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

.