We use the LSE-Hendry general to specific approach to analyse if US gasoline price adjustments are asymmetric with respect to changes in crude oil prices. Furthermore, we modify some weaknesses in the earlier works by Boreinstein, Cameron and Gilbert (1997) and Bachmeier and Griffin (2003) and shows that if the price adjustment equations are properly specified and estimated, alternative specifications and temporal aggregation of data do not affect the results. Monthly US data are used to show that alternative specifications give equally good results and there is no asymmetry in the US gasoline price adjustments.Asymmetric price adjustments, Market power, General to specific approach, Error correction models and Gasoline and crude oil prices

B Bhaskara Rao

Gyaneshwar Rao

English

Research Papers in Economics

Asymmetric Gasoline Price Responses 1
.
ARE US GASOLINE PRICE ADJUSTMENTS
ASYMMETRIC? ∗
B. Bhaskara Rao
rao b@usp.ac.fj
Gyaneshwar Rao
rao gr@usp.ac.fj
University of the South Paciﬁc, Suva (Fiji)
Abstract
We use the LSE-Hendry general to speciﬁc approach to analyse if US
gasoline price adjustments are asymmetric with respect to changes in
crude oil prices. Furthermore, we modify some weaknesses in the ear-
lier works by Boreinstein, Cameron and Gilbert (1997) and Bachmeier
and Griﬃn (2003) and shows that if the price adjustment equations are
properly speciﬁed and estimated, alternative speciﬁcations and tempo-
ral aggregation of data do not aﬀect the results. Monthly US data are
used to show that alternative speciﬁcations give equally good results
and there is no asymmetry in the US gasoline price adjustments.
JEL: Q4, Q40, D82, C22, C32.
KEYWORDS: Asymmetric price adjustments, Market power, General
to speciﬁc approach, Error correction models and Gasoline and crude
oil prices.
∗ We are grateful to Professor Lance Bachmeier of the Kansas State University
and Bill Horvath of the U.S. National Energy Information Center for valuable advice
on the U.S. data. We take responsibility for the errors in data and analysis.2 B. B. Rao & G. Rao
.
I. INTRODUCTION
World-wide escalation of gasoline prices have often been under public
scrutiny since expenditure on gasoline is signiﬁcantly visible in the con-
sumer budget. Gasoline price rises have led to speculations as to their
causes, including the view that the multinational oil companies have
been manipulating prices in an oligopolistic market to earn economic
proﬁts. Many also claim to have observed an asymmetric relationship
between the retail prices of gasoline and the crude oil prices–that is
retail prices respond more quickly to crude price increases than when
they decrease. This is described by Bacon (1991) as the ’rocket and
feathers’ phenomenon in his examination of the UK gasoline market.
The Bacon rockets and feathers phenomenon was found to be also
valid to the US gasoline prices by Borenstein, Cameron and Gilbert
(1997). They have used a series of bivariate error correction models
(ECM), at various stages of the production and distribution chain of
gasoline, and found strong evidence for asymmetric price adjustment
with weekly US data. Essentially their speciﬁcations of the price ad-
justment equations are misspeciﬁed variants of the LSE-Hendry gen-
eral to speciﬁc (GETS) approach. Subsequently, Bachmeier and Griﬃn
(2003) have examined the robustness the BCG ﬁndings, by using both
the GETS type and the well-known ECM equations based on the Engle-
Granger two-step estimation method. They have used both weekly and
daily data. Their main ﬁndings are that there is no asymmetric price
adjustment in the US gasoline market and data for longer frequencies,
e.g., weekly or quarterly data, are likely to be favourable to asymmetric
price adjustment.
Our objectives in the present paper are two fold. First, we ex-
amine the nature of price adjustments in the US gasoline market and
second we show that GETS is a useful approach when it is used prop-
erly. This latter objective is important because the LSE-Hendry GETS
approach, in spite of its computational attractiveness, is not widely
used for modeling time series models. GETS is not popular, especially
with the North American researchers, compared to the alternatives like
VAR and cointegrating VAR approaches. Smith (2000) provides an
excellent methodological perspective to evaluate these alternative tech-
niques and Hoover and Perez (1999, 2004), by using the Monte Carlo
approach, show that GETS is a useful approach.
The outline of this paper is as follows. Section II discusses theAsymmetric Gasoline Price Responses 3
speciﬁcation of our price adjustment equation. Empirical results of the
estimated equations with monthly US data are presented in Section III.
Summary and conclusions are in Section IV.
II. SPECIFICATION
It would be useful to brieﬂy discuss ﬁrst the speciﬁcations of sym-
metric and asymmetric price adjustment equations using the Engle and
Granger (EG) two step procedure. If the equilibrium (long run) rela-
tionship between gasoline and crude oil prices is:
PG= γ0 + γ1 PC+ ε (1)
where PG and PC are, respectively, gasoline and crude oil prices and
ε is an error term with the usul classical propertie. The short run
dynamic price adjustment equation, without any asymmetry, based on
the error correction model is:
∆PGt =
n1 X
i=0
βci ∆PCt−i
n2 X
i=1
βgi ∆PGt−i
− π b Zt−1 + ￿ti (2)
where b Zt−1 = b εt−1. It is well known that the OLS estimates of the
parameters in (1) are super consistent and a parsimonious version of
(2), by eliminating the insigniﬁcant lagged ﬁrst diﬀerences of variables,
would be consistent with the underlying DGP. Granger (1997, p.174),
for example, favours this general to speciﬁc type of approach in the sec-
ond stage of developing DGP consistent error correction models. Note
that βci and βgi measure the short run impact of changes in PCand PG
respectively. π is the speed of adjustment to the long run equilibrium.
The asymmetric price adjustment variant of (2) is as follows:
∆PGt =
n1 X
i=0
β+
ci ∆PC+
t−i
n2 X
i=1
β+
gi ∆PG+
t−i + π+ b Zt−1
n3 X
i=0
β−
ci ∆PC−
t−i
n4 X
i=1
β−
gi ∆PG−
t−i + π− b Zt−1 + ￿ti (3)
Equation (3) can be split into two parts. The part with the super-
script + on the coeﬃcients and the variables, is relevant when prices
increase. Similarly the second part, with superscript −, is relevant4 B. B. Rao & G. Rao
when prices fall. This interpretation was originally used by BCG and
BG. They assumed that β+
ci apply when ∆PCt−1 > 0 and β+
gi apply
when ∆PGt−1 > 0. π+ is applicable when ∆PCt > 0 and π− when
∆PCt ≤ 0. The coeﬃcients and variables with the superscript − are
relevant when the corresponding prices decrease.
To capture the asymmetric eﬀects of crude oil price changes on
gasoline prices, the BCG and BG interpretation of (3) is unsatisfactory
because it is not clear why changes in the past gasoline prices should
have asymmetric eﬀects on the current changes in the gasoline prices.
It may be noted that the error correction part, given by Zt−1 correctly
excludes such eﬀects of gasoline prices. Equation (3) can, therefore,
be modiﬁed by reinterpring that β+
gi apply when ∆PCt−i > 0 and β−
gi
apply when ∆PCt−i ≤ 0.1 Our main interest in estimating (3) is to
determine if the two price adjustment coeﬃcients viz., π+ and π− are
signiﬁcantly diﬀerent and whether | π+ |>| π− |. If this latter condition
is satisﬁed, then the data are consistent with the Bacon rockets and
feathers hypothesis.
The GETS variants of the asymmetric equation is:
∆PGt =
j1 X
i=0
β+
i ∆PC+
t−i +
j2 X
i=0
β−
i ∆PC−
t−i
j3 X
i=1
α+
i ∆PG+
t−i +
j4 X
i=1
α−
i ∆PG−
t−i
+ θ+ (PGt−1 − φ0 − φ1 PCt−1 − φ2T)
+ θ− (PGt−1 − φ0 − φ1 PCt−1 − φ2T)+ ξti (4)
where T is time trend. In GETS, Zt−1 of the ECM in (2) or (3) is
replaced with its equivalent (PGt−1 − φ0 − φ1 PCt−1 − φ2T). In (4)
θ+ and θ− are the speed of adjustment coeﬃcients. The intercepts and
trend variable can be removed from the error correction part of (4) and
may be freely estimated, for example, as in BCG. The rearranged GETS
speciﬁcation is as follows:
1 Price changes were never zero in our sample.Asymmetric Gasoline Price Responses 5
∆PGt = γ0 + γ1 T
+
j1 X
i=0
β+
i ∆PC+
t−i +
j2 X
i=0
β−
i ∆PC−
t−i
j3 X
i=1
α+
i ∆PG+
t−i +
j4 X
i=1
α−
i ∆PG−
t−i
+ θ+ (PGt−1 − φ1 PCt−1)
+ θ− (PGt−1 − φ1 PCt−1)+ ξti (4A)
In our empirical estimation we found that (4A) gives more plausible
estimates than (4). We take the view that there is no basic weakness
in the speciﬁcations of (4) or (4A) based on the LSE-Hendry GETS
approach. Nevertheless, it is often criticised because it does not test for
cointegration but simply assumes that PG and PC are cointegrated.
It can be said that GETS accepts the underlying theory behind the
relationship between the dependent and explanatory variables in their
levels. If that is valid, it is not appropriate to criticise GETS for mix-
ing I(0) and I(1) variables, because if the levels of the variables are
cointegrated, their linear combinations are I(0).
III. EMPIRICAL RESULTS
Our data covers the period from January 1978 to December 2004. PG
is all types of gasoline in the U.S. city average retail price and PC is
the crude oil domestic ﬁrst purchase price. Data are obtained from the
Energy Information Administration’s Monthly Energy Review of March
2005. We have searched for optimal lags with PcGets of Hendry and
Krolzig (2001) starting with a long general unrestricted model (GUM).
Seven lags for the ﬁrst diﬀerences of the variables and eleven monthly
seasonal dummies are used. The automatic model selection procedure in
PcGets yielded parsimonious short run dynamic adjustment equations.
We have reestimated these parsimonious PcGets equations with Microﬁt
and found that it gives the same coeﬃcient estimates but for minor
changes in the fourth decimal places. Use of Microﬁt was necessary to
conduct the Wald tests and estimate the GETS equation with NLLS.
Our estimates and test results with Microﬁt are reported in Table-1.
The ﬁrst stage OLS equation to generate Zt for the ECM-EG equa-
tion in column 1 is at the bottom of Table-1 and it is similar to the BG
equation, except that the mark-up of gasoline prices seems to have in-6 B. B. Rao & G. Rao
Table-1
Asymmetric Price Adjustment Equations
Monthly US Data: 1978-2004
Asymmetric ECM-EG Equation Asymmetric GETS Equation
OLS NLLS
Regressor Coeﬀ. t-ratio Coeﬀ. t-ratio
Intercept -0.029 3.68 0.034 3.28
Trend 0.000 3.63 0.000 3.44
∆PG+
t−1 0.354 6.66 0.883 23.89
∆PG+
t−2 -0.252 4.24 — —
∆PG+
t−5 -0.168 3.13 -0.062 1.72
∆PC+
t 0.687 3.59 — —
∆PC+
t−3 -0.280 3.72 0.201 3.14
∆PC+
t−6 —— ——
∆PG−
t−1 0.270 6.66 0.170 3.21
∆PG−
t−2 -0.252 4.24 -0.110 2.29
∆PC−
t 0.615 6.15 0.528 7.85
∆PC−
t−1 0.301 2.58 0.332 3.65
∆PC−
t−3 0.262 2.51 — —
∆PC−
t−5 -0.346 3.66 — —
∆PC−
t−6 0.405 4.12 — —
π+ -0.083 2.72
π− -0.132 4.52
θ+ — — -0.068 3.45
θ− — — -0.074 3.73
φ1 — — 1.016 9.13
OLS equation in the ﬁrst stage ECM-GE
PGt =0 .706 + 1.129 PCt
(27.65) (22.17)
Notes:
In the ﬁrst equation seasonal dummies for August, September and October
were signiﬁcant and in the second equation seasonal dummies for May, June
and September were signiﬁcant. All the residual based χ2 test statistics for
serial correlation, heteroscedasticity, normality of errors and functional form
misspeciﬁcation are insigniﬁcant at the 5% level. These are not reported to
conserve space.Asymmetric Gasoline Price Responses 7
creased from about 6% in GB to 13%. Both the ECM-EG and the GETS
equations are well determined. All the 16 coeﬃcients in the ﬁrst equa-
tion (excluding the seasonal dummies) are signiﬁcant at the 5% level.
Similarly, all but one coeﬃcient are signiﬁcant in the GETS equation
at the 5% level. The remaining coeﬃcient of ∆PG+
t−5 is signiﬁcant at
the 10% level.
It is noteworthy that the dynamic lag structure in both equations
is diﬀerent. The asymmetric price adjustment coeﬃcients π+ and π−
in the ECM-EG equation are well determined and signiﬁcant. Al-
though their point estimates imply that downward adjustments are
faster, the Wald test indicated that there is no signiﬁcant diﬀerence
between them at a marginally less than the 5% level but conclusively
at the 1% level.2 The test statistic, with the p value in the parentheses,
is χ2
1 =3 .9728 (0.046).
In the GETS equation, the asymmetric price adjustment coeﬃcients
θ+ and θ− are much closer. The Wald test indicated that the null that
these two adjustment coeﬃcients are equal could not be rejected at
the 5% level. The computed test statistic and the p value are χ2
1 =
1.6322 (p =0 .201).
On the basis of these results it is hard to say that GETS based
speciﬁcations are unsatisfactory. In fact the GETS equation seems to
have performed better than the ECM-EG equation. Our results thus
highlight some weaknesses in the speciﬁcation and estimation of these
price adjustment equations in the earlier works of BCG and BG. Fur-
thermore, temporal aggregation does not seem to be the main reason
for the BCG ﬁnding of asymmetric price adjustments. The results of
BG cover the period 1985-1998 and our sample is from 1978 to 2004
and both reach the conclusion that there is no evidence of asymmetric
price adjustments in the US gasoline market. Therefore, it may be said
that the US regulation policy has been eﬀective and/or the oil ﬁrms
have become sensitive to the perceptions of the public and media about
their unfair price adjustment policies.
IV. CONCLUSIONS
In this paper we have shown that temporal aggregation and the GETS
speciﬁcation are not the main sources for the BCG conclusion that
gasoline price adjustments are asymmetric in the USA. We have ex-
plained the underlying rationale of the GETS speciﬁcation and showed
2 Interestingly in the BG ECM-EG equation the point estimate of the downward
adjustment coeﬃcient was also more than the upward adjustment coeﬃcient.8 B. B. Rao & G. Rao
that if it is properly speciﬁed with a lag structure consistent with the
DGP and properly estimated by imposing the constraints on the co-
eﬃcients, it is as good as or better than the ECM-EG speciﬁcation.
The main weaknesses in the previous works seem to be a restricted and
uniform lag structure in the dynamic adjustment equations, inappro-
priate speciﬁcations and estimation methods. We have not presented
dynamic impulse responses for two reasons. Firstly, the lag structure
in our equations is complicated, needing simulations with seventh or-
der diﬀerence equations. Secondly, these simulation results are perhaps
unnecessary when the estimated price adjustment coeﬃcients are ad-
equate for testing the asymmetric price adjustment hypothesis. It is
hoped that our methodology and techniques would be useful to esti-
mate price adjustment equations in other oligopolistic markets and in
other countries that may diﬀer in the enforcement of regulation policy.3
3 It may be of interest to point out that Rao and Rao (2005) used both the ECM-
EG and GETS based gasoline price adjustment equations for Fiji. Both equations,
with quarterly data, gave similar estimates of the price adjustment coeﬃcients and
imply that gasoline price adjustments in Fiji are highly asymmetric. This ﬁnding is
not surprising because Fiji is a small developing country and, unlike in the developed
countries, regulation policies are diﬃcult to implement and police in the developing
countries.Asymmetric Gasoline Price Responses 9
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ARE US GASOLINE PRICE ADJUSTMENTS ASYMMETRIC?

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ARE US GASOLINE PRICE ADJUSTMENTS ASYMMETRIC?

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