product,
once shocked, to re-establish the long-run equilibrium varies across prod-
ucts. Light and middle distillates show faster adjustment speeds whereas
conclusions.
24
the convergence process takes longer for heavy products. A second result
is the long-run exogeneity of Brent relative to all products. This result
confirms our hypothesis on the crude-product feedback mechanism and im-
ply that crude oil price can be taken as exogenous in the Brent-oil product
price equations. Lastly, we modify our error correction model by including
a double asymmetry to investigate a potential asymmetric role of the refin-
ing margin. In the new specification asymmetries arising from input price
changes and those depending on the sign of last’s period refining margin
are distinguished. The results of the estimated coefficients confirm both the
common perception of different responses of product prices to changes in the
crude oil price and the presence of a refining margin effect. We are therefore
tempted to conclude that “rockets and feathers” seem to dominate the price
adjustment mechanism in the European oil product markets. Conventional
Wald tests largely reject the symmetry hypotheses giving statistical support
to our findings.
25
Table 1: Mean and Coefficient of Variation
(Weekly crude and oil product prices Jan 1990 - Sept 2005)
1990 −2005 1990 −1997 1998 −2005
Variable Mean Coeff of Var(%) Mean Coeff of Var(%) Mean Coeff of Var(%)
Brent 23.26 41.09 19.07 20.32 27.63 41.84
Naphtha 219.51 35.60 184.24 16.48 252.49 36.97
Gasoline 248.54 42.07 191.36 12.00 290.18 41.36
Kerosene 240.53 42.51 201.65 23.66 281.06 44.70
Gasoil 216.79 42.03 181.04 20.02 250.94 44.74
Fuel Oil 1% 127.08 34.11 106.33 17.70 148.70 33.99
Fuel Oil 3.5% 108.24 39.64 87.31 21.73 130.05 38.10
Brent: U.S.$/bbl; refined products: U.S.$/metric ton.
26
2.0
2.4
2.8
3.2
3.6
4.0
4.4
1990 1992 1994 1996 1998 2000 2002 2004
BRENT
4.4
4.8
5.2
5.6
6.0
6.4
1990 1992 1994 1996 1998 2000 2002 2004
NAPHTHA
4.4
4.8
5.2
5.6
6.0
6.4
6.8
1990 1992 1994 1996 1998 2000 2002 2004
GAS OLINE
4.4
4.8
5.2
5.6
6.0
6.4
6.8
1990 1992 1994 1996 1998 2000 2002 2004
KEROSENE
4.5
5.0
5.5
6.0
6.5
1990 1992 1994 1996 1998 2000 2002 2004
GASOIL
4.0
4.4
4.8
5.2
5.6
6.0
1990 1992 1994 1996 1998 2000 2002 2004
FUEL OIL 1%
3.6
4.0
4.4
4.8
5.2
5.6
6.0
1990 1992 1994 1996 1998 2000 2002 2004
FUEL OIL 3. 5%
Figure 1: Time series of crude and oil log prices over the period 1990 −2005
27
Table 2: Price Level Correlations
(Weekly crude and oil product prices Jan 1990 - Sept 2005)
Brent Naphtha Gasoline Kerosene Gasoil Fuel Oil 1%
Naphtha 0.9766
Gasoline 0.9749 0.9727
Kerosene 0.9766 0.9673 0.9599
Gasoil 0.9762 0.9653 0.9577 0.9941
Fuel Oil 1% 0.9388 0.9149 0.9315 0.9076 0.9096
Fuel Oil 3.5% 0.9173 0.8863 0.9081 0.8834 0.8801 0.9639
Table 3: Price Change Correlations
(Weekly crude and oil product prices Jan 1990 - Sept 2005)
Brent Naphtha Gasoline Kerosene Gasoil Fuel Oil 1%
Naphtha 0.5699
Gasoline 0.6135 0.6413
Kerosene 0.6475 0.6066 0.5961
Gasoil 0.6564 0.6152 0.5925 0.8948
Fuel Oil 1% 0.4792 0.4713 0.4787 0.4773 0.4543
Fuel Oil 3.5% 0.4771 0.4801 0.4665 0.5149 0.4798 0.6866
28
Table 4: Augmented Dickey-Fuller and Philip-Perron Tests Results
Augmented Dickey-Fuller Philip-Perron
Variable Levels First Differences Levels First Differences
Brent −1.16 −23.41∗∗∗
−1.03 −23.25∗∗∗
Naphtha −1.41 −21.09∗∗∗
−1.32 −21.02∗∗∗
Gasoline −0.51 −19.91∗∗∗
−0.06 −19.81∗∗∗
Kerosene −1.04 −20.17∗∗∗
−1.01 −20.17∗∗∗
Gasoil −0.71 −22.06∗∗∗
−0.41 −21.69∗∗∗
Fuel Oil 1% −2.17 −18.49∗∗∗
−1.65 −17.47∗∗∗
Fuel Oil 3.5% −1.69 −19.61∗∗∗
−1.51 −19.63∗∗∗
∗∗∗ statistical significance at 1% level
Table 5: Bivariate Johansen cointegration tests for crude and oil products
H0: rank=P Trace statistics Critical value Max-eigen statistics Critical value
at 5% at 5%
Naphtha
None∗∗ 43.86 20.26 42.74 15.89
At most 1 1.11 9.16 1.11 9.16
Gasoline
None∗∗ 40.46 20.26 39.47 15.89
At most 1 0.99 9.16 0.99 9.16
Kerosene
None∗∗ 62.16 20.26 60.09 15.89
At most 1 2.07 9.16 2.07 9.16
Gasoil
None∗∗ 62.68 20.26 61.09 15.89
At most 1 1.59 9.16 1.59 9.16
Fuel Oil 1%
None∗∗ 40.72 20.26 38.71 15.89
At most 1 2.01 9.16 2.01 9.16
Fuel Oil 3.5%
None∗∗ 22.12 20.26 20.05 15.89
At most 1 2.08 9.16 2.08 9.16
∗∗ statistical significance at 5% level
Table 6: Brent Weak Exogeneity Test Results
Variable Adjustment Speed Variable Adjustment Speed
Brent vs. Naphtha −0.01 Brent vs. Gasoil −0.003
(0.21) (0.02)
Brent vs. Gasoline 0.04 Brent vs. Fuel Oil 1% 0.008
(2.89∗∗) (0.29)
Brent vs. Kerosene 0.02 Brent vs. Fuel Oil 3.5% 0.01
(0.55) (0.87)
Wald χ2-statistics in parentheses;
∗∗ statistical significance at 5% level
29
Table 7: OLS Estimation: Long-Run Elasticities and Short-Run Coefficients
(Weekly Data from January 1990 to September 2005)
Naphtha Gasoline Kerosene Gasoil FO 1% FO 3.5%
Proportionality 2.62∗∗∗ 2.55∗∗∗ 2.43∗∗∗ 2.35∗∗∗ 2.26∗∗∗ 1.81∗∗∗
Coefficient, β0(121.19) (100.55) (104.59) (99.14) (68.89) (42.27)
Long-Run 0.88∗∗∗ 0.94∗∗∗ 0.97∗∗∗ 0.96∗∗∗ 0.82∗∗∗ 0.91∗∗∗
Elasticity, β1(126.35) (115.19) (129.72) (125.78) (77.87) (65.83)
Adjustment −0.115∗∗∗
−0.071∗∗∗
−0.114∗∗∗
−0.118∗∗∗
−0.087∗∗∗
−0.093∗∗∗
Speed, α+
p(−4.93) (−3.32) (−5.99) (−6.05) (−4.08) (−4.88)
Adjustment −0.121∗∗∗
−0.096∗∗∗
−0.069∗∗∗
−0.071∗∗∗
−0.044∗∗∗ 0.001
Speed, α−
p(−5.33) (−3.89) (−3.41) (−3.24) (−2.36) (0.09)
∆Brent, γ+
00.472∗∗∗ 0.546∗∗∗ 0.533∗∗∗ 0.622∗∗∗ 0.278∗∗∗ 0.358∗∗∗
(12.11) (12.51) (14.59) (16.17) (5.41) (6.58)
∆Brent, γ−
00.464∗∗∗ 0.543∗∗∗ 0.459∗∗∗ 0.515∗∗∗ 0.464∗∗∗ 0.463∗∗∗
(12.38) (13.09) (13.86) (14.52) (10.56) (9.71)
∆Dep−1,ω10.266∗∗∗ 0.249∗∗∗ 0.205∗∗∗ 0.191∗∗∗ 0.447∗∗∗ 0.358∗∗∗
(9.68) (8.69) (7.95) (7.31) (14.37) (12.41)
∆Dep−2,ω2−0.059∗∗∗
−0.084∗∗∗
−0.046
(−2.19) (−3.21) (−1.40)
Adj.R20.49 0.49 0.48 0.50 0.44 0.41
AR(1-7) 3.12∗∗∗ 1.47 2.49∗∗ 1.38 3.17∗∗∗ 1.05
(p-value) (0.00) (0.17) (0.02) (0.21) (0.00) (0.39)
ARCH(7) 9.99∗∗∗ 4.15∗∗∗ 15.43∗∗∗ 23.76∗∗∗ 5.91∗∗∗ 6.18∗∗∗
(p-value) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
Normality 50.83∗∗∗ 11.97∗∗∗ 156.53∗∗∗ 629.89∗∗∗ 17.79∗∗∗ 9.48∗∗∗
(p-value) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
∗∗∗ statistical significance at 1% level
∗∗ statistical significance at 5% level
∗statistical significance at 10% level
Unless differently specified, t-statistics are in parentheses.
30
-.15
-.10
-.05
.00
.05
.10
.15
.20
1992 1994 1996 1998 2000 2002 2004
Gaso il
-.10
-.05
.00
.05
.10
1992 1994 1996 1998 2000 2002 2004
Napht ha
-.12
-.08
-.04
.00
.04
.08
.12
93 94 95 96 97 98 99 00 01 02 03 04 05
Gaso li ne
-.15
-.10
-.05
.00
.05
.10
.15
1992 1994 1996 1998 2000 2002 2004
Kerosene
-.12
-.08
-.04
.00
.04
.08
.12
1992 1994 1996 1998 2000 2002 2004
Fuel Oil 1%
-.12
-.08
-.04
.00
.04
.08
.12
1992 1994 1996 1998 2000 2002 2004
Fuel Oil 3.5%
Figure 2: OLS Residuals
31
Table 8: GARCH Estimation Results
(Weekly Data from January 1990 to September 2005)
Naphtha Gasoline Kerosene Gasoil FO% FO 3.5%
Proportionality 2.62∗∗∗ 2.55∗∗∗ 2.43∗∗∗ 2.35∗∗∗ 2.26∗∗∗ 1.81∗∗∗
Coefficient, β0(121.19) (100.55) (104.59) (99.14) (68.89) (42.27)
Long-Run 0.88∗∗∗ 0.94∗∗∗ 0.97∗∗∗ 0.96∗∗∗ 0.82∗∗∗ 0.91∗∗∗
Elasticity, β1(126.35) (115.19) (129.72) (125.78) (77.87) (65.83)
Adjustment −0.128∗∗∗
−0.086∗∗∗
−0.094∗∗∗
−0.101∗∗∗
−0.072∗∗∗
−0.095∗∗∗
Speed, α+
p(−6.82) (−4.61) (−5.56) (−5.69) (−4.17) (−5.42)
Adjustment −0.141∗∗∗
−0.094∗∗∗
−0.070∗∗∗
−0.078∗∗∗
−0.051∗∗∗ 0.014
Speed, α−
p(−5.79) (−3.46) (−3.97) (−4.24) (−2.96) (0.85)
∆Brent, γ+
00.433∗∗∗ 0.516∗∗∗ 0.525∗∗∗ 0.619∗∗∗ 0.247∗∗∗ 0.316∗∗∗
(12.16) (14.59) (17.78) (22.48) (5.49) (6.87)
∆Brent, γ−
00.434∗∗∗ 0.509∗∗∗ 0.485∗∗∗ 0.538∗∗∗ 0.442∗∗∗ 0.475∗∗∗
(15.39) (15.37) (16.04) (17.66) (13.68) (15.08)
∆Dep−1,ω10.288∗∗∗ 0.291∗∗∗ 0.188∗∗∗ 0.173∗∗∗ 0.479∗∗∗ 0.387∗∗∗
(11.11) (10.57) (6.91) (6.51) (15.09) (13.74)
∆Dep−2,ω2−0.058∗∗∗
−0.061∗∗∗
−0.088∗∗∗
(−2.19) (−2.57) (−3.01)
ARCH 1 0.149∗∗∗ 0.047∗∗∗ 0.184∗∗∗ 0.188∗∗∗ 0.238∗∗∗ 0.168∗∗∗
(3.86) (2.61) (3.65) (3.57) (4.42) (3.48)
ARCH 2 −0.242∗∗∗
(−3.69)
ARCH 3 0.104∗∗∗
(3.25)
ARCH 4 −0.076∗∗∗
(−3.29)
GARCH 1 0.693∗∗∗ 0.045 0.629∗∗∗ 0.618∗∗∗ 0.673∗∗∗ 0.586∗∗∗
(10.57) (0.05) (7.32) (6.96) (3.58) (5.38)
GARCH 2 0.895∗∗∗
(8.73)
Adj.R20.51 0.49 0.48 0.50 0.44 0.40
ARCH(7) 0.76 1.14 0.95 1.37 0.83 0.83
(p-value) (0.62) (0.33) (0.47) (0.21) (0.56) (0.56)
Normality 1.81 2.99 2.19 0.66 7.19∗∗ 4.90∗
(p-value) (0.41) (0.22) (0.33) (0.72) (0.03) (0.09)
∗∗∗ statistical significance at 1% level
∗∗ statistical significance at 5% level
∗statistical significance at 10% level
Unless differently specified, t-statistics are in parentheses.
32
Table 9: Wald test of Long-Run and Brent Change Asymmetric Coefficients
Null Hypothesis Naphtha Gasoline Kerosene Gasoil Fuel Oil 1% Fuel Oil 3.5%
Long-Run Asymmetry
α+
p=α−
p0.14 0.04 0.79 0.64 0.61 13.56∗∗∗
(p-value) (0.71) (0.84) (0.37) (0.42) (0.43) (0.00)
Short-Run Asymmetry
γ+
1=γ−
10.00 0.01 0.76 3.29∗9.06∗∗∗ 5.99∗∗
(p-value) (0.98) (0.91) (0.38) (0.07) (0.00) (0.02)
∗∗∗ statistical significance at 1% level
∗∗ statistical significance at 5% level
∗statistical significance at 10% level
33
Table 10: GARCH Estimation: Refining Margin Effects
(Weekly Data from January 1990 to September 2005)
Naphtha Gasoline Kerosene Gasoil FO 1% FO 3.5%
Constant, c0.328∗∗∗ 0.212∗∗∗ 0.158∗∗∗ 0.162∗∗∗ 0.124∗∗∗ 0.049∗∗∗
(9.53) (5.91) (5.55) (5.51) (5.31) (2.61)
Lagged −0.128∗∗∗
−0.085∗∗∗
−0.068∗∗∗
−0.071∗∗∗
−0.054∗∗∗
−0.029∗∗∗
Dependent, λp(−9.92) (−6.16) (−5.94) (−5.78) (−5.62) (−3.47)
Lagged 0.116∗∗∗ 0.080∗∗∗ 0.068∗∗∗ 0.069∗∗∗ 0.044∗∗∗ 0.029∗∗∗
Brent, λb(9.76) (6.05) (6.01) (5.73) (5.49) (3.55)
Rising Brent & 0.419∗∗∗ 0.483∗∗∗ 0.452∗∗∗ 0.562∗∗∗ 0.178∗∗∗ 0.256∗∗∗
Positive Margin, γ1(9.48) (12.31) (14.39) (20.03) (3.18) (4.91)
Rising Brent & 0.486∗∗∗ 0.615∗∗∗ 0.626∗∗∗ 0.761∗∗∗ 0.323∗∗∗ 0.455
Negative Margin, γ2(8.51) (7.84) (10.19) (12.46) (5.69) (8.01)
Falling Brent & 0.486∗∗∗ 0.528∗∗∗ 0.487∗∗∗ 0.553∗∗∗ 0.509∗∗∗ 0.531∗∗∗
Positive Margin, γ3(14.40) (13.03) (12.16) (14.01) (13.83) (14.95)
Falling Brent & 0.331∗∗∗ 0.459∗∗∗ 0.501∗∗∗ 0.487∗∗∗ 0.329∗∗∗ 0.332∗∗∗
Negative Margin, γ4(6.04) (8.22) (11.09) (9.49) (5.59) (5.65)
∆Dep−1,ω10.282∗∗∗ 0.282∗∗∗ 0.178∗∗∗ 0.162∗∗∗ 0.481∗∗∗ 0.372∗∗∗
(10.52) (10.18) (6.91) (6.01) (15.68) (13.15)
∆Dep−2,ω2−0.069∗∗∗
−0.065∗∗∗
−0.086∗∗∗
(−2.65) (−2.66) (−2.93)
ARCH 1 0.152∗∗∗ 0.048∗∗∗ 0.184∗∗∗ 0.191∗∗∗ 0.266∗∗∗ 0.163∗∗∗
(3.77) (2.66) (3.73) (3.59) (4.97) (3.36)
ARCH 2 −0.276∗∗∗
(−3.81)
ARCH 3 0.112∗∗∗
(3.22)
ARCH 4 −0.071∗∗∗
(−2.98)
GARCH 1 0.693∗∗∗ 0.049 0.634∗∗∗ 0.618∗∗∗ 0.699∗∗∗ 0.593∗∗∗
(10.79) (0.46) (7.60) (6.86) (3.47) (5.34)
GARCH 2 0.889∗∗∗
(8.11)
Adj.R20.52 0.50 0.48 0.50 0.44 0.41
ARCH(7) 0.98 1.02 0.97 1.52 0.77 0.83
(p-value) (0.44) (0.42) (0.45) (0.16) (0.61) (0.56)
Normality 1.54 1.99 3.21 0.52 5.48∗4.99∗
(p-value) (0.46) (0.37) (0.20) (0.77) (0.06) (0.08)
∗∗∗ statistical significance at 1% level
∗∗ statistical significance at 5% level
∗statistical significance at 10% level
Unless differently specified, t-statistics are in parentheses.
34
Table 11: Wald test of Refining Margin Asymmetric Coefficients
Null Hypothesis Naphtha Gasoline Kerosene Gasoil Fuel Oil 1% Fuel Oil 3.5%
No asymmetry
γ1=γ2=γ3=γ42.84∗∗ 1.28 2.52∗∗ 3.74∗∗∗ 8.61∗∗∗ 8.46∗∗∗
(p-value) (0.04) (0.28) (0.05) (0.01) (0.00) (0.00)
Brent’s Rise asymmetry
γ1=γ21.16 2.69∗2.84∗∗ 7.06∗∗∗ 4.49∗∗∗ 8.80∗∗∗
(p-value) (0.28) (0.10) (0.00) (0.00) (0.03) (0.00)
Brent’s Drop asymmetry
γ3=γ47.33∗∗∗ 1.25 0.06 1.16 8.57∗∗∗ 10.61∗∗∗
(p-value) (0.00) (0.26) (0.80) (0.28) (0.00) (0.00)
∗∗∗ statistical significance at 1% level
∗∗ statistical significance at 5% level
∗statistical significance at 10% level
35
Appendix A: Data Description
Platt’s weekly price series are used in this study. The complete description
of each price is as follows:
Crude: Brent, Dated 10-15 days, Spot Price, Cargo Average, U.S.$ per
Barrel; Density Class: Brent Blend United Kingdom;
Naphtha: Cargoes Northwest Europe, Spot Price, CIF∗, Cargo (Physical)
Average∗∗, U.S.$ per Metric Ton; Density Class: Naphtha;
Gasoline Premium: Gasoline Premium Unleaded, Northwest Europe, Spot
Price, CIF∗, Cargo Average∗∗, U.S.$ per Metric Ton; Density Class:
Unleaded Gasoline;
Kerosene: Northwest Europe, Spot Price, CIF∗, Cargo Average∗∗ , U.S.$
per Metric Ton; Density Class: Jet Kerosene;
Gas Oil: Gasoil 0.2 PCT (NO. 2), Northwest Europe, Spot Price, CIF∗,
Cargo Average∗∗, U.S.$ per Metric Ton; Density Class: Gasoil 0.2;
Light Fuel Oil: Fuel Oil 1.0 PCT (NO. 6), Northwest Europe, Spot Price,
CIF∗, Cargo Average∗∗, U.S.$ per Metric Ton; Density Class: NO.6
1.0%;
Heavy Fuel Oil: Fuel Oil 3.5 PCT (NO. 6), Northwest Europe, Spot Price,
CIF∗, Cargo Average∗∗, U.S.$ per Metric Ton; Density Class: H.S.F.O.
- EUROPE 3.5%.
∗CIF: Cost, Insurance, and Freight. This is a trade term requiring the
seller to arrange for the carriage of goods by sea to a port of destination,
and provide the buyer with the documents necessary to obtain the goods
36
from the carrier.
∗∗ For each series we compute the mean of cargoes high NWE and cargoes
low NWE.
37
Appendix B: the Refining Margin Computation
In order to calculate the refining margin, we use a standard approach de-
scribed in the Users’ Guide (2000) released by the International Energy
Agency. The refining margin is there defined as follows:
Gross Product Worth: the weighted average value of all refined product
components (less an allowance for refinery fuel and loss) of a barrel of
the marker, computed by multiplying the spot price of each product
by its percentage share in the yield of the total barrel of crude
less Crude price: Brent FOB
less Transport costs: marginal crude freight, insurance and ocean loss, in
case of an FOB crude, assuming a single voyage for an appropriately
sized tanker chartered on the spot market
less Marginal refinery operating costs: defined to include only the marginal
costs for chemicals, additives and catalyst
less Credit allowance representing the financial effect of the time delay
between paying for crude and receiving receipts for its products, such
as crude credit, crude transit and product credit, assuming a crude
residence time in the refinery of five days and a product credit time of
ten days.
Price quotations used to calculate the GPW are the mean of FOB cargoes
high NWE and FOB cargoes low NWE for gasoline, kerosene, and 1% and
3.5% fuel oils and the mean of the CIF cargoes NWE quotations for naphtha
and gasoil. Since the product price series at our disposal are in U.S.$/Metric
Ton whereas that for Brent is in U.S.$/Barrel, we convert each product price
38
in U.S.$/Barrel by using the conversion factors in table 12. The background
and the assumptions behind the refining margin calculations are different
for each refining centre. The resulting product yields and the additional ele-
ments used in calculating the refining margin for Rotterdam Brent reported
by the International Energy Agency are summarised in table 13.
Table 12: Refined Petroleum Products Conversion Factors
Product Barrels per Metric Ton
Naphtha 8.82
Gasoline 8.46
Jet Fuel, Kerosene-type 7.88
Distillate Fuel Oil(Gasoil) 7.46
Fuel Oil 1% 6.49
Table 13: Product Yields and Parameters for Refinery Margin Calculations
(% volume)
Product Yields
Hydroskimming Cracking
Naphtha 6.49 9.08
Gasoline 17.00 28.56
Jet Kerosene 9.39 8.88
Distillate Fuel Oil(Gasoil) 35.98 37.45
Fuel Oil 1% 28.41 14.36
Total 97.27 98.32
Refinery Fuel and Loss (% on crude) 2.73 1.68
Parameters
Hydroskimming Cracking
Marginal Operating Costs ($/bbl) 0.30 0.40
Ocean Loss and Insurance Factor (% on crude) 0.48 0.48
Credit Factor (% on crude) 0.33 0.33
39
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