Retail Pricing under Contract Self-Selection: An Empirical Exploration

doi:10.4236/ti.2013.41B007

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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

Email: Yuanfang.lin@ ualberta.ca, lianh [email protected]

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

ααα

=−Φ −++

(1)

( )

0112 2

Pr []

idp

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.

is the cdf of a standard

normal distribution,

is a vector of variables

representing market condition with1

being the corres-

ponding coefficients, 2

zis a vector of variables

representing station characteristics with

being the cor-

responding coefficients, and0

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

ctl ctlidp

XISS ISSI

ββ βββε

=++ +++

(3)

where

is the vector of exogenous variables

representing the relevant market and station characteris-

tics with1

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

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).

( )( )

( )

/1SS YY

=−−Φ −

(4)

( )( )

/SSY Y

= −Φ−

(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

ααα

=++

(6)

For comparison purpose, a pricing regression without

correcting for the contract self-selection can be specified

01 2

ctl

γγ γε

=++ +

(7)

where the station’s contract choice is merely treated as an

exogenous variable, same as those in the vector

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

Wash

0.22

0.42

Full

0.12

0.33

Conv

0.91

0.29

Day

0.69

0.46

Serv

0.20

0.40

Brd

0.42 0.49 0 1

Noz

16.56

9.46

Cmp

3.22

3.11

Mhi

45255.00 21444.00 0 200001

Pop

1635.00

1058.00

7667

RUP

960.32

54.04

1159

Cvis

0.36

0.48

Nea f

0.21

0.41

Nea c

0.20

0.40

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

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 (

)

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

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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