The Decompositionof Promotional Response: An ... · The Decompositionof Promotional Response: An EmpiricalGeneralization ... On average, we ﬁnd that 25% of the elasticity is due

Marketing Science � 1999 INFORMSVol. 18, No. 4, 1999, pp. 504–526

0732-2399/99/1804/0504/$05.001526-548X electronic ISSN

The Decomposition of PromotionalResponse: An Empirical Generalization

David R. Bell • Jeongwen Chiang • V. PadmanabhanMarketing Department, The Wharton School, University of Pennsylvania, 1400 Steinberg Hall,

Philadelphia, Pennsylvania 19104, [email protected] Department, Hong Kong University of Science and Technology, Clearwater Bay, Kowloon, Hong Kong,

[email protected] Department, Olin School of Business, Washington University, 100 Brookings Drive,

St. Louis, Missouri 63130, [email protected]

AbstractPrice promotions are used extensively in marketing for onesimple reason—consumers respond. The sales increase for abrand on promotion could be due to consumers acceleratingtheir purchases (i.e., buying earlier than usual and/or buyingmore than usual) and/or consumers switching their choicefrom other brands. Purchase acceleration and brand switch-ing relate to the primary demand and secondary demandeffects of a promotion. Gupta (1988) captures these effects ina single model and decomposes a brand’s total price elastic-ity into these components. He reports, for the coffee productcategory, that the main impact of a price promotion is onbrand choice (84%), and that there is a smaller impact onpurchase incidence (14%) and stockpiling (2%). In otherwords, the majority of the effect of a promotion is at thesecondary level (84%) and there is a relatively small primarydemand effect (16%).

This paper reports the decomposition of total price elas-ticity for 173 brands across 13 different product categories.On average, we find that 25% of the elasticity is due to pri-mary demand expansion (i.e., purchase acceleration) and75% to secondary demand effects or brand switching. Thus,while Gupta’s finding that the majority of promotional re-sponse stems from brand switching is supported, the averagemagnitude of the effect appears to be smaller than firstthought. More important, there is ample evidence that pro-motions have a significant primary demand effect.

The relative emphasis on purchase acceleration and brandswitching varies systematically across categories, and thesecond goal of the paper is to explain this variation as a func-tion of exogeneous covariates. In doing this, we recognizethat promotional response is the consumer’s reaction to aprice promotion, and therefore develop a framework for un-derstanding variability in promotional response that is basedon the consumer’s perspective of the benefits from a pricepromotion. These benefits are posited to be a function of: (i)category-specific factors, (ii) brand-specific factors, and (iii)

consumer characteristics. The framework is formalized as ageneralized least squares meta-analysis in which the brand’sprice elasticity is the dependent variable. Several interestingresults emerge from this analysis.

• Category-specific factors, brand-specific factors, andconsumer demographics explain a significant amount of thevariance in promotional response for a brand at both the pri-mary and secondary demand levels.

• Category-specific factors have greater influence on vari-ability in promotional response and its decomposition thando brand-specific factors.

• There are several instances where exogenous variablesdo not affect total elasticities yet significantly affect individ-ual components of total elasticity. In fact, the lack of a sig-nificant relationship between the variables and total elasticityis often due to offsetting effects within two or more of thethree behavioral components of elasticity. This is particularlytrue for brand-specific factors, which typically have no effecton total elasticity, yet have important effects on the individ-ual behaviors.

• There is some evidence to suggest that not all promotion-related increases in primary demand are due to forward-buying—in some cases promotions appear to increaseconsumption.

We use these results to illustrate how category- and brand-specific factors work to drive primary and secondary de-mand elasticities in different directions.

In short, this paper offers an empirical generalization of akey finding on promotional response—how elasticities de-compose across brand choice, purchase incidence, and stock-piling—and new insights into factors that explain variancein promotional response. These findings are likely to be ofinterest to researchers who are concerned with theory de-velopment and the generalizability of marketing phenom-ena, and to managers who plan promotion campaigns.(Price Elasticity; Promotion; Brand Choice; Purchase Incidence;Stockpiling; Primary Demand; Secondary Demand; Meta-Analysis)

THE DECOMPOSITION OF PROMOTIONALRESPONSE: AN EMPIRICAL GENERALIZATION

Marketing Science/Vol. 18, No. 4, 1999 505

1. IntroductionEach year billions of dollars are spent on promotionsfor a simple reason—promotions work. In an era ofincreasing competitiveness, however, it has become vi-tal that promotions and promotional response be ad-dressed with sophistication that goes beyond the rec-ognition that promotions enhance sales. Prior researchhas documented that promotions can enhance sales by:(i) influencing sales of the category (i.e., they have pri-mary demand effects) and thereby sales of the brand,and/or (ii) influencing sales of the brand directly (i.e.,they have secondary demand effects).1

Managers need more precise answers to the ques-tions: Is the impact of a promotion for the brand(s) theymanage on primary demand, secondary demand, orboth? If the effect is largely on primary demand, arethe sales spikes due to altered timing (purchase inci-dence) and/or consumer stockpiling? If the effect is onboth, what is the split between primary and secondarydemand? How do these effects of a promotion differacross brands? Across categories?

Knowledge at this level of detail would allow man-agers to draw better guidelines for promotion policies,set priorities for promotional dollars, align promo-tional campaigns, and anticipate the moves and coun-termoves of rivals. This paper, through a careful in-vestigation of promotional response for a set of 173brands across 13 categories, attempts to provide guid-ance to brand managers involved in addressing theseissues. The paper also provides empirical regularitiesfor other researchers working on promotionalresponse.

1.1. Research on Price PromotionsThere is a wide body of literature employing econo-metric models calibrated on scanner panel data to eval-uate market, segment, or household-level response topromotions, across some combination of brand choice,

1Brand switching corresponds directly to secondary demand. Thelink between primary demand and incidence and quantity elastici-ties, however, is less clear. This is because consumers may, over timechoose to forward-buy or stockpile, yet not ultimately increase con-sumption. Thus higher incidence and quantity elasticities are nec-essary but not sufficient to indicate increases in primary demand.For ease of exposition we will relate incidence and quantity effectsto primary demand, and will return to this issue in §4.1.

purchase incidence, or purchase quantity behaviors.Early work demonstrating the impact of promotionson consumer brand choices (Ehrenberg 1972,Guadagni and Little 1983) has given way to more so-phisticated models of price promotions (e.g., Neslin etal. 1985, Rossi et al. 1996, Bucklin et al. 1998). The morecomplex models either calibrate individual-level re-sponse, and/or look at interactions in response acrossbehaviors. A common emphasis, however, is the focuson consumers as the unit of analysis.

A different stream of research that attempts to un-derstand the drivers of promotional response acrossmultiple brands, categories, or market conditions isseen in the work of Bolton (1989) and others that havesince followed (Raju 1992, Fader and Lodish 1990,Narasimhan et al. 1996). Here, the focus is typically ona summary measure of brand elasticity as the unit ofanalysis. Thus, the emphasis in past literature tends tobe either on promotions as they affect consumers, orbrands, but not both.

Ironically, as pointed out by Blattberg et al. (1995, p.130), the field is in short supply of the general empir-ical regularities which frame a more integrated per-spective of promotions. In a similar vein, Narasimhanet al. (1996, p. 29) note:

In the final analysis, . . . promotional policy must be set forspecific brands (their emphasis), and more work is needed tounderstand how promotional elasticities vary across brands. . .

Our work, which looks at empirical regularities in pro-motional response across brands and at the same timeacross underlying consumer behaviors, is a step in thisdirection.

1.2. Research Objective and ApproachBass (1993, p. 2) describes an empirical generalizationas “a pattern or regularity that repeats over many dif-ferent circumstances” and notes the important role ofempirical generalization in (marketing) science. Thispaper examines the empirical generalizability of pre-vious research on the decomposition of promotionalresponse into primary and secondary demand effects(Gupta 1988, Chiang 1991, Chintagunta 1993). Thesestudies report that secondary demand effects (i.e.,

BELL, CHIANG, AND PADMANABHANThe Decomposition of Promotional Response

506 Marketing Science/Vol. 18, No. 4, 1999

brand switching) are the dominant consequence ofprice promotion.2

We begin by examining the decomposition acrossmultiple product categories. Our objective is to deter-mine the extent to which the emphasis on primary andsecondary effects varies across product categories. Sec-ond, we formalize, via meta-analysis, the linkages be-tween exogenous category, brand and consumer co-variates, and the three components of a brand’selasticity. Our objective here is to provide a rationalefor the effects of the covariates and to demonstrate thatthey explain a significant amount of the variance inprimary and secondary demand elasticities.

To achieve these goals, we estimate the price pro-motion effect on primary and secondary demandusingmarket basket scanner panel data from 250 house-holds. In all, 519 price elasticities are generated for 173brands in 13 different product categories. Ourhousehold-level choice model allows for dependenciesacross the purchase incidence, brand choice, and pur-chase quantity decisions within a product categoryand may be viewed as a variant of Chiang (1991).

To analyze variability in the elasticities, we developa conceptual framework that captures the consumer’sview of the characteristics of individual brands andproduct categories. Our conceptualization is moti-vated by Bolton (1989, p. 167) who notes:

. . . (although) market characteristics are associated with dif-ferences in price elasticities, customer tastes (i.e., the custom-ers’ values for the particular attributes or benefits offered bythe category) seem to be important in explaining differencesin promotional price elasticities across categories.

The key premise is that variability in brand-level priceelasticities will be driven by: (1) consumer perceptionsof the attractiveness of a price promotion, conditionalupon the category environment, (2) the consumer’sview of how a price promotion on a given brand influ-ences perceived quality-per-dollar of that brand, and(3) the characteristics of consumers themselves.3

2Our analysis takes the perspective of a manufacturer. It is for thisreason that the brand switching effect reflects change in secondarydemand. From a retailer’s perspective, brand switching could reflecta primary demand effect if it is accompanied by store switching aswell.3There is an emerging literature in marketing that examines the issue

The unit of analysis is the brand-level elasticity as thisis the metric of most interest to the manager. We ex-amine the extent to which variance in a brand’s choice,incidence, and quantity elasticities can be attributed tothree sets of exogenous variables:

• Category Factors. Category factors influence theconsumer’s budget allocation process. In particular, theycapture consumer perceptions of the assortment on of-fer, and the economic benefits associated with buyingin a particular product category.

• Brand Factors. Brand factors capture consumer per-ceptions of the brand’s quality-per-dollar. They includevariables which reflect marketing effort and thebrand’s position in the marketplace.

• Consumer Factors. Consumer factors reflect the eco-nomic profile of the brand’s clientele. They are sum-marized by the demographic characteristics of con-sumers who purchase the brand.The framework is formalized as a generalized leastsquares meta analysis in which the brand’s price elas-ticity is the dependent variable.

1.3. A Brief Overview of the Key FindingsThe substantive findings are:

1. The basic conclusion of Gupta (1988) and Chiang(1991) that the dominant effect of a promotion is onswitching (i.e., secondary demand) is valid. The mag-nitude, however, is considerably lower than previ-ously reported. That is, promotions can have a signifi-cant impact on primary demand for a product (i.e.,purchase incidence and quantity choice).

2. The magnitude of primary and secondary demandeffects vary substantially across brands and categories.Our framework built on category-, brand- andconsumer-specific factors explains a significantamount (up to 70%) of this variance in promotionalresponse.

3. It is important to decompose total promotionalresponse into its primary and secondary componentsif one is to fully understand the effect of exogenous

of whether price-responsiveness of consumers is driven by the en-vironment, consumer traits, or some combination of the two (see,for example, Ainslie and Rossi 1998). Our conceptualization and em-pirical results allow an additional perspective.



Exhibit 1

Consumer Behavior

SecondaryDemand Primary Demand

Class of Factor Brand Choice Purchase Incidence Purchase Quantity

Category Factors Strong Moderate StrongBrand Factors Moderate Moderate ModerateConsumer Factors Weak Weak No Effect

covariates. There are several instances where exoge-nous variables do not affect total elasticity, yet signifi-cantly affect individual components of total elasticity.In fact, the lack of a significant relationship betweenthe variables and total elasticity is often due to offset-ting effects within two or more of the three behavioralcomponents of elasticity. This is particularly true forthe brand-specific factors.

4. Category-specific factors explain most of the vari-ability in promotional response. Brand-specific mar-keting variables play a modest role, and the character-istics of the brand’s core clientele have relatively littleexplanatory power.

5. Promotions result in demand dynamics that varysystematically across categories and this variance is re-lated to the apparent effect on consumption. In partic-ular, some categories (e.g., bacon, potato chips, soft-drinks, and yogurt) show increased average purchasequantities on promotion but no subsequent change ininterpurchase times, which implies that promotions in-crease consumption in these cases.4 In other categories(e.g., bathroom tissue, coffee, detergent, and papertowels) stockpiling effects are more consistent withforward-buying only (i.e., increased purchase quanti-ties and increased interpurchase times).

An overview of the meta-analysis findings is pro-vided by the following matrix. It highlights how ex-ogenous factors operate differently on the separatecomponents of promotional response. Entries in thematrix indicate the relative strength of the effect of theexogenous factors on each consumer behavior (see Ex-hibit 1).

The finer details of these effects, along with theirmanagerial implications, are discussed in §5.

1.4. CaveatsIt is important to note the following caveats. First,while we take a theory-based approach to developingour conceptual framework for the meta-analysis, it isnot derived explicitly from the underlying choicemod-els. To date, no such integrated model exists in the lit-erature, although recent work by Lee and Staelin

4We also test for the presence of a consumption increase by com-paring, for each household the ratios of average quantity to averageinterpurchase time under promotion and nonpromotion purchases(as this number is a straight proxy for the rate of consumption) andpresent the results in §4.1.

(1999) which seeks to develop multicategory demandsystems from consumer utility structures is a step inthis direction. Our framework, however, is largely con-sistent with the spirit of choice models in which con-sumers seek to maximize utility in the presence ofbudget constraint.

Second, the unit of analysis is a single elasticity foreach brand. That is, we do not explicitly model con-sumer heterogeneity in choice model response param-eters prior to computing the brand-level elasticities (asin Bucklin et al. 1998). We do, however, include pref-erence heterogeneity and purchase event feedback inthe model and allow for correlation between thebehaviors.5

Third, we do not attempt to address store switching.Clearly, the total elasticity can be defined at a higherlevel of generality by including the consumer’s storeselection decision (e.g., Bell and Lattin 1998.) An inte-grated approach to encompass all aspects of these con-sumer decisions is a desirable direction for futureresearch. Fourth, the spirit of the analysis is cross-sectional (i.e., across-brand and category differences inthe three types of elasticity). Our model and approachdoes not address dynamic or long-term effects of pro-motions (e.g., Mela et al. 1997). We do, however, usethe results of our analysis to inform the issue ofwhether or not promotions increase consumption.

5Abramson et al. (1996) show that it is most important to accountfor preference heterogeneity and purchase event feedback, and that“under-specifying b heterogeneity does not result in any significantbias of the parameters estimated” (p. 18). This view is corroboratedby Ailawadi et al. (1998) who show that inclusion of preference het-erogeneity and loyalty variables may be sufficient to ensure reliableestimates.



The remainder of the paper is organized as follows.The next section provides background and developsthe conceptual framework which motivates the exo-nenous variables for the meta-analysis. Section 3 de-scribes the data and methodology. We discuss the re-sults and their managerial implications in §4. Section5 concludes the paper.

2. Background and ConceptualFramework

We briefly highlight two streams in the literature onconsumer response to price promotions: (1)individual-level models of elasticity decomposition,and (2) regression-based models that relate exogenousvariables to variation in elasticities. Subsequently, wedevelop a framework for conducting the meta-analysisand compare and contrast this to existing work.

2.1. Elasticity Decomposition and Drivers ofElasticity

Gupta (1988) presents a model to simultaneously cap-ture the primary and secondary demand effects of apromotion and his results, and the subsequent workby Chiang (1991) suggests that the majority of pro-motional response (upwards of 80%) is due to brandswitching—that is, secondary demand effects domi-nate. Bucklin et al. (1998) report an overall primary-secondary breakdown of 58%�42% in the yogurtcategory. Given these differences, the obvious questionarises: Is there a pattern to the elasticity decomposi-tion? This issue is the focus of the first part of this pa-per. The second goal of the paper is to then examinevariability in the brand-level choice, incidence, andquantity elasticities themselves.

Bolton (1989) was among the first to investigate themarket characteristics associated with differences inpromotional price elasticities. She developed a modelthat related the differences in promotional elasticitiesto factors such as brand market share, manufacturerand retailer advertising levels, and promotional activ-ity at the brand and category level. Her data trackedsales of three brands in each of four categories acrossa set of 12 stores. The results indicate that these brandand market characteristics explain a substantialamount of the variation in promotional price elastici-ties. In particular, brands with smaller market shares,

lower levels of category and brand display activity,and higher levels of category and brand couponing aremore elastic. Interestingly, she finds that the effects ofcategory display and feature activity on promotionalelasticities are much larger than the effects of brandprices, display, and feature activity.

Fader and Lodish (1990) use IRI Marketing Factbookdata from 331 product categories to explore the rela-tionship between category structure (e.g., purchase cy-cle, penetration, etc.) and promotional movement (e.g.,volume sold on price cuts, display and feature, etc.).They report systematic relationships between categorycharacteristics and promotional policies. For example,high penetration, high frequency products were themost heavily promoted (although they did not receivea disproportionate share of manufacturer couponing).Raju (1992) has a focus similar to that of Fader andLodish (1990) in that he explores the relationship be-tween category characteristics and category sales. Hisdependent variable is the standard deviation in cate-gory sales over time. He finds that higher variabilityin category sales is associated with deeper, albeit in-frequent, dealing in the category, cheaper products,and the ability of consumers to stockpile.

Narasimhan et al. (1996) study the relationship be-tween product category characteristics and promo-tional elasticity using data from 108 product catego-ries. They consider three types of promotions (regular,featured, and displayed price cuts) and seven categorycharacteristics (penetration, interpurchase time, price,private label share, number of brands, impulse buying,and the ability to stockpile). Their measures of pro-motional response were generated from the IRI Info-Scan Topical Marketing Report and the category char-acteristics were generated from IRI’s scanner paneldata. They report that promotions get the highest re-sponse for brands in easily stockpiled, high penetra-tion categories with short purchase cycles. To sum-marize, factors which have been found to increaseelasticities are given in Exhibit 2.

2.2. This ResearchOur focus on the elasticity breakdown is motivated byGupta (1988) and by the information needs of categorymanagers. Our model relating variability in elasticitiesto exogenous brand, category, and consumer covari-ates is closest to Bolton (1989) and Narasimhan et al.



Exhibit 2

Author Factors Increasing Elasticity

Bolton (1989) Smaller market sharesLower levels of display (brand and category)Higher couponing (brand and category)

Fader and Lodish (1990)1 High penetrationHigh frequency of purchase

Raju (1992)1 Deeper, infrequent dealingConsumer ability to stockpile

Narasimhan, Neslin,and Sen (1996) High penetration

Short purchase cyclesConsumer ability to stockpile

1They do not study elasticities directly; however, their study implies this.

(1996). Table 1 summarizes the key differences be-tween our study and previous literature.

First, we choose to model elasticities using anindividual-level choice framework. The rationale isthat market-wide assessment of higher or lower elas-ticities for a brand, can be traced back to the underly-ing behavior of individuals. Second, we obtain elastic-ity estimates across brands and categories from thesame set of household data. Thus, all purchase deci-sions are subject to the same budget constraints andconsumers are exposed to common store environ-ments. Therefore, any potential cross-category substi-tution effects are implicitly absorbed in the elasticitycalculation. A side benefit is that typical store-levelsales data are generated weekly by different batches ofconsumers who happen to shop that week. In this sit-uation, it is impossible to know how this traffic issueaffects elasticity estimates, whereas using observationsfrom the same panelists avoids this potentially con-founding factor.

Third, as in Narasimhan et al. (1996) we incorporatefactors that account for across-category differences. Toenhance consistency we calculate these variables di-rectly from our panel data instead of using nationalaverages. Fourth, we use an iterated GLS method(Montgomery and Srinivasan 1996) for our meta-analysis to account for potential heteroscedasticityfrom two sources: measurement errors in the left-hand-side (elasticity estimates), and cross-category

modeling errors. This approach leads to better modelfits than those found in previous work. Last, we de-velop a conceptual framework that relates promotionalresponse in the form of primary and secondary de-mand effects to category, brand, and consumer covar-iates. The variables in the conceptual framework sum-marize a utility-maximizing consumer’s view of theattractiveness of a price promotion given the brand’scategory environment and the perceived status of thatbrand in the category.

The “empirical generalization” contribution of thepaper takes place at two levels. First, we present find-ings on the decomposition or promotional elasticity.Second, we explain the variability in promotional re-sponse by modeling the elasticities as a function of ex-ogenous factors suggested by our framework.

2.3. Conceptual FrameworkIn building the conceptual framework we rely heavilyon the classic notion of a utility-maximizing consumeroperating under a budget constraint (Varian 1992) andon the prior literature discussed above. Our rationaleis that the derived elasticities come from choicemodelswhich assume utility-maximizing consumers; the con-ceptual framework should also share this view. Asnoted previously, the conceptual framework incorpo-rates three broad classes of factor (category, brand, andconsumer), and Table 2 lists the variables and the hy-pothesized effects of each. (Details of the operationalmeasures are given Appendix A.)

2.3.1. Category Factors. Category factors influencethe value of the economic opportunity (as perceivedby the consumer) that price promotions offer in a par-ticular product class. For example, a price promotionin a storable category might be viewed very favorablybecause the consumer can manage inventory and time-shift purchases to take advantage of the promotion.

• Share of Budget. Given that all product categorieson the consumer’s shopping list are subject to the samebudget constraint, we anticipate that consumers aremore likely to accelerate their purchase for items thathave a higher share of budget. The hypothesis is thatconsumers are likely to adjust incidence and purchasequantity to take advantage of a promotion in this typeof category. This is analogous to the idea that heavyusers in a category are likely to be the most responsive



Table 1 A Comparison of Frameworks for Promotional Response

Study Exogenous Endogenous Data Objective

Bolton (1989) Market CharacteristicsCategory Price ActivityBrand Market ShareMfr AdvertisingCoupon MagnitudeDisplay ActivityRet Advertising

Brand Elasticity Store Explanatory

Fader and Lodish (1990) StructuralHH PenetrationPurchases per HHPurchase CyclePrivate Label SharePrice

Promotional% Vol on Feature% Vol on Display% Vol on Price Cut% Vol on Mfr Cpn% Vol on Ret Cpn

Aggregate Exploratory

Raju (1992) Category CharacteristicsExpensiveness of CatBulkiness of CatCompetitive IntensityMagnitude of DiscountsFrequency of Discounts

Variability in Sales Aggregate Explanatory

Narasimhan, Neslin, and Sen (1996) Category CharacteristicsCat penetrationInterpurchase TimePricePrivate Label ShareNumber of BrandsImpulse BuyingAbility to Stockpile

Price ElasticitiesFeatured Price CutDisplayed Price CutFeatured Price Cut

Aggregate Explanatory

Our Study Category CharacteristicsShare of BudgetBrand AssortmentSize AssortmentStorabilityPerceived DifferentiationNecessityPurchase Frequency

Price ElasticitiesTotal ElasticityBrand ElasticityIncidence ElasticityQuantity Elasticity

Panel Explanatory

Brand CharacteristicsRelative Price PositionPrice VariabilityDeal FrequencyDeal DepthBrand ExperienceBrand Loyalty

Consumer CharacteristicsIncomeAgeEducation



Table 2 Summary of Meta-Analysis Hypotheses1

Secondary Demand Primary Demand

(1) Category FactorsShare of Budget � �

Brand Assortment � �

Size Assortment � �

Storability � �

Perceived Differentiation � �

Necessity � �

Purchase Frequency � �

(2) Brand FactorsRelative Price Position � �

Price Variability � �

Deal Frequency � �

Deal Depth � �

Brand Experience � �

Loyalty (Repeat Purchase) � �

(3) Consumer FactorsIncome � �

Age � �

Education � �

1 �(�) indicates this variable leads to lower (higher) elasticities.

to promotions. The impact of share of budget on sec-ondary demand is less clear. Consumers are morelikely to have well-formed preferences for items thatconstitute a large share of budget. This suggests lessswitching.6

• Brand Assortment (breadth of variety).Narasimhan etal. (1996) utilize number of brands as an independentvariable in their study of promotional elasticities. Theyobserve a negative effect on total elasticity which theyattribute to brand switching. The rationale for this re-sult is the presence of many brands reflects broaderproduct differentiation. This, in turn, protects an in-dividual brand from “the enticement offered by a com-petitor’s promotion (p. 20).” Bawa et al. (1989) find thatlarger assortments tend to generate higher trial for newproducts. Thus, we expect the primary demand effectto increase with brand assortment.

• Size Assortment (depth of variety). Consumersshould be more elastic in categories that offer a broad

6Raju (1992) utilizes expensiveness in his study of sales variability.The share of budget variable here captures similar information.

variety of size assortments, because they have moreoptions and more refined information about the unit(Russo 1977 indicates that unit-price knowledge in-creases price sensitivity). Furthermore, consumersmayeither buy larger sizes, or switch brands depending onthe way in which unit price information is presentedand/or processed. Guadagni and Little (1983) also findthat, when offered price promotions, consumersswitch up to larger sizes. Thus we expect positive pri-mary and secondary demand effects.

• Storability. Storable products facilitate stockpilingand therefore intertemporal purchase displacement(Litvack et al. 1985; Raju 1992; Narasimhan et al. 1996).That is, consumers can purchase at irregular intervalsin response to deals, which means they can buy more,but are not compelled to buy on any particular trip.We therefore expect a higher overall primary demandresponse to promotions. The effect on secondary de-mand is not as clear. If, however, the storable productis also a nonfood item (e.g., detergent) wemight expectto see a positive effect on secondary demand too. Thisis because consumers appear more willing to switchbrands in categories where they are not consuming theproduct directly, and are therefore less vulnerable totaste incompatibilities.

• Perceived Differentiation. This construct is a refine-ment of the brand assortment constructs presented ear-lier. Assortment is determined by the retailer—all con-sumers are exposed to the same degree of assortmentwithin a given category, but may perceive it differ-ently. Perceptions of differentiation are based on con-sumer experience with different brands. Categorieswhere brand alternatives are perceived as highly dif-ferentiated will be characterized by greater respon-siveness in primary demand and less responsivenessin secondary demand.

• Necessity. Narasimhan et al. (1996) hypothesizethat promotional elasticity is higher for categories thatare characterized by a higher degree of impulse buy-ing. The notion is that impulse buying is an in-storeresponse often attributable to promotional activity.Wetherefore expect nonimpulse (i.e., relative necessity)products to be less elastic with respect to purchase in-cidence and stockpiling and hence, exhibit a lower pri-mary demand effect. Given that a product is a neces-sity and as such consumers have little flexibility to



adjust primary demand, their only outlet for savingmoney is via brand switching. This suggests a highersecondary demand effect.

• Purchase Frequency. We expect to see greaterswitching effects for more frequently purchased prod-ucts, but less stockpiling (Fader and Lodish 1990).

2.3.2. Brand Factors. Brand Factors influence theconsumer’s perception of how brand characteristics in-teract with promotions to affect the perceived quality-per-dollar assessment for a brand. For example, a pricepromotion on a market leader might be viewed morefavorably than a price promotion on a lesser brand.

• Relative Price Position. The consumer’s perspectiveon whether or not a given brand is a “premium” brandwill influence elasticity. Blattberg and Wisneiwski’s(1989) finding on asymmetric switching—that pre-mium brands draw more consumers when they pro-mote—implies a higher primary demand effect due toincreased incidence and a higher secondary demandeffect due to increased switching.

• Price Variability. From the consumer’s perspective,relative price stability improves the ability to distin-guish between regular and promoted prices, and there-fore take advantage of price promotions by strategi-cally accelerating purchases or switching brands. Thisleads to Bolton’s (1989) suggestion that greater pricevariability will be associated with lower response.Consequently, we expect greater price variability willlead to a lower primary demand effect and lower sec-ondary demand effect.

• Deal Frequency. More frequent dealing leads tomore opportunities for the consumer to exploit pricepromotions. All other things equal, however, very fre-quent dealing implicitly reduces the attractiveness ofany individual deal in any time period. Prior researchshows that consumers are able to accurately detect pro-motion frequency (Krishna et al. 1991). Furthermore,Thaler (1985) and Winer (1986) imply that frequentpromotions will lead to lower reference prices. Con-sequently, brands with more frequent deals shouldhave lower elasticities.

• Deal Depth. A higher percentage discount from thebase price greatly improves the quality-per-dollarequivalent of a brand. Consequently, greater depth

should be accompanied by higher purchase accelera-tion (Golabi 1985, Ho et al. 1998). Raju (1992) hypoth-esizes that deep discounts can induce some consumerswho are loyal to competing brands to switch to thepromoted brand. Hence, greater deal depth shouldalso be associated with a positive secondary demandeffect.

• Brand Experience. A promotion on a brand that hasbeen tried by a large fraction of consumers, will, allelse equal, have higher primary elasticities of demand,due to higher drawing power. “Double jeopardy” sug-gests that these brands with high trial also experiencemore frequent purchase and higher than expected re-peat, and “excess” behavioral loyalty (Fader andSchmittlein 1993). As discussed below, higher brandloyalty leads to lower secondary demand elasticities.

• Brand Loyalty. Brands with more repeat purchasingand a more loyal franchise will be less elastic in brandchoice and more elastic with respect to purchase quan-tity (Krishnamurthi and Raj 1991). This is also conjec-tured by Tellis (1988). We might also expect thesebrands to have a higher drawing power and as suchgenerate higher incidence elasticities.

2.3.3. Consumer Factors. Consumer Factors influ-ence the ability or disposition of the brand’s core cli-entele to respond to a price promotion. For example, abrand with a predominantly higher income clientelemight see less response to its promotions.

• Income. Brands with higher income consumersshould be less sensitive to price in brand choice(Ainslie and Rossi 1998). Conversely, they may expe-rience stockpiling because their consumers have moreability to take advantage of deals when the opportu-nity arises.

• Age. To the extent that older households shouldhave more time available to shop and search for deals,one could argue that they should be more elastic.Ainslie and Rossi (1998, p. 99) however, find direc-tional support for the idea that older consumers are infact less price sensitive, which leads us to expect lowerelasticities for brands with older clienteles.

• Education. More educated consumers are expectedto be more diligent in taking advantage of price vari-ability. Brands with a more educated clientele will seemore response to their price promotions.



3. Methodology and Data3.1. Choice Models and Price ElasticityIn deriving the choice models, we assume that con-sumers (households) have a linear additive utilityfunction and for each product category there is a setof brands available which consumers perceive to besubstitutes. To conserve space, we simply describe theessence of the model and our modeling decisions here,and place the details in Appendix B.

Gupta (1988) modeled the category decision usinginterpurchase time. Our dataset allows us to model the“buy/no buy” decision directly. In addition, whilesome authors (e.g., Bucklin et al. 1998) have modeledquantity as a discrete variable, we adopt a continuousformulation. We make this trade-off in order to allowfor correlation between the choice and quantity deci-sions (e.g., Krishnamurthi and Raj 1988).

We assume consumer i at each purchase occasion thas to decide whether to purchase, respectively, ineach of the product categories, and if so, which brandto choose and what amount to buy. For brand choice,we assume that, conditional on purchase incidence, abrand is selected if and only if it yields the highestindirect utility in that category. Furthermore, consum-ers can forego purchasing in the category if the pur-chase utility threshold is not crossed.

In specifying the purchase quantity equations, weemploy either a system of log-log or semi-log demandequations in which each demand equation corre-sponds to a selected brand. For a given category, wechoose among alternative formulations of the purchasequantity model on the basis of model fit. It is importantto note that in integrated choice, incidence and quan-tity models of this type, the quantity portion of themodel typically generates the least reliable parameterestimates and the poorest model fits of the three be-havioral pieces. A poor-fitting model, may in turn, leadto a downward bias in the estimated quantityelasticity.

Given the choice model structure just described (andlaid out in Appendix B), we can derive the exact ex-pression for each elasticity component (see AppendixC), and it follows immediately that the total elasticityis given by the sum of the three component elasticities:gT � gC � gI � gQ (Gupta 1988). Given that our focus

is on examining the elasticity differences across brandsand categories, we have to first ensure that these elas-ticities are indeed comparable. To establish consis-tency, we first normalize all sizes within a category bythe most commonly purchased size in that category(prices are adjusted accordingly). In this way, we en-sure that all categories are measured in their respectivepurchase units and eliminate any potential “magni-tude” problem in the meta-analysis which follows.Once the coefficients of themodel have been estimated,the elasticities are calculated for each observation andhousehold and then averaged over all households.7

3.2. Meta-Analysis Explanatory ModelLet ebjc denote the elasticity estimate for consumer be-havior b (i.e., choice, incidence, or quantity) for brandj in category c. The following equations detail our ap-plication of the Montgomery and Srinivasan (1996)Generalized Least Squares approach to meta-analysis.Their approach is predicated on the notion that errorsacross observations in the meta-analysis will not bei.i.d. This intuition is relevant in our setting for thefollowing reason. Our elasticity estimates are gener-ated from choice model parameter estimates that havebeen estimated with error (we apply the Delta Methodto derive the standard errors for the elasticity esti-mates), therefore the relationship between the true andestimated elasticities is given by (where the b subscriptis dropped for ease of exposition)

2e � e � � , � � N(0, r ). (1)jc jc jc jc �

Furthermore, the true model that relates the elasticityto exogenous factors that determine that elasticity is

F Kf

2e � � � b X � v , v � N(0, r ), (2)jc � � fk fkjc jc jc vk�1f�1

where is the unique variance in the true elasticity2rvmeasure, f indexes the classes of exogenous factors,and Kf the number of variables in each class of factor.We assume that the estimation errors (Equation (1))and unique errors (Equation (2)) are uncorrelated so

7Note that due to nonlinearities in the elasticity expression thismethod is preferred to the method where one simply inserts averagevalues of the covariates into the analytical expression for the elastic-ity (see Ben-Akiva and Lerman 1985).



Table 3 Description of Product Categories

Category Alternatives1 Purchases Storable Necessity Price Range2

Bacon 6 844 No No (1.60, 2.69)Margarine 10 1,504 No Yes (0.55, 1.44)Butter 4 388 No Yes (1.30, 1.85)Ice Cream 11 1,168 No No (1.60, 4.01)Paper Towels 10 1,442 Yes Yes (0.54, 1.08)Sugar 6 686 No No (1.61, 2.15)Liquid Detergents 25 886 Yes Yes (4.41, 9.80)Coffee 18 750 Yes No (4.65, 8.97)Softdrinks 15 967 Yes No (0.22, 6.99)Bath Tissue 20 2,192 Yes Yes (0.92, 2.11)Potato Chips 20 1,179 No No (1.09, 2.82)Dryer Softeners 18 288 Yes No (1.49, 2.76)Yogurt 10 318 No No (0.33, 2.35)

Totals 173 12,612

1Number of unique brand-size alternatives.2In the model estimation, prices are normalized to a common unit.

that the total error is partitioned into the sum of thesetwo components: wjc � �jc � vjc and wjc � N(0, 2r ��

).2rvFrom the conceptual framework in §2 we have three

sets of variables: (1) Category Factors, (2) Brand Fac-tors, and (3) Consumer Factors which contribute theexogenous variables for the meta-equation

K K1 2

e � � � b X � b Xjc � 1k 1kjc � 2k 2kjck�1 k�1

K3

� b X � w , (3)� 3k 3kjc jck�1

where the subscripts 1, 2, and 3 denote the three cate-gories of exogenous variables and wjc denotes the totalerror in the elasticity estimate. This partitioning of themeta-regression error is especially important when es-timates of the left-hand side variable are drawn frommany studies conducted under different conditions.8

While in this paper the elasticity estimates are devel-oped from the same choice models and households,the estimates do come from a wide range of productcategories. A further conceptual and practical advan-tage of the GLS procedure is that it allows us to controlsomewhat for heterogeneity in the meta-analysismodel rather than in the parameters of the underlyingchoice models. That is, we recognize that the brand’selasticity estimate follows a distribution that varies bybrand and category and take this into account in per-forming the meta-analysis. Estimates of the coefficientvectors, and the variance partitioning are obtained it-eratively, with standard errors of the elasticities serv-ing as GLS weights in the initial estimation. Subse-quent weights are obtained by further iteration and wefind that in all cases convergence occurs rapidly in 5–6 iterations.9

3.3. DataSource and Description. The data were generated froma market basket database provided by IRI. Purchase

8For example, meta-analyses often combine work from several dif-ferent authors, conducted over many different time periods and da-tasets.9The interested reader is referred to Montgomery and Srinivasan(1996) for complete details on this iterative scheme.

records for a random sample of 250 panelists, shop-ping in three supermarkets over a period of 78 weekswere used in the analysis. The 250 panelists were cho-sen at random from a total pool of 494 households.These panelists reflect the underlying demographics ofthe larger pool (which, in turn, was selected by IRI tobe representative of the whole market). The first 26weeks of data were used to initialize within-householdmarket share variables; the remaining 52 weeks wereused for calibration of the choice models derived inAppendix B.Category Selection and Explanatory Variables. The se-

lection of product categories for the analysis was de-liberate. We sought to include a range of categoriesheterogeneous on several dimensions (e.g., share ofbudget, storability, etc.). Our chosen products cover 3out of 4 PROMCLUS and PURCLUS groups, respec-tively, as defined in Fader and Lodish (1990). Table 3presents some basic descriptive information on theproduct categories in the dataset.

4. ResultsRecall that this paper has two goals: (1) to investigatevariability in the elasticity percentage decomposition



Table 5 Elasticity Decomposition Across Categories1

Percent of Total ElasticityDue to Demand

Category Choice Incidence Quantity Secondary Primary

Margarine 93.9% 5.7% 0.4% 93.9% 6.1%Softdrinks 85.6% 5.8% 8.5% 85.6% 14.4%Sugar 84.1% 13.3% 2.5% 84.1% 15.9%Paper Towels 83.2% 6.0% 10.8% 83.2% 16.8%Bathroom Tissue 81.2% 3.6% 15.2% 81.2% 18.8%Dryer Softeners 78.9% 1.4% 19.7% 78.9% 21.1%Yogurt 78.4% 12.2% 9.4% 78.4% 21.6%Ice Cream 77.4% 18.9% 3.7% 77.4% 22.6%Potato Chips 72.0% 4.5% 23.5% 72.0% 28.0%Bacon 71.6% 20.3% 8.2% 71.6% 28.4%Liquid Detergents 69.6% 0.7% 29.7% 69.6% 30.4%Coffee 52.6% 2.8% 44.6% 52.6% 47.4%Butter 48.8% 42.3% 8.9% 48.8% 51.2%

Average 75.2% 10.6% 14.3% 75.2% 24.8%Std. Deviation 0.13 0.11 0.12 0.13 0.13Minimum 48.8% 0.7% 0.4% 48.8% 6.1%Maximum 93.9% 42.3% 44.6% 93.9% 51.2%

Storable 75.2% 3.4% 21.4%Nonstorable 75.2% 16.7% 8.1%

Necessity 75.3% 11.7% 13.0%Nonnecessity 75.1% 9.9% 15.0%

1Based on share-weighted brand elasticities.

Table 4 Mean and Standard Deviation of Elasticity Estimates1

CategoryTotal

(XT, r )T

Choice(XC, r )C

Incidence(XI, r )I

Quantity(XQ, r )Q

Bacon (1.57, 0.078) (1.25, 0.216) (0.20, 0.143) (0.13, 0.009)Margarine (2.34, 0.003) (2.22, 0.064) (0.11, 0.116) (0.01, 0.051)Butter (1.98, 0.004) (1.24, 0.075) (0.57, 0.456) (0.17, 0.382)Ice Cream (2.58, 0.004) (1.89, 0.206) (0.58, 0.524) (0.10, 0.319)Paper Towels (4.74, 0.061) (4.00, 0.179) (0.22, 0.255) (0.52, 0.122)Sugar (4.60, 0.026) (4.03, 0.498) (0.46, 0.727) (0.11, 0.241)Liquid Detergents2 (5.66, 0.600) (3.95, 0.704) (0.07, 0.306) (1.63, 0.139)Coffee2 (3.06, 0.049) (1.65, 0.060) (0.06, 0.065) (1.36, 0.036)Softdrinks (3.09, 0.066) (2.66, 0.108) (0.11, 0.106) (0.31, 0.062)Bath Tissue (4.66, 0.214) (3.85, 0.308) (0.09, 0.488) (0.71, 0.079)Potato Chips (3.38, 0.046) (2.50, 0.089) (0.07, 0.105) (0.81, 0.054)Dryer Softeners2 (5.28, 0.097) (4.08, 0.128) (0.12, 0.359) (1.07, 0.187)Yogurt (1.92, 0.069) (1.57, 0.084) (0.15, 0.139) (0.20, 0.114)

1Based on raw (unweighted) elasticities.2Primary demand elasticities � 1.0.

across product categories, and (2) to analyze more for-mally, via meta-analysis, the variability in the brand-level elasticities themselves.

4.1. Elasticity Percentage DecompositionDispersion in Elasticities. We report the mean and var-iance of the brand-level elasticities for all 13 categoriesin Table 4.

Examination of the results reveals the following.First, there is considerable across category variation inbrand-level elasticities. Second, there is variationacross behaviors, within a category, but the pattern isconsistent: choice elasticities are much larger than ei-ther incidence or quantity elasticities. The choice (i.e.,secondary demand) elasticities are all greater than oneand the incidence plus quantity (i.e., primary demand)elasticities are generally less than one. The exceptionsare liquid detergents, coffee, and dryer softeners.

The overall pattern of results is consistent with ourexpectations for mature packaged goods. That is, itseems unlikely that promotions in most of these typesof categories will expand primary demand, althoughrecent empirical and analytical studies (e.g., Assuncaoand Meyer 1993, Ailawadi and Neslin 1998, Ho et al.1998) that link consumption dynamics to promotionresponse, have shown that there can be important pri-mary demand effects even for these types of products.We return to this issue shortly.

The Decomposition of Elasticities. Table 5 shows thepercentage decomposition due to choice, incidence,and quantity for each of the 13 categories.

With the exception of sugar, the breakdowns for anumber of categories differ from those reported inGupta (1988) and Chiang (1991). The choice elasticityvaries from a minimum of 49% of total elasticity forbutter to a maximum of 94% for margarine; the inci-dence elasticity ranges from a minimum of 1% of totalelasticity for liquid detergents to a maximum of 42%for butter; the quantity elasticity ranges from almostzero for margarine to a maximum of 45% for coffee.10

10Our results for the coffee category differ somewhat from Gupta(1988). We attribute this to two factors: (i) we have newer and dif-ferent data, and (ii) while Gupta’smodel addresses the “when” ques-tion of purchase timing, we focus on the “whether” decision of pur-chase incidence.



These ranges are reflected in the overall average of 75/11/14 which places less emphasis on choice and moreon quantity, relative to previous work.Role of Storability. Further sorting of the estimates in

Table 5 reveals: (1) all refrigerated products (marga-rine, yogurt, ice cream, bacon, and butter) have muchhigher proportions for the incidence effect than for thequantity effect, and (2) all storable products (soft-drinks, paper towels, bathroom tissue, dryer softeners,liquid detergents, and coffee) have just the oppositepattern. Both observations have intuitive appeal andare consistent with the experimental findings ofLitvack et al. (1985). The result is highlighted in Table5 where even though the choice percentage is constantbetween storable and nonstorable products (75% inboth cases), the quantity effects are much higher forstorable products (21% versus 8%). (We discuss thetwo categories—potato chips and sugar—that do notfall into these two groups, shortly.)Role of Consumption Dynamics. Further analysis is re-

quired in order to understand whether promotions: (a)increase consumption, (b) cause stockpiling but noconsumption increase, or (c) have no appreciable effecton either stockpiling or consumption. All three resultshave been observed in the literature. For instance,Ailawadi and Neslin (1998) show that promotionslead to increased consumption in yogurt andKrishnamurthi and Raj (1991) document stockpiling bybrand loyal consumers. Krishna et al. (1991) show thatwhen promotions are very frequent, consumers do notneed to stock up on deals.

To make this issue more concrete, consider the de-compositions for sugar and potato chips. Neither cate-gory is refrigerated, yet both are nonstorable due tofreshness considerations—the decompositions suggestthat consumers purchase more potato chips but notmore sugar when these products are on sale. Ourspeculation is that consumers buy more potato chipsbecause they want to consume more and this is lesslikely to occur with sugar. Softdrinks are another in-teresting category. It is well known that softdrinks areone of the most frequently promoted categories11, yet

11Totten and Block (1987) report that Coke promotes 41% of the timeand Pepsi 47%. In our data the comparable figures are 50% and 58%,respectively. We should also note here that it is possible that the

Table 5 shows that softdrinks have a somewhat smallstockpiling effect (8%), despite being a storable item.In addition, Lal (1990) provides a theoretical explana-tion for alternating promotions by major softdrinkbrands (e.g., Coke and Pepsi)—this ensures that rivalstore brands are effectively kept out of the market.

To investigate consumption dynamics in more de-tail, we analyzed panelist purchases in all productcategories during promotion and nonpromotion pe-riods. One important observation here is that the elas-ticity estimates themselves are insufficient to deter-mine whether or not consumption increases as a resultof promotion. This is because one needs a temporalanalysis to uncover this—the elasticity estimates reflecthow consumers respond to price changes at givenpoints in time, but do not indicate how long it takesbefore these consumers return to the market.

To ascertain whether consumption increases wereoccurring we computed summary statistics from thedata. First, we measured average quantities on pro-motion and nonpromotion and also measured averageinterpurchase times subsequent to promotion and non-promotion purchases. In addition, we computed theaverages for household ratios of quantities to inter-purchase times under both promotion and nonprom-otion purchases.12

Exhibit 3 is based on this exploratory analysis andis therefore only indicative of presence and absence ofconsumption increases—a thorough examination ofthis issue requires additional research.

In Exhibit 3, Q, , and represent average quan-IP Q/IPtities, interpurchase times, and rates of consumption,respectively, and all three quantities are calculated forboth promotion and nonpromotion purchases.

Prior to interpreting the data in Exhibit 3, severalfacts need to be noted. First, all of the calculations inthe exhibit have been performed conditional on a pur-chase having taken place. We know, however, that

switching effect for this category is overstated. It is well known fromthe Totten and Block data and other studies, that deal-to-deal buyingfor softdrinks is widespread. If it is also the case that quantities ondeal-to-deal purchases are relatively unchanged, the model will ac-count for the large swings via the brand choice part of the model.12This ratio is an estimate of the rate of consumption.



Exhibit 3

Promotional Purchases Nonpromotional Purchases t-ratios

Category Q IP Q/IP Q IP Q/IP Quantity Time Cons.

Stockpiling OnlyBathroom Tissue (roll) 6.76 27.65 0.30 4.83 22.38 0.28 4.47 1.59 0.53Coffee (oz) 35.71 58.84 0.80 24.76 43.75 1.19 4.45 1.67 �1.15Detergent (oz) 132.42 77.32 2.37 82.70 48.12 2.71 4.05 2.35 �0.52Paper Towel (roll) 2.00 45.12 0.08 1.40 34.77 0.08 4.98 1.71 0.20

Increased ConsumptionBacon (oz) 27.23 46.57 0.92 19.92 47.49 0.68 4.42 �0.12 1.47Potato Chips (oz) 10.25 44.63 0.64 7.37 41.78 0.41 4.44 0.32 1.62Softdrinks (oz) 240.32 45.28 9.18 135.86 45.86 6.27 5.69 �0.06 2.02Yogurt (oz) 33.12 37.69 1.43 25.12 38.32 1.10 3.75 �0.08 1.85

“No Effect”Butter (oz) 21.09 41.96 0.70 20.62 38.67 0.83 1.03 0.70 �1.08Dryer Softeners (sheets) 45.83 69.50 0.88 41.24 67.63 0.81 1.02 0.15 0.42Ice cream (oz) 66.63 38.76 1.72 66.33 35.79 1.85 0.28 0.67 �0.64Margarine (oz) 19.27 40.01 0.59 18.46 38.65 0.67 1.21 0.28 �1.10Sugar (lb) 5.42 59.37 0.18 5.41 58.21 0.23 0.09 0.13 �0.69

consumption may increase as a result of greater con-sumption by a fixed number of consumers, or, throughexpansion to additional consumers. Hence, we use thelabel “No Effect” with some caution, and with this inmind, return to discuss the case for ice cream shortly.

Second, there are several ways to infer consumptionincreases from the data in the exhibit. The most directwould be to simply compare our estimates of the con-sumption rate (i.e., ) under promotion and non-Q/IPpromotion purchases. There are, however, two poten-tial difficulties here. The first is simply statistical—theestimates of the consumption rates are created by av-eraging ratios across trips and households—and thisprocess makes it more difficult to detect effects. Thesecond reason that we want to look beyond just theconsumption rate estimates is substantive. It could bethe case that even though the estimates of the con-sumption rates are not different from each other, thereis still some intertemporal purchase displacement as aresult of promotion. Consider bathroom tissue. In thisinstance, the average consumption rates of 0.28 and0.30 rolls of tissue per day under promotion and non-promotion are not significantly different from each

other. Looking at the average purchase quantities andaverage interpurchase times separately does, however,provide additional information. The average purchasequantity at regular prices is 4.83 rolls and consumerstake about 22.38 days before buying again, yet whenfaced with promotion, consumers buy an average of6.76 rolls, but take much longer (27.65 days) beforepurchasing again. That is, they buy significantly more,but take significantly longer before buying again,which suggests that promotions on bathroom tissueencourage consumers to stockpile.

Beginning at the top of Exhibit 3, we list four storablecategories (bathroom tissue, coffee, detergent, papertowels) that show evidence of stockpiling. In each case,average quantities are significantly higher and averageinterpurchase times significantly longer following apurchase on promotion. The second grouping containsfour categories (bacon, potato chips, softdrinks and yo-gurt), which show some increase in average consump-tion rates across the nonpromotion and promotionconditions (for bacon p � 0.10 and for the other threecategories p � 0.05 on a one-tailed test). The probableconsumption increases that result from promotions is



also manifest in the fact that average purchase quan-tities are significantly higher, but average interpur-chase times are not significantly longer. It is interestingto note that the only storable category which seems toexperience increased consumption is softdrinks. Wespeculate that this could be due to the extraordinarilyhigh levels of promotion documented earlier.13

The “No Effect” group warrants one further com-ment. As noted above, the statistics in Exhibit 3 arecomputed conditional upon a purchase having oc-curred. Thus, they are only able to detect consumptionincreases for a fixed group of consumers. If, however,promotions also draw additional consumers into thecategory, overall consumption may increase too. Forexample, while we classify ice cream in the “No Effect”category, we note from Tables 4 and 5 that ice creamhas a relatively large incidence elasticity. Our calcula-tions suggest that when ice cream goes on promotion,overall penetration for the category is up by about 2%.In a way, this implies increased consumption as moreconsumers are moved from “no buy” to “buy,” al-though it does not allow us to say whether the averageconsumption for the individual consumers increases.

This final point also highlights the advantages anddisadvantages of this sort of exploratory analysis vis-a-vis model-based analysis. While the elasticity esti-mates do not fully capture intertemporal consumptionchanges (which must be captured in order to makestatements about ultimate primary demand increases),they do have the advantage of being model-driven andcalculated with everything else constant. Furthermore,they capture the interrelationship between the threeconsumer behaviors. The sample averages on the otherhand provide a preliminary indication of consumptioneffects, but any differences in these raw estimatescould be due to a host of uncontrollable factors. De-spite these offsetting benefits, we would expect thedata-based proxies in Exhibit 3 and the model-basedproxies of primary demand expansion (i.e., the quan-tity elasticities) to be positively correlated. For ourdata, the correlation between the 13 quantity elastici-ties in Table 4 and the percentage change in average

13We do not address the “reverse causality” or endogeneity issuehere. That is, firms may promote more because they realize that con-sumers will consume more. For an analysis of the endogeneity issuein a brand choice context, see Villas-Boas and Winer (1997).

quantities under promotion and nonpromotion isabout 0.47.

To summarize, the results from the investigation ofthe elasticity decomposition reveal that the majority ofthe promotion effect (75%) is due to brand switching.This proportion is smaller than previously reportedand suggests a larger than expected primary demandcomponent. Storable products have a proportionallygreater quantity effect than do nonstorables. Furtherexamination of this issue shows that most storables aresimply stockpiled (i.e., even though promotions in-crease average purchase quantities, interpurchasetimes also increase so that there is no apparent increasein total consumption). Blattberg et al. (1981) performan analysis very similar to ours and find evidence ofstockpiling in aluminum foil, facial tissue, liquid de-tergent and waxed paper (Tables 1 and 2, p. 124–125).They also derive a theoretical model to explain con-ditions under which storable products are dealt in or-der to transfer inventory carrying costs to the con-sumer. For softdrinks and some food products,promotions do appear to increase consumption. Ourempirical findings for the yogurt category parallelthose of Ailawadi and Neslin (1998). The more generalevidence for promotions increasing consumption isconsistent with the models of Assuncao and Meyer(1993) and Ho et al. (1998) who show that rational con-sumers increase consumption when faced with pro-motions. As highlighted above, this is a very importantand complex problem and will require a different typeof model to fully investigate it. Silva-Risso et al. (1999)develop a decision support system for determiningoptimal promotion calendars—their model capturesall three consumer decisions (choice, incidence, andquantity), and has the potential to estimate consump-tion effects and their relationship to promotionaleffectiveness.14

4.2. Meta-Analysis ResultsFor ease of exposition and brevity we do not focus onthe effect of each and every variable on all three con-sumer behaviors. Rather, we: (i) discuss the generalpattern of findings as they relate to the conceptual

14Their empirical application, however, used data from the tomatosauce category—a category which is unlikely to exhibit consumptionincreases due to promotions.



Table 6 Standardized GLS Parameter Estimates

Secondary Demand Primary Demand

Choice Incidence Quantity Total

Variable Parameter t-ratio Parameter t-ratio Parameter t-ratio Parameter t-ratio

(1) Category FactorsShare of Budget �0.599 �10.93a 0.001 0.01 0.148 2.68a �0.409 �7.74a

Brand Assortment �0.031 �0.45 0.079 0.87 0.583 8.64a 0.278 4.30a

Size Assortment 0.097 1.82b �0.340 �4.48a 0.386 7.33a 0.177 3.38a

Storability 0.586 8.34a 0.105 1.07 0.486 6.84a 0.676 9.99a

Perceived Differentiation �0.196 �2.59b 0.305 2.92a 0.295 3.85a �0.010 �0.14Necessity 0.328 5.22a �0.185 �1.86c �0.018 �0.31 0.247 4.11a

Purchase Frequency 0.003 0.05 0.097 1.03 �0.294 �4.54a �0.122 �1.97b

(2) Brand FactorsRelative Price Position �0.099 �2.38b �0.027 �0.46 0.016 0.38 �0.016 �0.39Price Variability �0.129 �2.11b �0.185 �2.40b �0.146 �2.62a �0.157 �2.88a

Deal Frequency 0.025 0.59 0.028 0.47 0.025 0.59 0.074 1.64Deal Depth 0.076 1.56 �0.007 �0.11 0.131 2.81a 0.035 0.85Brand Experience �0.059 �1.17 0.540 7.98a �0.068 �1.41 �0.016 �0.33Brand Loyalty (Repeat Buying) �0.164 �2.71a 0.096 1.10 0.191 3.13a �0.022 �0.37

(3) Consumer FactorsIncome �0.070 �1.59 �0.025 �0.41 �0.018 �0.41 �0.066 �1.53Age �0.087 �1.78c �0.043 �0.63 0.044 0.92 �0.066 �1.39Education �0.011 �0.23 0.135 2.10b �0.047 �1.04 0.008 0.19

Willet-Singer (1988) R2 0.74 0.38 0.69 0.75

a � p � 0.01, b � p � 0.05, c � p � 0.10.

framework and hypotheses (Tables 1 and 2), (ii) high-light results that are consistent with prior literature,and (iii) address some counterintuitive findings. Sec-tion 4.3 expands on the managerial implications of theframework.

4.2.1. An Overview of Main Findings. Table 6reports the standardized GLS parameter estimates foreach of the three behaviors, and for the total elasticity.

The model fits are substantially higher than thosefound in previous work and we are better able to ex-plain brand choice and purchase quantity elasticities,than we are able to explain purchase incidence elastic-ities. Category-specific factors are especially powerfulin explaining variability in brand-level elasticities andbrand-factors somewhat less so. Consumer factorshave relatively little explanatory power. Nevertheless,we do observe two small but significant effects.

Bolton (1989) speculates that the reason for weakereffects of the brand factors (e.g., relative price levels)is that their values tend to be similar across categories,making it difficult to detect any effect in the regression.For example, the degree of variance in relative nor-malized prices in category A might be very similar tothat in category B.15 Thus, we believe that Bolton (1989)is correct, if one is looking only at the effects of brand-specific factors on total elasticities. Total elasticity,however, fails to tell the full story. It is interesting tonote that the number of significant effects for the brandfactors is much higher when we look at individual be-haviors. Here the number of significant brand factors

15We examined the cross-category variability in the one variable,Deal Frequency, that was nonsignificant for all behaviors. A v2 testfor equality of variances across categories for this variable fails toreject the null hypothesis.



(8/18) approaches one half, in contrast to 1/6 for totalelasticity.

A comparison of the hypotheses expressed in Table2, with the empirical findings in Table 6, yields thefollowing:

• Hypotheses relating 6 of the 16 variables (Share ofBudget, Storability, Perceived Differentiation, Necessity,Price Variability, and Loyalty) to the primary and sec-ondary demand effects are supported. For example,brands in high share of budget categories see lessswitching in response to promotions (bC � �0.599 t� �10.93), but more stockpiling (bQ � 0.148, t �

2.68).• Hypotheses relating another 6 of the 16 variables

(Brand Assortment, Purchase Frequency, Deal Depth,Brand Experience, Age, and Education) to one of the twoeffects (i.e., either primary or secondary demand) aresupported. That is to say we have one finding signifi-cant in the expected direction and the other nonsignif-icant. For example, increased brand assortment leadsto higher primary demand elasticities (bQ � 0.583, t �

8.64), but does not lead to the expected reduction insecondary demand elasticities (bC � �0.031, t �

�0.45).• We have null results for Deal Frequency16 and In-

come. The remaining two results for Size Assortment andRelative Price Position are somewhat counter-intuitiveand require additional explanation. We discuss theseshortly.

4.2.2. Relationship to the Literature. A total of12 of the 16 variables influence primary and secondarydemand elasticities in a manner consistent with ourexpectations and the results in prior literature. Thissuggests that we have a relatively stable andinternally-consistent pattern of results that are infor-mative for explaining variability in brand-levelelasticities.

Although increased size assortment produces the ex-pected positive effect on secondary demand elasticities

16The null result is different from Mela et al. (1997). They examinethe impact of promotional frequency on a given brand over time andfind that consumer sensitivity increases. In our case, we examinedeal frequency cross-sectionally for a variety of brands and catego-ries in a shorter time horizon. It is possible that our null result is dueto aggregation and the shorter time span.

and a positive effect on stockpiling, it is hard to inter-pret the negative effect for purchase incidence. Onepossible explanation is that consumer size loyalty (e.g.Guadagni and Little 1983, Bucklin and Gupta 1992) un-dermines the ability of promotions to increase pur-chase acceleration. We predicted that brands with arelative price premiumwould, on average, have higherswitching. This argument follows the Blattberg andWisneiwski (1989) conjecture that lower-tier buyersswitch up when given the opportunity. One alternativeinterpretation of our opposite result is simply that buy-ers of relative premium brands are less price-sensitiveand that these brands therefore have lower switchingelasticities—it might be the case that these regularpremium brand buyers who are relatively price-insensitive in choice, outnumber the potential numberof buyers who trade up.

An important feature of our work is that we relatevariability in elasticities to the underlying behaviors.17

Table 6 shows seven instances in which an analysis oftotal elasticity reveals that an exogenous variable hasno influence, yet significant effects can be seen for oneor more of the underlying behaviors. As noted above,this is especially true for the brand-specific factors. Ourresult is important because if managers simply exam-ined total elasticities, they could be misled into think-ing their actions have no impact. For example, in-creased Deal Depth affects primary demand throughstockpiling (bC � 0.131, t � 2.81), yet no effect appearsfor total elasticity. Similarly, the null result for Loyaltywith respect to the total elasticity is due to the coun-tervailing effects on secondary (bC � �0.164, t �

�2.71) and primary demand (bQ � 0.191, t � 3.13).These primary and secondary effects are consistentwith what one would expect given the findings ofKrishna (1992) and Krishnamurthi and Raj (1991).

4.3. ImplicationsThe results can be used to: (i) better inform managersand researchers of general patterns in promotional re-sponse, and (ii) project consequences ofmanagerial de-cisions regarding promotional activity.

We illustrate the first point in two different ways.

17Narasimhan et al. (1996) develop hypotheses based on underlyingconsumer behaviors (e.g., brand switching, purchase acceleration,etc.) but their data only allow analysis of effects on total elasticity.



Exhibit 4

High Share of Budget Low Share of Budget

High Loyalty Low Loyalty High Loyalty Low Loyalty

Storable 31/691 25/752 22/783 15/854

Nonstorable 19/815 28/726 19/817 21/798

First, note that the overall elasticities for coffee andsoftdrinks reported in Table 4 are approximately equal.A more careful analysis of the breakdown in elasticityreveals that a relatively large fraction (47%) of the cof-fee elasticity is attributable to primary demand, whilethe analogous figure for softdrinks is only 15%. Themanagerial implication is that promotions on coffeemight encourage forward-buying and therefore gen-erate very little in the way of incremental sales. Al-though forward-buying does not lead to incrementalsales, it does produce desirable competitive effects—aconsumer with a pantry full of Maxwell House haslittle need for Folgers. On the other hand, if all pro-motions on softdrinks were to do is increase switching,then the benefits of the promotion (to the manufac-turer) may be shortlived. Recall, however, that in thisparticular case of softdrinks, we also obtained evi-dence that promotions increase consumption (see§4.1), but did not find this effect for coffee.

Second, the results allow us to make directionalstatements regarding how promotions are likely to af-fect elasticity components for a particular brand.18

Among the exogenous factors listed in Table 6, it islikely that the manager has immediate access to prox-ies for the share of budget his category consumes, andthe extent of brand loyalty. Furthermore, it is straight-forward to assess storability for the product in consid-eration. The following 2 � 2 � 2 exhibit illustrateshow each of these forces push primary and secondarydemand elasticities in different directions. The entriesin Exhibit 4 refer to the primary/secondary percentagedecomposition.

Several comparisons are possible from Exhibit 4.First, comparing cells 1 and 2, we see that for highbudget share, storable products, higher loyalty reducesthe relative impact of secondary demand elasticitiesand increases the impact of primary demand elastici-ties. Second, a comparison of the breakdown in cells 1and 3 illustrates that high share of budget categories

18In developing the example, we note that this is just one of manypossible illustrations of how our framework can be used. Our inten-tion is not to list all in detail, but merely illustrate the usefulness ofthe meta-analysis results. We believe that such speculation is fruitfulgiven the high level of agreement between the underlying resultsand those from prior research, and the high meta-analysis modelfits.

will see greater primary effects. Third, a comparisonof cells 1 and 5 highlights our findings that storabilityleads to a greater primary demand effects. Clearly, sev-eral such Exhibits and comparisons can be drawn outof our framework. This illustrative example showshow a manager or researcher might use the matrix to:(1) make an educated guess as to how market condi-tions and other factors influence elasticities, and (2) un-derstand the likely reward frommarketing efforts (e.g.,efforts to increase loyalty).

A final application of the framework takes a “deci-sion support” approach. In this case, we use explicitknowledge of the values of the exogenous variables tosimulate changes in elasticity, given certainmanagerialactions.

For example, assume that the brand manager forDannon yogurt is considering a change in promotionalpolicy for the 8 oz. size. At present the brand promotes30% of time, and offers an average discount of 15%.The corresponding elasticity breakdown is 79%, 14%,and 7% for choice, incidence, and quantity respec-tively. Now imagine that he considers reducing dealfrequency by 50% and at the same time increasing thedeal depth by 50% over the current value. Using theparameter estimates in Table 6, we estimate the newbreakdown is closer to 63%, 24%, and 13%. Thus, theincreased emphasis on depth of promotion sees a shiftin favor of primary demand effects. This may be animportant insight for the Dannon manager, given ourearlier finding that this category appears to experienceincreased consumption, and the similar empirical re-sult of Ailawadi and Neslin (1998). That is, the Dannonbrand manager might be better off stimulating con-sumers to accelerate purchase and stock up, as thisleads to increased consumption, rather than focusingas much on encouraging switching. This is especiallytrue in our Dannon example, where the brand already



has a healthy share position. Finally, this change inpolicy might also be palatable for retailers who haveprivate label yogurt (as many do), as they could po-tentially benefit from a reduction in brand switchingto Dannon.19

5. ConclusionOne of the significant advances in the promotions lit-erature was the development of a methodology for de-composition of promotional response into primary andsecondary demand components. To date, this meth-odology has been applied to only two categories, sothe generalizability of the substantive finding from thiswork is unknown.

Our research has two goals. First, to document cross-category differences in the decomposition of brand-level promotional response, and in particular, differ-ences in the relative importance of primary andsecondary demand elasticities. Second, to formalizevia meta-analysis, a consumer-based framework forunderstanding the impact of exogenous factors onvariability in brand-level elasticities.

The important takeaways from this research effortare:

1. Primary and Secondary Demand. We confirm that,with the exception of butter (where the split is approx-imately 50/50), the largest percentage of the elasticitydecomposition falls on secondary demand, or brandswitching. This is consistent with the findings ofLeeflang and Wittink (1996) who show that managerstend to overreact (relative to a normative benchmark)to the promotional activities of competitors, thus re-inforcing the switching effects.

2. The Decomposition. The earlier breakdown of 84/14/2 appears to be an exception. Within the spectrumof these decompositions, we find that a 75/11/14 splitis about the average across all product categories. Stor-ability is an important moderator. We find that the de-composition becomes 75/3/22 for storable productsversus 75/17/8 for nonstorable products.

3. Elasticity Drivers. Category-specific factors aremore powerful than brand-specific factors in explain-ing the variability in elasticities. For example, share of

19We thank Dick Wittink for this insight.

budget and storability are two category characteristicsthat play a large role. Share of budget decreases theswitching elasticity, but increases the quantity elastic-ity, while storability increases both. Price variabilityand deal depth are important brand-specific factors,but they have less marginal impact. Variability de-creases all three types of elasticity, whereas increaseddeal depth increases the quantity elasticity. Consumer-factors (as measured in terms of demographics alone)have relatively little impact in explaining across-branddifferences in elasticities. It is the case, however, thatfor a given brand, elasticity response might differacross consumers (Bucklin et al. 1998). Furthermore,variables that describe consumer shopping patternsmight be more valuable in capturing price responsethan are demographics alone (e.g., Ainslie and Rossi1998, Bell and Lattin 1998).

4. Total Versus Component Elasticities. It is insufficientto simply examine drivers of total elasticity. In manyinstances a variable has no effect on total elasticity be-cause it has countervailing effects on primary and sec-ondary demand elasticities. This is particularly true inthe case of brand-specific factors.

5. Promotions and Consumption. There is evidence thatpromotions increase consumption in some categories(e.g., bacon, potato chips, softdrinks and yogurt). Con-versely, we observe that other categories (e.g., bath-room tissue, coffee, detergents, and paper towels) ex-perience forward-buying, yet they see no apparentcorresponding increase in consumption. As noted inour discussion in §4.1, this is a complex issue and likelyto be a very fruitful avenue for future research.

To summarize, the words of Bass (1995, p. G6) onthe state of marketing knowledge are relevant to thestatus of the choice literature:

. . . the field has matured to the point where it seems desirableto take stock of where we are, what we have learned, andfruitful directions for extending the knowledge base.

We show that there are regularities in the decom-position of brand-level price elasticities and that theycan be explained by variables derived from a frame-work that reflects the consumer’s view of price pro-motions. The empirical regularities identified in thispaper should be useful to researchers developingmod-els of promotional response, and as an aid to managers



in making better-informed promotion allocation andexecution decisions.20

Appendix A. Operational Measures• Category Factors

— Share of Budget is computed by determining total dollars spentin the category by each panelist and then expressing this as a fractionof total grocery expenditures. The resulting fractions are then aver-aged across all households.

— Brand Assortment is the total number of brand alternatives of-fered in the category.

— Size Assortment is the total number of size alternatives offeredin the category.

— Perceived Differentiation is computed from the household-levelchoice data. First, we compute the within-household market sharesfor each brand in the product category under consideration. Eachelement of the household’s choice-share vector is then squared andall elements are summed together.21 This measure is then weightedacross all users in the product category, to obtain a category-specificmeasure of the consumers’ view of interbrand substitutability.Higher values mean that consumers perceive the brands in the cate-gory to be more differentiated and less substitutable.

— Storability is a dummy variable indicating whether the cate-gory is storable.

— Necessity is a dummy variable indicator of whether or not thecategory is a necessity product according to accepted IRI definitions.

— Purchase Frequency reflects likelihood that a product appearson the shopping list on any randomly selected trip. It is the fractionof all trips and individuals who buy the category.

• Brand Factors— Relative Price Position. We estimate the extent to which a brand

is perceived as a premium brand in its product category by firstcomputing brand-specific average prices. These brand-specificpricesare then normalized within the category to create a measure that iscomparable across categories.

— Price Variability is the coefficient of variation of the brand’sprice. Higher values indicate more variability.

— Deal Frequency measures the proportion of times a brand is

20The authors thank seminar participants at the Marketing ScienceConference, University of California, Berkeley and INFORMS, SanDiego for their comments. We are grateful to John Carstens, PeterDanaher, Dan Horsky, Dipak Jain, Jim Lattin, Don Morrison,Chakravarthi Narasimhan, P. B. Seetharaman, Seenu Srinivasan,Dick Wittink, and especially Randy Bucklin and Carl Mela for manycomments and suggestions. We also thank the previous Editor,Richard Staelin, the Area Editor and two anonymous Marketing Sci-ence reviewers for advice, insights, and constructive suggestions onearlier versions of this paper. Our appreciation to Doug Honnold ofIRI for providing us with the data.21This calculation provides a household-specific version of theHerfindahl index and varies from 1/n to 1, where n is the numberof choice alternatives in the category.

found on deal, normalized according to relative deal frequency inthe category.

— Deal Depth gives the average percentage discount for a brand,conditional upon the brand being on promotion. This variable isnormalized with respect to category activity.

— Brand Experience is the fraction of consumers who have triedthe brand, of all those who have bought in the category.

— Brand Loyalty is the average number of purchases of the brand,by all consumers who purchase the brand. This variable is normal-ized across categories to take into account different purchase ratesin different categories.

• Consumer Factors— Income reflects the modal income level of consumers who pur-

chase the brand. Empirically, we found the mode to be a better dis-criminator than the mean—this is consistent with recent work byDhar and Hoch (1997).

— Age. The modal age of panelists who purchase the brand.— Education. The modal education (higher values indicate higher

levels of education) of the panelists who buy the brand.

Appendix B. Model and Likelihood FunctionFor each product category, let Iit denote a dichotomous indicator sothat Iit � 1 if consumer i purchases that category at occasion t andIit � 0 otherwise. Furthermore, let B � {1, . . . , J} denote the set ofbrands so that Dijt � 1 indicates that brand j is chosen by the con-sumer and Dijt � 0 otherwise. Thus, conditional onJ D � 1� ijtj�1

a purchase.Following the spirit of Hanemann (1984) and Chiang (1991), the

choice decisions and the interdependence between decisions are de-scribed as follows:

¯ ¯Q � X b � � iff U � g � Max{U � g , ∀ k � j},ijt ijt j ijt ijt ijt ikt ikt

¯ ¯U � g � U � g ,ijt ijt i0t i0t

¯ ¯0 iff U � g � Max{U � g , ∀ k},i0t i0t ikt ikt

where j � B, Qijt is the quantity demanded for brand j, Xijt denotesthe associated covariates, bj contains the corresponding coefficients,Uijt represents the perceived benefits of brand j per dollar, Ui0t is theutility threshold for category purchase, and �ijt and gijt are unob-servable error terms. To reflect the interdependency between deci-sions, �ijt and gijt are assumed correlated. Moreover, Uijt may containvariables also in Xijt.

Note that to avoid unnecessary estimation complications, we as-sume decisions across categories are independent except they are allsubject to the same budget constraint.22 By assuming �j and gj are

22This is not a serious flaw because we eventually adopt a General-ized Extreme Value (GEV) distribution for g error terms. Chiang andLee (1992) show that the GEV distribution satisfies the necessary andsufficient conditions which ensure the unbiasedness of the estimateswhen other categories are intentionally omitted.



correlated, the model in effect can be viewed as a hybrid ofKrishnamurthi and Raj (1988) and Chiang (1991).

We assume �j is normally distributed and g � (gi0t, gi1t, . . . , gijt, . . .giJt) are jointly GEV distributed and i.i.d across all households andoccasions. Specifically, let H(g) � exp(�G(�e�g)) denote the jointcdf such that G(�e�g) � [�k�B exp(�gk/(1 � d))](1�d) � exp(�g0)where 0 � d � 1. Given the model structure and these assumptionson the errors, the incidence and the choice probabilities can be de-rived, respectively, as

(1�d) ln 0 /(1�d)• ikte e�� k�B

Pr(I � 1) � ,it¯(1�d) ln 0 /(1�d) U• ikt i0te e � e��

k�B

�d ln•U /(1�d)ikt ¯e e � U /(1 � d)� ijt� � � �

k�BPr(D � 1|I � 1) � .ijt it

(1�d) ln 0 /(1�d)• ikte e�� k�B

This specification is equivalent to a nested logit model (McFadden1978) in which the “inclusive value” has a special form of ln �k�B

exp[Uikt/(1 � d)] and its corresponding coefficient is (1 � d). d isinterpreted as the degree of similarity between brands.

Let J� � {0, 1, 2, . . ., B} denote the option set (including the non-purchase option), and let � {0, 1, . . . , j � 1, j � 1, . . . , B} denote�J�j

the set without the jth option. The joint condition of Dijt � 1 and Iit� 1 can be rewritten as follows (i and t are suppressed):

�¯ ¯U � g � Max{U � g , k � J },j j k k �j

�¯ ¯U � Max{U � g , k � J } � g ,j k k �j j

U � g*.j j

Given g � GEV as described above, it is straightforward to showthat � Fj(•) such thatg*j

�d* *g /1�d 0 /1� g /(1�d)j je � e d • e� k� �

k�J,k�jF (•) � .j 1�d

*U g /1�d 0 /1�d0 je � e � e� k� �k�J,k�j

We assume (�k, ), k � 1, . . . , B has a pairwise joint distributiong*kdenoted by B(�k, , qk), where qk represents the correlation. Thoughg*kwe do not know the shape of B(•, •, •), we know both marginal dis-tributions. Thus, the following transformation identity, which main-tains the same correlation coefficient can be established (Lee 1983):

B(� , g*, q ) � BN(n , n , q ),k k k 1k 2k k

where BN is a bivariate normal distribution, n1k � U�1(U(�k/rk)) �

�k/rk, and n2k � U�1(F( )). For any observation Qikt, k � J, the cor-g*kresponding sample likelihood function is

�1 ¯U (F(U ))ikt Q � X bikt ikt kL � f , n dn ,ikt bn 2k 2k� � �� rk

where fbn(•, •, •) is the bivariate normal density. The evaluation ofU�1(F(•)) can be carried out numerically during the MLE iterations.The sample likelihood for I � 0 is 1 � Pr(I � 1). Thus, the loglikelihood function is

1�I D I•it ikt itLL � ln Pr(I � 0) • (L ) . it ikt� � ��i T k�Ji

B.1. VariablesVariables included in Xijt, Uijt, and Ui0t, respectively, are

• Xijt � (constant, log price, feature, display, inventory, familysize, log expenditure, family size*log price)

• Uijt � (brand constant, log price, feature, display, last brandpurchased, last size purchased, brand loyalty, size loyalty, familysize*log price)

• Ui0t � (constant, log expenditure, inventory, family size)

Appendix C. Price ElasticitiesIt is straightforward to show that the purchase incidence, brandchoice, and purchase quantity elasticities are

pe � h • p • Pr(D |I) • (1 � Pr(I)),I j j

phe � • p • (1 � Pr(D |I)),D |I j jj (1 � d)

�1p �(U (Pr(D ))j jpe � • b � rQ |D ,I j j�j j E(Q |D , I) Pr(D )j j j

�1�U (Pr(D ))j�1U (Pr(D ))j� �pj

ph� (1 � dPr(D |I) � (1 � d)Pr(D )) ,j j ��(1 � d)

where h p is the price coefficient in Pr(Dj|I). The variance of eachelasticity estimate is calculated via the delta method (Rao 1973). Fur-thermore, it can be shown (Gupta 1988) that the total elasticity is thesum of the elasticities of the three components.

ReferencesAbramson, Charles, Imran Currim, Morgan Jones. 1996. Diagnostic

validity of the multinomial logit model. Working Paper, Uni-versity of California, Irvine, CA.

Ailawadi, Kusum L., Scott A. Neslin. 1998. The effect of promotionon consumption: buying more and consuming it faster. J. Mar-keting Res. 35 (August) 390–398.

——, Karen Gedenk, Scott A. Neslin. 1998. Purchase event feedbackand heterogeneity in choice models: a review of concepts andmethods with implications for model building. Working Paper,Tuck School of Business, Dartmouth College, Hanover, NH.

Ainslie, Andrew, Peter E. Rossi. 1998. Similarities in choice behavioracross multiple categories. Marketing Sci. 17 (2) 91–106.

Assuncao, Joao, Robert J. Meyer. 1993. The rational effect of pricepromotions on sales and consumption. Management Sci. 39 (5)517–535.



Bass, Frank M. 1993. The future of research in marketing: marketingscience (JMR 30th anniversary guest editorial). J. Marketing Res.30 (February) 1–6.

——. 1995. Empirical generalizations and marketing science: a per-sonal view. Marketing Sci. 14 (Summer) G6–G19.

Bawa, Kapil, Jane T. Landwehr, Aradhna Krishna. 1989. Consumerresponse to retailers’ marketing environments: an analysis ofcoffee purchase data. J. Retailing, 65 (Winter) 471–495.

Bell, David R., James M. Lattin. 1998. Shopping behavior and con-sumer preference for retail price format: why ‘large basket’shoppers prefer EDLP. Marketing Sci. 17 (1) 66–88.

——, Teck-Hua Ho, Christopher S. Tang. 1998. Determining whereto shop: fixed and variable costs of shopping. J. Marketing Res.,35 (August) 352–369.

Ben-Akiva, Moshe, Steven R. Lerman. 1985. Discrete Analysis: Theoryand Application to Travel Demand. MIT Press, Cambridge, MA.

Blattberg, Robert C., Gary D. Eppen, Joshua Lieberman. 1981. Atheoretical and empirical evaluation of price deals for consumernondurables. J. Marketing 45 (Winter) 116–129.

——, Kenneth J. Wisneiwski. 1989. Price induced patterns of com-petition. Marketing Sci. 8 (Fall) 291–309.

——, Richard A. Briesch, Edward J. Fox. 1995. How promotionswork. Marketing Sci. 14 (Summer) 122–132.

Bolton, R. N. 1989. The relationship between market characteristicsand promotional price elasticities,Marketing Sci. 8 (Spring) 153–169.

Bucklin, Randolph E., Sunil Gupta, S. Siddarth. 1998. Determiningsegmentation in sales response across consumer purchase be-haviors. J. Marketing Res. 35 (May) 189–197.

——, Sunil Gupta. 1992. Brand choice, purchase incidence, and seg-mentation: an integrated modeling approach. J. Marketing Res.29 (May) 201–215.

Chiang, Jeongwen. 1991. A simultaneous approach to the whether,what, and how much to buy questions. Marketing Sci. 10 (Fall)297–315.

——, Lung-Fei Lee. 1992. Discrete continuous models of consumerdemand with binding nonnegativity constraints. J. Econometrics54 (1) 79–93.

Chintagunta, Pradeep K. 1993. Investigating purchase incidence,brand choice and purchase quantity decisions of households.Marketing Sci. 12 184–208.

Dhar, Sanjay K., Stephen J. Hoch. 1997. Why store brand penetrationvaries by retailer, Marketing Sci. 16 (3) 208–227.

Ehrenberg, Andrew S. C. 1972. Repeat Buying, North-Holland,Amsterdam.

Fader, Peter S., Leonard M. Lodish. 1990. A cross-category analysisof category structure and promotional activity for groceryproducts. J. Marketing, 54 (October) 52–65.

——, David C. Schmittlein. 1993. Excess behavioral loyalty for high-share brands: deviations from the Dirichlet model for repeatpurchasing. J. Marketing Res. 30 (November) 478–493.

Golabi, Kamal. 1985. Optimal inventory policies when orderingprices are random. Oper. Res. 33 (May/June) 575–588.

Guadagni, Peter, John D. C. Little. 1983. A logit model of brandchoice calibrated on scanner data. Marketing Sci. 2 (3) 203–238.

Gupta, S. 1988. Impact of sales promotions on when, what, and howmuch to buy. J. Marketing Res. 25 (November) 342–355.

Hanemann, W. M. 1984. Discrete continuous models of consumerdemand. Econometrica 52 541–561.

Ho, Teck-Hua, Christopher S. Tang, David R. Bell. 1998. Rationalshopping behavior and the option value of variable pricing.Management Sci. 44 (December) S145–160.

Krishna, A., I. C. Currim, R. Shoemaker. 1991. Consumerperceptionsof promotion activity. J. Marketing 55 (April) 4–16.

——. 1992. The normative impact of consumer price expectations formultiple brands on consumer purchase behavior.Marketing Sci.11 (Summer) 266–286.

Krishnamurthi, L., S. P. Raj. 1988. A model of brand choice and pur-chase quantity price sensitivities. Marketing Sci. 7 (1) 1–20.

——, ——. 1991. An empirical analysis of the relationship betweenbrand loyalty and consumer price elasticity. Marketing Sci. 10(2) 172–183.

Lal, R. 1990. Manufacturer trade deals and retail price promotions.J. Marketing Res. 27 (November) 428–444.

Lee, Eunkyu, Richard Staelin. 1999. A general theory of demand ina multi-product, multi-outlet market. Working Paper, FuquaSchool of Business, Duke University, Durham, NC.

Lee, L. F. 1983. Generalized econometric models with selectivity.Econometrica 51 507–512.

Leeflang, Peter S. H., Dick R. Wittink. 1996. Competitive reactionversus consumer response: do managers overreact? Internat. J.Res. in Marketing 13 (April) 103–119.

Litvack, D. S., R. J. Calantone, P. R. Warshaw. 1985. An examinationof short-term retail grocery price effects. J. Retailing 61 (3) 9–25.

McFadden, D. 1978. Modeling the choice of residential location. A.Karlquist et al., eds. Spatial Interaction Theory and Residential Lo-cation. North-Holland, Amsterdam.

Mela, Carl F., Sunil Gupta, Donald R. Lehmann. 1997. The long termimpact of promotion and advertising on consumer brandchoice. J. Marketing Res. 34 (May) 248–261.

Montgomery David B., V. Srinivasan. 1996. An improved methodfor meta-analysis: with application to new product diffusion.Working Paper, Graduate School of Business, Stanford Univer-sity, Stanford, CA.

Narasimhan, C., Scott. A. Neslin, Subrata K. Sen. 1996. Promotionalelasticities and category characteristics. J. Marketing 60 (April)17–30.

Neslin, Scott A., Caroline Henderson, John Quelch. 1985. Consumerpromotions and the acceleration of product purchases. Market-ing Sci. 4 (2) 147–165.

Raju, J. S. 1992. The effect of price promotions on variability in cate-gory sales. Marketing Sci. 11 (3) 207–220.

Rao, C. R. 1973. Linear Statistical Inferences and Its Applications. 2ndEd., John Wiley & Sons, New York.

Rossi, Peter E., Robert E. McCulloch, Greg M. Allenby. 1996. Thevalue of purchase history data in target marketing. MarketingSci. 15 (4) 321–340.

Russo, J. Edward. 1977. The value of unit price information. J. Mar-keting Res. 14 (May) 193–201.



Silva-Risso, Jorge M., Randolph E. Bucklin, Donald G. Morrison.1999. A decision support system for planning manufacturers’promotion calendars. Marketing Sci. 18 (3)274–300.

Tellis, Gerard J. 1988. The price elasticity of selective demand: ameta-analysis of econometric models of sales. J. Marketing Res.25 (November) 331–341.

Thaler, Richard H. 1985. Mental accounting and consumer choice.Marketing Sci. 4 (Summer) 199–214.

Totten, John C., Martin P. Block. 1987. Analyzing sales promotion:text and cases. Commerce Communications Inc., Chicago, IL.

Varian, Hal R. 1992. Microeconomic Analysis. 3rd Edition, Norton,New York.

Villas-Boas, J. Miguel, Russell S. Winer. 1997. Endogeneity in brandchoice models. Working Paper, Haas School of Business.

Willet, John B., Judith D. Singer. 1988. Another cautionary note aboutR2: it’s use in weighted least squares regression analysis.Amer.Statistician 42 (3) 236–238.

Winer, Russell S. 1986. A reference price model of brand choice forfrequently purchased consumer products. J Consumer Res. 13(September) 250–256.

This paper was received May 5, 1997, and has been with the authors 14 months for 3 revisions; processed by Scott Neslin.

Documents

The Decompositionof Promotional Response: An ... · The Decompositionof Promotional Response: An EmpiricalGeneralization ... On average, we ﬁnd that 25% of the elasticity is due