Measuring the Impact of Promotions on Brand Switching When Consumers Are Forward
Looking
Author(s): Baohong Sun, Scott A. Neslin, Kannan Srinivasan
Source: Journal of Marketing Research, Vol. 40, No. 4 (Nov., 2003), pp. 389-405
Published by: American Marketing Association
Stable URL: http://www.jstor.org/stable/30038874
Accessed: 28/01/2010 14:55
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless
you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you
may use content in the JSTOR archive only for your personal, non-commercial use.
Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
http://www.jstor.org/action/showPublisher?publisherCode=ama.
Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed
page of such transmission.
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 support@jstor.org.
American Marketing Association is collaborating with JSTOR to digitize, preserve and extend access to
Journal of Marketing Research.
http://www.jstor.org
BAOHONGSUN, SCOTTA. NESLIN,and KANNANSRINIVASAN*
Logitchoice models have been used extensivelyto studypromotion
elasticities
response. This articleexamines whether brand-switching
derivedfromthese modelsare overestimated
as a resultof rationalconsumeradjustmentof purchasetimingto coincidewithpromotion
schedules andwhethera dynamicstructural
modelcan addressthisbias.Using
simulateddata,the authorsfirstshow thatif the structural
modelis corelasticitiesare overestimatedby stand-alonelogit
rect,brand-switching
models.A nestedlogitmodelimprovesthe estimates,butnotcompletely.
Second,the authorsestimatethe modelson realdata.The resultsindicate thatthe structural
modelfitsbetterandproducessensiblecoefficient
estimates.The authorsthenobservethe same patternin switchingelasticitiesas they do in the simulation.Third,the authorspredictsales
assuminga 50% increase in promotionfrequency.The reduced-form
modelspredictmuchhighersales levelsthandoes the dynamicstructural
model. The authorsconcludethat reduced-formmodel estimates of
elasticitiescan be overstatedand thata dynamicstrucbrand-switching
turalmodelis bestforaddressingthe problem.Reduced-form
modelsthat
includeincidencecan partially,
not
address
the issue.
though completely,
The authorsdiscuss the implicationsfor researchersand managers.
Measuring the Impact of
Brand
Switching When
Forward
Looking
Logit choice models have proved an invaluabletool for
studying consumer decision processes. The models have
generatedinsights into issues such as marketsegmentation
(Bucklin, Gupta,and Siddarth1998; Chintagunta,Jain, and
Vilcassim 1991; Kamakuraand Russell 1989), statedependence (Guadagniand Little 1983; Keane 1997a, b; Seetharaman, Ainslie, and Chintagunta 1999), and competitive
asymmetries(Allenby and Rossi 1991). A fundamentalfind-
Promotions
on
Consumers
Are
ing is that promotions influence consumer choice; that is,
they cause consumers to switch from BrandA to Brand B.
Gupta(1988), Chintagunta(1993), Chiang (1995), Bucklin,
Gupta,and Siddarth(1998), and Bell, Chiang,and Padmanabhan (1999) have examined the magnitudeof the brandswitching effect, at least relativeto dynamic effects such as
stockpiling, and have found that brandswitching accounts
for the majorityof the currentperiod promotioneffect.
A relatedresearchstreamhas studiedconsumers'dynamically rationaldecisions aboutquantityand purchasetiming:
Golabi (1985), Assunq.o and Meyer (1993), Meyer and
Assunqdo (1990), Helsen and Schmittlein (1992), and
Krishna(1992, 1994a, b) study how promotionuncertainty
determines consumers' optimal forward-buyingbehavior.
Erdem and Keane (1996) and G6nialand Srinivasan(1996)
develop stochastic structuraldynamic programmingmodels
to accommodate consumers' forward-looking behavior.
G6ntil and Srinivasanfind that consumerscan accelerateor
deceleratepurchasesto coincide with a promotionschedule
as long as they have sufficient inventory.Erdem,Imai, and
Keane (2003) develop a dynamic structuralmodel in which
consumersform futureprice expectationsand decide when,
what, and how much to buy. These articlesdemonstratethat
dynamic structural models are important for capturing
*Baohong Sun is AssistantProfessorof Marketing,Kenan-FlaglerBusiness School, University of North Carolina (e-mail: sunb@bschool.unc.
edu). Scott A. Neslin is AlbertWesley Frey Professorof Marketing,Tuck
School of Business, Dartmouth College (e-mail: Scott.Neslin@Dartmouth.edu).KannanSrinivasanis H.J. Heinz II Professorof Management,
Marketing, and Information Systems, Graduate School of Industrial
Administration,Carnegie Mellon University (e-mail: kannans@andrew.
cmu.edu). The authorsthankTilin Erdem, Eric Bradlow,and participants
in the marketingseminarat Universityof Michigan;the Tuck School Marketing Workshop;National Universityof Singapore;Universityof California, Riverside; HarvardUniversity;Yale University; WashingtonUniversity; and Duke Universityand in the MarketingSummerCamp at Carnegie
Mellon Universityfor valuablecomments on previousversions of this article. They also thankAndrewHayes, Tuck School of Business, for valuable
researchassistance.The authorsthankthe threeanonymousJMRreviewers
for several constructivesuggestions.
389
Journal of MarketingResearch
Vol. XL (November2003), 389-405
JOURNALOF MARKETING
RESEARCH,NOVEMBER2003
390
rational consumer adjustmentsin purchase timing due to
expectationsof futurepromotionactivity.
Our researchbuilds on the study of the brand-switching
effect by (1) demonstratinga potentialupwardbias in logitestimated switching elasticities and (2) showing that a
dynamic rationalmodel can significantlyalleviate this bias.
The intuitionbehind the bias is that the logit choice model
does not take into account consumers' rational purchasetiming adjustmentsmade to take advantageof a deal. The
bias misidentifies the promotion purchases as brand
switches and therefore overestimatesthe switching effect.
Keane (1997a, p. 311) describes the situation as follows:
"Suppose after a few years of shopping I realize that my
favorite supermarketalways cuts the price of my favorite
detergent,say Era, from $4.00 to $3.50 duringone week of
every month. Most other shoppers at the store realize this
too. So those who like Era adopt a decision rule that says:
'Only buy Era if the price is $3.50, and then buy enough so
that my inventorywill last at least 7 weeks (the longest possible time until the next sale)'.... If one were to estimate a
MNL [multinomiallogit] model for detergentchoice in the
store, the price elasticity of demand for Era would appear
enormous."'
The subsequent numerical example is motivated by
Keane's (1997a) research.1Consider two consumers: One
prefersBrandA and one prefersBrandB. In a no-promotion
environment,their purchasesmight be as follows:
Week
1
Consumer1
2
Consumer
A
B
2
3
4
A
B
5
6
A
B
7
8
A
B
Now consider that BrandA is promotedin Weeks 2 and 6.
Assume that Consumer2 does not react to this promotion;
there is no switching effect. Consumer 1 reacts by accelerating the second purchaseforwardfrom Week 3 to Week 2,
not purchasingin Week 5 in anticipationof a promotion,and
purchasingin Week 6 when the promotionoccurs:
Week
1
2
Consumer1
2
Consumer
A
B
A
3
B
4
5
B
6
7
A
A
B
8
Note that the promotion has not changed consumers'
brandchoices; it has only changed the timing of Consumer
l's purchase.However,when a logit model is used, it reads
data from purchaseobservationsonly and associates higher
probabilitiesof purchasingBrandA with promotionsavailable for Brand A. The model overestimates the brandswitching effect because it is designed to "fit"the statistical
relationshipbetween purchase probabilitiesand promotion
availability without recognizing the purchase-timeadjustment of a forward-lookingconsumer.2
A nested logit model may partlyalleviate the overestimation problemby calculatingbrandswitching conditionalon
a promotion-drivenpurchase-timingdecision. However,this
]Weacknowledgethe stimulatingcommentsraisedby an anonymous
revieweron a differentarticleby one of theauthors,whichalso servedto
motivatethisexample.
andit
canalso inducelargerpurchasequantities,
2Notethatpromotions
is not difficultto constructexamplesthatshowthatthis effectcan also
effects.This thereforemay
inducean upwardbias in brand-switching
accentuatethe bias. However,we simplifythe analysisby focusingon
brandchoiceandpurchaseincidence.
model is a reducedform in thatit does not model the process
of dynamic decision making: It still "fits" the relationship
between probabilityof purchasingand promotionavailabilities of Brand A. In general, logit and nested logit choice
models are too simple to take into account consumers'
forward-lookingbehavior.For example, nested logit models
naturally capture purchase acceleration but do not easily
capturepurchasedeceleration.A dynamic structuralmodel
in which the purchase-timingdecision is endogenized is
designed to model this behaviorexplicitly.
In additionto more accurateestimation of brandswitching as a result of marginal additional promotion, another
potential advantageof a dynamic rational model is that it
can avoid overpredictionof brandswitching when there is a
shift in promotion policy. Keane (1997a) conjectures that
the logit model would be especially ineffective if a brand
were to change its promotionpolicy, because the model does
not describe how consumerpurchasestrategiesadaptto the
new policy.
The intuition that logit choice models overstate the
switching effect makes sense but simplifies the problem in
two ways. First, logit models completely ignore the
purchase-timingdecision and consider promotionsolely as
a brand-switchinggame. As we mentionedpreviously,techniques exist to examine choice and timing decisions jointly
(Bell, Chiang, and Padmanabhan1999; Chiang 1991; Chintagunta 1993; Gupta 1988). Second, the intuition does not
explicitly take into accountconsumerpreferences.Modeling
heterogeneityis an inherentpartof any logit model and may
help alleviate the bias.
Therefore, we undertakethe following steps to demonstrate the existence of bias and prescribe a solution for it:
First, we develop a dynamic structuralconsumer-decision
model of incidence and choice. The potential advantageof
the structuralmodel is more accuratebrand-switchingelasticity estimatesbecause it endogenously models the process
by which rationalconsumersadjusttheirtiming decisions in
response to promotion uncertainty. In accordance with
Keane (1997a), we believe this will be particularlyeffective
in evaluatingchanges in promotionpolicy. Second, we comparethis model to variationsof both stand-alonelogit choice
models and choice/incidence models, taking into account
heterogeneityin consumerpreferences.We conduct the following analyses:
*Syntheticdata simulation:Assuming that the structuralmodel
is correct, we generate purchase-timingand choice decisions,
modelson the
andwe estimatelogit,nestedlogit,andstructural
data.This simulationshows thatthe logit and nested logit models produce upwardly biased estimates of promotion-induced
brandswitching, comparedwith the true effect as generatedby
the structuralmodel. The logit model resultsare more upwardly
biased thanthose of the nested logit model, suggesting thattaking into accountpurchasetiming at least partiallyaddressesthe
bias issue.
*Empiricalestimation:We estimate the logit, nested logit, and
structuralmodels on real data and compare brand-switching
elasticities across the models. We find that the structuralmodel
fits the databetter,and the elasticity resultsmirrorthe synthetic
datasimulation.The logit model elasticities are greaterthanthe
nested logit elasticities, which in turnare greaterthanthe structuralmodel elasticities.
*Policy simulation:Startingwith the real data, we increase the
promotionfrequencyfor one brandand use our models to predict sales with and without the policy change. This is a test of
on BrandSwitching
Impactof Promotions
theLucascritique(Lucas1976),whichstatesthatpolicymodels thatdo notaccountforadjustments
agentsmakein response
to a "regime"change producebiased predictions.As we
expected,we findthatthelogitandnestedlogitmodelspredict
muchhighersalesforthebrandwithincreasedpromotion
than
does the structural
model
model;this is becausethe structural
addressesthe Lucas critiqueby modelinghow consumers
changetheirpurchasetimingin responseto policychange.
Overall,the results suggest that logit choice models overestimate brand-switchingelasticities. Although nested logit
models partially mitigate the problem, a structuralmodel,
such as the one we propose, addresses the problem
comprehensively.
We proceed as follows: First, we develop the structural
model. Second, we present our synthetic data simulation,
our empiricalestimation,and our policy simulation.Finally,
we conclude with a summaryand discussion of the implications for both researchersand managers.
MODELINGCONSUMERDECISIONSIN A
STRUCTURAL
FRAMEWORK
Dynamic StructuralDecision Models
There is a growing body of literaturethat establishes that
consumersare forwardlooking in their purchasedecisions.
The evidence includesthe observationthatconsumersstockpile product in response to promotions (Blattberg,Eppen,
and Lieberman1981; Neslin, Henderson,and Quelch 1985).
The apparentreasonconsumersstockpile is thatthey realize
the lower price, which is availableonly temporarily,is worth
the additionalfutureinventorystoragecosts. Severalarticles
have models that formalize this process (Assunqdo and
Meyer 1993; Blattberg, Eppen, and Lieberman 1981;
Erdem, Imai, and Keane 2003; Gbntiland Srinivasan1996;
Krishna 1992, 1994a, b; Sun 2003).
We propose a dynamicstructuralmodel for analyzingthe
effect of promotionon brandswitching in an uncertainpromotion environment.Our primary theme is that forwardlooking, rational consumers make it difficult for nondynamic models to measurebrandswitching. Therefore,the
key phenomenawe incorporateare promotionexpectations,
brandchoice and incidence, and dynamic utility maximization. The need to model promotionexpectations and brand
choice is obvious given our purpose.The dynamic rational
model literatureassumes that consumers either maximize
long-term utility or minimize long-term costs under a
weekly consumptionconstraint.We believe thatutility maximization,is more appropriatefor our needs, because we
want consumersto have the option of forgoing or accelerating consumption.
Comparingthese aspects with those in previousliterature,
Blattberg,Eppen, and Lieberman(1981) focus on promotion but assume that the promotion schedule is known; in
addition,they do not model brandchoice, and they assume
that the consumerminimizes costs subjectto a consumption
constraint.Assunglioand Meyer (1993) maximize consumer
utility and model promotionexpectationsbut do not model
brand choice. Krishna (1992, 1994a, b) considers brand
choice and models promotionexpectationsbut assumes that
customers minimize costs subject to a consumption constraint,as do Blattberg,Eppen, and Lieberman.Erdem and
Keane (1996) maximize utility and examine brand choice
but consider product attributes,not promotion. Gbntil and
391
Srinivasan(1996) consider promotionexpectations, but do
not model brand choice, and consider cost minimization.
Erdem, Imai, and Keane (2003) consider brandchoice and
purchasequantityin a dynamic utility maximizationframework. Our model is similarto theirs in that it also drawson
the generalframeworkof Hanemann(1984) to model utility
for consumption.However, we tailor our model to investigate the impactof promotionon brandswitching. For example, we treat heterogeneity using a continuous distribution
rather than the latent class approach adopted by Erdem,
Imai, and Keane.We also use a simpler promotionexpectations model that focuses on the promotionschedule of individual brand-sizes. This article differs from that of Sun
(2003), who endogenizes the consumption decision and
investigatespromotioneffect on endogenous consumption.
Model Specification
We model the consumer decision process as a dynamic
programming problem under promotion uncertainty.We
assume thatconsumeri = 1 ..., I visits the storeon the periodic (e.g., weekly) basis t = 1 ..., T. On each store visit, the
consumer decides whether to buy and which brandto buy
given the observed promotionsand expected future promotions of the j = 1, ..., J brand-sizes. We denote the nopurchasechoice by j = 0. The objective of consumer i is to
determine, for each of a series of store-visit occasions,
whetherto purchasethe category and if so which brand,so
as to maximize the sum of discounted expected futureutility, Uit, over the finite planninghorizon.
T
d
ijt
1
at-iuj
max E
(1)
T
The indicatorvariabledijt= 1 if consumeri chooses brandj
at time t, and dijt= 0 otherwise for j = 1, ..., J. Because j =
0 indexes the category decision, diot = 1 means that consumer i decides not to buy the product category (i.e.,
"chooses"alternative"0"),and diot= 0 means thatconsumer
i decides to buy the productcategory in week t. The length
of the finite decision horizon is T, and 0 < 8 < 1 is the discount factor to reflect that consuming now is preferredto
consuming later (Erdemand Keane 1996; G6ntil and Srinivasan 1996). We denote the mathematicalexpectationoperator as E(.).
Foreach week t, we define the consumer'sutilityfunction
over thatweek's consumptionof each brand-size,Cijt,and of
consumptionof a composite of other goods, Zit. Thus, the
utility is given by
J
(2)
(2)
+cx1Z,
U
UitI =
j=lI
ijtCijt +cliZit,
where xli measures the benefit from consuming the composite of other goods.3 The term Vijtdenotes the consumption benefit associated with consuming brandj. We model
this as follows:
(3)
ijt=
2ij X3iLastijt.
3Note thatwe assume thatthe composite good is not storable,so we view
Zit as either purchaseor consumption.This is to simplify our model, the
purposeof which is to explain behaviorin the focal category.
JOURNALOF MARKETING
RESEARCH,NOVEMBER2003
392
The utility function is state dependent and stochastic, as
Hanemann(1984) introduces.The variableLastijtindicates
whetherconsumeri purchasedbrandj at purchaseoccasion
t- 1. The benefit from consumptionof brandj depends on
Lastijt.The coefficients X2ijmeasure consumer i's intrinsic
preferencefor brandj. The parameterX3icapturesthat consumers' learning of the quality of a productor their familiarity with a productcan influence their consumptionpreference for a product.This state dependencephenomenonis
also referred to as purchase-event feedback (Ailawadi,
Gedenk, and Neslin 1999).
We normalizethe price of the composite goods to be one.
At each period, consumeri has income yit and incurs costs
as a result of purchasingbrandsin the category,consuming
other goods, managing category inventory, and incurring
stockouts, in accordancewith budget constraint:4
J
(4)
yit =
i
Pijtdijt + Zit + 81i
j=l
+ 82il
Invijt
j=1
-
Invijt
jjl
where
(5)
Pijt= Priceijt- PromijtDscntijt.
The variablePijtis the net price paid by consumeri, Priceijt
is the everydayprice consumeri pays for brandj in week t,
Promijtis a dummy variablefor the presence of a price promotion, and Dscntijtdenotes the value of the price promotion. The consumer'sinventoryof brandj at the beginningof
week t, Invijt,is given by
(6)t
=
ijt = Invij(t- 1) + qijt- Cijt.
The variableqijtis the purchasequantityduringperiodt. We
calculate consumption, Cijt, on the basis of previous
research(Gupta 1988; see also Ailawadi and Neslin 1998),
except we keep track of consumption and inventoryat the
brandlevel. We first calculate Cit, total category consumption in each week, as Cit =
Ci), where Ci is
consumer i's average weekly
lInvijt,
consumptioncalculated from
min(_
the data (Ailawadi and Neslin 1998; Gupta 1988). The calculation shows thatthe consumerwill consume Ci as long as
he or she has that much inventoryon hand.To calculateCijt,
we assume that if the consumer has positive inventory of
various brands,he or she consumes the brandsin order of
preference(Vijt).Given that Invijtis the inventoryof brandj
at time t, 81i6 = Invijtmeasurestotalholdingcost; 81idenotes
unit holding cost. In addition, I(=
Invijt- Ci) is an indi< Ci and equal to
cator function equal to 1 when 11
costs (for a more thor0 otherwise. This capturesstockoutqlInvijt
ough treatment,see Erdem, Imai, and Keane 2003). The
combinationof Equations2, 4, and 5 yields the following:
4Note that we include inventorycosts in the budgetconstraint,which is
equivalentto including it directly in the utility function.For a similartreatment, see Erdem,Imai, and Keane (2003).
J
(7)
Uit =
li(Priceijt-
V[ijtCijt-
PromijtDscntijt)dijt]
j=l
-
Invijt- xli2iI
txli li
j=1
Invijt Ci +
j= 1
Oxliyit.
We add a few adjustmentsto Equation7. First, note that
ali represents price response. Previous researchers have
found that response to changes in regularprice is different
from response to promotional price discounts (Guadagni
and Little 1983; Mulhernand Leone 1991). We allow for the
possibility of having differentialresponse to price promotions and regularprice by introducinga new parameter,a4.
Second, we set -cli6li = c5i, where a5i represents the
change in utility from increasing inventory by one unit.
Third,we set -Cli2i = x6i,where x6irepresentsthe change
in utility if the consumer is out of stock. Fourth,note that
choices are mutually exclusive so that 1j = odijt = 1, and
+
when no category purchase is made, Uit = 1 =
lijtCijt
+
Ci) + liYit.Therefore, yit,
5i =
6iI( across alternatives,
is independentof
which does
not change
lInvijt
__InVijt
or
the
decision.
and
will
not
affect
brand
choice
category
dijt
We thereforetreat it as a constant and set it equal to zero
(Erdem,Imai, and Keane 2003)5 and thus can state our utility function as follows:
(8) Uit =
(WijtCijt
cxliPriceijtdijt
+ C4iPromijtDscntijtdijt)
j=l
1
+
Invijt+
Invijt Ci
6iI{
x5i
We model promotion availability and consumer perceptions of promotionavailability.As do Gntil and Srinivasan
(1996) and Assunqdo and Meyer (1993), we assume that
promotionof each brand-sizefollows a first-orderMarkov
process and is independentacross alternatives:6
(9)
Prob(Promjt= lIPromj(t-1)= 1) = tj1, and
(10)
Prob(Promjt= lIPromj(t-1) = 0) = tjo,
for j = 1 ..., J, where denotes the probabilityof promojl there was
tion in periodt, given that
promotionin period t 1 for brand-sizej. Similarly, itjodenotes the probabilityof
promotionin period t, given that there was no promotionin
periodt - 1. The parametersdescribethe frequenciesandthe
5We can relax this assumptionand allow total shopping expenditureto
affect purchasedecision by assuming a nonlinearutility function.We leave
modeling expenditureeffect for furtherresearch.
6Wechecked this assumptionby calculatingand comparingEquations9
and 10 and then doing the same using Promj(t- 2) insteadof Prom(t- 1).We
found thatthe t - 1 conditionalswere differentwhereasthe t - 2 conditionals were virtually the same. For example, for the Heinz 14 oz. bottle,
- 1)=
Prob(Promjt=1IPromj(t-1)= 1) = .02, whereasProb(Promjt= 1IPromj(t
0) = .06 (the chance of a promotionin week t is greaterif the brand-sizehas
not just been promoted).The second-orderconditionalsfor this brand-size
are Prob(Promjt= 1IPromj(t- 2) = 1) = .05 and Prob(Promjt= lIPromj(t- 2)=
1) = .05, or virtually identical. Similar patternshold for the other brandsizes.
on BrandSwitching
Impactof Promotions
temporal correlationof promotions over time. We assume
that consumers learn these probabilities;G6ntil and Srinivasan (1996), who also estimatea structuralmodel, find evidence thatconsumerscan do so, as do Krishna,Currim,and
Shoemaker(1991), who use a consumersurvey.
Note thatthe utility function(Equation8) andperceptions
of promotion availability imply that loyal consumers are
especially likely to adjustpurchasetiming (e.g., by acceleration). Considerthe consumerwho entersthe store in time t
and finds Brand A on promotion. The consumer does not
need to buy the product category now (inventory is high)
and realizes that doing so only adds inventorycosts in the
future. However, the consumer realizes that because the
brandis on promotionnow, it may not be next week, and by
buying now, the consumercan ensurefutureconsumptionof
BrandA. This futureconsumptionbenefit is especially high
for consumerswho preferBrandA, and that is why they are
intrinsicallymore likely to adjust purchasetiming. Timing
adjustmentby loyal purchasersis the key intuitivereasonfor
the upwardbias in switching estimates; in taking this phenomenoninto account,the dynamic structuralmodel should
provide more accurateswitching estimates.
Our focus is the impactof promotionon brandswitching,
so it is naturalthat we model consumerpromotionexpectations ratherthan price expectations. Our emphasis on promotion expectationsis also based on the following reasons:
First, modeling price expectations would add more complexity by increasingthe size of the dynamic programstate
space. Second, including these expectations would only
make our case stronger,because there would be even more
consumer adjustmentof purchase timing. Third, the three
price-relatedquantitiesare regularprice (Priceijt),availability of a promotion (Promijt),and depth of a promotion
(Dscntijt).We believe thatconsumersare most likely to form
expectations for the availability of a promotion. Krishna,
Currim, and Shoemaker (1991) find that consumers are
more likely to have opinions of promotionfrequency than
promotion depth. Fourth,the variationin regularprice per
ounce was fairly small in our data (mean and standarddeviations are $.0561 and $.0015, $.0389 and $.0017, $.0461
and $.0015, $.0480 and $.0016, $.0274 and $.0010, and
$.0349 and $.0014 for the six brand-size combinations in
our application).So plus or minus two standarddeviationsis
on the order of an 8% change, whereas the average price
promotiondiscountis on the orderof a 15%to 30% change.
Finally,we assume thatit is easier to learnthe probabilityof
promotionon the next occasion conditional on currentpromotion than to learn the likelihood of a change in regular
shelf price. Therefore,it is more rationalto make the effort
to learnwhen promotionswill be availablebecause it is easier and the payoff is higher.
The simplest way to incorporatefutureprices when solving consumers'dynamicprogramsis to treatthe prices constantover the time horizon.Gt~ntiland Srinivasan(1996) follow this approach.We insteadrepresentthe prices as random
draws from a normal distributionwith mean and variance
specific to the brand.The mean and variance remain constant over time. The results we reportin this article use this
specification.We also follow a similarapproachfor depthof
promotions. We observe that constant prices yield similar
parameterestimates and identical managerialimplications.
393
The solutionto the dynamicprogramdefinedby Equation
1 and the specificationof our utility function is such that at
any time period and given any state, the optimal solution is
the solution to the dynamicprogramfrom that time forward.
The consumer's optimal choice is thus the solution to the
Bellman equation:
(11)
= maxE
Vit(Lastit,Invit,Promit)
dijt
YST-tUiT
T= t
+ 8Et
= maxfUit
[Vi(t +1)(Lasti(t +1), Invi(t +1), Promi(t +1)]1
d ijt
There are three state variables:last purchase,inventory,and
promotion;Lastit,Invit,and Promitare vectors that denote
consumeri's previouschoice, inventory,and currentpromotion status for all brands, respectively. The value function
Vit depends on the state at time t for consumer i. It is the
maximum expected discounted consumption utility for a
consumer who makes decisions about purchase incidence
and brandchoice given Invitunits of currentinventory,last
purchaseLastit,and observed promotionPromit.
Heterogeneityand Estimation
Previous research suggests that consumers are heterogeneous in their preferences, sensitivities to marketing-mix
variables, holding costs, and stockout costs (e.g., Allenby
and Rossi 1991; Chang, Siddarth, and Weinberg 1999;
G6ntil and Srinivasan 1993; Kamakuraand Russell 1989;
Krishna, Currim, and Shoemaker 1991). It is also known
that ignoring unobservedconsumerheterogeneitymay lead
to biased parameter estimates (Heckman 1981). Let (pi
denote a vector of length J + 5 that representsconsumeri's
utility parameters((Xli,(X2ij,(X3i,(4i, 5i, (X6i)Tfor j = 1,
....is
J, whereT denotes the transpose.Then, we assume that pi
multivariatenormally distributedwith the following mean
vector and covariancematrix:
N(90,
-i-
(12)
where po= (a1, a21'
9),
2J, a3, (X4, X5,a6) is the mean of
....,
matrixof dimensionJ +
pi, and Xp is a variance-covariance
5 in which the diagonal elements denote the corresponding
variance of each parameter.Thus, we need to estimate the
mean and variancefor each of these parameters.In addition,
we capturethe potential for loyal users to be more promotion sensitive by allowing the intrinsic preferencea2ij and
promotioncoefficients (a4i) to be correlatedwith correlation
p. Thus, all the off-diagonal elements of lp except p are
constrainedto be zero. A positive (negative)p indicatesthat
consumers who like the brand are more (less) promotion
sensitive than average.Let 0 = (a1, a2j, a3, a4, a5, a6, al
Qxa4(Ta5(a6,
forj = 1, ..., J represent
1j0)We then have the
all
the ac33
Ga2j,
jl,
parametersto be estimated.
probability of choosing brandj conditionalon piand 0 (Pijt0,qi]):
(13)
Pijt(e, pi) = Prob(dijt= 10, (pi).
We assume that the value function of choice j is distributed
by an i.i.d. errorterm tijt, which follows an extreme value
distribution. The probability of consumer i making a
sequence of purchasedecisions dijt,j = 0, ..., J is given by
JOURNALOF MARKETING
RESEARCH,NOVEMBER2003
394
(14)
Pi(,
= 17
(Pi)
t
lj
dijtPijt(O,
(Pi)-
Integrationover the distributionof (piyields the likelihoodof
observing consumeri's sequence of purchasedecisions:
Pi(6) = E[Pijt(0,
qPoi)O]
(15)
=
1
17
t1t
dijtPijt(O,
(pi)fpi6O)d(pi,
where ( is the domain of the previous integration, and
f(@pi|)is the multivariatenormalprobabilitydistribution
function for yi conditional on 0. Thus, the log-likelihood
function to be maximizedis
(16)
log L(6) =
log[Pi(0)].
i=1
There is no closed-form solution for the underlyingpurchase probabilitiesin Equation 13. In addition, calculating
Equation15 requirescomputationof multipleintegrals.The
dimensionof the integralsis too large for traditionalnumerical integrationmethods; instead, we use simulated maximum likelihood, which employs Monte Carlo methods to
simulatethe integralsratherthan evaluatethem numerically
(Keane 1993; McFadden1989; Pakes 1986). Because inventory is continuous, we have the problem of a large state
space. We adopt Keane and Wolpin's (1994) interpolation
method by calculating the value functions for a few state
space points and using these to estimate the coefficients of
an interpolationregression. We then use the interpolation
regressionfunction to provide values for the expected maxima at any other state points for which values are needed in
the backwardrecursionsolution process.
The adoptionof simulationand interpolationsignificantly
reduces the computationburden, which also enables us to
take into account unobserved consumer heterogeneity.We
begin the simulation with a starting value for 0. Next, we
draw a set of parametersfor a given consumer. We then
solve the dynamicprogrammingproblemfor the entire time
span. We repeatthe process for that same consumer,with a
different set of pi. This generates Pijt.We then go through
this process for the next consumer.After all consumersare
finished, we have Pijtfor each consumer,and we can calculate the likelihood function. Using simulation, we then
numerically calculate gradients and obtain a new 9. We
repeatthe entire process until we can no longer improvethe
likelihood function.7
(17)
We compare our structuralmodel with several conventional reduced-formmodels that are used to study consumer
responseto promotion.Using a multinomiallogit model, we
model the conditional probabilitythat a household chooses
brandj. The probabilityof choosing brandj given thata purchase is made is
7Note that taking into account unobservedheterogeneityassuming continuousheterogeneitydistributionrequiresthe dynamicprogrammingproblem to be solved for each draw. A simpler treatmentof heterogeneity is
latentclass approach,as Erdem,Imai, and Keane (2003) adopt.
=
J
liut
.
where
(18) Wilt = -xliPriceijt +
+
2ij + oX3iLastijt
X4iPromijtDscntijt.
Note thatEquation18 correspondsto the structuralmodel in
its specification of intrinsic preference, state dependence,
price, and price promotion.However, it does not consider
purchaseincidence or dynamicdecision making.
Nested logit is one method for modeling purchase incidence, though it does not explicitly model optimal dynamic
decision making. In this framework,the probabilityof category purchaseincidence dependson the expected maximum
utility from the brand-choicedecision. This expected maximum utility is given by CatVal = log(IJ lewit), which
reflects the established brand preferences and marketing
activity in the category at purchase occasion t (Ben-Akiva
andLerman1985). Purchaseincidence is thenrepresentedas
(19)
(20)
Pit(diot
=
Rt
ioi +
R*
eRit
0) =
=
1+eiR*
+
lliCit
+
t32iCatValit
and
E
1j3i
Invijt
j=I
+
34iI
InVijt - Ci +5iPromTimeit.
tj=lt
We define inventoryand consumptionas we did previously.
The variable PromTimeitrepresentsthe time since the last
promotion.It is meant to capturethat consumers may hold
out until the next promotionin a reduced-formsense (Mela,
Jedidi, and Bowman 1998).8 To calculate PromTimeit,we
calculate the average time between promotionsin the category, which is 1.6 weeks. If the time since the latest promotion in the category seen by consumeri is greaterthan half
the average, PromTimeitequals 1; otherwise, it equals 0.
Given this definition,we expect P5ito be negative.The likelihood function for this nested logit model is
Dijt
-Dit
-
(2j1)
L
l"
ewrt
/
1.*.R
+ e
lt
ijt
1 + e
e
Reduced-FormModels
e W.*.t
Pit(dijt = ldiot = 0) =
1+
Dit
R* it
eR
jt
where Dijt is a dummy variable that equals 1 if brandj is
chosen by consumeri in week t, and Dit is a dummyvariable
that equals 1 if the productcategory is purchasedby consumer i on trip t.
We examine two additional models of incidence and
choice. First is a logit model with no-purchaseas an alter8Note that including the variable PromTimein the nested logit model
enables consumers to consider a next-periodpromotion possibility when
makinga purchasedecision that maximizes theircurrentutility.It is far too
simple and ad hoc to capturethe complicateddecision process generatedby
forward-lookingbehaviorand its interactionwith promotionexpectations.
on BrandSwitching
Impactof Promotions
native (Chiang 1991; Erdem and Keane 1996; Erdem and
Sun 2002). Our motivationfor considering this model is to
make the purchase incidence model more similar to our
model, which also treats no-purchaseas a distinct alternative. Second, we estimatea static version of our model. This
assumes the discountfactor8 = 0, so consumersdo not consider future periods. Accordingly, we also do not include
inventoryand stockout costs because they requiredynamic
optimizationon the partof the consumer.
ANALYSES
SyntheticData Simulation
In our first analysis, we simulate synthetic data using the
structuralmodel with a known set of parameters,and we
estimate various logit models and the structuralmodel on
these data. We intend to show that if consumers follow a
rationalpurchasestrategy,conventionallogit models overestimate brandswitching due to promotion.
We generate the data from our proposed dynamic structuralmodel for 200 consumersduringa 50-week horizon.In
essence, we assume that the structuralmodel is the "true"
model. There are two brandswith marketsharesof 70% and
30%.Table 1 shows the trueparametervalues for generating
the synthetic data. We compare five models: (1) a logit
choice model with brandpreference,price, and promotion
as independentvariables;(2) a nested logit model; (3) a logit
model with no purchaseas a choice alternative;(4) the static
version of our dynamic model;9 and (5) the dynamic
model.10
Table 1, Column 2, shows the true parameter values
(mean and standard deviations) for the synthetic data.
Columns 3-7 reportthe averagemean and average standard
deviations over 100 simulationsfor each parameter.Table 1
shows the following: First, the structuralmodel is estimated
correctly; the average estimated parametersin Column 7
correspondto the trueparameters.Second, the nonstructural
models consistently overestimatedthe coefficient for promotion. The upwardbias is highest for the logit model and
lower for the three choice/incidence models. The results
conform to our expectationsbut do not clearly demonstrate
an upwardbias in switching elasticities, which can be equal
even if the raw coefficients are unequal(Ailawadi, Gedenk,
and Neslin 1999).
We calculate promotion-switchingelasticity as the percentage change in purchaseprobabilityof brandj with and
without promotion, conditional on category purchase, for
consumeri for brandj at week t:
(22)
esijt = Prob(dijt= ldiot = 0, Promijt= 1)
-
=
=
=
Prob(dijt ldiot 0, Promijt 0)]
/Prob(dijt= Idiot = 0, Promijt= 0).
9This is a structuralmodel that assumes immediateutility maximization.
Consumersdo not take into account future utilities. We thereforeassume
the discount parameter8 = 0 and that there are no inventoryeffects.
10Notethat to simplify, we assumed for the simulation that consumers
know future regular prices. This assumption is relaxed in our empirical
application,in which we assume that consumersview futureregularprices
as randomdraws from a normaldistributionwith constant mean and variance over time.
395
We calculatethis quantityfor each householdfor brandj for
an arbitrarilyselectedWeek 8, a week when Brand1 was not
promoted.We simulatepromotionavailabilityand use average price discountto representpresentpromotiondepth.We
use 100 randomdraws to simulate consumerheterogeneity.
Note that to make the promotion elasticities comparable
across models, we calculate the preceding equation for the
same consumersfor each model, specifically the consumers
who makea categorypurchasein Week8 in the no-promotion
case. In this way, we focus only on the brand-switching
aspects of the variousmodels. To complementthe switching
elasticity,we also calculatethe percentageof the immediate
sales "bump"thatis due to switchingratherthanacceleration
or deceleration.11This quantityis comparableto that calculated by other researchers who investigate the switching
effect of promotions(e.g., Bell, Chiang, and Padmanabhan
1999; Gupta1988). Using the same simulationmethodas we
do to calculate the switching elasticity, we classify
promotion-weekincrementalpurchases as brand switches
(A), acceleratedpurchases (B), and deceleratedpurchases
(C). The switchingpercentageis thusA/(A + B + C).
Table 1 presents the switching and switching percentage
results and shows the following: First, logit models overestimatepromotionelasticities more thanthe structuralmodel.
The t-tests show that the differences are significant.We use
the word "overestimate"because the structuralmodel is the
true model, we estimate its coefficients accuratelywith that
model, and its elasticities are thereforethe true elasticities.
Second, all the reduced-form models overestimate the
brand-switchingeffect. The upwardbias is highest for the
stand-alonelogit choice model and second highest for the
nested logit model with purchaseincidence. Logit with nopurchaseoptions and the static structuralmodels also result
in higher switching elasticities.
The results suggest that logit choice models overestimate
the brand-switchingeffect of promotions.The addition of
purchase incidence helps alleviate this bias but not completely, apparently because the incidence models are a
reducedform of dynamic decision making.Therefore,such
a model does not fully capturethe consumer'srationalpurchase strategy and confounds switching with purchase
timing.
EmpiricalApplication
Data. We used ketchup data collected by ACNielsen.12
The calibrationsample consists of 8823 observationsof 173
households that made 1473 purchasesof ketchupduring51
weeks from 1986 to 1988 in Sioux Falls, S.Dak. We
excluded occasional purchasers by randomly selecting
householdsthatmade more than4 purchasesof ketchupduring the 51 weeks. We also only chose households that purchased at most one unit of ketchup on each purchaseoccasion; single-unitpurchasersrepresent98% of all households
11Notethat we cannot calculate this quantity for the stand-alonelogit
models or the static structuralmodel because these models either do not
consider purchase displacement (logit) or do not enable consumers to
accelerateor deceleratepurchases(static structural).However,it providesa
useful basis for comparing the nested logit and no-purchaseoption logit
with the dynamic structuralmodel.
12Areason for using ketchupdata is that the consumptionrate is relative
insensitiveto promotion,as Ailawadi and Neslin (1998) show. However,for
otherproductcategories,ignoringflexible consumptionratemay also cause
overestimationof brand-switchingelasticities. This supportsour findings.
JOURNALOF MARKETING
RESEARCH,NOVEMBER2003
396
Table 1
SIMULATION
BASEDON SYNTHETIC
DATA
Parameters
Price-a,
BrandpreferenceoC2
Brand 1
Brand2
Promotiona4
Unit inventorycost
a05
Stockoutcost (X6
Static
Structural
Model
(4)
Dynamic
Structural
Model
(5)
TrueValuesa
Logita
(1)
Nested Logit
(2)
Logit with
No-Purchase
Alternative
(3)
-2.00
1.00
-3.40 (.34)
1.26 (.27)
-2.68 (.16)
1.34 (.44)
-2.61 (.22)
1.10 (.44)
-2.30 (.19)
1.03 (.25)
-2.22 (.21)
1.01 (.26)
-.50
.50
-1.00
.50
1.50
1.00
-.10
.05
-.20
.05
2.51 (.29)
1.16 (.24)
1.57 (.41)
.91 (.49)
2.77 (.20)
1.19 (.21)
2.05 (.33)
1.43 (.25)
-.55 (.14)
.56 (.15)
-1.08 (.26)
.51 (.19)
2.09 (.24)
1.31 (.35)
-.06(.03)
.05 (.02)
-.22(.10)
.06 (.02)
-.55 (.20)
.54 (.09)
-1.07 (.20)
.48 (.22)
1.74 (.24)
.98 (.30)
-.54 (.19)
.52 (.07)
-1.07 (.18)
.50 (.20)
1.51 (.18)
.94 (.24)
-.08(.04)
.05 (.02)
-.18(.07)
.06 (.02)
lo0
tE1
T20
Rt21
Purchase Incidence
Categorypreferencet0
.50
.25
.30
.15
.55 (.13)
.26(.11)
.33 (.09)
.16 (.07)
1.24 (.20)
.13 (.06)
.69(.25)
ConsumptionP
.25(.10)
Unit inventorycost 33
Stockoutcost 34
Breakdownof Short-TermPromotionEffect
Brandswitching
Purchasedisplacement
.30(.09)
.58 (.23)
.31 (.15)
-.08 (.03)
.03 (.04)
-.03 (.02)
.02 (.03)
Categoryvalue P2
Marginal Promotionof Brand 1 in Week8
Short-termpromotionalswitching
elasticities
Long-termpromotionalswitching
elasticities
.62(.18)
.351 (.044)
.275 (.027)
.266 (.021)
.237 (.019)
.198 (.015)
.164(.023)
.156(.027)
.130(.016)
.121 (.013)
.101 (.011)
N.A.
72%
28%
69%
31%
N.A.
56%
44%
.222 (.029)
.186 (.025)
.187 (.025)
.099 (.017)
.054 (.016)
Increased PromotionPerception(i) of Brand 1 by 50%
Percentagechange of Brand 1 aggregate
sales
aNumbersin the first and second lines are the means and standarddeviations of each generatedparameter.
Notes: N.A. = not applicable.Numberof households= 200; numberof weeks = 50; numberof observations= 10,000; numberof simulations= 100. Numbers not in parenthesesare estimatedparameters;numbersin parenthesesare the standarderrorof the correspondingparameters.The results are obtainedon
the basis of 100 simulations.Average means, standarddeviations, and their standarderrors are reportedover 100 simulations.The standarddeviation of
promotion-switchingelasticities are reportedin parentheses.To test whetherthe elasticities differencesamong Models 1, 2, 3, 4, and 5 are statisticallysignificant, we performedt-tests for the first brand.The t-values are 4.12, 4.26, 3.97, 3.86, and 4.06 for short-termmarginalpromotionelasticities; 4.18, 3.96,
4.21, 4.19, and 4.40 for long-termmarginalpromotionelasticities; and 4.85, 4.75, 5.36, 4.86, and 5.02 for policy-changeelasticities.
and 96% of all purchaseoccasions. We selected six leading
brand-sizesthatconstitutemore than 85% of the (unit) market share:Heinz 14 oz., 28 oz. and 32 oz., 40 oz. and 44 oz.,
and 64 oz.; Hunt's 32 oz.; and Del Monte 28 oz. and 32 oz.
We groupedsimilar sizes (e.g., 28 oz. and 32 oz., 40 oz. and
44 oz.) togetherto reduce the computationburden.The six
sizes we consideredcover more than98% of the sales of the
three brandsin our study.Table 2 reportsdescriptivestatistics. The average price per oz. is $.0561, $.0389, $.0461,
$.0480, $.0274, and $.0349 for the six brand-sizes.Average
category purchase is 5.344 ozs. per week. We reserved an
additional 4131 observations of 81 households that made
647 purchase of ketchup during 51 weeks in Springfield,
Mo., for holdout sample validation.In estimatingthe models, we quantifiedprice, price discount, and inventoryrelative to a 32 oz. bottle. Thus, if a consumer purchaseda 44
oz. bottle, there is 1.375 additionto inventory(qijt= 1.375).
This is a matterof rescaling that does not affect the results.
We chose the ketchupcategorybecause it is a productthat
consumerscan use flexibly and that has relativelylow holding costs. It is also a well-promotedcategory.As a result,
ketchup is a category for which consumers can plan their
Impactof Promotionson BrandSwitching
397
Table2
DESCRIPTIVE
STATISTICS
OF KETCHUPDATA
Store Special Price
BrandName
Heinz 14 oz. (1)
Heinz 28 oz. and 32 oz. (2)
Heinz 40 oz. and 44 oz. (3)
Heinz 64 oz. (4)
Hunt's 32 oz. (5)
Del Monte 28 oz. and 32 oz. (6)
MarketShare
Mean Price per Ouncea
Frequency
Mean
4.31%
39.68%
5.14%
3.37%
13.52%
19.47%
(85.49%)
5.61
3.89
4.61
4.80
2.74
3.49
5.8%
19.0%
8.5%
10.9%
12.5%
18.1%
.896
1.114
1.022
1.201
.481
1.065
aln the estimation,we scaled the prices relativeto 32 ozs.
Notes: We selected frequentketchupusers who made at least five purchasesduringthe 51 weeks. The averagesample category purchaseis .167 bottle per
week. The averagecategorypurchaseis .043 bottle per week in the originaldata from ERIM.
purchasing.Most of the purchasesare single unit, and consumptionis relativelystable, as Ailawadi and Neslin (1998)
demonstrate. Ketchup therefore seems an ideal category,
though certainlynot an atypicalone, for illustratingrational
consumerplanning.
We operationalizedprice as regular,everyday shelf price.
We follow Abraham and Lodish (1987) to construct the
price discount,Dscntijt.We definedpromoequal to 1 if there
was a price discount in that week and equal to 0 otherwise.
We defined Last equal to 1 for the brand-sizethat was chosen most recently and equal to 0 otherwise (see Ailawadi,
Gedenk, and Neslin 1999; Seetharaman,Ainslie, and Chintagunta 1999).13The 8 is fixed at .995 (Erdem and Keane
1996).14
Comparative model fit. The fit statistics for both insample (calibration)and out-of-sample (holdout) are provided in Table 3. Because choice models (Model 1 and 2)
and choice/incidencemodels (Models 3-7) fit data to different model structures(incidence and/or brand), the overall
log-likelihood values and Bayesian information criteria
(BICs) are not directlycomparable.Thus, we also reportthe
log-likelihood values of the brandchoice componentfor the
nested logits (Models 3 and 4) to compare the performance
of various reduced-formchoice models. In terms of this
choice component, model fit improves from Model 1 to
Model 4; Model 4 is the best-fittingchoice model. We then
compared the overall log-likelihood value and BICs for
Models 3-7. The overall log-likelihood (absolute)value and
BICs are lower for Model 7 than for Models 3-6, indicating
that the dynamic model fits data the best.15Holdout sample
fit statistics supportthis finding. To better assess the fit of
each model, we reportpredicted average probabilitiesand
counts of each choice alternativein comparison with the
sample frequency and sample count of the calibratedsample. In addition, we reportthe percentageof correctly predicted choice alternativesand Efron's R2 for both the cali3Weestimated all the reduced-formmodels with smoothed use experience ("BLOY,"or brandloyalty, as in Guadagniand Little's [1983] study).
There is some improvementof log-likelihood value and BIC, but it does not
affect the estimation of other parameterssignificantly.Comparisonof the
model estimationcan be obtainedfrom the authors.
14Althoughthe 51-week time horizon seems long, we note that the discounted factor implies that the distanttime periods are less importantthan
immediatetime periods.
15Akaikeinformationcriterionis calculatedas -lnL + numberof parameters, and BIC is calculatedas -lnL + (numberof parameters)/2x In(number of observations).
bration sample and the holdout sample.16These indexes
paint the same picture. The comparisonof Models 6 and 7
suggests thatthe static version of our model performsworse
than the dynamic version, which suggests that dynamics
indeed matter.
Overall, the dynamic structuralmodel fits betterthan the
other models in terms of log-likelihood, BIC, and hit rates
for the calibrationand holdout samples.17This suggests that
our proposed model provides a better descriptionfor consumer rational purchase behavior in the ketchup category.
Models 3-5 underperform the forward-looking model
because they try to capture the dynamics of consumer
rationalstrategyby an exogenously imposed statisticalrelationship. The assumedrelationshipis too simple and ad hoc
to incorporatethe complex effects of purchasetiming and
forward-looking inventory effects. The choice models
(Models 1 and 2) ignore purchasetiming and cannot completely capture consumer rational purchase strategy. The
static structuralmodel (Model 6) performsworse than the
dynamic model because the former leaves out all the
dynamics.
Estimated coefficients. Table 4 reports the estimation
results of the seven competingmodels; meanparameterestimates are reportedin the first line, and the standarddeviation estimates across households are reportedin the second
line. We first focus on the structuralmodel (Model 7). All
the mean coefficients are significant and have expected
signs. The standarddeviations are also significant for all
coefficients except that for stockoutcost. This providesevidence that consumers are heterogeneous. Brandconsumption preferences for the six brand-size combinations are also significantly estimated, and there are
indications of significant heterogeneity in preference. The
significance of the last purchase parameterreinforces the
16Efron'sR2 is calculatedas follows:
x1
1 -
i=
1
j
t= 1
,
i
i
( Y
j=--1 (Yijt
-
-
-
jt
ijt)2
t =
It conveys the proportion of the variance of the dependent variable
explained by the independentvariableand is a more reliable model selection criterionfor discrete-choicemodels (Amemiya 1985).
l7Note that the holdout sample consists of households in a differentcity
than the calibrationsample households, so this predictive validity test is
more stringentthan predictingthe choices of the same households in a different period or of differenthouseholds in the same period.
398
JOURNAL
Model
(7)
Dynamic
tion
Predic-
72 84992 63 83
RESEARCH,
299
out
7365 Hold-
.970
.064
8829.4
8988.4 4840.1
tion .973
.064
.1000
.0082
.0102
.0071
.0090.0339
.8316
Average
CalibraProbability
Structural
tion
Predic(6)
Structural
Model
OF MARKETING
68 85897 58 84
306
out
7352 Hold-
.941
.053
8920.5
9006.8 4868.0
Static
tion .954
.055
.0081
.1017
.0067
.0087.0346
.8296
.0106
CalibraAverage
Probability
No-
tion
Predic-
Alternative
with
(5)
Logit
Purchase
with
Logit(4)
PromTime
Nested
71 86195 63 82
300
out
7351 Hold-
.940
.050
8937.79060.3 4870.4
tion .953
.053
.1010
.0082
.0108
.0070
.0089.0335
.8306
Average
CalibraProbability
NOVEMBER
choices
example,
For brand
of
sample.
values
entire
considered.
the
of are
log-likelihood
outand
the
report
occasions
purchases
we
of
purchase
are
Therefore,
percentage
and
tion
Predic-
69 85895 60 84
models.
302
out
7355 Hold-
.941
.051
8910.4
9042.1
4859.2
(1438.7)
(2555.2)
(2617.2)
tion .954
.054
.0082
.1027
.0107
.0068
.0093.0338
.8285
Average
CalibraProbability
observations
these
8823
probabilities
theacross
of
predicted
tion
Predic-
68 86196 57 84
305
out
7352 Hold-
.935
.050
16.75%
comparable
not
average
only
are
of
8947.3
9069.9
4881.8
(2569.3)
(2638.4)
(1458.4)
purchases.
when
tion .952
.052
COMPARISONS
.0080
.1030
.0107
.0065
.0094.0339
.8285
values
Average
CalibraTable
1473 product
Probability
FIT
model
are the
logit
81 98 56 79
out .880
868
307
tion
.043
HoldTherereport
PredicMODEL
the models.
log-likelihood
with
we
by logit
(2)
8823.
2729.12791.1 1473.7
4131.
Logit
Correlation
tion .904
.046 = =
overall
.1041
.0090.0380
.0110
.0090
.0059
CalibraAverage
models nested
Probability
the
predicted
two
logit
sets,
82 99 54 78
the
for.05627,
out .873
870
310
tion
.039 observations
Holdobservations
Predicfor
of of is data
oz.
(1)
models,
Logit
2815.9 1485.3
2757.7
14
tion
number
all
.891
.041 numberdifferent
.1051
.0092
.0057
.0088.0381
.0112
Average
Calibrafit occasions
51;51; Heinz
Probabilityc
= = across
for
models
74 84288 65 81
purchase
293
weeks
7380
Count
of
weeks
Sample
logit
of of
comparable
those
probability
nested
.0084
.0074
.0092
.0332
.8364
.0954
.0100
number
Sample
number and
Frequency
and
173;
81; average
= =
probabilities
The
occasion
models
oz.oz.
and
32 44
logit
.1635.
oz.
average
x
andand
households
purchase
households
28
predicted
oz.oz.oz.oz.oz.
of of the
on
R2
Frequency
Because
14 28 40 64 32
.05627
oz.
Monte
make
=
purchase
32
-LL BIC
-LL
Rate
Statistics
In-samplea Out-of-sampleb
Heinz
Heinz
Heinz
Heinz
Hunt's
Del No
Efron's
aNumber
bNumber
cTo Notes:
Correctly
.0092conditional
Fit
Parameter
Predicted
Hit
3
(3)
Logit
Nested
2003
on BrandSwitching
Impactof Promotions
existence of state dependence in brand preference. The
results also show that price has a negative impact on purchase, and promotion increases the attractivenessof the
price discount, as we expected.
The coefficients for inventoryand stockoutcosts are negative and significant,as we expected. In monetaryterms,the
holding cost is equivalentto a weekly price reductionof .05/
.44 = $. 11. Given an average price of approximately$1.25
per bottle, a consumerwould be indifferentbetween a 20%
price cut ($.25) and holding a 32 oz. bottle of ketchup in
inventory for slightly longer than two weeks. This shows
much flexibility in that the consumer would be willing to
stockpilea bottle of ketchupeven if it meantit was not going
to be consumed immediately.
The estimatesof the promotionexpectationsare sensible.
The estimatedperceivedconditionalprobabilityof a promotion in period t, given that there was not a promotion in
periodt - 1, is greaterthanthe probabilityif therewas a promotion in period t - 1. The implied promotionfrequencies,
calculated as l0j/(1 + tjo - tjl), are 7.0%, 19.0%, 9.5%,
7.0%, 12.9%, and 15.7% for the six brand-sizes, respectively, which correspondnicely to the observed frequencies
in Table2 (Heinz 64 oz. is the one exception).Overall,these
results are notable:They show that the estimatedperceived
promotiontransitionprobabilitiesrecoverthe actualpromotion frequencies ratherwell. This suggests that consumers
indeed learn the promotion schedule. The correlation
between brandpreferenceand promotionresponse is positive, showing that consumers who have a higher-thanaverage intrinsic preferencefor a particularketchup brand
are also more promotion sensitive than average. Thus,
brand-loyalcustomers are more likely to adjust their purchase timing to meet the promotion schedule of their
favoritebrand.
We now focus on the purchase incidence parametersin
Model 4. The inventoryand stockoutvariablesare negative,
as we expected (though only weakly statistically significant). The positive estimate of CatValitshows that consumersare more likely to acceleratepurchaseon promotion;
the negative estimate of PromTimeitimplies that consumers
delay theirpurchaseuntil next promotionwith the belief that
the longer the time since the last promotion,the higheris the
probabilityof promotion in the next period. The CatValit
variable is standardfor nested logit models, but the PromTimeit variable is relatively new. Our results support its
inclusion as an ad hoc way to model deceleration.
Finally, the promotioncoefficient was consistentlyhigher
as we moved from the structuralmodel to Model 5 and
through to Model 1. These results are similar to our synthetic data simulation.We next turnto estimatedelasticities
and switching percentagesto determine whether the logit,
nested logit, and nondynamic structuralmodels produce
greaterswitching effects.
Estimatedelasticities and switchingpercentages. Table 5
shows the comparativeshort-termand long-term switching
elasticities and percentage breakdownof switching versus
purchase displacementfor a marginalpromotion of Heinz
28 oz. and 32 oz. in Week 11. It also reportssales elasticities when the promotionperceptionsof Heinz 28 oz. and 32
oz. are increasedby 50%.The resultsare quite similarto our
simulation in that the switching effects are consistently
higher for the logit, nested logit, logit with no-purchase
option, and static structuralmodels than for the dynamic
399
structuralmodel. The nondynamicmodels infer more brand
switching than does the dynamic structuralmodel. Given
our concerns about not taking into account consumer
rationaltiming adjustmentsand given our previous simulation results, the empiricalresults suggest that reduced-form
models overstate switching effects compared with a
dynamic structuralmodel.
It is notablethat thereis not much differencebetween the
two logit choice models or among the four reduced-form
choice/incidence models, though PromTimeseems to help.
The key seems to be the additionof purchaseincidence, but
how incidence is addeddoes not make much of a difference,
except in the dynamic structuralmodel.
The difference between the reduced-form choice/incidence models and the structural model is managerially
meaningful. The difference in short-termbrand-switching
elasticities between Model 5 and the structuralModel 7 is
.346 - .242 = .104. That means that Model 5 finds an additional 10.4%change in base probabilitiescomparedwith the
structuralmodel. Assuming a base of roughly .40 purchase
probabilityfor Heinz 28 oz./32 oz. (its marketshare) means
a difference in .104 x .40 = 4.16 sharepoints. A sharepoint
in the ketchupcategory is worth roughly $3 million dollars
in revenue,so the differencebetween these models is a matter of $12.5 million, or $240,000 per week.18The difference
between the logit choice models and the structuralmodel is
.426 - .242 = .184 x .40 = 7.4 sharepoints, or $22.1 million,
or $424,615 per week. These are manageriallymeaningful
differences (see, e.g., Abrahamand Lodish 1987).
Policy-ChangeAnalysis
Senior managersare often more interestedin evaluating
the effect of a significantchange in promotionpolicy rather
than the effect of marginalpromotion.It is in this area that
we expect the dynamic structuralmodel to distinguishitself
even more from the nondynamicmodels, because the structuralmodel explicitly takes into accountthe promotionpolicy throughthe frequencyperceptioncoefficients, n. Keane
(1997a, p. 312) states our expectations best: "To successfully forecast behavior after a regime change one needs to
model how agents tailor their decision rules to particular
regimes. One needs a so-called 'structural'model whose
parametersare 'primitives'of agents' preferences,information processing systems,... which remain fixed across
regimes."
We expect that the structuralmodel will predictless of a
gain in marketsharethanthe othermodels for the brandthat
experiences a quantum increase in promotion frequency.
This is because these models do not explicitly enable consumers to adjust their purchasetiming as a function of the
firm's overall promotionpolicy. The choice/incidence models try to achieve this by including inventory and ad hoc
variables such as PromTimeijt,but they do not do as complete a job as the structuralmodel, which models rational
consumeradjustmentsexplicitly in a dynamicprogramming
framework.
We run a simulationin which we increasethe actualpromotion frequencies of Heinz 28 oz./32 oz. by 50% and
18Source: Information Resources (1995). Volume of mustard and
ketchup per 1000 households is 5916 units; ketchupaccounts for 77% of
the category and is priced at $.73 per unit. The assumptionof 90 million
households translatesto a category sales volume of $5,916 x .77 x .73 x
90,000 = $299.3 million.
400
JOURNAL
OF
MARKETING
RESEARCH,
NOVEMBER
2003
Model
(.08)
(.01)
(.21)
(.20)
(.09)
(.12)
(.10)
(.22)
(.02)
(.005)
(.08)
(.10) (.09)
(.03)
(.09)
(.05)
(.03)
(.04)
(.08)
(.04) (.16)
(.11)
(.06)
(.10)
(.24)
(.30)
(.05)
(.02)
(.01)
(.03)
(.04)
(.03)
(.03)
(.06)
(.07)
(7)
Dynamic .11
.209
.110
.072
.34 .05 .20 .20 .15 .341.31
.98.09.10 .018 .16 .18.074
.011
.099
.054.056
.141
.173
.049
-.49 -.50
-.05 -.25
-.44
-.94 -.17 -.70
-1.13
Structural
parameter.
the
of
deviation
(.16)
(.13)
(.06) (.13)
(.08)
(.06)
(.01)
(.06)
(.22)
(.07)
(.10)
(.22) (.26)
(.29)
(.06)
(.03)
(.08)
(6)
Structural
Model .10
.29 .04 .20 .22 .15 .30(10)
.17
.08
.98
-.51 -.58 1.41
-.40
-.97 -.20 -.80
-1.17
Static
(.07)
standard
.16
estimated
the
is
No(.07)
(.05)
(.08)
(.02)
(.29)
(.10)
(.29)
(.14)
(.15)
(.03)
(.02)
(.007)
(.08) (.07)
(.14)
(.07) (.22)
(.10)
(.08)
(.33)
(.08)
(.07)
(.09)
(.07)
(.07)
Alternative
with
(5)
.33 .06 .23 .28 .17 .401.76
.55.19.08 .010 .09 .17
.16
-.06 -.11
-.47
-.14 -.86 -1.10-.50 -.64
Logit
-1.05
Purchase
.36.17
(.01)parentheses
(.02)
in
.03
-.08 not
is
that
it
DATA
beneath
with
4
(.07)
(.12)
(.06) (.06)
(.002)
(.29)
(.13)
(.02)
(.01)
(.05)
(.04)
(.09)
Logit(4)
KETCHUP
.17
.05 .54 .04 .01.63.27
PromTime
-.46
-.16 1.49 -.07 -.21
Nested
WITH
(.19)
(.22)
(.08)
(.05)
(.08)
.58.22.08
1.86
.13
(.19)
(.03)
(.02)
(.07)
(.08)
(.02)
(.02)
(.11)
(.04)
(.08)
(.07)
(.05)
number
.27.11.54.22.19.09 .04 .03 .04 the
-.05 -.06 -.06
Table
parameter;
(3)
Logit
ESTIMATION
Nested
(.12)
(.02)
(.08)
(.22)
(.06)
(.06) (.07)
(.32)
(.01) (.04)
(.01)
(.15)
(.14)
.57 .04 .09.61.25(.07)1.89
.45.24.09(.04)
.051.51
.19
-.08 -.19(.06)
-.51
-.17
(.03)
(.21)
(.07) (.04)
(.02) (.13)
(.10)
.13
.52.23.18(.06)
.25(.07)
.12(.05)
.07 .03 .04
-.04 -.08(.09)
the
of
value
mean
MODEL
with
(.002)
(.12)
(.006)(.03)
(.03)
(.09) (.05)
(.21)
(.01)
(.32)
(.18)
(.07)
.60 .02 .07 .19(.11) .54.31.11
.20
.021.43
-.59(.12) -.14
-.05 -.17(.05)
-.37(.11) 2.36
Logit
Correlation
(2)
(1)
Logit
(.002)
(.27)
(.14)
(.009)
(.005)(.02)
(.10) (.03)
(.18)
.23
-.61
(.09)
estimated
.15
the
is
estimates.
various
parentheses
in the
of
not
(.31)
(.19)
(.07)
(.07)
.01 .62 .02 .06 .20(.11) .67.33.16
-.12 1.48 -.05 -.15(.04)
-.39(.12) 2.40
errors
number
top
standard
the
the
(6)
(2) (3)
oz. oz.
32 44
oz.
32
and
p
are
30o
brand
promotion
PI
a5
parameter,
P2
rate
(1) and and (4) (5) oz.
cost a6
28 a3
each
P5
and
parentheses
value 33 4
preference
oz. oz. oz. oz. oz.
between
a4
Incidence
in
For
cost
14 28 40 64 32
Monte
preference
purchase inventory
1
Inventory
Stockout
PromTime
Notes:
Hunt's
Consumption
Heinz
Heinz
Del
Category
Category
HeinzHeinz
preference
t6o
t61 Purchase
t41ts0 7t51
Numbers
Brand
Last Promotion
Unit Stockout
7E40.071
Correlation
'tlo~1720721730
7E31
Parameter
Price-axl
a2
on BrandSwitching
Impactof Promotions
assume that perceived promotionfrequencies also increase
by that amount in the dynamic structuralmodel (t20 and
Given that the base promotionfrequencyis 19%for
c21).-19
Heinz 28 oz./32 oz., we randomly select 10% more of the
weeks when therewas no promotion,assume thattherewere
promotionsrunningin those weeks, and calculate the predicted percentagechange in Heinz 28 oz./32 oz. sales. The
results in Table 5 confirm our expectations. The logit and
nested logit models all predict substantially greater
increasesin sales thanthe dynamicstructuralmodel, and the
results are even more dramaticthan those for a marginal
additionalpromotion.The predictedsales changes for Heinz
28 oz./32 oz. are more than double for the nonstructural
models compared with the dynamic structuralmodel. For
example, the nested logit model with PromTimepredicts a
19.1% increase in sales, whereas the structuralmodel predicts only an 8.5% increase.
The results suggest that reduced-form models significantly overestimatethe effectiveness of a policy increase in
promotionfrequencybecause they do not explicitly enable
consumersto adjusttheir purchasetiming strategiesrationally in response to the new regime, and they assume the
same promotionsensitivities hold for the new regime.
Limitations
As we noted in the model development section, we
assume a simple mechanism for consumers' future price
expectations. We focused on expectations of promotions;
notably, regular price variations were quite modest (see
"Model Specification").Therefore,we resortedto a simplifying assumptionto enhancethe computationalfeasibility of
our model. Erdem,Imai, and Keane (2003) and Hendel and
Nevo (2002) systematically examine the price expectation
process. A comprehensive specification of both price and
promotionexpectationsis desirable,particularlywhen analyzing a category in which price fluctuationsare considerable. We hope to address this issue in a future research
effort.
We also implicitly assume that consumersexpect promotions to be independentacross alternatives.Erdem, Imai,
and Keane (2003) and Hendel and Nevo (2002) find thatthe
promotionsacross alternativesmay be correlated.A simple
pairwiseempiricalanalysis shows thatonly 5 of the 15 average within-storecorrelationsamong our six brand-sizesare
significantlydifferentfrom 0. The magnitudeof the significant ones ranges from -.16 to .27. As partof increasingthe
sophisticationof consumer expectations,we might select a
higher-orderMarkov model that allows for covariation in
promotions across alternatives.This would complicate the
model development significantly; however, it would be a
worthytopic for furtherresearch.In the interim,we conjecture that any better specification of consumer expectations
should strengthenthe findings reportedhere. As consumers
hold more sophisticatedexpectations of the firms' promotional strategies,they will become more adept at adjusting
theirpurchasetiming, which increasesthe need for dynamic
19Notethatwe assume thatconsumerslearnthe new scheduleand update
their frequency perceptions (it). The consumer may not be perfectly
informed of the policy change. Because our article focuses more on how
consumers adjustpurchasegiven their perceptionson promotionschedule
than on how they form promotionperceptions, we make this assumption
and leave perceptionformationfor furtherresearch.
401
rational models to unravel purchase-timingdecisions from
brandswitching.
Finally, we have assumed that the consumption rate is
deterministic.As a result, the advent of a stockout is deterministic. This happensbecause our model predictsthe same
choices for householdswith identicalpurchasehistoriesand
holds taste parametersconstant.This may result in a bias in
elasticities (for details, see Erdem, Imai, and Keane 2003).
With six alternatives,the possibility of identical purchase
histories should decrease as the purchasehistory increases.
Given the long historyfor each household in our model, we
believe that the bias arisingfrom deterministicconsumption
should be minimal.
SUMMARYAND DISCUSSION
The themes of this article are that logit decision models
can overestimate the extent of promotion-inducedbrand
switching because they do not completely account for consumers' rationaladjustmentsin purchasetiming and that a
dynamicstructuralmodel can addressthis problem.We have
investigatedthis thesis by developing a dynamic structural
model of choice and incidence and comparing it with a
stand-alone logit choice model, a nested logit model with
incidence, a logit model with a no-purchasealternative,and
a static version of the dynamic model. The dynamic model
differs from these reduced-formstatic models by explicitly
modeling the process by which consumersdecide what and
when to purchase,taking into account their currentinventory status and their perceptionsof future promotionactivity. Our key findings are as follows:
*Ina simulation
thatusesdatagenerated
model,
by thestructural
the reduced-form
modelsconsistentlyoverpredicted
switching
elasticitiesandthepercentage
of thepromotion
salesbumpdue
to brandswitching.
*Thestructural
modelfits thedatabetterthanthereduced-form
choice/incidence
models.
models,includingthereduced-form
*Inestimatingthesemodelson realdatafor the ketchupcategory,we observedthesamepatternof estimatedelasticitiesand
thatwe foundin thesimulation.
switchingpercentages
*Inevaluating
thetotaleffecton salesof a 50%increasein promotionfrequency,the reduced-form
modelspredictedmuch
model.
highersalesgainsthanthedynamicstructural
The results suggest that, as we expected, reduced-form
models overstatethe brand-switchingeffects of promotion.
All four analyses contributeto this conclusion.Forexample,
the simulationconvinces thatthe reduced-formmodels overstate elasticities on simulateddata,but there is no guarantee
thatthe simulateddata,based on the structuralmodel, reflect
reality.The betterfit of the dynamicstructuralmodel on real
data, togetherwith its sensible coefficient estimatesand our
observationof the same patternin estimated elasticities in
real data, suggests that the simulation reflects reality well
and that the higher switching effects by the logit models in
the empirical test are truly overstated.The policy analysis
drives home the point that the real gain from the structural
model is in evaluatingmajorpolicy changes, because that is
an areain which the model's explicit accountingfor the current promotionpolicy works to advantage.
As we expected, in all our analyses, the stand-alonelogit
model exhibits the most bias. Much, though not all, of the
bias can be alleviated by estimating nested logit models
with incidence; at least these models try to attain similar
402
JOURNAL
OF MARKETING
RESEARCH,
3.59
Model
(7)
Dynamic
(.045)(.007)
56%
44%
.242 .074
Structural
(6)
Structural
Model
and
(.0017)elasticities.
3.44,
.085
2.92,
2.69,
policy-change
for
3.03,
(.040)
3.80
3.81,
.190 and
(.052)(.006)
N.A.
.333 .099
Static
3.49,
3.75,
are
3.57,
No(.066)
Alternative
with
(5)
Logit
Purchase
77%
23%
.346 .109(.026)
with
(.067)
26%
74%
PromTime .347 .108(.023)
Nested
Logit(4)
5
(.070)
(3)
Logit
Nested
ELASTICITIES
79%
21%
.378 .117(.028)
t-values
(.038) 3.23,
The
.190 3.08,
Heinz.
4.06,
for
4.01,
t-tests
and
(.031)
.191
performed
elasticities;
we
promotion
(.026)
significant,
.196
Table
marginal
statistically
are
7 long-term
for
(.040)
Model
3.47
.235 andand
6
...,
2 3.53,
1,
= 2.48,
m
(.041) 2.08,
PROMOTION
with
(.064)(.031)
N.A.
Logit
Correlation .426 .135
(2)
(.062)(.033)
N.A.
.431 .137
(1)
Logit
.253
Model
2.81,
2.37,
between
50%
by
11
Week
in
effect
2.88,
difference
Heinz
of
elasticities;
sales
(ir)
elasticities
promotion
oz. the
oz. oz.
aggregatepromotion
elasticity
elasticity
Heinz
32 32
parentheses.
of 32
Perception
of
in
and
and andshort-term
whether
are
oz.
oz.switching
oz.of displacement
marginal
change
switching
test
switching
28
28 28
PromotionTo errors
Promotion
PurchaseHeinz
HeinzHeinzBrand
short-term
Short-term
Breakdown Percentage
Notes:
Long-term
Increased forStandard
Scenarios
Marginal
NOVEMBER
2003
on BrandSwitching
Impactof Promotions
phenomena as the structuralmodel by including variables
such as PromTimeas a means to model consumers'holding
out for the next promotion.They can also account for loyal
consumers' taking most advantage of promotions. These
steps improvethe elasticities and sales predictionsbut not as
completely as does the dynamic structuralmodel.
We have also learned the following from the particular
coefficients and results of our empiricalstudy:
aremorelikely
withintrinsically
*Consumers
higherpreference
fortheirpreferred
brand.
to takeadvantage
of a promotion
*Consumers
appearto haveaccurateperceptionsof promotion
frequencyin that our estimatedparametersfor promotion
well to actualpromotion
expectations
corresponded
frequency.
is a realphenomenon,
as exhibitedmostdirectly
*Deceleration
variable.
by the significanceof thePromTime
fits the data
*A dynamicstructural
modelof choice/incidence
betterand performsbetteron holdoutdata testingthan do
modelsthatattemptto coverthe samephenomreduced-form
ena.Thissuggeststhattheeffortof runningconsumersthrough
a dynamicprogrampaysoff in betterfit andprediction.
Our findings have several important implications for
researchers.First,the choice promotion-elasticityestimates
derived from reduced-formmodels, especially stand-alone
logit models, shouldbe interpretedwith caution.These elasticities are probablyoverstated.Second, researchersshould
devote more attentionto dynamicstructuralmodels. We perceive movement in this direction (Erdem, Imai, and Keane
2003; Erdem and Keane 1996; G6ntil and Srinivasan1996;
Sun 2000) and encourageresearchin this area. The cost of
computationfor these models is high, but with improved
computing power they are becoming more practical.That
the benefit of these models is relevant to managers (i.e.,
more accuratepredictionsof brandswitching and sales levels) should spur the movement even more. Third, in the
event that a researcheris unable to estimate a structural
model, the next best model is an ad hoc choice/incidence
model that includes variables such as PromTime. These
variables are statistically important and help improve
switching elasticity estimates. Fourth,our results encourage
theoreticalresearchthatemphasizespurchasedynamics as a
reason for promotion(see Blattberg,Eppen, and Lieberman
1981). There is a need for additionaleconomic models that
examine the effects of dynamic rationalconsumerbehavior
on promotionpolicy in a competitiveframework.
MANAGERIAL
IMPLICATIONS,
CONCLUSION,AND
FURTHERRESEARCH
First,promotionsmay be more of a purchase-timinggame
than a brand-switchinggame, as was previously believed.
This is consistent with recent research that has shown the
importanceof stockpiling and deceleration (Bell, Chiang,
and Padmanabhan1999; Kopalle, Mela, and Marsh 1999;
Mela, Jedidi, and Bowman 1998; Seetharaman,Ainslie, and
Chintagunta1998; van Heerde, Gupta, and Wittink 2003;
van Heerde, Leeflang, and Wittink2000).
Second, managersshouldbe cautiousof panel data-based
simulationsof forecastedchanges in sales due to majorpolicy changes, if the forecastingmodels do not explicitly take
into account how consumers will adjust to the new policy.
Such forecasts may be overoptimisticbecause they do not
consider how consumers will adjust to the policy change.
403
For example, if relianceon promotionis doubled,manyconsumers who formerly bought at regularprice will structure
their buying habits to purchase during promotions.These
are not truly incrementalsales.
Third, because loyal customers are more likely to purchase on promotionby adjustingpurchasetiming, manufacturersshould find ways to distinguishloyal customersfrom
nonloyal customers and target the latter for promotion
effort.
Fourth,because consumerrationalpurchasestrategiescan
have a negative impact on profit, manufacturersshould find
ways to discourage consumers from taking advantage of
promotionby adjustingpurchasetiming. For example, specifying the maximum numberof units purchasedon promotion can increasethe promotioneffect of attractingnew purchases switched from other brands or other stores but can
limit stockpilingbehavior.
Although our results are quite encouraging, there are
remaining issues that suggest topics for further research.
First, it would be worthwhile to find reduced-formmodels
that capturethe incidence and choice process as well as the
structuralmodel. We believe this would be possible if the
reduced-formmodels contained the correct variables; for
example, promotion frequency could be incorporated
directly in the model (see Kopalle, Mela, and Marsh 1999).
Second, as we mentioned previously, we can relax the
assumptionthat consumptionis constant.For some product
categories, promotionalso has a significant impact on consumption rate, which contributesto the incrementalsales
increase that promotion induces (for a structuralmodel in
which consumers endogenously decide how much to consume, see Sun 2003). Third,it would be beneficialto examine profit. Promotion causes brand switching, which contributes positively to profit; however, promotion induces
purchaseaccelerationor decelerationand stockpiling,which
may contributenegatively to profit. What promotionstrategy can balance these considerationsin the presence of a
consumer who will rationallyadjustto any policy change?
Fourth, as we also mentioned previously, regular price
expectationsand promotiondepth as well as promotionfrequency could be modeled. This would add complexity
because of the additionalcontinuousstatespace variableand
is unlikely to change our basic result. However,the added
insight of distinguishing between promotion and price
would be important.Relatedly,ratherthan treatthe promotion schedules as independent,furtherresearchcould incorporate dependencies.Fifth, it would be especially useful to
model the process by which consumers learn promotion
schedules. This would enhancethe message from our Lucas
critique simulation, which, for the sake of illustration,
assumed that consumersreadily learnedthe new promotion
schedule. Finally, estimates of brandswitching are at least
indirectly related to the problem of estimating the "postpromotiondip" (e.g., Neslin and Stone 1996). The structural
model we develop, embellished,for example, by incorporating endogenous consumption, the number of units purchased, and transactioncosts, would be useful for identifying the key factors that mask the postpromotiondip.
Although we demonstrate the merit of the structural
model, we must recognize some of the limitations of the
approach.These models pose difficultestimationchallenges
that necessitate simplifying assumptions. More important,
JOURNALOF MARKETING
RESEARCH,NOVEMBER2003
404
developing and estimatingsuch a model may be beyond the
reach of most practitioners.Therefore,managersmay continue to rely on reduced-formmodels that are far simpler to
estimate. By developing several reduced-formmodels for
comparisonpurposes, we offer guidance for specifications
that might alleviate, at least partially,the potentialbias for
overestimatingthe impactof promotionon brandswitching.
In conclusion, this researchprovidesencouragingsupport
that more accurateestimates of brand-switchingelasticities
can be obtainedby incorporatingforward-lookingconsumer
behavior into structural models. This calls for further
researchprojectsin this area.As the buying public becomes
more and more informedabout prices and shopping issues,
we believe that taking into account the rational consumer
(Keane 1997b) will become more importantin evaluating
the effectiveness of sales promotions.
REFERENCES
Abraham, Magid M. and Leonard M. Lodish (1987), "PROMOTER:An AutomatedPromotionEvaluationSystem,"Marketing Science, 6 (2), 101-123.
Ailawadi, Kusum L., Karen Gedenk, and Scott A. Neslin (1999),
"Heterogeneityand PurchaseEvent Feedback in Choice Models: An EmpiricalAnalysis with Implicationsfor Model Building," InternationalJournal of Research in Marketing, 16 (3),
177-98.
and Scott A. Neslin (1998), "The Effect of Promotionon
Consumption:Buying More and ConsumingIt Faster,"Journal
of MarketingResearch, 35 (August), 390-98.
Allenby, Greg M. and Peter E. Rossi (1991), "QualityPerceptions
and Asymmetric Switching Between Brands,"Marketing Science, 10 (3), 185-204.
Amemiya, Takeshi (1985), Advanced Econometrics. Cambridge,
MA: HarvardUniversityPress.
Assunqdo,Jodo L. and RobertMeyer (1993), "TheRationalEffect
of Price Promotionson Sales and Consumption,"Management
Science, 39 (5), 517-35.
Bell, David R., Jeongwen Chiang, and V. Padmanabhan(1999),
"The Decomposition of Promotional Response: An Empirical
Generalization,"MarketingScience, 18 (4), 504-526.
Ben-Akiva, Moshe and Steven R. Lerman(1985), Discrete Choice
Analysis. Cambridge: Massachusetts Institute of Technology
Press.
Blattberg,Robert C., Gary Eppen, and Joshua Lieberman(1981),
"ATheoreticaland EmpiricalEvaluationof Price Deals for Consumer Nondurables," Journal of Marketing, 45 (January),
116-29.
Bucklin, Randolph E., Sunil Gupta, and S. Siddarth (1998),
"Determining Segmentation in Sales Response Across Consumer PurchaseBehaviors,"Journal of MarketingResearch, 35
(May), 189-97.
Chang, Kwangpil, S. Siddarth,and Charles B. Weinberg(1999),
"The Impact of Heterogeneity in Purchase Timing and Price
Responsiveness on Estimates of Sticker Shock Effect,"Marketing Science, 18 (2), 178-92.
Chiang, Jeongwen (1991), "A Simultaneous Approach to the
Whether,What, and How Much to Buy Questions,"Marketing
Science, 10 (4), 297-315.
(1995), "Competing Coupon Promotions and Category
Sales,"MarketingScience, 14 (1), 105-122.
Chintagunta, Pradeep K. (1993), "InvestigatingPurchase Incidence, Brand Choice, and Purchase Quantity Decisions of
Households,"MarketingScience, 12 (2), 184-208.
, Dipak C. Jain, and Naufel J. Vilcassim (1991), "Investigating Heterogeneityin Brand Preferencesin Logit Models for
Panel Data," Journal of MarketingResearch, 28 (November),
417-28.
Erdem,Tilin, SusumuImai, and Michael P. Keane (2003), "Brand
and Quantity Choice Dynamics Under Price Uncertainty,"
QuantitativeMarketingand Economics, 1 (1), 5-64.
and Michael P. Keane (1996), "Decision-Making Under
Uncertainty: Capturing Dynamic Brand Choice Processes in
TurbulentConsumer Goods Markets,"Marketing Science, 15
(1), 1-20.
and Baohong Sun (2002), "An EmpiricalInvestigationof
the Spillover Effects of Advertising and Sales Promotions in
Umbrella Branding," Journal of Marketing Research, 39
(November),408-420.
Golabi, Kamal (1985), "OptimalInventoryPolicies When Ordering Prices Are Random,"OperationsResearch, 33 (3), 575-88.
Gtntil, Fusun and KannanSrinivasan(1993), "ModelingMultiple
Sources of Heterogeneity in Multinomial Logit Models:
Methodologicaland ManagerialIssues,"MarketingScience, 12
(3), 213-29.
and
(1996), "Impactof ConsumerExpectationsof
Coupons on Purchase Behavior,"Marketing Science, 15 (3),
262-79.
Guadagni,Peter M. and John D. Little (1983), "A Logit Model of
BrandChoice Calibratedon ScannerData,"MarketingScience,
2 (3), 203-238.
Gupta, S. (1988), "Impactof Sales Promotions on When, What,
and How Much to Buy," Journal of Marketing Research, 25
(November),342-55.
Hanemann,W. Michael (1984), "Discrete/ContinuousModels of
ConsumerDemand,"Econometrica,52 (3), 541-61.
Heckman, J. (1981), "Heterogeneityand State Dependence," in
Studies in Labor Markets,S. Rosen, ed. Chicago: University of
Chicago Press, 91-139.
Helsen, Kristianand David C. Schmittlein(1992), "Some Characterizationsof StockpilingBehaviorUnder Uncertainty,"Marketing Letters,3 (1), 5-17.
Hendel, Igal and Aviv Nevo (2002), "Measuringthe Implications
of Sales and Consumer,"working paper,University of California, Berkeley.
Information Resources Inc. (1995), IRI Marketing Factbook.
Chicago: InformationResources.
Kamakura,WagnerA. and GaryJ. Russell (1989), "AProbabilistic
Choice Model for Market Segmentation and Elasticity Structure,"Journal of MarketingResearch, 26 (November),379-90.
Keane, Michael P. (1993), "SimulationEstimationfor Panel Data
Models with LimitedDependentVariables,"in Handbookof Statistics, G.S. Maddala,C.R. Rao, and H.D. Vinod, eds. New York:
Elsevier Science Publishers.
(1997a), "CurrentIssues in Discrete Choice Modeling,"
MarketingLetters,8 (3), 307-322.
(1997b), "ModelingHeterogeneityand State Dependence
in ConsumerChoice Behavior,"Journal of Business and Economic Statistics, 15 (3), 310-27.
and KennethI. Wolpin(1994), "Solutionand Estimationof
Dynamic ProgrammingModels by Simulation,"Review of Economics and Statistics,"76 (4), 648-72.
Kopalle, Praveen K., Carl F. Mela, and Lawrence Marsh (1999),
"TheDynamic Effect of Discountingon Sales: EmpiricalAnalysis and NormativePricing Implications,"MarketingScience, 18
(3), 317-32.
Krishna,Aradhna (1992), "The Normative Impact of Consumer
Price Expectationsfor Multiple Brands on ConsumerPurchase
Behavior,"MarketingScience, 11 (3), 266-87.
(1994a), "The Effect of Deal Knowledge on Consumer
PurchaseBehavior,"Journal of MarketingResearch, 31 (February), 76-91.
(1994b), "The Impact of Dealing Patterns on Purchase
Behavior,"MarketingScience, 13 (4), 351-73.
Imran C. Currim, and Robert W. Shoemaker (1989),
,
"ConsumerPerceptions of Promotional Activity," Journal of
Marketing,55 (April), 4-16.
on BrandSwitching
Impactof Promotions
Lucas, Robert,Jr. (1976), "EconometricPolicy Evaluation:A Critique," in The Phillips Curve and Labor Market, CarnegieRochester Conference on Public Policy Series, Vol. 1, Karl
Brunnerand Allan H. Meltzer, eds. New York:AmericanElsevier, 19-46.
McFadden,Daniel (1989), "A Method of Simulated Moments for
Estimation of Discrete Response Models Without Numerical
Integration,"Econometrica,57 (5), 995-1026.
Mela, Carl F., Kamel Jedidi, and Douglas Bowman (1998), "The
Long-Term Impact of Promotions on Consumer Stockpiling
Behavior,"Journalof MarketingResearch, 34 (May), 248-61.
(1990), "The Optimalityof
Meyer, Robert J. and Joo
Assunq.o Marketing Science, 9 (1),
Consumer Stockpiling Strategies,"
18-41.
Mulhern, Francis J. and Robert P. Leone (1991), "ImplicitPrice
Bundlingof Retail Products:A MultiproductApproachto Maximizing Store Profitability,"Journalof Marketing,55 (October),
63-76.
Neslin, Scott A., Caroline Henderson, and John Quelch (1985),
"ConsumerPromotions and the Acceleration of Product Purchases,"MarketingScience, 4 (3), 147-65.
405
and Linda G. Schneider Stone (1996), "ConsumerInventory Sensitivity and the PostpromotionDip,"MarketingLetters,
7 (1), 77-94.
Pakes, Ariel (1986), "Patentsas Options: Some Estimates of the
Value of Holding European Patent Stocks," Econometrica, 54
(4), 755-84.
Seetharaman,P.B., Andrew Ainslie, and Pradeep K. Chintagunta
(1999), "Investigating Household State Dependence Effects
Across Categories," Journal of Marketing Research, 36
(November),448-500.
Sun, Baohong (2003), "PromotionEffect on Endogenous Consumption,"workingpaper,Kenan-FlaglerBusiness School, University of North Carolina.
van Heerde, HaraldJ., Sachin Gupta,and Dick R. Wittink(2003),
"Is 75% of the Sales PromotionBump Due to BrandSwitching?
No, Only 33% Is,"Journal of MarketingResearch,40 (November), 481-91.
, Peter S.H. Leeflang, and Dick R. Wittink (2000), "The
Estimation of Pre- and PostpromotionDips with Store-Level
Scanner Data," Journal of Marketing Research, 37 (August),
383-95.