R. Godby et al. r Energy Economics 22 2000 349]368 354
previous literature. Gasoline price data used here is regional, as opposed to the Ž
. Ž
. aggregate data used in Kirchgassner and Kubler 1992 , Borenstein et al. 1997 ,
¨ ¨
and the crude costrgasoline price relationship is estimated in several centres, as Ž
. opposed to the single centre studied in Bacon 1991 . Additionally, the econometric
method employed is less restrictive than that used in either of the previous studies. We fully describe our method, while reviewing and comparing it to previous
methods, in the following section.
3. Partial and full adjustment models
One model used to explain the response of gasoline prices to input cost shocks is the partial adjustment model. The current price y , is set at last period’s price with
t
an adjustment for any differences between last period’s price and the target level, y
U
, according to the following relationship:
ty 1
Ž . Ž
U
. Ž .
y s y q
1 y f y
y y
q « 1
t ty
1 ty
1 ty
1 t
where f is the speed of adjustment. From an equilibrium where y s
y
U
, a shock
ty 1
t
to y
U
will result in an infinitely slow adjustment toward the new equilibrium if
ty 1
f s 1 and an instantaneous adjustment to the new target if f s 0. Given that
Ž crude cost is the single determining factor in gasoline prices Natural Resources
. Canada 1997b , it is assumed that the target price is the long-run equilibrium price,
U
Ž . y s c q c c q «
, 2
1
Ž .
where c is other costs and margins which we consider to be essentially constant , c
is the crude cost, and c , represents the proportion of the crude cost which is
1
passed through to the retail gasoline price. In this long-run relationship, whether or not c , is equal to one will depend on the market under study.
1
Ž .
Bacon 1991 observed that a partial adjustment would not allow for a proper assessment of the asymmetric responses to two separate shocks in the target price
Ži.e. an unanticipated crude cost decrease followed by an unanticipated crude cost .
increase unless the researcher were able to split the sample into the appropriate sub-samples. Since it is not possible, a priori, to know the appropriate sample split,
Ž .
Bacon 1991 proposed the following quadratic partial adjustment mechanism,
2
U U
Ž .
Ž .
Ž . y s y
q a y
y y
q a y
y y
q « 3
t ty
1 ty
1 ty
1 1
ty 1
ty 1
t ,
where the hypothesis that a s 0 reflects a symmetric pricing response. If both a
1
and a , are greater than zero, the response to a crude cost increase will be more
1
rapid early on than a crude cost decrease. If a - 0 and a 0, the response is
1
Ž .
more rapid to a crude cost decrease. Bacon 1991 found the former to be true in the UK.
The weaknesses of the quadratic partial adjustment model are that a proportio- nal and equal change is imposed as an adjustment toward the new equilibrium in
R. Godby et al. r Energy Economics 22 2000 349]368 355
all periods after a shock and the asymmetry must become proportionately larger with an increase in the difference between current and long-run equilibrium prices
Ž .
Borenstein et al., 1997 . Subsequently, an asymmetric full adjustment model is proposed,
p
U
q q
y y
Ž .
Ž .
Ž . y s y
q u y
y y
q u D
c q u D
c q «
4
Ý
t ty
1 ty
1 ty
1 k
tyk k
tyk t
,
ks
where p is the number of lags over which the shock is felt, D c
q
are the positive
tyk
changes in the crude cost, and D c
y
are the negative changes in the crude cost. In
tyk
Ž .
order to ensure that the error term is white noise, Borenstein et al. 1997 included lagged changes in past gasoline prices in their estimation. After estimating the
crude cost series by instrumental variables, the second stage involved estimating,
p
q q
y y
Ž .
D y s yu c q u y
y u c c
q u D
c q u D
c
Ý
t 0 ty1
1 ty1 k
tyk k
tyk
ks r
q q
y y
Ž .
Ž . q
u D y
q u D y
q « 5
Ý
k tyk
k tyk
t ,
ks 1
The coefficients on the lagged price level and the lagged crude oil price can be used then to uniquely determine the pass-through coefficient, c .
1
Ž .
Kirchgassner and Kubler 1992 adopted an approach which is similar to Boren-
¨ ¨
Ž .
U
stein et al. 1997 . For both models, the long-run price, y , was estimated in the
t
Ž . first stage using Eq. 2 . The second stage involved estimating an unrestricted and
restricted model,
p
Ž .
Ž . D
y s u z q
u D
c q «
6
Ý
t ty
1 tyk
tyk t
,
ks p
q q
y y
Ž .
Ž . D
y s u z q
u D c
q u D c
q « ,
7
Ý
t ty
1 k
tyk k
tyk t
ks
ˆ ˆ
where z s
y y c y c
c represents the lagged residuals from the first
ty 1
ty 1
1 ty1
regression and is referred to as the error correction term. To motivate the differences between the full adjustment error correction model
and the approach adopted in this paper, consider a full adjustment model with a lag length of only one period. All else equal, the short-run response in current
retail price will be determined by a change in the current crude cost only. A symmetric response would be represented by the dashed line in Fig. 1. The solid
line represents an asymmetric response such that the price is adjusted upwards by a larger proportion of the crude cost change when crude prices are increasing than
Ž
q y
. when decreasing u u
. Suppose that the actual response follows a more complicated process:
R. Godby et al. r Energy Economics 22 2000 349]368 356
Fig. 1. ] ] ]
symmetric } asymmetric.
X
Ž . D
y s a D c , D
c F g 8
1 X
Ž . D
y s d D c , D
c g 9
1
In Fig. 2, the threshold formulation is the darker solid line. The response to a crude cost change is to increase the retail price by a
X
D c for all changes in crude
cost less than or equal to g. When the crude cost changes by more than g, the response is to change the retail price by d
X
D c , where a
X
- d
X
. The asymmetric full adjustment model allows that there is a different response
to crude cost increases and decreases, but it requires that the threshold for this
Fig. 2. —
threshold } asymmetric.
R. Godby et al. r Energy Economics 22 2000 349]368 357
asymmetric response be a zero change in the crude cost and does not allow for a dynamic threshold effect. The Threshold Regression model does not impose these
restrictions.
4. The Threshold Autoregressive TAR model
