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Promotion Effect on Endogenous Consumption

Author(s): Baohong SunSource: Marketing Science, Vol. 24, No. 3 (Summer, 2005), pp. 430-443Published by: INFORMS

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romotion E f f e c t o

Endogenous onsumption

BaohongSunTepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue,

Pittsburgh, Pennsylvania 15213, [email protected]

Marketing ScienceVol. 24, No. 3, Summer 2005, pp. 430-443

issn 0732-23991 issn 1526-548X1 5 12403 10430

M

doi 10.1287/mksc.l040.0110©2005 INFORMS

the years,researchershave found that promotionmakes consumersswitch brandsand purchaseear-lier or more.However,it is unclearhow promotionaffectsconsumption,especiallyfor product categories

thatareperceivedto be versatileand substitu able.In this paper,we proposea dynamicstructuralmodel with

endogenousconsumptionunderpromotionuncertainty o analyze the promotioneffect on consumption.This

model recognizesconsumersas rationaldecisionmakerswho formpromotionexpectationsand plan theirpur-chase and consumptiondecisions in light of promotionschedule. Applying the proposedmodel to packagedtunaand yogurt,we find that endogenousconsumption respondsto promotionas a resultof forward-lookingand stockpilingbehavior.This is the firstempiricalpaperthat recognizesconsumptionas an endogenousdeci-

sion variableand proposes a structuralmodel to offer behavioralexplanationson whether,how, and whypromotionencouragesconsumption or product categorieswith flexibleconsumption.

Keywords:promotion;consumption;categoryexpansion;dynamicstructuralmodel;forward-lookingconsumers

History:Thispaperwas receivedJuly21, 2003,and was with the authors 8 months for 2 revisions;processed

by TulinErdem.

1. IntroductionDoes consumption respond to promotion? Manystudies have focused on the effects of promotionon

brand switching, purchasequantity,and stockpilingand have documented that promotion makes con-

sumersswitch brandsand purchaseearlieror more.1

The consumers'consumptiondecision has long been

ignored, and it remains unclear how promotionaffectsconsumption(Blattberget al. 1995).Conven-

tional choice models cannotbe used to address this

issue because many of these models assume con-

stant consumptionrates over time (usually defined

as the total purchasesover the entire sample peri-ods divided by the number of time periods). While

this assumptioncan be appropriatefor some prod-uct categoriessuch as detergentand diapers,it mightnot hold for many other product categories, such

as packaged tuna, candy, orange juice, or yogurt.For these categories,promotion can actually stimu-

lateconsumption n additionto causingbrandswitch-ing and stockpiling.Thus,forproductcategorieswith

a varyingconsumptionrate,it is criticalto recognize

the responsivenessof consumption to promotioninorder to measure the effectiveness of promotiononsales moreprecisely.

Emerging literature in behavioral and economic

theory has provided supporting evidence that con-

sumptionfor some

product categories respondsto

promotion.Using an experimentalapproach,Wansink

(1996)establishesthat significantholding costs pres-sure consumers to consume more of the product.Wansinkand Deshpande (1994)show that when the

product is perceived as widely substitutable,con-sumers will consume more of it in place of its closesubstitutes.They also show that higher perishabilityincreases consumption rates. Adopting scarcitythe-

ory,Folkeset al. (1993)show that consumerscurb con-

sumptionof productswhen supply is limited because

they perceive smaller quantities as more valuable.Chandon and Wansink(2002) show that stockpilingincreasesconsumptionof high-convenienceproducts

more than that of low-convenience products. In ananalytical study, Assuncao and Meyer (1993) showthatconsumptionis an endogenous decisionvariabledriven by promotionand promotion-inducedstock-

piling resultingfromforward-lookingbehavior.In this paper,we develop a forward-looking truc-

tural model that recognizes consumers as rationaldecision makers who plan their future purchasesand consumptionto coincide with promotionsched-ules. Optimal consumption decisions are made in

light of inventoryand promotionin both currentand

1For disaggregate models, see Guadagni and Little (1983), Gupta

(1988), Bucklin and Lattin (1991), Chintagunta (1993), Krishna

(1994b), Chiang (1995), Bucklin et al. (1998), Bell et al. (2000),

Seetharaman (2003), Neslin et al. (1985), Mela et al. (1998), and

Kopalle et al. (1999), among others. For aggregate models, see Mela

et al. (1998a, b), Kopalle et al. (1999), Dekimpe et al. (1999), Paapand Franses (2000), Nijs et al. (2001), and Pauwels et al. (2002),

van Heerde et al. (2004), Pauwels and Srinivasan (2004), etc.

430

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Sun: PromotionEffecton EndogenousConsumption

Marketing cience24(3),pp. 430-443,©2005 INFORMS 431

futureperiods. This is the first empirical paper that

recognizes consumptionas an endogenous decisionvariable and proposes a structural model to offerbehavioralexplanationson whether, how, and why

promotionencouragesconsumption.2Applying our model to packagedtuna and yogurt

data,ouranalysisshedsnew insightson the followingissues, which cannotbe addressedby previous mod-els with fixed or exogenousconsumptionrates.First,how does endogenous consumptionreact to promo-tion? Managersare interested in the circumstancesin which categoryexpansionoccurs and the reasonsbehind these situations(Blattberg t al. 1995).Second,if there is a positive relationshipbetween consump-tionand promotion,how is this relationshipmodified

by productand promotion-related ariables,such as

holding costs and promotionuncertainty?This pro-vides

importantmplications

ormanagers o promotethe appropriateproductcategoryin a more effective

way.Third,how to quantifythe importanceof a con-

sumption increase relative to brand switching and

stockpiling?Suchan understandingwill allow a man-

ager to promote the brand that will cause the least

brand switching and purchasedisplacementbut the

greatestconsumption ncrease.Fourth,as an applica-tion, can the proposed model be adopted to explainthe absenceof a postpromotion ip?

2. LiteratureExaminingconsumers'optimalpurchase,stockpilingor consumptionbehavior under price or promotionuncertaintyhas attractedincreasing attention fromtheoreticalresearchers see Golabi 1985, Meyer and

Assuncao1990,Helsen and Schmittlein1992,Krishna

1992).Assuncao and Meyer (1993) advance existingtheoretical rameworkby allowingconsumer'srate of

consumption o be a decisionvariable.Theyconclude

thatconsumptionshould rationally ncreasewith the

size of existinginventories.Ho et al. (1998)show that

the averageoptimalconsumptionrate increaseswith

price fluctuation.Bell et al. (2002)show that flexible

consumptioncauses more intense price competition.

Althoughthese papers provide importanttheoretical

justifications or forward-lookingpurchasebehaviorand

promotioneffect on

consumption,their norma-

tive conclusionsneed to be empiricallytested.

There are some recentempiricalpapersaddressingthe promotioneffect on consumerstockpilingbehav-ior under price or promotionuncertainty.Erdem andKeane(1996)and Gonul and Srinivasan(1996)estab-

lish thatconsumers are forwardlooking.Erdemet al.(2003)explicitlymodel consumers'expectationsaboutfuture prices with an exogenous consumption rate.In their model, consumers form future price expec-tations and decide when, what, and how much to

buy.3Sun et al. (2003)demonstratethat ignoringfor-ward looking behavior leads to an overestimationof promotion elasticity.4However, the frameworks

developed in these papers cannot be adopted to

study promotioneffect on consumptionbecausetheyassume constant orexogenousconsumption,which is

independentof promotion.5The only published empirical paper that studies

the promotioneffect on consumption s Ailawadi and

Neslin (1998),which adopts nested logit model andestablishesa positive statisticalrelationshipbetween

consumption and inventory. Compared with theirreduced formapproach,our proposeddynamicstruc-tural model with endogenous consumption decisionunder promotion uncertainty offers several advan-

tages to study the promotioneffect on consumption:(1) It treats both promotion and inventory as state

2Althoughthe importanceof empirically esting how promotion

encouragesendogenous consumptionhas long been recognized

(e.g.,Neslinand Stone1996), t remainsa challenging askin terms

of both modeling and computation.Endogenizingconsumption

requires hat the optimizationproblembe solved for optimalcon-

sumption.In a dynamicmodel, optimalconsumptionneeds to be

solved over multiple periods of time. With multiple brandsand

quantitydecisions, he curse of dimensionality f endogenouscon-

sumption n dynamicprogrammingstimationsbecomescomputa-

tionallyvery intensive.

3Erdemet al. (2003)develop several novel componentsin their

model, such as household'susage rate,fixed cost associatedwith

purchase, nventorycost, and comprehensiveprice process.These

componentsallow them to provide detailed behavioralexplana-tions on consumerbrandandquantitychoicedynamicsunderprice

uncertainty.Consumptions assumed to be exogenouslygiven.Dif-ferent rom theirpaper, he focus of our study is to investigatehow

endogenousconsumptionresponds o promotion,an issue that has

never beenexaminedbefore.To focus on endogenousconsumption,we do not include all the novel componentsfromtheirpaperbut

instead follow Gonul and Srinivasan 1996)and Sun et al. (2003)in modelinginventoryandprice process.Thissignificantly educesthe computationalburden and offers us the flexibilityto endoge-nize consumption.4Sun et al. (2003)study whether brand switching elasticities are

overestimatedf consumers'stockpilingbehavior s ignored.Theyassumeconsumptionrate is exogenousand constant.On the con-

trary,this paper establishesthat consumers make strategiccon-

sumptiondecisionsin responseto promotion.5There s a recentworking paperby Hendeland Nevo (2002),who

proposea dynamicmodel of purchaseand consumptiondecisions.

Theyassume that consumers olvea dynamicquantitychoiceprob-lem and thenseparately olve a staticbrandchoiceproblem,which

breaks down when there is consumerheterogeneity. n addition,

they assumethatthe price processof differentbrands s described

by a single categorypriceindex,which fails when differentbrands

have differentprice processesand cannotbe used to conductpol-icy simulations n which one brand alters its pricing.The focus of

theirpaper s to show thatprice elasticitycan be significantly ver-estimatedif we ignore dynamics.On the contrary,n our model,consumerssolve a jointquantityand choiceproblem.Weincorpo-rate unobservedheterogeneityand allow price processto be differ-ent acrossbrands. Most importantly, ur focus is on endogenousconsumptionrather hanpriceelasticity.







Sun: PromotionEffecton EndogenousConsumption432 Marketing cience24(3),pp. 430-443,©2005 INFORMS

variables driving a sequence of endogenous purchaseand consumption decisions; (2) it provides behav-

ioral explanations on not only whether consumptionvaries with respect to promotion, but also why (e.g.,

promotion-induced stockpiling) and how (e.g., thepromotion-consumption relationship increases with

holding cost and decreases with promotion uncer-

tainty) it occurs; and (3) it provides more reliable sim-

ulation results because it is not subject to the Lucas

critique that parameters estimated using reduced

form models are not robust to policy change.

3. Dynamic Model with EndogenousConsumption under Promotion

Uncertainty3.1. Model Setup

3.1.1. Consumption Utility. Suppose consumers

/ = 1,...,/ visit stores on a periodic (e.g., weekly)basis for t = 1, . . . , T. In the store, there are ; = 1, . . . , /

competing brand choices in addition to the default

nonpurchase choice ; = 0. Each consumer observes

prices and promotions for all the competing brands in

a product category of interest.6 At each time period,consumer i decides which brand ; to purchase and

how much to consume. For each brand ;, the con-

sumer can choose among a discrete set of available

quantities q. We assume that household / has the fol-

lowing per period utility function at time t:7

J

Ut=E<l>j(Cjt-yclt) + aZt, (1)7=1

where c;, is the quantity of consumption of the focal

category for brand ;, and Zt is the quantity of all

other goods consumed in week t. The parameter a

measures the benefit from consuming the compositeof other goods. The parameter 0y represents the unit

consumption benefit associated with brand ; for con-

sumer /. The parameter y represents the degree of risk

aversion.

3.1.2. Budget Condition, Purchase, and Expenses.

At time t, consumer i has an exogenous budget ytallocated for all purchases and inventory costs. Let P-f

denote the price associated with purchasing brand /.Because the unit of the composite goods is scalable,we normalize the price of the composite good to one.

Let qjt denote the purchase quantity and 7;f denote

the inventory of brand j for consumer i at time t.We assume that the goods are durable and goods not

consumed can be stored at a unit holding cost of 6.

Then we have the following budget constraint:8

/, q 7=1

where a dummy variable djqt= 1 denotes a purchase

of brand ; and quantity q?

if the consumer chooses brand jand quantity q at time t, (3)

0, otherwise.

The inventory of brand / evolves according to the fol-

lowing relationship:

Ijt=

Ij(t-i)+ fyc-i)~

c/('-i)* (4)

Substituting the budget condition (2) into the utilityfunction (1), we get the following expression for the

per-period utility function:

7=1

Vj.q 7=1

7

To simplify the notations, we define It =Y,)=\Ijt as

the category inventory at time t. Moreover, oecause

yt enters the utility function for different brand-

quantity decisions in the same way, it will not

affect brand-quantity decisions. Dropping this com-

mon term across brand-quantity choices, the per-

period utility function can be written as

U,= E 4>j(c}lycjt) a E Witty- hi,, (6)

7=1 j' q

where h = aO. In Equation (6), parameter a mea-

sures consumer sensitivity to total price (or expen-

diture). The parameter h measures the unit holdingcost, which is assumed to be linear with respect to

inventory and constant over the planning horizon.

6In the following discussion, we do not explicitly differentiate

priceand promotion.Wereferchangeof priceas price promotion.Becausebothpriceandpromotionarestatevariables f treatedsep-arately, his simplification ignificantlyreduces the computationalburden without affectingthe main result and is consistentwithErdemet al. (2003).7For the ease of exposition,we ignorethe subscript in all vari-ables.Later,we add heterogeneityand subscript to relevantvari-ablesstarting n §3.2.

8We ncludeinventorycostsin thebudgetconstraint.This s equiv-alent to including inventorycosts directlyin the utility function.See Erdemet al. (2003)and Sun et al. (2003) or a similar reatmentof inventorycost.9Note we treatbrand-quantity ombinationas a discrete choice.This is consistentwith recentpapersin economicsand marketingthatdevelop dynamicstructuralmodels to studythe effectsof pro-motion on stockpiling.







Sun: PromotionEffecton EndogenousConsumptionMarketing cience24(3),pp. 430-443,©2005 INFORMS 433

3.1.3. Dynamic Programming.We model the con-sumer's purchase and consumption decisions asa dynamic optimization problem under promotionuncertainty.The consumer's task is to decide which

brand to buy, how much to buy and how much toconsume given currentinventory and promotionsoas to maximizethe sum of discountedexpectedfuture

utility Utover the infinite horizon.

MaxE,jf;8'-'(tfT+ eT)|. (7)C/ <V I T=t J

The variable8 is the discount factorto reflect thefact that consuming now is preferred to consum-

ing later (for example, the interest rate).The opera-tor Et[] denotes the conditionalexpectationoperatorgiven the consumer's nformationat time t. Thevari-able et is a random shock to utility that affects con-

sumer i's decision. We assume that et = J2j,qdjqt€jqtwhere e^t has an i.i.d. extremevalue distribution toobtainmultinomial ogit choiceprobabilities.

Given the one-periodutility function,we have the

followingBellmanequationfor the optimaldecisions:

/V(Ft)= max£ ^.(c,-, yc)t)

- a £ djqtPjtqjthlt

+ 6,+ 8E[V(F,+1)|F,]/ (8)

whereFtdenotes the information et availableto con-

sumer/ at time t. The consumerknows the inventorylevel at the end of last period and observes current

prices. We let St denote the state variables, whichincludethe exogenousstatevariablessuch as current

prices and endogenous state variables such as cur-rentinventories.The decisionvariablesaresequencesof brand-quantitychoices djqtand consumption cyf.Following Equation (8), the optimal consumption

maximizes the value function given the optimalbrand-quantitydecision,d*t:

r /

cJt argmax\V(Ft)J2<f>j(cjt-ycjt)-aJ2d]qtPjtqjtcjt I/=1 j,q

-W,+e,+5E[V(Ff+1)|F,]J,

9)

where c*tdenotes the optimal currentconsumption,which depends on the exogenous state variablesPjt;endogenous state variables I;7;the brand-quantitydecision d*qt;arameters uch as 5, h, y; and parame-tersthatdescribethe price processof differentbrands.As shown in Figure 1, currentoptimal consumptiondepends on the inventories throughthe dependenceof V(Ft+l)on the inventories. Currentoptimal con-

sumptionis also relatedto pricefor the followingrea-

son:It will affectexpectationsof futureprices,whichaffects the next period value function 8E[V(Ft+l)Ft]and thus changesthe relative trade-offsbetween cur-rent and futureconsumption.The indirecteffect aboutfuture value function will also affect the level of cur-rent consumption. Moreover,optimal consumptiondepends on the optimal brand-quantitydecision d*which is also directlyaffectedby inventorylevel and

prices.The time line of the decision process is as follows:

At the beginning of time t, the consumer is awareof the leftovers from last period. She also observes

promotionavailableat the store and forms expecta-tions for future promotion.Given currentinventory,

currentpromotion,and expected future promotion,she makes a purchasedecision at the store. Return-

ing home, the consumer decides how much to con-sume based on her available inventory (the sum ofleftovers from last week and optimalnew purchases),currentpromotionand futurepromotionexpectation.

Figure AGraphicalescriptionf theRelationship mong urchase,Consumption,ndStateVariables







Sun: PromotionEffecton EndogenousConsumption434 Marketing cience24(3),pp. 430-443,©2005INFORMS

The consumer's decisions are time consistent in that

she knows what she will do in the future periods, and

her decision in the future will be subgame perfect (i.e.,the consumer's decision in future periods is optimal

conditional on the information she has in the future).Thus, both current and future purchase and consump-tion decisions are interdependent and depend on cur-

rent inventory and promotion.

3.1.4. Store Visits. We observe from the data that

consumers sometimes do not visit the store. If the con-

sumer visits the store, her behavior is described bythe above model. If she does not visit the store, she

chooses only the amount of consumption and does so

to maximize the current consumption utility, minus

inventory costs, plus discounted future expected util-

ities. It is important to model store visits because ran-

dom store visits create extra precautionary incentive

to hold inventories. Consumption also varies withduration between visits.

We use a binomial distribution to model store visit

behavior.10In each period, there is a probability p that

she will visit the store next period. Let the value func-

tion in periods of store visits be V(Ft) and the value

function of no store visit be W(Ft).The Bellman equa-tions for store visit and no store visit are given below:

/

V(Ft)= max £ </>c7 -yc2jt) a £ djtPjtqjt hlt + et

+ 8E[pV(Ff+1) (1 -P)W(Ft+1) F,], (10)

W(Ft) max£^(ty -yc£)- W,

+ SE\pV(FM) + (1 -p)W(FM) | F,]. (11)

We approximate the value of p using the sample fre-

quency of store visits.

3.1.5. Expectation of Price Promotion. We as-

sume that the log price of brand / follows a first-order

Markov process. We also take into account competi-tive reaction and the time trend of price. Thus,

lnPjt=

A1;. A2lnP;.(f_1)A3- -^ItiVdJ A

¥j

+ A4t ty/ (12)

where As are coefficients. The variable r/y7 s the

random shock of brand / at time t. We assume the

random shocks in prices of all / brands, 77,, ollow a

multivariate normal distribution:

tj,-N(0,2,,). (13)

Competitor reaction is captured by entering the

mean price of all competing brands in the price

process. The diagonal elements in Xv denote the

corresponding variance of r/;, and the off diagonal

elements denote the covariance between prices of dif-ferent brands. Allowing random shocks to be corre-

lated can further capture the co-movement of pricesof the competing brands. The price process parame-ters are estimated using the price data prior to the

estimation of the model. The price process parametersare then treated as known in the model estimation

when we solve the consumer's dynamic optimization

problem.

3.2. Heterogeneity and Estimation

In this section we introduce heterogeneity to the

coefficients in Equations (10) and (11). Let w; =

(0/;, yx, aif h{) be the multivariate normal distributionthat generates these coefficients:

(Oi-xNfaXJ, (14)

where aj=(<£;,y , a, h) is the mean of coifand Sw is

a diagonal variance /covariance matrix of dimension

/H-3 with the diagonal elements denoting the corre-

sponding variance of each parameter.

Formally, for a given value of the parameter, the

log-likelihood function of the sequence of choices of

all the households is

£log(Pr(D?TS*.)) i>g(7 nL Pr(D, S,,1=1 i=\

I^htD^.^dF^dFilS), (15)

where lx denotes the initial inventory and Df, =

(D;1, . . . , Dit) denotes the history of D/Tfor r from 1

up to t. Similarly, S-}= (Sn, . . . , Sit) denotes the cor-

responding history of exogenous state variables, pur-chase prices and store visits from 1 up to t. Let ^denote the set of time periods in which consumer i

visits the store. Given the extreme value distribution

of the error term, the probability of observing con-

sumer i making decision Dit at time t e <Ji s

P^D.IS,,/,^,^^^, (16)

where

4-,=I>p(v^)*V (17)

^ =£exp(V^), (18)

and dijqtdenotes the observed brand and quantitychoice at time t for consumer /, V{jqts the value

10Hendel and Nevo (2003)also use binomialdistribution o modelstorevisits.







Sun: PromotionEffecton EndogenousConsumptionMarketing cience24(3),pp. 430-443,©2005INFORMS 435

function for choice ;, q for consumeri at time t and

is given by

/

Vijqt= max X>//(<^~

Jic%)~

aipjtqijt~

hflitcijt>dijqt

y=1

+ SE[pVi(F/+1)(1- p)W,+1) | F,]. (19)

Insummary, he statevariablesareprice, inventory,andstorevisits.Amongthese,inventory s anendoge-nous state variable,while price and store visits are

exogenous state variables.Because of the complex-

ity of the dynamicprogrammingproblem,we adoptsimulatedmaximum ikelihoodtechniquesemployingMonteCarlomethods(Keane1993) n addition to the

interpolationmethod(KeaneandWolpin1994) o esti-

mate the model,which significantlyreducesthe com-

putationalburden and makes the endogenizationofconsumptionpossible.11

4. EmpiricalApplication4.1. Data DescriptionWe use lite tuna and yogurt data collected by the

A. C. Nielsen Company and focus on purchasesof leading brands, which comprise more than 93%

and 74% of the marketshare for tuna and yogurt,

respectively.Forboth categories,the calibration am-

ples consist of 6,200 observationsfrom 50 randomlyselected households during 124 weeks from 1986 to

1988in Sioux Falls,SouthDakota.These householdsmade 839 purchases of tuna and 1,440 purchasesof yogurt during the observation period. Table 1

reportsthe descriptivestatistics.Consumersusually

buy morethantheiraverageconsumption.For exam-

ple, the averagepurchasesper incidenceare2.77 and

2.57cansof 6.5-oz.for StarKist nd CKN.Consumers'

averageconsumptionper week for StarKistand CKN

is 0.48and 0.31 cans of 6.5-oz. tuna, respectively.We

reserve980observations rom49 households over the

courseof 20 weeks who made 145purchasesof tuna

and 248 yogurt in Springfield,MO for cross samplevalidation.

Table 1 Descriptive Statistics

Average price Average purchase

Brands Market share per ounce (cents) quantity3

Tuna categoryStarKist 67.73 0.111 2.77

CKN 32.27 0.104 2.57

Yogurt category

Nordica 34.61 0.0642 1.99

Yoplait 28.16 0.0983 2.18

Private label 19.92 0.0450 1.82

Dannon 17.31 0.0871 1.93

aThepurchase quantities are number of units. The unit refers to 6.5 oz. for

tuna and 6 oz. for yogurt.

4.2. Estimation and ComparisonWe compare our dynamic structural model withfour baseline models.12The first baseline model is a

nested logit model with fixed consumption.The sec-ond model is similar to Ailawadi and Neslin (1998),which is a nested logit model with a varying but

exogenously given consumption rate. Model 3 is astatic version of our proposed model. Model 4 is a

forward-lookingmodel with constant consumption.It is similar to Sun et al. (2003) and Erdem et al.

(2003)because it assumes that the consumptionrateis not endogenouslydrivenby inventoryand promo-tion. Model 5 is our proposed structuralmodel with

endogenous consumption under promotion uncer-

tainty.As indicated in Table 2a, for tuna category,the comparisons of log-likelihood values, AIC andBIC show that model fit

improves

from Model 1 to

Model 5 with Model 5 being the best-fittingmodel.Model 4 fits the data worse than Model 5, whichindicatesthat it is importantto treatconsumptionasa decision variable that can be endogenously driven

by promotion and inventory. Model 3 underper-forms Model 5, indicatingthat consumerare indeed

forward-lookingand strategicallyplan theirpurchaseand consumptiondecisions. Models 3 and 4 are our

proposedmodels without dynamicsand endogenousconsumption,respectively.The comparisonof thesetwo models with our proposed model reveals thatboth componentsareimportant n improvingdata fit-

ting. The model comparisonresultsfrom the holdout

sample support our hypothesis that consumers notonly strategicallyplan theirfuturepurchases,but alsotheir future consumption in light of inventory and

promotion.

11We point out three issues in the empiricalapplication.First,because he statevariablePjt s continuous, t is impossible o solve

exactlyfor V^f,Wijqtt every statepoint.Weconsider12 invento-

riesand 10prices(drawn .i.d.froma uniformdistribution)orthe

two brandsin analysis.Thus,we calculatethe value functionon

G= 14,400grid points.Second,althoughwe specify the DP prob-lem over an infinitehorizon,we findconvergenceof the backward

inductionprocesswhen T= 248,whichis twicethe numberof sam-

ple periods.Third,we startwith an initial inventoryof zero and

solve the dynamicprogramming roblem or the whole time spanfor M = 10 times to simulatethe initial inventorydistribution or

a consumer.

12The estimationand simulation resultsare similarfor tuna and

yogurt categories.To save space,we reportmodelcomparisonand

coefficient stimationresultsonly for tunacategory.Thepolicysim-

ulation resultsare reportedfor both categories.We point out the

majordifference n simulationresults between the two categories.Interested eaderscan obtainthe estimationresults of yogurtcate-

gory fromthe author.








Table 2a Model Comparison

Tuna category

Reduced form

models Structural models

Model fit statistics Model 1 Model 2 Model 3 Model 4 Model 5

Calibration sample3

Log-likelihood 6,659.0 6,627.1 6,620.2 6,609.2 6,575.8

AIC 6,687.0 6,656.1 6,630.5 6,619.2 6,585.8

BIC 6,781.3 6,753.7 6,663.9 6,652.9 6,619.5

Holdout sample

Log-likelihood 1,035.2 1,004.2 1,000.1 992.2 957.3

AIC 1,063.2 1,033.2 1,010.1 1,002.2 967.3

BIC 1,131.6 1,104.1 1,034.6 1,026.7 991.9

Calibration sample: Number of households = 50; Number of weeks =

124; Number of observations = 6,200. Holdout sample: Number of

households = 49; Number of weeks = 20; Number of observations = 980.

Table 2b Sample and Simulated Purchase Incidence, Choice, and

Quantity

Tuna category

Sample Model 3 Model 4 Model 5

Percentage distribution of duration between purchases (weeks)1 5.31 5.24 5.26 5.28

2 4.87 4.90 4.89 4.86

3 3.82 3.80 3.80 3.79

4 4.57 4.63 4.62 4.6

5 8.92 9.01 8.99 8.97

6 13.47 13.39 13.41 13.51

7 20.35 20.04 20.18 20.3

8 18.22 18.15 18.16 18.18

9 12.56 12.50 12.49 12.5310+ 7.91 8.34 8.20 7.98

Choice probabilities

No purchase 86.11 84.74 84.99 85.79

StarKist 9.52 11.26 11.13 10.01

CKN 4.37 4.00 3.88 4.20

Average purchase quantity

StarKist 2.77 2.80 2.79 2.75

CKN 2.57 2.55 2.56 2.61

The advantage of the structuralmodel is that it

explains the behavior process ratherthan fits the

data, as does a reduced form model (a very reducedform model can fit better than a structuralmodel

without explaining consumer decision process). Wenow demonstratehow the proposedstructuralmodel

approximates he data. In Table 2b, we comparethe simulated frequency distribution of durationsbetween visits, choice probabilities,and average pur-chase quantity with those from the sample. The fitof our proposed model is remarkably good on allthese dimensions,indicatingthatthe proposedmodel

approximates he data very well.Table 3a reports the maximum likelihood esti-

mates of parameters n the price process.Most of the

Table 3a Estimates of the Price Process

Tuna category

Parameter Estimate

Brand constant A^

StarKist -0.551 (0.16)

CKN -0.265 (0.08)

Lagged price A2: -0.134 (0.06)

Average prices A3: 0.063 (0.021)

Time trend A4: 0.0008(0.0007)

Variance covariance matrix 2,:

2^:0.074 (0.023)

2 : -0.011 (0.007)

2,22: 0.087 (0.029)

coefficients are significantlyestimatedexcept that ofthe time trend and covariance.The coefficientof the

averageof

competitors'priceis

positiveand

signifi-cant implying StarKist ncreases ts price if the aver-

age last period price of competitorsis higher. ThecovariancebetweenStarKist nd CKN is insignificant,indicatingthat there is no cleartendencyforthe priceshocks to move in the same direction.Thisfindingisconsistentwith Erdemet al. (2003).

In Table 3b, we report the estimation results ofthe five competingmodels with meanparameter sti-mates reported in the first line and the standarddeviation estimatesacross householdsreported n thesecond line.13We follow the convention and fix the

weekly discount factorat 0.995.Because Model 5 isthe best fitting model, we focus on the estimation

resultsof Model 5 in the followingdiscussion.All themean coefficientsaresignificantlyestimatedand havethe expected signs. The standard deviations of allthe coefficientsare significant,indicatingconsumersare heterogeneous in responding to consumption,price, and holding cost. The mean of consumptioncoefficient </>s positive, implying that consump-tion increases consumerbenefit.Also, unit consump-tion benefit is higher for StarKist han for CKN.Therisk coefficienty is significantlypositive implying aconcave utility functionand that consumersare riskaverse. Consumersbecome saturatedwhen consum-

ing too much of a product. The coefficient of total

price (a) indicates that total expenditurehas a neg-

ative effect on utility. The coefficient of inventory(h) implies that the higher the inventory,the lowerthe probabilityof purchasingbecause of the cost of

storage.

4.3. SimulationIn this section, we use the estimated parametersofour proposed structuralmodel as inputs for Monte

13We also estimateda model with last purchase, eature,and dis-

play as additionalexplanatoryvariables.This marginallyaffectedthe estimationand simulationwithoutchangingthe main results.








Table3b Model Estimation3

Tuna ategory

Reducedorm

model Structuralmodel

Parameter Model1 Model Model3 Model Model5

Consumptionenefit >:StarKist 2.36 2.18 1.65 1.65 1.54

(0.22b) (0.25) (0.30) (0.19) (0.24)0.84 0.81 0.29 0.18 0.20

(0.18) (0.22) (0.06) (0.08) (0.05)CKN 1.25 1.01 0.64 0.60 0.65

(0.19) (0.32) (0.19) (0.21) (0.21)1.14 0.82 0.20 0.19 0.18

(0.22) (0.21) (0.09) (0.07) (0.07)

Riskaversion : -0.24 -0.37 -0.22 -0.21 -0.18

(0.14) (0.10) (0.12) (0.11) (0.08)0.13 0.14 0.16 0.12 0.11

(0.16) (0.093) (0.06) (0.05) (0.05)Pricea: -4.01 -3.47 -2.99 -2.32 -2.18

(0.52) (0.15) (0.29) (0.41) (0.31)0.89 -0.99 0.43 0.41 0.34

(0.34) (0.32) (0.10) (0.10) (0.06)

Unitholding ost h: -0.036 -0.014 -0.062

(0.022) (0.021) (0.012)0.030 0.012 0.044

(0.017) (0.022) (0.016)fb

Purchase-incidence 0.010

(0.0091)

Category reference80: 0.18 0.15

(0.08) (0.06)0.08 0.07

(0.03) (0.03)

Consumptionate a: 1.19 1.17

(0.19) (0.18)

0.88 0.84(0.44) (0.41)

Inventory32: -0.13 -0.07

(0.04) (0.03)0.08 0.06

(0.08) (0.04)

Categoryalue 33: 0.38 0.34

(0.18) (0.14)0.57 0.53

(0.20) (0.24)

Purchase-quantity

Quantityreference0: 2.10 2.09

(0.45) (0.44)1.16 1.10

(0.20) (0.19)

Average uantity : 1.11 1 20

(0.34) (0.29)0.32 0.36

(0.06) (0.13)

Inventory2: -0.14 -0.12

(0.04) (0.04)0.06 0.04

(0.10) (0.03)Pricey3: -3.01 -2.96

(0.79) (0.83)1.90 1.94

(0.26) (0.22)

standard errorsarereportedn parentheses.Parameterf is defined imilarly s in Ailawadi nd Neslin(1998).

Carlo simulations to explore the effect of promo-tion on consumption.Specifically,we are interestedin using the model to derive the following implica-tions:(1) How do purchaseand consumptionchange

differentlywith a price cut (Figure2)? (2) Will con-sumption respond directly to promotion(Figure3)?(3) How is consumption driven by inventory (Fig-ure 4)? (4) How is the consumption-inventoryrela-

tionship modified by holding cost and promotionuncertainty (Figure 4)? (5) How important is the

consumption ncreaserelative to brandswitchingand

stockpiling (Tables4 and 5)? (6) Can the proposedmodel be adopted to explain the absence of a post-promotion dip (Figure5)?

In Figure2, we randomlyselect week 10 (week 12)and cut prices for all sizes of StarKist una (Yoplaitfor yogurt) by 25%. We then plot the average pur-chases and

average consumptionof the

promotedbrandacross consumersagainst time. The change of

pricein the promotionweek will alterexpectedfuture

prices. Comparing Figures 2a and 2b for tuna (Fig-ures 2c and 2d for yogurt), we obtain the follow-

ing results.First, t shows thatconsumptionincreaseswhen there is a price promotion.This indicates that

consumption is not constant. Second, a significantsales increase occurs in week 10 (week 12). Thereare some noticeable adjustmentsin the first two orthree weeks (firsttwo or threeweeks) before sales goback to baseline sales aftereight weeks (five weeks).Different rompurchase,promotioncauses consump-tion to increasesignificantlyfor threeweeks (fortwo

weeks). Consumptionthen graduallymoves back tobaseline level about nine weeks (fourweeks) afterthe

promotion.Allowing consumersto strategicallymake

consumptiondecisions in light of promotionexpecta-tions, our dynamicmodel results in a smoothercon-

sumption paththan thepurchasepath.Thisis becauseconsumersare allowed to strategicallydecide not toconsume everythingavailablerightaway but insteadto save for future consumption.Thus, how much toconsume is optimallydecidedby consumers.Note theincreaseof consumptionin the simulated promotionweek is bigger for yogurt than for tuna. The promo-tion induced additionalpurchases are consumed ata fasterpace for yogurt than for tuna. This indicates

that promotion effect on consumption is bigger forproduct categoriesthat are easily perishable.

In Figure3, we plot averageconsumptionacrossallconsumersagainstvarious levels of permanentpricechanges (pricecuts or priceincreasesof x% n all peri-ods).Since we assumeconsumersareaware of thefactthatpricechangesareofferedpermanently, forward-

looking consumer is less likely to stockpile duringpromotion.Thus, most of the increase of consump-tion can be attributed to direct effect of promotionon consumption.When the price of StarKist(Yoplait)








Figure Purchase ndConsumptionhangewithPromotion Figure AverageConsumptionncreaseswithPromotion

dropsfor all periods,we find an increaseof the aver-

age consumptionof StarKist Yoplait),but a decreaseof the average consumptionof CKN (otherbrands).Nevertheless,the average categoryconsumptionstillincreases.Our resultsindicatethataverageconsump-tion could directly respondto pricechanges.

Figure4a (Figure4c) plots consumption(averagedacross consumerand time) as a functionof availableinventories (Y.)=\hjt-\+ £/=i fy-f-i)/which we defineas consumption function.We plot _theconsumptionfunction when the holding cost (h) is 0.01, 0.062,and 0.10 for tuna (0.15,0.074,and 0.035 for yogurt).It shows that consumption is an increasing func-tion of inventory.How promotioninduced stockpil-ing resultsin increasedconsumption s endogenouslycapturedby our proposed model. It also shows thattheconsumptionfunction ncreaseswith holdingcost.The higher the disutility of holding inventory,themore consumers are willing to consume given thesameinventory.Similarly,n Figure4b (Figure4d),we

plot the consumptionfunctionfor Sr?110.150, 0.074,and 0.035 for tuna (Xmi= 0.200,0.105,and 0.052 for

yogurt).Thehighertheuncertainty,he lowerthe con-

sumption given the same inventory.In otherwords,the consumptionfunction decreaseswith promotionuncertainty.Knowing that promotionsare becoming








Figure 4 Consumption Function (Consumption Increases with

Inventory)

less predictable,forward-lookingconsumers realizethat the productmightnot be availableat lowerpricesin the near future.Theylower their currentconsump-tion and save for future demand given the same

availableinventory.Thus,given the same stockpiling,increasedpromotion uncertainty discourages a con-

sumptionincrease.

To better understandpromotioneffect on contem-

poraneoussales, we breakdown the promotionsalesincrease in week 10 for tuna (week 12 for yogurt)into brandswitching, consumption ncrease,and pur-chase displacementand reportthe results in Table4.Brandswitching is defined as the total units of CKN

(Yoplait) onsumersgive up to purchaseStarKist theother yogurt brands) due to promotion of StarKist

(Yoplait).These are purchases made by consumerswho are

expectedto

buyCKN

(theother

brands)without promotion but switch and buy the sameamount of StarKist Yoplait).Consumptionchange is

defined as the differencebetween total consumptionwith promotionand total consumptionwithout pro-motionin the week of promotion.Theremainingpartof the sales increase n the promotionweek is defined

as purchasedisplacement.We report the breakdowns of the sales change in

week 10 (week 12). We find that 33%(43%)of the

sales increase s attributed o a consumption ncrease,42%(39%) s due to brandswitching,and 25%(18%)is from stockpilingas predicted by Model 5. Ignor-

ing flexible consumption or stockpiling behavior,Models 1, 3, and 4 attribute he ignoredconsumptionincreaseor stockpiling to brand switching. Model 2

also attributesa larger portion of the sales increase

Table 4 Breakdown of Promotion Effect on Short-Term Sales Increase

Tuna category

Brand Consumption Purchase

switching (%) increase (%) displacement (%)

Model 1 93 NA 7

Model 2 66 25 9

Model 3 60 40 NA

Model 4 52 NA 48

Model 5 42 33 25

Yogurt category

Brand Consumption Purchase

switching (%) increase (%) displacement (%)

Model 1 89 NA 11

Model 2 58 33 9

Model 3 54 46 NA

Model 4 53 NA 47

Model 5 39 43 18








Table 5 Consumption Elasticities

Tuna category

Consumption

elasticities

StarKist CKN

Model 1 NA NA

Model 2 0.19 0.12

Model 3 0.35 0.25

Model 4 NA NA

Model 5 0.29 0.19

Yogurt category

Consumption

elasticites

Yoplait Private label

Model 1 NA NA

Model 2 0.25 0.18Model 3 0.42 0.29

Model 4 NA NA

Model 5 0.38 0.25

to brandswitching.14'5Consistent with our previous

findings, consumption elasticity is higher for yogurtthanfor tuna.

To betterdemonstratehow promotioncan stimulatecurrentconsumption,we also calculateconsumptionelasticities or the simulatedpromotion n week 10 forStarKistweek 12forYoplait)and compare he resultswith competing models. We report in Table 5 the

percentage ncreasein consumptionof the promotedbrandgiven the 25%price promotion.The results con-firmthatModels 1, 2, and 4 underestimatepromotioneffect on consumption, and Model 3 overestimatesthis effect.We conduct a similar simulation for CKN

(private abel)and find the same result.We notice that

consumptionelasticityis higher for StarKist han forCKN(higherforYoplait hanforprivate abel).This isbecauseStarKist(Yoplait)s a strongerbrand,and thebenefits of consuming a preferredbrand are greaterthanthose of consuminga less preferredbrand.Thus

promotionhas stronger impact on the consumptionof strongerbrands.

As an example of application,our model can beused to better understand why the postpromotion

dip predicted by some conventional choice mod-els is not significant using actualweekly sales fromscanner panel data (Blattbergand Neslin 1990). In

Figures 5a and 5b, we draw average weekly cate-

gory sales againstweeks and comparehow averageweekly categorysales reactto the simulatedpromo-tion using the threecompetingstructuralmodels.Wefocus on structuralmodels because the underlyingdecision processesare known as opposed to reducedform models. As expected, the actual sales do notshow a significant dip for both tuna and yogurt.Model 5 allows consumersto predict futurepromo-tions and optimally plan their purchasesto coincidewith

promotionschedules. Consumers

delaytheir

Fioure 5 Postoromotion Dio

14Consistentwith van Heerdeet al. (2003),we also find thatignor-

ing categoryexpansion eads to an overestimation f brandswitch-ing.However,ourmodel canseparatea consumptionncrease rombrand switching and stockpiling,which cannot be achieved byexistingmodels.15We also calculate the breakdowns for all the periods followingthepromotion.We find thatthe saleschangeassociatedwith a tem-

porary promotionlasts for about eight weeks for tuna (5 weeksfor yogurt), most of which is concentrated n the first two orthreeweeks.Usingdisaggregatemodel,we confirm he findingsofPauwels et al. (2003),who find that temporarypromotionhas an

adjustment ffect due to dynamicfactors uch asinventory,promo-tion expectation,consumptionincrease,stockpiling,etc. The per-manent effectis not significant.







Sun: PromotionEffecton EndogenousConsumptionMarketing cience24(3),pp. 430-443,©2005INFORMS 441

purchasesuntil promotion,making sales before pro-motionrelatively ow. Withmoreinventory, hey alsoconsumemore,makingthe dropof sales afterpromo-tion less significant.Thus,for productcategorieswith

flexibleconsumption, he postpromotiondip could beinsignificantbecauseof the consumptioneffect at pro-motion and the purchase decelerationeffect before

promotion.Models 3 and 4 still result in a postpro-motiondip becausethey ignore purchasedecelerationand consumption ncrease,respectively.

Below we summarize the calibrationresults usingthe packagedtuna and yogurt.

• For products that are perceived to be versatileand substitutable,consumption is not constant butrather ncreaseswith inventoryand promotion.

• The consumptionfunction(consumption ncrea-ses with inventory) ncreasesas holdingcost increasesand

promotionuncertaintydecreases.

• Promotionnot only causes brand switching and

purchaseaccelerationbut also stimulates consump-tion. Promotionhas a stronger impact on the con-

sumptionof strongerbrands.• Conventionalmodels assuminga constant or an

exogenous consumptionrateoverestimate he impor-tance of the brand-switching ffect.

• Our simulation demonstrates that the lack ofevidence fora postpromotiondip could be due to pur-chase decelerationbeforepromotionand a consump-tion increaseatpromotion orproductcategorieswithflexibleconsumption.

• The dynamicstructuralmodel with endogenous

consumption approximatesthe data the best. Thus,to measurepromotioneffect on sales accurately,t is

important o treatconsumers as rationalagents whoform promotion expectations and optimally adjusttheirpurchase ime and quantityas well as consump-tion to coincide with the promotionschedule.

Note the above empiricalfindings are drawn fromthe applicationof our proposed model to tuna and

yogurt categories.Whenapplyingto othercategories,these conclusion may be modified by the degreeof consumption flexibility of those categories. We

speculatethat the higher the degree of flexibilityof

consumption,the bigger the effect of promotionon

consumption.

5. ManagerialImplications,Conclusion, and FutureResearch

Managersrely on periodic price promotionsto stim-ulate demand,and this trend is expected to increaseover time.Ifpromotionsimply induces brandswitch-

ing and purchase displacement without encourag-ing consumption,promotionbecomes a less effective

strategyunless it can significantlyattract new usersfrom other stores or other categories.Conventional

choice models cannothandle the promotioneffect on

endogenous consumptionbecause they assume con-stantor exogenousconsumptionrates.It is importantto understandhow consumptionrespondsto promo-tion.Inthispaper,we allow consumptionto be a deci-sion variableendogenouslydrivenby promotionand

propose a dynamic structuralmodel with endoge-nous consumption under promotion uncertaintytoexaminethe promotioneffect on consumption.Basedon this model, we investigatethe issue whetherpro-motion has any effect on consumptionand provideinsightful behavioralexplanationson whether,why,and how consumptionis affectedby promotion.

Manufacturersusually initiatepromotionto attractnew users or brand switchers. Retailers frequentlyofferpromotionsto increasestoresales. Applying the

proposed model to tuna and yogurt data, we find

some interestingempiricalresults thathave importantimplications for manufacturersand retailers. First,

managersshouldbe awarethatforproductcategorieswith versatile and substitutableconsumption, pro-motion can encourage consumption in addition tobrand switching and purchase displacement.There-

fore,manufacturers hould take into accountthe pro-motion effect on consumption when designing an

optimal promotionstrategy.Retailers should chooseto promote categories whose consumption is most

likely to increasewithout cannibalizingconsumptionof other categories. Second, because the increasingrelationshipbetween inventory and consumption isenhanced

by holdingcosts,the

consumptionncreases

even more if retailerschoose to promoteproductcat-

egories thatareeasily perishableor bulky.Our analysis is subjectto limitations which open

avenues for future research.First,it will be interest-

ing to apply our model to additionalcategories(e.g.,candy, orange juice, pasta) and study explicitly howthe promotioneffect on consumptionvaries with the

degree of flexibilityof consumption.Second,retailersand manufacturerswill be interested to know what

type of consumers are more likely to consume more.

Third,manufacturers nd retailers nitiatepromotionfor various reasons, e.g., attractingmore shoppers,getting rid of inventory,creating demand of com-

plementary categories.It will be interestingto studyhow to take advantage of the promotion effect on

consumptionto achieve those goals (e.g., Villas-Boas

2004). Fourth,we have focused on consumption of

only one category.The model can be extended to mul-

tiple categories to study the cross-categoryeffect of

promotionon consumption.Finally,given the com-

plexity of estimating a DP model, we have ignoredother promotion variables such as coupon, feature,

display,referenceprice,and brandloyalty,which willbe interestingto explorein futureresearch.







Sun: PromotionEffecton EndogenousConsumption442 Marketing cience24(3),pp. 430-443,©2005 INFORMS

AcknowledgmentsAn earlier version of this paper was under the title Pro-motion Effects on Category Expansionwith EndogenizedConsumptionUnder PromotionUncertainty/'The author

thanks participantsat marketing seminars held at RiceUniversity, ndianaUniversity,Universityof Pennsylvania,Ohio State University, Cornell University, University ofNorthCarolina,PennsylvaniaStateUniversity, he Market-

ing SummerCampat CarnegieMellonUniversity,and the

MarketingScienceConference or their valuable comments.

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