Technology and Investment, 2013, 4, 31-35
Published Online Febr uary 2013 (http://www.SciRP.org/journal/ti)
Retail Pricing under Contract Self-Selection: An Empirical
Exploration
Yuanfang Lin, Lianhua Li
School of Business, University of Alberta, Edmonton, Canada
Received 2012
ABSTRACT
Using cross-sectional survey data on prices, station and market characteristics for 730 gasoline stations in the Greater
Saint Louis area, we estimate a switching regression model of station decisions. We employ a binary probit choice
model to study a station’s decision to enter a contract relationship with greater control from the upstream refinery, or a
contract relationship with greater degree of independence, as a function of market and station characteristics. We then
estimate stations’ pricing decisions with self-selecti vity corrections for the station’s contract decision. We show that
incorrect inferences about retail gasoline station’s pricing behavior would result if the endogeneity in the choice of con-
tract type were treated as exogenous condition in the estimation.
Keywords: Retail Gasoline Markets; Marketing Channel; Pricing Strategy; Selection Bias; Switching Regression
1. Introduction
As a channel intermediary, a retailer obtains product
from manufacturers and resell to the end consumers in
the market. When selecting a certain contract relationship
with the upstream manufacturer, a retailer considers and
compares the benefits versus the levels of control from
the manufacturer on its marketing activities, associated
with different types of contract relationship. If a retailer
agrees to become a lower level division or a franchise of
the manufacturer, the retailer’s marketing activities in
terms of daily prices, promotional events, etc will be
largely controlled by the manufacturer. On the other hand,
if the retailer maintains its independence by only paying
wholesale prices to get product from manufacturer, the
above mentioned marketing activities can then be largely
determined by the retailer itself or least with greater de-
gree of flexibility.
This paper examines a retailer gasoline station’s pric-
ing decision after accounting for its endogenous, compa-
ratively longer-term decision on the contract relationship
with upstream refinery. The model and analysis pre-
sented here are inspired by work done by Iyer and See-
th ar ama n (2003) which examines a firm’s incentive to
price discriminate after self selecting the product offering.
We model a gasoline station’s decision to be in a more
“controlled” or “independent” relationship with upstream
refinery as a function of the market and station characte-
ristics. We then model the retail price set by the gasoline
station conditional on its prior endogenous contract deci-
sion. The study allows us to explicitly and comprehen-
sively investigate the interaction between two important
Marketing “4Ps”, namely, price and place (channel) in
the retail gasoline industry.
2. Literature Background
When it comes to the marketing “4Ps” about a retail gas-
oline station, the “Price” and “Place” (including both
geographic location and contract choice) have been of
strong interests in existing economic studies.1
Slade (1996) argues that when there is a high degree of
The fol-
lowing we briefly review a few key references before
stating the contribution of this paper.
Shepard (1993) argues that gasoline refiners will
choose contractual forms with strong performance incen-
tives, i.e., lessee-dealerships or open dealerships, at gaso-
line stations where unobservable effort is more important
(e.g. auto repair, full service), and contractual forms, i.e.
company-owned, that allow more direct control but offer
weaker performance incentives, at stations where ob-
servable effort is more important (e.g. convenient store).
Pricing regression using cross-sectional data on contrac-
tual forms and other characteristics from 1,527 gasoline
stations in Eastern Massachusetts showed that compa-
ny-owned stations indeed have lower prices than other
stations, all else being equal.
1 Interested readers are referred to Lin and Seetharaman (2012) for
details.

Y. LIN, L. LI
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 ,
Pridp
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.
Φ
is the cdf of a standard
normal distribution,
1
z
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
2
α
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
X
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.
idp
I
is an indicator variable which
equals 1 for stations with contract of strong “indepen-
dence” from the upstream refinery and 0 otherwise. The
variable
1
SS
is a self-selectivity correction for the “con-
trol” contract regime, while the variable
0
SS
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).
( )( )
( )
1
/1SS YY φ =−−Φ −
(4)
( )( )
0
/SSY Y φ = −Φ−
(5)
whe re
φ
is the pdf of the standard normal distribution and
Y
represents the estimates from the binary probit model
in step 1.
0112 2 Y zz
ααα =++
(6)
For comparison purpose, a pricing regression without
correcting for the contract self-selection can be specified
as
01 2
P
ctl
XI γγ γε =++ +
(7)
where the station’s contract choice is merely treated as an
exogenous variable, same as those in the vector
X
.
32

Y. LIN, L. LI
4. Data and Estimation
We employ a survey data2
9) Mhi, a non-negative continuous variable that cap-
, collected during 1999, which
covers 730 retail gasoline stations in the Greater Saint
Louis area. The survey data contain information on retail
prices and various service and local market characteris-
tics pertaining to the 730 gasoline stations. We also em-
ploy the 2000 U.S. census records and information from
the Missouri Census Data Center for demographic cha-
racteristics of the local markets where these gasoline
stations operate.
4.1. Empirical Measures
We use the Type-of-Operation recorded in the station
survey to construct the dependent variable for the binary
probit model at step 1. Stations in the survey are classi-
fied into four different types of operation: 1) owned by
refinery; 2) franchise of refinery; 3) independent retailer;
and 4) local jobbers. We group the first two types of op-
eration (company-owned, franchise) into the “con-
trol”-type contract relationship (Ctl), while the remaining
two are grouped into the “independent”-type contract
relationship (Idp). This practice is consistent with the
literature studies on marketing channel coordination (e.g.
McGuire and Staelin 1983). Consistent with the literature,
we include the following variables in the estimation of
contract choice model and pricing regression, which
contains station and market characteristics, as well as
demographics of the local area where the station is oper-
ated.
1) Wash, i.e., a dummy variable that takes the value 1
if the station offers car wash and 0 otherwise.
2) Full, i.e., a dummy variable that takes the value 1 if
the station sells full-service gasoline and 0 otherwise.
3) Conv, i.e., a dummy variable that takes the value 1
if the station has convenience store and 0 otherwise.
4) Day, i.e., a dummy variable that takes the value 1 if
the station opens 24 hour a day and 0 otherwise.
5) Serv, i.e., a dummy variable that takes the value 1 if
the station has service station and 0 otherwise.
6) B rd , i.e., a dummy variable that takes the value 1 if
the station is a brand-name station (Amoco, Shell, or
Exxo n-Mobil) and 0 otherwise.
7) No z, a discrete variable, whose values range from 2
to 8, that captures the number of pumping nozzles at the
gasoline station.
8) Cmp, a non-negative discrete variable that captures
the number of gasoline stations (other than the focal one)
that operate in the same local market (defined by census
track).
2 The survey data was collected by New Image Marketing Ltd.
tures the median household income of the census track
where the station operates.
10) Pop, a non-negative discrete variable that captures
the size of population for the census track where the sta-
tion operates.
The station survey includes, for each gasoline station,
the prices of three grades – 87, 89 and 93 octane levels.
Since 87-octane level is the most commonly sold grade
of gasoline in retail gasoline markets, and is available at
all the stations in our dataset, we operationalize the de-
pendent variable (Rup) for the pricing regression at step 2
using the observed (posted) price of self-service gasoline
in cents per gallon. And the following variables are in-
cluded in the pricing regression to assess the potential
impact from local demand and competitive condition.
11) Cvis, a dummy variable that takes the value 1 if
there is another station visible from the location of the
focal station and 0 otherwise.
12) Neaf, a dummy variable that takes the value 1 if
the station is within 1 mile distance from a highway en-
trance and 0 otherwise.
13) Neac, a dummy variable that takes the value 1 if
the station is near a business entity (e.g. grocery store,
shopping plaza, etc).
Table 1 reports the descriptive statistics for all the va-
riables.
Table 1. Descriptive Statistics
Variable
Mean
Std Dev
Min
Max
Ctl
0.34
0.48
0
1
Wash
0.22
0.42
0
1
Full
0.12
0.33
0
1
Conv
0.91
0.29
0
1
Day
0.69
0.46
0
1
Serv
0.20
0.40
0
1
Brd
0.42 0.49 0 1
Noz
16.56
9.46
1
66
Cmp
3.22
3.11
0
17
Mhi
45255.00 21444.00 0 200001
Pop
1635.00
1058.00
0
7667
RUP
960.32
54.04
19
1159
Cvis
0.36
0.48
0
1
Nea f
0.21
0.41
0
1
Nea c
0.20
0.40
0
1
4.2. Contract Choice Results
Table 2 reports the probit model estimation results from
step 1. Stations are more likely to choose a “con-
trol”-type contract with a major brand refinery. Stations
are also likely to be in a “control”-type contract if offer-
ing car wash or full-service gasoline product. Also longer
opening hours and greater number of pumping nozzles
are both more likely associated with a “control”-type
contract. Consistent with the literature (e.g. Shepard
33

Y. LIN, L. LI
1993), stations are more likely to be in a “independent”-
type contract if offering auto repair service where unob-
servable effort is more important. Different from the li-
terature, we did not find significant impact on the “con-
trol”-type contract from the presence of convenience
store, which could be explained by the increasing
co-existence of convenience stores inside gasoline station
in recent years. Stations are less likely to choose a “con-
trol”-type contract when operating in a local area with
higher medium household income. Finally the presence
of competing stations in the same local area marginally
reduces a station’s likelihood of choosing a “con-
trol”-type contract as reaming independence would help
the station react more promptly in competitive situation
such as promotional decisions.
Table 2. Probit Model Results
Variable Coeff
Std.
Error T-Stat P-Value
Cons t
-1.098
0.245
-4.489
0.000
Wash
0.301
0.144
2.093
0.036
Full 0.827 0.191 4.321 0.000
Conv -0.190 0.194 -0.978 0.328
Day
0.415
0.147
2.827
0.005
Serv -0.017 0.182 -0.093 0.926
Brd 0.949 0.123 7.689 0.000
Noz
2.501
0.383
6.534
0.000
Cmp -0.028 0.018 -1.588 0.112
Mhi -0.881 0.513 -1. 718 0.086
Pop
-0.482
0.471
-1.023
0.306
4.3. Pricing Regression Results
Table 3 reports the estimation results of the pricing re-
gression from Step 2.
Table 3. Pricing Model Results
Variable
Coeff
Std.
Error
T-Stat
P-Value
Cons t
0.000
0.007
-0.018
0.985
Day
-0.020
0.007
-3.085
0.002
Brd
0.007
0.014
0.535
0.592
Mhi
0.033
0.021
1.569
0.107
Pop
-0.023
0.021
-1.125
0.261
Cvis
0.003
0.007
0.402
0.687
Nea c
-0.014
0.006
-2.513
0.012
Nea f
-0.006
0.006
-0.969
0.333
Ctl
0.045
0.037
1.221
0.222
SS1
-0.080
0.046
-1.750
0.080
SS0
0.023
0.050
0.468
0.640
The visibility of another station does not seem to sig-
nificantly impact the focal station’s pricing decision, a
finding prompts us to further consider a better measure
of the competitive intensity in the local market. Among
all the variables indicating the potential demand from
local market, closeness to another business entity (e.g.
grocery store, shopping plaza) has the most significant
impact. In particular, a retail station tends to lower its
gasoline price in order to attract traffics likely going to
the nearby business locations. The covariance between
the “control”-type contract choice and the pricing (
3
β
)
is significantly negative, i.e., if a station is more likely to
be in a “control”-type contract relationship with upstream
refinery, it is also more likely to charge a lower price.
4.4. Effect of Endogeneity Correction
The main objective of this paper is to demonstrate the
importance of incorporating a gasoline station’s endo-
genous contract choice when studying its pricing strategy.
For this purpose, we also separate estimate the pricing
equation specified in Equation 7 and the results are re-
ported in the following Table 4.
Table 4. Pricing without Contract Self-Selection
Variable Coeff
Std.
Error T-Stat P-Value
Cons t
0.008
0.005
1.508
0.132
Day
-0.018
0.006
-3.186
0.001
Brd
0.021
0.007
3.157
0.002
Mhi
0.024
0.019
1.267
0.205
Pop
-0.025
0.019
-1.294
0.196
Cvis
0.002
0.007
0.295
0.768
Neac
-0.014
0.006
-2.545
0.011
Neaf -0.006 0.006 -0.974 0.330
Ctl
-0.001
0.006
-0.076
0.939
When a station’s contract type (Ctl) is merely treated
as an exogenous variable in the pricing regression, the
estimate coefficient is statistically insignificant, which
implies that there is no covariance between a station’s
contract relationship with upstream refinery and its pric-
ing decision. This is different from the result of step 2
pricing regression as reported in Table 3. A likelih-
ood-ratio test is further conducted with the null hypothe-
sis being the pricing model with contract self-selection
correction (Table 3) and the alternative hypothesis being
the pricing model without contract self-selection correc-
tion (Table 4). Test statistics favors the self-selection
correction model with high significance (P<.001).
5. Conclusion
This paper investigates a gasoline station’s endogenous
decision to choose a specific contract relationship with
upstream refinery and the corresponding pricing decision.
We find that a pricing regression that does not endogen-
ize the gasoline station’s contract decision to station and
34

Y. LIN, L. LI
local market characteristics leads to incorrect inferences
in the pricing estimation. The most interesting direction
to further expand the current study is to identify other
station decisions that are also endogenously set. One
such factor would likely be the geographic location of the
station where a potential study will then involve a
three -stage decision sequence where stations choose
geographic location first, followed by contract decision
with upstream refinery, and finally the competitive pric-
ing behavior in the local market.
6. Acknowledgements
We thank the Social Sciences and Humanities Research
Council of Canada for funding that supports this research
project.
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