Econometric Model of Location and Pricing in the Gasoline Market

8/21/2019 Econometric Model of Location and Pricing in the Gasoline Market

1/15

An Econometric Model of Location and Pricing in the Gasoline MarketAuthor(s): Tat Y. Chan, V. Padmanabhan and P. B. SeetharamanSource: Journal of Marketing Research, Vol. 44, No. 4 (Nov., 2007), pp. 622-635Published by: American Marketing AssociationStable URL: http://www.jstor.org/stable/30162507 .

Accessed: 14/01/2015 11:03

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

.

American Marketing Association is collaborating with JSTOR to digitize, preserve and extend access to

Journal of Marketing Research.

http://www.jstor.org

http://www.jstor.org/action/showPublisher?publisherCode=amahttp://www.jstor.org/stable/30162507?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/30162507?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=ama


2/15

TAT

.

CHAN,

V.

PADMANABHAN,

nd

P.B.

SEETHARAMAN*

The authors

ropose

an econometric odel

of both he

geographic

locations

f

gasoline

retailers

n

Singapore

nd

price ompetitionmong

retailers onditionaln theirgeographic ocations.Althoughmarket

demand

for

asoline

s

not

observed,

he authors

re able to infer

he

effectsf such

demand

from tations'

ocations nd

pricing

ecisions

using

available

data

on local market-level

emographics. sing

the

proposed

ocation

model,

which s based

on

the

assumption

f social

welfare

maximization

y

a

policy

planner,

he authors

ind hat ocal

potential asoline

demand

depends positively

n the ocal

demographic

characteristics

f

the

neighborhood.

sing

he

proposedpricing

model,

which s based

on the

ssumption

fBertrand

ompetition

etween

etail

chains,

he uthors

ind

hat

etail

margins

or

asoline

re

approximately

21%.

The authors lso

find hat

onsumers

re

willing

o travel

p

to a

mile or

savings

f

$.03

per

iter.

sing

he estimates

fthe

proposed

econometric

odel,

he authors

nswer

policy uestions

ertaining

o a

recent

merger

between

two firms

n the

industry. nswering

hese

questionshas importantolicymplicationsor othgasolinefirmsnd

policy

makers

n

Singapore.

An

Econometric

odel

fLocation

nd

Pricing

n he

Gasoline

Market

Location

s

repeatedly

tressed

n

the

business

ress

s

one,

f not he

only, equirement

or

uccess

n

retailing.

t

is also

recognized

n the academic

iterature

s

being

an

*Tat

. Chan

s Associate

rofessor

f

Marketing,

ohn

M. Olin School

of

Business,

Washington niversity

n St.

Louis

(e-mail:

chan@wustl.

edu).

V. Padmanabhan

s INSEAD

Chaired

Professor

f

Marketing,

INSEAD,

Singapore

e-mail:

[email protected]).

.B.

Seetharaman

s

Professor

f

Marketing,

esse

H.

Jones

Graduate

chool

of

Management,

ice

University

e-mail:

[email protected]).

he authors

re

listed

n

alphabetical

rder.

hey

thank

uanfang

in

for

etting

p

the

data

n usable

form or he

mpirical

nalyses.

hey

lso

thank

rofessors

Glenn

MacDonald

nd

MarkDaskin

for heir aluable

uidance

nd

com-

ments uring hepreliminarytagesof thisproject. hey ppreciatehe

many

nsightful

omments

y

participants

t

the

Summer

nstitute

f

Competitive

trategy

n

Berkeley,

alif.

July

003);

the

Marketingamp

at the

Kellogg

School

of

Management,

Northwestern

niversity,

n

Chicago September

003);

the

eminars

t Jesse

H. Jones

chool

ofMan-

agement,

ice

University

November

003),

NSEAD

(November

003),

The Wharton

chool,

University

f

Pennsylvania

January

004),

ndian

Institute

f

Management,

hmedabad

August

004),

National

University

of

Singapore

August

004),

Korea

University

usiness

chool

KUBS),

Seoul

(May

2006),

and

Vellore

nstitute

f

Technology

VIT),

Vellore,

India

February

007).

Finally,

hey

ratefully

cknowledge

he

ssistance

of Professor

van

Png,

Mrs. Priti

Devi,

Mr.

Albert

an,

Mr. Low

Siew

Thiam,

Mr.

Henry

Wee,

nd

Mr.

Eng

Kah Joo.

To read

and contribute

o reader

and

author

dialogue

on

JMR,

visit

httpilwww.marketingpowercom/finrblog.

2007,007,

American

arketing

ssociation

ISSN:

0022-2437

print),

547-7193

electronic)

important

eterminant

f retail

ompetition

nd

perform-

ance.

ndeed,

ome

of

the

arliest

works

n retail

ompeti-

tion

e.g.,

D'Aspremont,

Gabszewicz,

and

Thisse

1979;

Hotelling

929)

werebased

on

models of

spatial

hetero-

geneity iven

etail

irms'

ocation

decisions.

This article

attempts

o understand

he

phenomenon

f retail

erform-

ance

by

developing

n econometric

odel

of ocation

nd

price

decisions.

The

simultaneous

onsideration

f both

location

and

marketing-mix

nteractions

nables

us to

address

broader

et

of

questions

elated

o

publicpolicy

and to

provide

more

omprehensive

nalysis

f the

ssues

of

firm onduct

ndmarket

erformance.

or

example,

we

can

now ddress he

following

uestions:

.What re the

mportant

actors

ontributing

o the

potential

demand

t

location?

.How

mportant

s

a retailer's

eographic

ocation

hen

on-

sumers

hoose

mong

lternativeetailers?

hat rade-offs

re

involved

or

retaileretween

acing

arge otential

emand

at

locationnd

eing

n lose

roximity

o

ompetitors

t

he

location?

'What sthe

mpact

f

merger

etween

wo

etail

hains n

prices

nd

rofits

n he

etail

ndustry?

The context

fthis rticle

s the

gasoline

market

n

Singa-

pore.

Using

a

primary

ata

set

that

epresents

censusof

all

gasoline

stations

n

Singapore

nd

tracks

eographic

locations,

asoline

prices,

nd

various tation

haracteris-

tics across

226

gasolinestations,

s

well as

the demo-

Journal

f

Marketing

esearch

622

Vol. XLIV

(November

007),

622-635

This content downloaded from 193.226.34.229 on Wed, 14 Jan 2015 11:03:55 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp


3/15

An

EconometricModel

of

Location and

Pricing

623

graphic

haracteristicsf the tations'ocal

neighborhoods,

we

estimate n econometric odelof ocation

nd

pricing

decisions f

gasoline

tations.

The

ocation

model s built

n

the

premise

which

s

con-

sistent

ith

nstitutionalealities

n

Singapore,

s we dis-

cuss furthernthe ection

Description

f

Data")

that he

Singapore overnment

etermines here o ocate

gasoline

stations n

the

city.

The

government,

s

a social welfare

planner,

s assumed to minimize

ggregate

ravel osts

incurred

y

consumers

n

their ffortso

buy gasoline

n

Singapore.

his eads to a

decision

model that

s

called a

"P-median

roblem."

Weuse a minimum-distanceethod

to

estimateuch location

model,

which nables s to nfer

the

geographic

istribution

f

potential asoline

demand

across ocal

markets

n

Singapore

nd the

dependence

f

suchdemand n ocal

demographic

haracteristics.

We

then

ropose

pricing

modelfor

gasoline

tations,

conditional

n

their

ocations,

based

on the

premise

f

Bertrand

ompetition

etween etail hains. The

pricing

model

equires

ocal firm-level

emand,

hich s

a

function

of

the

potential

emand

or

gasoline

t various

ocations,

prices,and gasolinecharacteristics,s inputs.Because

gasoline

emand s unobserved

n

the

data,

we use

equilib-

rium

conditions

of

demand and

supply

to obtain

an

estimablemodelof

pricing.

stimating

he

pricing

model

enables us

to

infer oththe cost

and demandfunctions.

Using

he

stimates

f

the

parameters

f the ocationmodel

and

pricing

model,

we answer

olicy uestions

ertaining

to the

relative

rofitability

f

various etail

hains nd the

consequences

f

a

merger

etween wo retail hains on

prices

nd

profits

f

firmsn

the

ndustry.

From

stimating

ur

proposed

ocation

model,

we

find

that

ocal

potential

asoline

demand

epends

ositively

n

the

following

ocal

demographic

haracteristicsf

the

neighborhood:opulation;

median

ncome;

umber f

cars;

and proximityo theairport, owntown,nd highways.

Using

he

stimated

otential

asoline

emand t each ocal

neighborhood

n

Singapore

s an

input,

we then

stimate

our

proposed

ricing

modelwith

mpirical

ata on

actual

prices

of

gasoline

at

various

tations.We find hat

etail

margins

or

asoline

re

approximately

1% and

that

mar-

ket hare or

gasoline

tations

negatively

nfluenced

y

the

price

of

gasoline

and

travel

ost. We find hat

on-

sumers re

willing

o

travel

p

to

a milefor

price

aving

of

$.03

per

iter

which

ranslatesnto

saving

f

approxi-

mately

1.3

on a

40-liter

ank f

gasoline).

RELATIONSHIPTO THE

LITERATURE

The

primary

ontributionf

this rticle s

to

develop

n

econometric odelof ocation nd

pricing

ecisions nthe

gasoline

market.We

position

t n

the

context

f

previous

research

oth n

gasoline

marketsnd on

retail

ompetition

models.

Gasoline

Markets

Shepard

1991)

and

yer

nd

Seetharaman

2003)

esti-

mate

pricing

models for

gasoline

stations

hathave

ocal

monopolypower.

Their

models

are not

applicable

for

competitive

arkets,

s inthis

rticle. lade

(1992)

esti-

mates

competitivericing

model

using

ime-series

ata

on

demand

nd

prices

t

13

gasoline

tationsnthe

Greater

Vancouver rea. n

focusing nly

on a

limited umber f

firms n the same geographicneighborhood,he model

ignores

herole of ocation

n

competition.

ssuming

hat

retail ocationdecisions re

exogenous,

ng

and Reitman

(1994)

and

yer

nd Seetharaman

2007)

address he

puzzle

of

why

etailers

n the

ame

geographicpace adopt

imilar

strategies

n certain ases and different

trategies

n others.

Pinkse, lade,

andBrett

2002)

estimate

competitive

ric-

ing

model hat ccommodates he ffects f firms'

patial

locations.

However,

ll these tudies ake reduced-form

approach

to

modeling

he effects f locationon

price

competition

etweenfirms.

n

contrast,

e estimate

n

economic-theoreticodel f

pricing

ehavior

n this

tudy

(see

also

Manuszak

1999).

Furthermore,

oneof the

previ-

ously

mentionedtudies

ttempt

o

explain

irms' ocation

decisions.We believe hat

he urrent

tudy

s

the

firstffort

to

model ocation

ecisions

n

gasoline

markets.

he insti-

tutional

eality

hat he

Singapore overnment

erves s

a

social

planner

n

determining

ocations

f

gasoline

tations

makes ur

ocationmodel oth ealistic

nd

mathematically

tractable.

Retail

Competition

odels

Models of firms'ntryndexitdecisions, ased on free

entry

f firms

as

opposed

o a social

planner etermining

the

optimal

ocations),

have been

recently roposedby

Mazzeo

(2002),

who

models hotels'

ocal market

ntry

decisions,

nd

by

Seim

2006),

who

models ideoretailers'

local market

ntry

ecisions

for

review f the iterature

on

entry

models,

see

Dube et al.

2005).

Our

modeling

approach

iffersrom heirsn

thatwe model he

ocation

decisions-rather

han he

ntry

nd exitdecisions-of a

fixed number

f

gasoline

stations n

geographic

pace,

using

theobserved

geographic

istributionf

geodemo-

graphic

ariables

n

that

pace.

A

rich

iteraturexists n

marketing

hat asts firms nd

consumers

n

a common

erceptual

map

to

analyze

firms'

optimalmarketingecisions Choi,Desarbo,and Harker

1990;

Hauser

1988;

Hauser and

Shugan

1983;

Moorthy

1988).

Marketing

odels f this

ype

ecognize

hat rands

occupy

different

ositions

n the

perceptual

map

n terms

of not

only

heir

bjective

ttributesut also consumers'

subjective

valuations f these

attributes,

hereas con-

sumers

avedifferent

deal

points

i.e.,

most

referred

om-

binations

f

attributes)

n thesame

perceptualmap.

Our

location

model an be

viewed n

ight

fthis

iterature,

uch

that

onsumers'

deal

points

orrespond

o their

laces

of

residence r

work,

whereas

rand

ositions

orrespond

o

the

geographic

ocations f

stores. onsumers'

deal

points

are

nferred

s

a

functionf

geographic

haracteristics

n

our

case,

unlike

n

the

perceptualmap

literature,

hich

measures

ubjectively

erceived

rand

ositions

nd con-

sumers' deal

points

or

ttributes

singmarketing

esearch

techniques.

ote thatocation s

a

horizontalttribute

i.e.,

different

onsumerswould

disagree

on

what

s

the best

location

for firm

ccording

o

where heir

deal

points

reside),

as

opposed

to,

for

example,

price

and

quality,

which

are vertical ttributes

i.e.,

all

consumerswould

agree

hat ower

price

s

preferable

o

higher rice,

higher

quality

s

preferable

o

ower

uality,

nd so

forth).

Thomadsen

2005)

has

developed

retail

rice

ompeti-

tion

model

based

on

the

ssumption

f

Bertrand

rice

om-

petition

etween

ast-foodetail

hains.This

modeluses a

multinomial

ogit

model f

demand s an

input

o

the

pric-

ingequations.Demandfor etailerss parameterizeds a




4/15

624

JOURNAL F

MARKETING

ESEARCH,

NOVEMBER

007

function

f observed

eographic

haracteristics,

rices,

nd

travel

istances f consumers

o stores. oth

demand- nd

supply-side

arameters

re

nferred

olely

from

bserved

prices

ecausedemand or arious etailerss not

bserved

in the

data. Because

we also do not

observedemandfor

gasoline

retailers n our

data,

we

adopt

Thomadsen's

approach

o

model

price

competition

etween

retailers.

However,

nlike

Thomadsen,

who

relies

on

the

pricingmodel

only,

we use a locationmodel that

exploits

the

observed

eographic

istributionf

gasoline

tationscross

localmarketso nfer

he

potential asoline

emand t each

local

market.

We

organize

he emainderfthis rticle s follows:We

develop

mpirical

models o estimate

ocation nd

pricing

decisions f

gasoline

tationsn

Singapore,long

with sti-

mation

echniques

o

estimatemodel

parameters.

hen,

we

describe ur

data.

Following

his,

we

present

he

mpirical

results f

our

nalyses.

We then iscuss

he

policy mplica-

tions of our results.

Finally,

we offer ome

concluding

remarks.

MODELOF LOCATIONNDPRICING ECISIONSOF

GASOLINETATIONSN SINGAPORE

We

present

his ection n two

parts.

irst,

we

develop

model

of

gasoline

tations' ocational hoices

by

the

gov-

ernment,

aking xplicit

he

parametricpecification

fthe

locationmodel nd

discussing

stimation etails.

econd,

we

develop

a model

of

gasoline pricing

ecisions ondi-

tional n the

bservedocational

hoices,

resenting spe-

cific

parameterization

f the

pricing

model nd

setting p

the stimation

rocedure.

LocationModel

It s useful

o note he

ollowing

wofeaturesfthe

gaso-

linemarketnSingapore thatmake t differentrom he

gasoline

market

n

the

United

tates):

1. Gasolinetationsanbe built n

only pecifiedlots

eter-

mined

y

he

overnment.

and s

offeredn

public

ender

in an

open-bidystem,

nd

ny ompany

an bid.

n

other

words,

idding

ecisions f oil

companies

etermine

nly

who wns ach

ocation,

otwherehe ocationshemselves

ought

o o

2.Price

ompetition

mong asoline

tationsn

Singapore

s a

relatively

ecent

henomenon.

efore

his,

asoline rices

were etermined

n

thebasis

of a

multilateral

greement

betweenhe

Singapore

overnment

nd

gasoline

etailers.

Therefore,

he

ingapore

overnment

ssumed

rices

o be

equal

while

determiningptimal

ocations

or

gasolinestations.

In

light

of

these two

features,

we make the

following

assumptions

or ur ocationmodel.

In

empiricallyxplaining

bservedocations

f

gasoline

ta-

tions

n

Singapore,

e assume hat he

ingapore

overnment

is

the ecision aker.

Because

gasoline

rices

re onstantcross

asoline

tations,

they

o not

lay

role

n

he ocation

odel.

The

government

icks eographic

ocationsor he

gasoline

stationsominimizehe otal

xpectedraveling

osts f ll

consumersn

Singapore

ho constitute

he otal

otential

demandor

asoline.

The

supplyapacity

f ach

asoline

tation

xceedsts

oten-

tial emand

i.e.,

n

undercapacityroblem

oesnot

xist).

We

acknowledge

hat

tation

haracteristics

e.g.,

conven-

ience

tore,

ar

wash)

lso

affect

onsumers'hoices

mong

stations

nd,

herefore,

onsumers' elfare

unctions.

ow-

ever,

he

ingapore

overnment

annot now

priori

hich

retail hain

will

successfully

id for

specific

ocation nd

the tationharacteristicshat he hainwill hen hoosefor

that ocation.

herefore,

t

s

impossible

or

he

government

to

determine

ocations

y

accounting

or tation

haracter-

istics t

various

ossible

ocations.

his underlies

he

hird

assumption.

Consistent

ith his

ssumption,

ur

estima-

tion esults romhe

pricing

model

how hat tation

har-

acteristics re not

as

important

s

price

or

travel ost

n

influencing

onsumer emand

or

asoline

tations;

e dis-

cuss

this

urther

ubsequently.)

anagers

t Exxon

Mobil,

Shell,

nd

Caltex,

he hree

major

il

companies

n

Singa-

pore,

onfirmedhe

inal

ssumption.

By

discretizing

he

two-dimensional

ap

of

Singapore

intoN

equally paced

grid oints,

we

define he

Singapore

government'sroblem s one ofchoosingP gridpoints,

among

he ull etofN

available

rid

oints,

o

ocate

gaso-

line stations o minimize he

sum

of

traveling

istances

across all consumerswho

constitute

otential asoline

demand.

Let

Yid

denote

binary

utcome hat akes the

valueof

1

if

consumers ithin

rid oint

choose he

gaso-

line station

n

grid oint

and 0

if

otherwise. n thebasis

of the

preceding

iscussion,

we

can thenwrite he

Singa-

pore

government'sbjective

unction

s follows

note

hat

our

conversations ith

overnmentlanners

ndicated

hat

models

of this

kind

are

routinely

used

in

urban

development):

(1)

m

such

hat

(2)

N

(3)

N

(4)

Yii

(5)

Y

(6)

x

where

(Zi;

a)

is the

potential

emand

or

asoline

t

grid

point

,

Zi

is a vector f all

relevant actors

hat

xplain

potential asoline

demand t

gridpoint

,

a

is the corre-

sponding

ector

f

unknown

arameters,

ii

s the

geo-

graphic

istance etween

rid oints

and

,

Xi

s an ndica-

torvariable hat akes hevalue

of

1

if

a

gasoline

tation

resides n

grid oint

and 0

if

otherwise,

nd

Yii

s a

binary

outcome hat akes hevalue

of

1

if

consumers ithin

rid

point

choose the

gasoline

tation

n

gridpoint

and 0

if

otherwise.

quation

1

is the

objective

unction

f

the

Sin-

gapore government.quation

2 embodies he constraint




5/15

An

Econometric

Model

of

Location and

Pricing

625

that onsumersithin

grid oint

can hoose ne nd

only

ne

gasoline

tation.

quation

embodies

he on-

strainthathe

overnment

s

working

ith stations

n

ts

location-planning

ecision.

quationcaptures

he

ogical

conditionhatonsumersannothooseo

go

o

grid oint

for heir

asolineurchase

fno

gasoline

tations ocated

at

.

Equation

implies

hatonsumerst

grid

oint

will

chooseithero

ravel

o

grid oint(Yii 1)

ornot

(Yii0).Finally,quation implieshat gasolinetations

eitheret

p

t

grid oint

(Xi

1)

or

not

(Xi

0).

We

pecifyotentialasoline

emandt

grid ointi

=

q(Zi;

)

in

log-linear

anner

sing

he

ollowing

ulti-

plicative

odel

which

as

been

xtensively

sed o sti-

mate

he ffectsf

marketing-mix

ariablesn

brand

ales;

see,

.g.,

an

eerde,

eeflang,

nd

Wittink

000):

(7)

ln(qi)

whereOPi sthe esidentialopulationfgrid oint,

INCi

s themedianncome

f

rid oint

,

CARi

s the

otal

number

f

wnedars

n

grid

oint

,

iAIRi

s an ndicator

variablehat

akeshe alue f

1

f

grid oint

is near he

airport

nd if

therwise,

ipTi

s

an

ndicatorariablehat

takeshe

alue

f1 f

grid oint

is

n

he owntownrea

and if

therwise,

nd

iHwYi

s an

ndicatorariablehat

takeshe alue f1 f

grid

oint

is close o

highway

nd

0

if

otherwise.

n

addition,

OP0, NCo,

nd

CARD

re

explanatory

ariablesor

reference

rid

oint,

hose

potential

emandevel

o

s fixedt

1

for

dentification

purposes).

herefore,

he

xplanatory

ariablesor

llother

grid oints

re

perationalized

elativeo

he

orresponding

variablesf hiseferencerid oint.ote hathe arame-ters

l, a2,

and

3

ofthe

multiplicative

odel anbe

directly

nterpreted

s the

lasticitiesf

potentialasoline

demando

hanges

n

he elative

alues f he

xplanatory

variablesith

espect

o

he eference

rid

oint.

t s also

useful

o reiterate

ere hat

houghotential

asoline

demandt

grid oint

s a

functionf ocal

emographic

variables,

t

depends

eithern he

rices

nd tation

har-

acteristics

f

tations

hat

ay

hooseo ocate

hemselves

at

r

near

he

rid

oint

or n he

ravel

istancesf on-

sumers ithinhe

rid

oint.

his s

consistentith

he

definitionf

potential

arketize n he

xisting

iterature

on

hoice

odels.

We

perationalize

he

eographic

istance

etween

rid

pointsand,denotedy ii, singhe uclideanistance

measure.

Using

ata rom

he ew ork

tate

epartment

of

Transportation,

hibbsnd uft

1995]

ind

correlation

of

987

between

traight-line

istancesnd

ravel

imes.

Other

tudieshat

se

Euclidean

istancess

proxies

or

travel

imesnclude

anuszak

1999],

homadsen

2005],

Davis

2007],

nd

McManus

2007].)

n

other

ords,

up-

pose

hat

xi, i)

nd

(xi, i)

re

he uclidean

oordinates

of

and

;

then,

ij

9211/2.

We

ssume

hat

he

onsumer'secision

ule

or hoos-

ing

gasoline

tation,

s

perceived

y

he

overnment,

s

the

ollowing:

ivenll

grid oints

such

hat

k

1,

(8)

Y

In

other

ords,

onsumersithin

given rid

oint

re

assumed

o

choose he losest

asoline

tationor heir

gasoline

urchases.

his temsromur

ssumption

hat

the

overnment

ssumes

rices

obe constant

cross ll

gasoline

tations

n

Singapore

hile

making

ts

ocation

decisions.1

To

estimate

odel

arameters,

e cast he ocation

modeln

stimableconometric

orms follows:

(9)

X

where

N

is

the bservedocation

f

tation

,

Ri(Z,

;

a0)

is the

redicted

ocation

based

n

olving

he

bjective

f

the

ingaporeovernment,

s

given

n

Equation

)

of

ta-

tion

,

a0

s

the

rue

alue

f

he nknown

arameter

ector

a

(that

s

knowno the

ingaporeovernment

ut s

unknowno he

conometrician),

nd

ei

s

themeasurement

error

with

mean f

ero).

Minimizing

his

measurement

errorn

some

way,

sing

n

appropriate

oss

function,

servess the

stimation

echnique

orecover

stimates

f

a.

It s

usefulo

ecognize

erehat

Xi

nd

Ri(Z,

;

a0)

are

bothwo-dimensionalariablesecauseheyepresentta-

tion

ocationsn

wo-dimensionaluclidean

pace.

We an

olve

he

ingaporeovernment's

ocation

rob-

lem,

epresentedy

quations

-6 nd

alled

he

-median

problem,

sing

he

agrangianlgorithm

for

etails,

ee

Daskin

995).2

or

given

, therefore,

t

s

possible

o

compute

he

redicted

ocations

Ri(Z,

P;

ao)

using

his

algorithm.

he stimation

bjective

sto

pick

he

alue

f

that

minimizes

he

followinguasi

mean

quare

rror

(QMSE):

(10)

QMSE(X,

(11)

QMSE(X,

(12)

Xjk

(13)

Xjk

where (x) ndX(Y) enotehe andycoordinatesfX,

respectively.

he ationalef

using

jk

n he

MSE

sas

follows:fter s

obtained

y olving

he

-median

rob-

lem,

t

s

necessary

o

pair

p

ach

f he

predicted

oca-

tions

ithne f he

observed

ocationsn

he ata

efore

computing

mean

quare

rror.

owever,

here

re umer-

ous

ways

o

undertakehis

airing

ask.

We

pick

he ne

that

minimizeshemean

quare

rror.

hat

s,

mong

ll

possible

airings

f

ocationsn

X,

nd

X,

we

pick

he

ne

lit s

possible

ouse

probabilistic

hoice

unction,

uch s

themulti-

nomial

ogit,

nsteadf he

inary

ndicator

unction,

or

1.

However,

his

renders

he

overnment's

ecision

roblem

onlinear

nd

omputationally

difficult

o olve.

2We

ick

he

tarting

alues

sing

he

xchange

lgorithm.




6/15

626

JOURNAL F MARKETING

ESEARCH,

NOVEMBER 007

that as minimum

ean

quare

rror.We achieve

his om-

putationally

sing

he

xchange lgorithm

for

details,

ee

Daskin

1995).3

The estimator or t

that

we

propose

s the

value that

minimizeshe

QMSE.

In other

words,

(14) a).

Therationale or his stimationlgorithms toemploy n

estimator

hatmatches heobserved

nd

predicted

tation

locations s

closely

s

possible.

n

this

ense,

ur

proposed

estimator

s a minimum istance

stimator,

ust

like the

least

squares

stimator.

e use

Nelder nd

Mead's

(1965)

nonderivative

implex

method o

search

or or

Note hat

ur ocationmodel

pecifies

he

potential

aso-

line demand t

a

grid oint

sing

ll relevant

emographic

variables,

uch

as local

residential

opulation,

umber

f

cars

owned,

nd median

ncome. Previous

ntry

models

have used

only

ocal

population

o characterize

otential

local demand

or

product

see,

e.g.,

Seim

2006).

In these

models,

irms'

ntry

nd exitdecisions

n

given

ocal mar-

kets retreated s endogenous.n ourmodel,however, e

treathe

geographic

ocations

f a

given

umber

ffirmss

endogenous.

ur

research

nterest

ies n

understanding

he

dependence

f these ocations

n

theobserved

eographic

distribution

f

demographic

ariables.

Our ocation

model s also

unique

n

that

t

captures

he

objectives

fa social welfare

maximizer-specifically,

he

government-in

etermining

etail

ocations.

t can

be

gen-

eralized

o other

ecision ontexts

ertaining

o

retail

oca-

tion

n which

he

government

r

a

central

ity

lanner

s the

decision

maker

whose

objective

s to ncrease

ocial

wel-

fare

y

reducing

raveling

onsumers'

nconvenience.

t

can

also be

generalized

o

contexts

hat nvolve

reater

iscre-

tionon the

part

of firms

eciding

where o

locate

them-

selves, uch s supermarketocation ecisionsntheUnited

States.

The

objective

f the

P-median

roblem

would

hen

involve he

maximization

f some

firm-specific

easure

f

interest,

uch as

profit

r market

hare,

cross

all chosen

locations

or tores

elonging

o

that

hain,

onditional

n

chosen

ocations

f

competing

tores.

ur

model ould

be

extended

o

a

context

n which

firms'

ricing

nd

service

decisions

are also allowed

to

influence

heir

ocational

choices.

Such

a model

would

entail

he

pecification

nd

estimation

f a simultaneous

ystem

f

equations

overning

firms'

ocations,

prices,

nd

service

choices.

This is

an

important

nd

challenging

xtension

f ourmodel

for ur-

ther esearch.

PricingModel

Givenrelative

ocations

f

P

gasoline

tations,

s deter-

mined

y

the

Singapore

overnment

nd

represented

sing

the

ocation

model

discussed

previously,

e

next

model

gasoline

prices

at the

P

gasoline

stations.

here

are

six

gasoline

retail

hains n

Singapore:

Shell,

Caltex,

Esso,

Mobil,

BP

(British

etroleum),

nd SPC

(Singapore

etro-

leum

Company).

he

merger

f

Exxon,

alled

Esso

in

Sin-

gapore,

with

Mobil reduces

the

number f

independent

chains

n

Singapore.

However,

t the

time

f data

collec-

tion,

hese tations

etained

heir

riginal

dentity.

e retain

this structure

ecause

it

helps

us

illuminate

etter

he

3Wepick he tartingaluesusing hemyopic lgorithm.

brand-specific

ffects n retail

ompetition

nd also eases

the

exposition.

More

recently,

P and

SPC

have also

merged.

We address he ffectsfthis

merger

n

the

Policy

Implications"

ection.

To

gain

n

understanding

bout

henature

f

price

orn-

petition mong

stations n the

gasoline

market,

we run

reduced-form

ricing egressions

we

report

hese

esults

n

the

Appendix).

hese

regressions

how hat

he ocal

pres-enceofother tations

elonging

o the ame chainhas an

increasing

ffect

n

price

t

thefocal

station,

hereas he

number f

stations

elonging

o

competing

hains

has

a

decreasing

ffect.

his eads us

to

assume

hat ach chain

manager

ets he

price

t

all stations

elonging

o his

or her

chain.

We also make the

standard)

ssumption

hat he

observed

rices merge

rom ertrand

rice ompetition

t

the chain evel.

An

alternative

ssumption

would be

that

each station

manager

maximizes ome

weighted

ombina-

tionof the

profits

t

his or her

station nd

the

profits

f

other tations. uch

a

model

would llow

for

tation-level,

as

opposed

o

chain-level,

rice ompetition

when

he sti-

mated

weights

or ther tations

re

zero).

It would also

allowfor ollusivepricingmong etail hains when he

estimated

eights

or tations

elonging

o other

hains re

nonzero).

We estimated

uch

model,

nd t reduced

o the

special

case

of chain-level

rofit

maximization

e discuss

here.Under hechain-level

rofit

maximization

model,

gasoline

etail

hain's

problem

s one

of

choosing possibly

different)

asoline

rices

or ll its tations

o maximize

he

total

ariable

rofits

rom

elling asoline

t all its

tations.

We can

thenwrite

etail hain

m's

objective

unction

at

time

)

as follows:

(15)

max

where

Cit

referso the

marginal

ost

of

selling asoline

t

station

during

ime

,

Qit

efers

o thedemand

or

asoline

atstation

during

ime

,

and

.5525pit

epresents

evenues

(after

axes)

hat ccrue

o

the etailer

rom

harging

price

pit.

n

Singapore,

he xcisetax

rate

harged

or

asoline

s

35%.

There

s

an

additional

orporate

ncome ax

rate

of

15%.

Thisresults

n

$1

-

.35

x

$1)

x

(1

-

.15)

=

$.5525

of

every

ollar

f

pretax

evenues

ccruing

o

the etailer:

(16)

Cit)c1Q11

We

specify

reduced-form

emand

unction

or

asoline

at stationduringime i.e.,Qit) s follows:

(17)

i

where

Qiit

s the

demand

n

grid

oint

for

asoline

t sta-

tion

during

ime and

s

specified

s follows:

(18)

Qijt

where

Siit

enotes

he

market

hare

n

grid oint

for

aso-

line

at station

during

ime

and

qi

denotes he

potential

demand

or

asoline

t

grid oint

(as

we

discussed

n the

subsectionLocationModel"). Furthermore,iit s speci-




7/15

An

Econometric odel fLocation nd

Pricing

627

feed

y

means f a

multinomial

ogistic

unction-which

s

consistent ith andom

tility

maximizationn the

part

f

individualonsumers

McFadden 974)-as

follows:

(19)

S

where

Wi

stands for a vectorof

station haracteristics

(number fpumping ays,pay-at-pumpacility,resence

of

convenience

tore,

pecialty

eli,

ervice

tation,

nd car

wash)

that rerelevantnterms f

nfluencing

arkethare

for

gasoline

t a

station,

3

s

the

corresponding

ector f

parameters,

ii

s the

geographic

istancebetween

grid

points

and

,

pit

efers othe

price

f

gasoline

t station

during

ime

,

nd8 and

y

stand or

he ravel ost nd

price

sensitivityarameters

f

consumers,

espectively.

he

prob-

abilistic hoice rule thatunderlies

he multinomial

ogit

model s

not

necessarily

nconsistent

ith

hefixed hoice

rule

determining

ii

n

the ocation

model

we

discussed

re-

viously.

his s becausethe

government

ssumes hat

rice

and ll other elevanttation

haracteristics-both

bserved

andunobserved-aredentical cross tations henmaking

location

ecisions.

n

such

case,

the andom

tility

odel

reduces oa deterministic

tility

odel

which

ets he an-

domness

n

the onsumer's

tility

unctiono

zero)

based

on

travel osts

nly.

The

preceding

markethare

pecification

ncludes 1 in

thedenominatoro

capture

he ffect f

theoutside

good

(i.e.,

consumers'

ption

ot o

purchase asoline

t

any

of

the vailable

asoline

tations,

hoosing

o travel

y

bus or

taxi

instead).

Under the

conditions

f

the market

hare

model,

onsumers

ithin

given

rid oint

re

assumed o

allocate

hemselvesetween

asoline

tations

and

the

ut-

side

good),

f we

taketwo

types

fstation

haracteristics

into ccount

Iyer

nd Seetharaman

003,2007): (1)

hori-

zontal haracteristics

i.e.,

geographic

ocations hat eter-

mine

did)

nd

2)

vertical

haracteristics

i.e.,

Wi

and

pit).

Our demand

pecificationgnores

he

ffects

f

both nob-

served

otential

emand hocks hat

may

hange

otalmar-

ket demandfor

gasoline

and

unobserved

tation-specific

demand shocks that

may

influencemarket

hares for

chains.

In

this

sense,

our

demand model

predicts

hat

demand or

ach station ill

be

a

deterministic

unctionf

station haracteristicsnd can

be

considered

reduced-

form

emand

pecification.

We

specify

he

marginal

ostof

firm at time

as follows

(as

in

Thomadsen

005):

(20) Cjt

where

Ct

refers

o

the

ime-varying

arginal

ost

of

gaso-

linethat s

assumed o be the

ame

cross

tationsnd

eit

s

a random

hock hat

epresents

he

ffects f

unobserved

(by

the

conometrician)

ariables n the

marginal

ost of

gasoline

t a

station.

Plugging quations

17-20 into

Equation

16

yields

the

following

irst-order

onditions,

epresented

n

matrix

orm,

for

asoline

tation that

elongs

o chain

m:

(21) .5525pt

where

t

s a P x 1

vector f

retail

rices

t

theP

stations,

p

is a P x 1 vector fones,andS2(pt, ) is a P x P matrix

whose

th diagonal

lement

s

given

y

y....5T.,

Siit(1

Siit)qi

andwhose

ff-diagonal

lement

j,

k)

is

equal

to

-y111_,Sikt

Siitqi

fstations andk

belong

o the amechainand 0

if

otherwise.

inally,

=

(13

y)'

is thevector

f

parameters

in the

market hare

model,

nd

Qt

s a

P

x

1

vectorwhose

jth

elements

given y

II,._.

Siitqi.

Although

he

ost shock

t captures

he ffects f unob-

served ariables rom he conometrician'standpoint,hey

include

variables

e.g.,

rental

ost

advantages

because

of

superior

easing

erms]

ssociatedwith

pecific

ocations)

that

re known

o

retail hain

managers

nd thereforere

incorporated

hen he

managers

maketheir

ricing

eci-

sions.This

ntroducesn

endogeneityroblem

n the sti-

mation ecauseof

possible

orrelation

etween

t

nd

et

n

Equation

1.

This s the

ypical rice

ndogeneity

roblem

(see,

e.g.,Berry,

evinsohn,

nd

Pakes

1995).

Furthermore,

it

s

possible

hat

etail hain

managers

ncorporatet

when

making

ecisions

ertaining

o station

haracteristics,

i.

This

eads

to

an

additional

ndogeneityroblem

nthe sti-

mation ecauseof a

possible

orrelationetween

Wi

and

et

in

Equation

1.We refero

this

s

the characteristics

ndo-

geneity

roblem."

Similar to

Thomadsen

2005),

we

used

generalized

method f

moments

GMM)

to estimate

quation

21. To

correct or

rice

ndogeneity,

e

choose four nstrumental

variablesfor

pit:

1)

an

indicator ariable

that akes the

value

of

1

if other

tations

elonging

o the same retail

chain s

station existwithin one-mile

adius f station

and 0 if

otherwise,

2)

the

og

of

the number f

stations

belonging

o

retail

hains ifferent

rom hat f

station that

existwithin

one-mile

adius f

station

,

(3)

the

verage

estimated

otential

asoline

demand

from

ur

location

model)

per

tation ithin

one-mile

adius f station

,

and

(4)

the

potential

emand t each

gridpoint

n

the

Singa-

poremapdividedby tsdistance o station andsummed

over

ll

grid

oints.

he

validity

fthe

irstwo nstruments

relieson an

assumption

hat

he ostshocks re

ocalized

and do not

spill

over to other

nearby

tations

within he

one-mile adius.

Another

rgument

n

favor fthese nstru-

ments

iven

n

Thomadsen

s

that

ecause ost shocks

may

be time

varying,

heymay

how

ittle

orrelation ith ta-

tions'

ocation

ecisions.)

or

example, uppose

hat tation

j's

cost

advantage

rises fromts

location

having

ower

lease

costs

e.g.,

because the

tation

egotiated

or

better

leasing

erms

hile

enting

he eal

state).

n

this

ase,

nei-

ther

he

number f

nearby

tations

elonging

o the ame

chain

nor

henumber f

nearby

tations

elonging

o com-

petinghains s likely obe a functionf such cost dvan-

tage

f

station

.

In other

words,

nstrumentsand

2

willbe

uncorrelated ith

hecost

shock.

However,

hese nstru-

mentswill

be

highly

orrelated ith he

price

t

station

to

the

xtent

hat tation will

be less

aggressive

hen

etting

price

n the

resence

f

other tations

elonging

o the

ame

chain

to

avoid

cannibalizing

ales of

the same chain's

stores)

nd

more

ggressive

hen

etting

rice

n

the

pres-

ence of

competitors.

ur reduced-form

riceregressions

(see

the

Appendix)

how

that

nstruments

,

2,

and

3

are

indeed

highly

orrelatedwith

heobserved

rices.

Simi-

larly,

because

the

average

estimated

otential

gasoline

demand t

nearby

tations

i.e.,

nstrument

)

depends nly

on

observed

emographic

haracteristicsfthe

neighbor-hood as

specified

nder he ocation

model),

nstrument




8/15

628

JOURNAL F

MARKETING

ESEARCH,

NOVEMBER 007

will also

be uncorrelated ith he

ost

shock.

Finally,

he

rationale or

hefourth

nstrumentalariable

s

that

t

s

a

more

global

measure f

competitive

ffects

han hefirst

three nstrumental

ariables hat

apture

ocal

effects

f

competition.

urthermore,

t accountsfor both how far

away

a

competing

tation s and the

ntensity

f

gasoline

demand n

that tation's

neighborhood. uppose

that

Ut

denotes P

x

18

matrix,

n

which

ach

row

epresents

dif-

ferenttation nd the18 columns

epresent

ne

ntercept,

two ndicator ariables

or

ime

representing

hreewaves

of data

collection),

ive ndicator ariables

or

hain

repre-

senting

he ix

chains),

ix

variables

epresenting

tation

characteristics

as

we

explain

subsequently),

nd four

instrumentalariables

as

we

discussed

previously);

hen,

the

following

moment ondition

nderlies heGMM esti-

mation

ignoring

haracteristics

ndogeneity):

(22)

E(EtlUt)=

When

he tation

haracteristicsorrelate

with he ost

shocks,

he

momentonditionn

Equation

2 is invalid.We

areunable o findppropriatedditionalnstrumentso cor-

rect or haracteristics

ndogeneity.

herefore,

e reesti-

mate ur

proposed

model

by excluding

he

tation harac-

teristics s

explanatory

variables within

Wi

and as

instrumentsithin

t,

hus

recluding

oncerns bout

pos-

sible

endogeneity

f such variables

n

the stimation.

We

compare

he stimatesf

the

ravel

ost

8)

and

price

ensi-

tivity

y) parameters

btained

sing

hismodified

pecifica-

tionwith hoseobtained

sing

our

original pecification.

This enablesus

to

understand

herobustness

f these wo

parameter

stimates-that

s,

their

sensitivity,

r lack

thereof,

o the nclusion

f

possibly

endogenous

tation

characteristics

n the stimation.

Under his

pecification

f the

pricingmodel,

bserved

price

variationsnthedata arisebecauseof differencesn

demand

haracteristicscross

stations,

ime-varying

ost

changes

which

re

equal

across

tations),

nd cost shocks

atthe tationevel.

Finally,

otential

asoline

demand

t

a

grid oint

i.e.,

qi)

is notobserved

n thedata.We use

the

estimated

otential asoline

demandn

grid

oint

,

which

we obtained

sing

he stimates

f the ocation

model,

s

a

proxy

or

i.

This not

only

allows

the

potential asoline

demand o

be

simultaneously

etermined

y

ocal

popula-

tion,

median

ncome,

umber

f cars

owned,

nd

presence

of

highway

nddowntown

ut lso allows

he

weights

sso-

ciated

with hese actors

obe

endogenously

stimatedrom

the bserved istribution

f

gasoline

tations.

hus,

we are

relieved rom heburden fneeding o estimate otential

gasoline

emand

in

addition

o

the

parameters

f the

pric-

ing

model)

from he

price

ata.

Identification

ssues and Caveats

We

now discuss ome

dentification

ssues.

We

identify

marginal

osts

from he

verage

rice

cross

ll

stations

nd

the

changes

in this

average price

across

periods

i.e.,

waves).

Although

tation-level

emand

s notobserved

n

the

data,

we can

dentify

he ame

by nvoking

he

quilib-

rium onditions

f demand nd

supply.

What dentifies

he

demandfunction

s the

sufficient

ystematic

ariation

n

prices

n

thedata

across

stations hat

esides

n

neighbor-

hoods

with

different

evels

of

local

potentialgasoline

demand nddifferentevels of ocal competitiventensity.

Proof f

sufficientariationn

prices

s

easily

observed n

the

esults f our

reduced-form

ricing

egressions

see

the

Appendix),

n

which

we find hat he effects

f

all the

competitive

nvironmentactors re

significant.

or

exam-

ple,

suppose

hat station

hat aces ittle ocal

competition

(i.e.,

few

nearby

tations)

riceshigher

han nothertation

that

aces

higher

ocal

competition

i.e.,

manynearby

ta-

tions);

for

the same level

of

local

potentialgasolinedemand,hiswould erve s the ource f dentificationor

the

travelcost and

price sensitivity arameters

n the

demand unction.

uppose

lso that wo tations

elonging

to differenthains

pricedifferently

ithin he ame ocal

market;

hiswould erve s the

ource

of

dentificationf

thebrand

ntercepts

n

thedemand unction.

Three aveats re

n

order.

irst,

ecausewe

rely

n

price

data to infer oth ost-side nd demand-side

arameters,

ourestimates f demand re

ikely

o be less efficienthan

estimates btained

sing

demand ata.

Second,

becausewe

rely

n

specific

ssumptions,

uch s Bertrand

rice ompe-

tition etween

etail hains nd

multinomial

ogit

demand

for

asoline

tations,

oachieve his

dentification,

t s

pos-

siblethat ur stimatesresubject omisspecificationias.

Third,

lthough

eallowfor nobservedemand hocks n

potential asoline

demand,

it,

we

ignore

uchunobserved

demand hocks

n

themarket hare

function,

ift.

n this

regard,

e

reiteratehat hese

ssumptions

re dictated

y

our

ack

of access to demand

ata

n

the

product ategory.

DESCRIPTION OF

DATA

Our data

pertain

o the

gasoline

market

n

Singapore,

which s a

good geographical

market or

xamining

irm

conduct or arious nstitutionalonsiderations.

irst,

t

s

a

self-contained arket f substantial

ize. For

example,

gasoline

sales

in

2002

alone were

n

excess of

a

billion

liters,nd more nfamously,ingapore anks econd next

to theUnited

tates)

n

global

arbon ioxide

mission

er

unit f

gross

domestic

roduct

The

Economist

003).

Sec-

ond,

ll

the

demand s

supplied

y

ocal

refiners,

nd there

is no

possibility

f

supply-side

eakage.

Before

rossing

he

border nto

Malaysia

(the

only possible

road

transit),

motoristsre

required

y

aw to have their

as

tanks illed

to at least

three-quarters.

hus,

supply-demandeakages

due to the

price

ifferences

etween he

womarkets o not

hold.4

hird,

hemarkets

increasingly

iewed s

a

mature

and

competitive

market.

Gasoline demand s stableand

expected

o

grow lowly

ecause

of the ontrolled

ncrease

in

automobile

wnership. raditionally,

etail

ompetition

has been

conducted

hrough onprice

nstruments

e.g.,

sweepstakes,reebies,oyalty rograms).ricepromotions

are

a recent ddition

past

three o five

years)

o thismix

and are

becoming ncreasingly

ommon

nd distributed

across he ntire

sland.

Currently,pward

f 25%

of

gaso-

line stations re

running romotions

anging

n

depth

rom

5%

to 15%

on

petrol

nd/or iesel.

Fourth,

heoil

majors

controlll elements

ftheir hannel

rom

roduction

o dis-

tribution

o

retailing.

owever,

he ocation

decisions

for

4The

price

differential

etween

he

two countriess

substantial.

he

price

f a

liter f

98-octane

etrol

n

May

2002 was

S$1.244

n

Singapore

and

S$.630

in

Malaysia.

ndustryarticipants

uggested

hat he ubstan-

tial

gasoline

tax

revenue

was one of

the reasons

for he

Singaporean

ordinance.




9/15

An

EconometricModel of Location and

Pricing

629

retail

utlets

re ecided

y

ingapore's

rban

edevelop-

ment

uthority.

We

mploy

urvey

ata,

epresenting

cross-section

f

226

gasoline

tations

n

Singapore

uring

ate 001

nd

early

002.We nclude

ll

gasoline

tations

nmainland

Singapore

n ur

mpirical

nalyses,

gnoring

asoline

ta-

tions hatre ocatedn slands

ff he

ingapore

oast.

There

re 29

gasoline

tations

n

mainland

ingapore.

e

excludedhreetationstwo elongingoMobil nd ne o

BP)

whose

eographic

ocations

ere

missing

n

he

urvey

data.

mong

he 26 tations

n

mainland

ingapore,

5

stations

re wned

y

hell,

3are wned

y

Mobil,

9 re

owned

y

sso,

2 are wned

y

Caltex,

9 are wned

y

BP,

nd

are wned

y

PC.For

ach

asoline

tation,

he

survey

ata ncludehe

rices

f

four

rades

f

petrol

(Premium,

8unleaded

UL], 5UL,

nd

2UL),

he

rice

of

iesel,

nd

large

umberf

tation-specific

haracteris-

tics

e.g.,

umber

f

pumpingays,

resence

f

onven-

ience

tore,

ay-at-pumpacility,

ar

wash,

ervice

tation,

automatedeller

achine,

tore

ours,

rices

f

goods

t

convenience

tore).

ur ata et

lso

ontains

emographic

informatione.g., population,ome wnership,ge,

employment

tatus,

ode

f

ransportation,

ncome)

er-

taining

o

ach

asoline

tation's

arket.

hree aves f

data

ollection,

llofwhich

sed

he

ame

urvey

nstru-

ment,

ere ndertaken

t he

ame et

f

26

gasoline

ta-

tions

uring

hemonths

f

November

001,

December

2001,

nd

January

002.

his

ielded

ime-seriesariation

in

gasoline

rices.

ecause8UL

sthemost

opularrade

of

gasoline

n

Singapore,

e

report

he stimationesults

for ur

ricing

odel ased

n

his

rade

f

gasoline.

sti-

mation

esultsor he

ther

rades

re

onsistentithhose

we

obtainedor he

8UL

grade

nd reavailable n

request.

For

he ocation

odel,

e

dividemainland

ingaporeinto rectangularridf1550 ridointshatre qually

spaced

n

both he orizontalnd

he erticalimensions.

Picking

550 s

opposed

o smallerumberf

rid

oints

ensureshatach

rid oint

as

no

morehan ne

asoline

station,

hichs

required

o

be

consistent

ithur

ocation

model

see

Equations

-6).

stimating

he ocation odel

enables

s to characterize

otential

asoline

emand

endogenously

t

ach

rid oint

n

ingapore.

e

llow he

followingemographic

haracteristicso nfluence

ocal

potential

asoline

emandt

ach

rid oint

i.e.,

i):

1)

POPi,

he ocal

opulationepresented

ithin

rid

oint

,

computed

s

the

otal

opulation

f

the ensus racto

which

he

rid oint

elongs

ivided

y

he otal

umberf

gridoints ithinhat ensusract;2) INCi,hemedian

incomef

he ensus

ract

o

which

rid

oint

belongs;

3)

CART,

he otal

umber

f

cars

epresented

ithin

rid

point

,

computed

s the otal

umberf

arswithinhe

censusractowhichhe

rid oint

elongs

ivided

y

he

total

umberf

grid oints

ithin

hat ensus

ract;

4)

AIRi,

n

ndicatorariablehat

akes

he

alue

f1

f

grid

point

is

ocated

djacent

o he

irport

nd

if

therwise;

(5)

DTi,

n

ndicatorariable

hat

akes he

alue f

1

f

grid

oint

is

ocated ithinhe

owntownrea

nd

if

otherwise;

nd

6)

HWYi,

n

ndicatorariable

hatakes

the

alue f1 f

grid oint

is

ocated

djacent

o

major

highway

nd

f

therwise.

For

he

ricing

odel,

e

use

he

ame et f

1550

rid

pointss inthe ocation odel ocomputeggregate

demandor ach

asoline

tation

see

Equation

7).

We

also

lug

he

stimated

aluesf

i

from

he

ocation

odel

directly

nto

quation

8

while

stimating

he

pricing

model. e llow he

ollowing

tationharacteristics

(Wi)

to nfluence

arket

haresor

asoline

tations

i.e.,

O

n

Equation

9:

1)

CHAIN,

five-dimensionalector

f

indicatorariables

epresenting

hichf ix

ifferent

etail

chainstation

belongso; 2)PUMPSi,

he otal

umber

f

gasolineumpingaysvailablen tation; (3)

PAYS,

n

indicatorariablehat

akeshe alue

f1 f

tation

has

pay-at-pump

acility

nd

if

therwise;

4)

HOURSi,

n

indicatorariablehat

akes he alue

f 1 if

tationis

open

4

hours

day

nd f

therwise;

5)

WASH,

n ndi-

cator ariablehatakes

he alue f

1 f

tation

has

car

wash

acility

nd

if

therwise;

6)

SERVi,

n

ndicator

variablehatakes he

alue f1

f

tationhas

service

station

nd if

otherwise;

nd

7)

DELIS,

n

ndicator

variablehatakeshe

alue f

1

f tationhas

specialty

deli nd

f

therwise.

Thevariableble

PUMPS.a

ariesromto 0

acrosstations

inour

ata et. he

emaining

ndicatorariables

PAYS,

HOURS.)

, JASH.' JERV.'ndDELI-take.1he alue f1

for

9%,

8%,

0%,

2%,

nd 2%of he tationsn

our

data

et,

espectively.

n

ddition

o

he tationharacteris-

tics,

hemarkethare odel

ncludeshe

rice

f

gasoline

at tation

,

PRICE,

nd ravel

istance,

ii,

s

explanatory

variables

see

quation

9).

Table

provides

he

meansnd

tandardeviationsf

prices

f

8UL

gasoline

tvariousetail

hains

n

Singa-

pore.

he

veragerice

f

8UL

asoline

s

approximately

$.05

owert PC han

t he theretailhains.he

tan-

dard

eviation

f

rice

f

gasoline

s

$.03

for

most

rades

and etail

hains),

hich

smuchmallerhanhe

tandard

deviation

f

price

bservedn

U.S.markets

see,

.g.,yer

and

eetharaman

003; hepard991). his riceariationincludesariationcrosstationsithinchainnd cross

time.

EMPIRICAL

RESULTS

We

eport

he

stimatesf ur

roposed

ocation

odel

(called ROPOS)

n

Column

ofTable

.

We

eport

he

standard

rrorsssociated

ithhesestimatesn

Column

3.We btain

hese

sing

bootstrappingrocedure,

s fol-

lows: n

he asis

f

he

stimate

,

using quation

,

we

generate

he

mpirical

istributionf

ei

as the

ifference

betweenhe

bserved

nd he

redicted

ocations.

sing

this

mpirical

istribution

f

rrorsnd he

stimate

,

we

simulate

ocationsor

he

asoline

tations.

aking

hese

simulatedocationssactualocations,ereestimatehe

proposed

ocation

odel.

e

hen

ycle hrough

he ame

Table

1

MEANS

AND

STANDARD

DEVIATIONS OF

98UL

GASOLINE

PRICES

AT

VARIOUS

RETAIL

CHAINS

Chain

Mean

Price

($

per

Liter)

Standard

eviation

of

Price

Shell

1.19

.03

Caltex

1.18

.04

Esso

1.19

.03

Exxon

Mobil

1.19

.03

BP

1.19

.03

SPC

1.14 .03




10/15

630

JOURNAL

F MARKETING

ESEARCH,

NOVEMBER

007

Table

2

ESTIMATED ARAMETERS F

THE

LOCATIONMODEL:

EFFECTS OF LOCAL

MARKET

HARACTERISTICS N

POTENTIAL

EMAND

OR GASOLINE

Parameter M

SE

POPi

2.3425 .2042

INC 2.5327 .0995

CART

.9462 .0975

AIRi

1.8075 .0900

DTi

1.8394 .1063

HWYi

2.9434 .0332

proceduregain.

We

do this

ntil

we

have50 sets f

a,

based nwhich e

compute

he tandardeviation.s we

expected,

he esultshow hat

otentialasoline

emandt

a

grid oint

s a

positive

unctionf he

opulation,

edian

income,

ndnumberf ars wnednthe ocal

neighbor-

hood.

his

validatesur

revious

ontentionhat

opula-

tion s

only

ne

mong

everal

emographic

ariableshat

influence

ocal

demand

or

asoline.

s

expected,

e also

find hat roximityo he irport,owntown,ndhighways

increasesocal

potentialasoline

emandnd hat

roxim-

ity

o

highways

ccountsor he

argest

ncrease.

ll

these

results re

intuitively

ensible nd

give

excellent ace

validity

oour

roposed

ocation odel.We lso stimate

benchmarkodel

called

BENCH)

that estricts

otential

gasoline

emandobe

equal

othe ocal

population

e.g.,

Seim

006).

To

understand

owwellwe are ble o

predict

observed

asoline

tationocations

sing

ur hosen et f

six

demographic

ariables,

e

compare

he

redictive

bil-

ity

fPROPOSwith hat fBENCH.The

QMSE

based n

PROPOS

s

7210,

nd

that ased

on

BENCH s

15,199,

thusndicatingore han 0%predictiveains romsing

demographic

ariableso

predict

ocal

potentialasoline

demand,

s

n

our

roposed

ocation odel.

Figure visuallyepresents

he stimatedocal

potential

gasoline

emandcross

rid oints

n the

ingapore ap.

Overlaying

he

istributionf stimated

otentialasoline

demand

cross

rid oints

n

top

f

he

bservedistribu-

tion f

gasoline

tationscross he ame et f

grid oints

enables s to

convey isually

he

government's

asisfor

placing large

umberf

gasoline

tationocationst ome

geographiceighborhoods

ndnot t others. o facilitate

interpretation,

e code

Figure

into our

equal-sized)

regions

f

varying

hades

from

ight

o

dark)

Low

Demand

lightest

hade),

Middle emand

lighter

hade),

Middle emand (lighthade), ndHighDemanddark

shade)-using

he

uartiles

f he stimatedistributionf

potentialasoline

emand. hedense lusterfobserved

gasoline

tationsnthe ortheast

ortion

f

Figure

,

long

with he estimated

igh degree

f

potential asoline

Figure

ESTIMATED OTENTIAL ASOLINE

EMAND N

SINGAPORE

Most

rofitabletation

Least

Profitabletation

LowDemand

Middle emand emand

Middle emand

1

High

emand

Gasoline tations

600

500

40000 60000

800 100000 700 900

400

300

200

100

100

0

0

Notes:

Higher

emandreas re darkerhan ower emand reas.




11/15

An

Econometric

odel

f

Location nd

Pricing

631

demand n this

part

f

the

map,

s

a

consequence

f three

effects:

he

presence

f downtownn the horizontal

ine

spanning

rom

380,

380)

to

620,

380),

the

presence

f the

airport

lose to

(700, 350),

and

the

presence

f

a

major

highwaypanning

he

egion

rom

700, 420)

to

800, 400).

Overall there s a

highdegree

of

agreement

etween

he

estimatedocations nd the ctual

ocations

f the

226

sta-

tions. or

example,

urestimated

ocations

re also

highlyconcentratedn thenortheast

ortion

f

Figure

.

In

Table

3,

we

present

he esults fthe

pricing

model

or

98UL

gasoline.

Column excludes

tation haracteristics

as

explanatory

ariableswithin

Wi

to

address he

ssue of

characteristics

ndogeneity,

s we

discussed

previously),

and

Column includes uchvariables.

nderstandably,

he

minimized riterionunction alue

s lowerunder olumn

3

(because

t ncludes

dditional

xplanatory

ariables)

han

under

olumn

,

but

he

stimates

f common

arameters

are similar o

each other. he

estimated

rice-costmargins

from

olumns and 3

are 21.3% and

21.2%,

respectively.

These

are

higher

han estimated

margins

n

the North

American

asoline

market. or

example,

Manuszak

1999)

estimatesetail rice-cost arginsnHawaiian asoline ta-

tions t

approximately

0%. This

perhaps

eflects

ower

intensity

f

price

competition

n

the

Singapore

market.

Price

promotions

ere

ong

bsent n

the

ingapore

market

andbecame

prevalent

etail

ctivitynly

ecently,

s dis-

cussed n

theEuromonitor

2004)

report.

n

terms f con-

sumers' ntrinsic

rand

references

reflected

n

theesti-

matedbrand

ntercepts

n the

demand

model),

we allow

them o

have two

components:

1)

one that

s

common

across

all

brands

called

CONSTANT in Table

3),

repre-

senting

onsumers' aseline

references

or

asoline

rands

relative

o the

outside

good,

and

(2)

one

(reported

epa-

rately

nder ach brand

name

n

Table

3)

that

epresents

Table3

ESTIMATED

PARAMETERS

(STANDARD

ERRORS)

OF

THE

PRICING MODEL:

EFFECTS OF

STATION

CHARACTERISTICS

ON STATION-LEVEL DEMAND

FOR

GASOLINE

Parameter

Model1

Model

2

Cost

Constant

.415

(.009)

.417

(.027)

Wave2

-.019

(.001)

-.020

(.000)

Wave3

.000

(.002)

-.001

(.001)

Demand

Constant

.115

(22.402)

.049

9693.489)

Shell

-.062

(.038)

-.058

(.023)

Caltex .052 (.022) .057 (.020)

Esso

.063

(.027)

.069

(.025)

Mobil

.039

(.028)

.049

(.024)

BP

.116

(.023)

.127

(.028)

PUMPS-

J

N.A.

.002

(.000)

PAY.

1

N.A.

.002

(.001)

HOURSi

N.A.

-.032

(.004)

WASH.

J

N.A.

.005

(.001)

SERVi

N.A.

-.009

(.001)

DELI.

J

N.A.

-.012

(.002)

PRICE.

J

DIST..

u

-2.845

(.086)

-.103

(.003)

-2.808

(.381)

-.106

(.014)

Criterion

unction

alue

.0028

.0021

Notes:

N.A.

=

not

pplicable.

consumers'dditional

reference

or ach

brand

elative o

SPC

(for

dentification

urposes).

The

component

hat s

shared

by

all

brands

CONSTANT)-and

mustbe inter-

preted

s the

baseline

preference

or ach

brand elative o

the

outside

ood-is

not

ignificantly

ifferent

rom ero.

With

he

highest

stimated

ntercept,

P

appears

o be the

strongest

rand

n

the

marketplace.

he

coefficientsssoci-

ated withboth

Documents

Econometric Model of Location and Pricing in the Gasoline Market