Y. LIN, L. LI
Copyright © 2013 SciRes. TI
complementarity between gasoline and other activities in
the station (e.g. convenient store), contract with high
salary and low commission must be offered, while when
there is a high degree of substitutability between gasoline
and other station activities (e.g. auto repair), contract
with low salary and high commission must be offered.
Slade (1998) tests whether strategic reasons could ex-
plain why manufacturers choose to remain separate from
their retailers in some markets. Using a binary probit
model on cross-sectional data on contractual forms and
other characteristics collected from 96 branded gasoline
stations in Vancouver during Fall 1991, the author de-
monstrates that a station’s likelihood of being a les-
see-dealership increases as the predicted difference in the
price-cost margins between vertical separation and ver-
tical integration increases.
Pinkse and Slade (1998) assess whether gasoline sta-
tions of a given contract form (e.g. vertically integrated)
cluster together in geographic space. Using spatial statis-
tics, and six different measures of geographic closeness,
the authors recovered positive spatial correlations, i.e.,
firms with similar contract forms are found to cluster.
Regarding stations’ contract choice, the authors found
pattern consistent with Shepard (1993) and Slade (1996).
Our paper contributes to the literature by further dis-
tinguishing comparatively longer versus shorter term
marketing factors. A gasoline station’s retail prices could
be adjusted due to demand and competitive situations
rather frequently within a short time frame. On the con-
trary, the investment of land acquisition, asset purchase
and contract selection tends to be decided earlier and
sustained throughout a longer period. Following this ra-
tionale, we propose that when studying retail stations’
pricing behavior in competition, their prior choice of
entering certain contract with upstream refinery needs to
be taken into consideration. Further the contract type of a
station cannot be merely treated as an exogenous variable
in the pricing equations, rather it has to be treated as an
endogenous decision of the gasoline station separately
and then incorporate into the later analysis of pricing
strategies. A close reference of our paper is Iyer and
Seetharaman (2003) where the authors investigate a gas-
oline station’s incentive to price discriminate by self se-
lecting to sell full -service as well as well as self-service
gasoline.
3. Econometric Model
We employ the “switching regression with endogenous
switching” (Trost 1977) to estimate a retail gasoline sta-
tion’s pricing decision conditional upon its endogenous
contract choice. Other econometric applications of this
model have been in the context of explaining dis-
crete/continuous choice decisions of households (e.g.
Hanemann 1984; Dubin and McFadden 1984; Chinta-
gunta 1993; etc). Details of the model specification are
descrited in the following two-step procedure:
Step 1: we estimate a binary probit model of the gasoline
station’s decision of contract relationship with upstream
refinery, which is represented by the following choice
probabilities:
( )
0112 2
Pr1 []
ctl
zz
ααα
=−Φ −++
(1)
( )
0112 2
Pr []
idp
zz
ααα
=Φ− ++
(2)
where Prctl ,
stand for the probability of a gasoline
station choosing a contract relationship which receives
stronger control from the refinery, or maintains more self
independence, respectively.
is the cdf of a standard
normal distribution,
is a vector of variables
representing market condition with1
α
being the corres-
ponding coefficients, 2
zis a vector of variables
representing station characteristics with
being the cor-
responding coefficients, and0
α
is the intercept term.
Step2: We estimate a linear regression for prices that
explicitly accounts for the effects of contract
self-selection as shown below.
012314 0
P
ctl ctlidp
XISS ISSI
ββ βββε
=++ +++
(3)
where
is the vector of exogenous variables
representing the relevant market and station characteris-
tics with1
β
being the corresponding coefficients. ctl
Iis
an indicator variable which equals 1 for stations with
contract of strong “control” from the upstream refinery
and 0 otherwise.
is an indicator variable which
equals 1 for stations with contract of strong “indepen-
dence” from the upstream refinery and 0 otherwise. The
variable
is a self-selectivity correction for the “con-
trol” contract regime, while the variable
is a
self-selectivity correction for the “independent” contract
regime. Incorporating these variables in the price regres-
sion corrects for the self-selectivity bias that would arise
in the parameters of a pricing model that ignores the sta-
tion’s endogenous contract choice. The self-selectivity
correction terms are computed as follows based on Mad-
dala (1983).
(4)
(5)
whe re
is the pdf of the standard normal distribution and
represents the estimates from the binary probit model
in step 1.
0112 2
Y zz
(6)
For comparison purpose, a pricing regression without
correcting for the contract self-selection can be specified
as
(7)
where the station’s contract choice is merely treated as an
exogenous variable, same as those in the vector
.