Flexible Decomposition of Price Promotion Effects. Using Store-Level Scanner Data

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1 Flexible Decomposition of Price Promotion Effects Using Store-Level Scanner Data Harald J. van Heerde, Peter S.H. Leeflang, and Dick R. Wittink* March 25, 2002 * Harald J. van Heerde is Assistant Professor at the Department of Marketing, Faculty of Economics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands. Peter S.H. Leeflang is Professor of Marketing at the Department of Marketing and Marketing Research, Faculty of Economics, University of Groningen, The Netherlands. Dick R. Wittink is the General George Rogers Clark Professor of Management and Marketing at the Yale School of Management, New Haven, CT, and Professor of Marketing and Marketing Research, Faculty of Economics, University of Groningen. The first author can be contacted by telephone ( ), fax ( ), or by heerde@kub.nl). All authors thank ACNielsen (USA and The Netherlands) for providing the data, and the editor, the area editor, the reviewers, seminar participants at Tilburg University, University of Leuven, Rotterdam (Erasmus), the DMSA Conference (Maastricht), London Business School, Yale School of Management, NYU s Stern School of Business, and the New York Modelers Group for valuable feedback.

2 Flexible Decomposition of Price Promotion Effects Using Store-Level Scanner Data Abstract We propose a model that estimates standard, enhanced, and flexible decompositions of price promotion effects based on store-level data. At present, decompositions of sales effects due to price promotions are available only for household models. These models decompose the sales elasticity into a category incidence elasticity, a brand choice elasticity and a quantity elasticity. We introduce a method that allows a unit sales effect, estimated from store data, to be decomposed into its constituent sources. The standard decomposition divides the own-brand unit sales effect into a cross-brand effect, a stockpiling effect, and a category expansion effect. The enhanced decomposition includes two extensions. One extension is the separation of the category expansion effect into a cross-store effect and a market expansion effect. This extension requires data on stores of multiple chains in geographic proximity. The other extension assumes the availability of item-level data so that a cross-item effect can be decomposed further into withinbrand (cannibalization) effects and between-brand effects. For improved understanding of promotion effects, we propose flexible decompositions. We allow the decomposition to depend on the type of promotion support, such as feature and/or display. A second type of flexibility is that we allow the decomposition to depend on the magnitude of the discount. We use a flexible, nonparametric, method to accommodate the latter dependency. We apply the models to four store-level scanner data sets. The decomposition results show that, on average, the secondary demand effect, captured by the sales decrease for other brands, is about 33 percent. This contrasts strongly with the finding from models of household data that about 75 percent of the sales elasticity is attributable, on average, to the brand choice elasticity. We also find that the contribution of the cross-brand effect decreases for increasing price discounts. In addition, except for feature-supported discounts, the stockpiling effect tends to decrease as a percent of the sales effect as the discount increases, while the contribution of the 2

3 category expansion effect tends to increase. We find that the flexible decomposition of promotion effects, separately for four types of support, provides superior insight into marketplace phenomena. The methodology and the empirical results are relevant to marketing scientists in academia and in the practice. Keywords: Econometric Modeling, Nonparametric Estimation, Deal Effects, Promotion, Regression and Other Statistical Techniques. 3

4 1. INTRODUCTION Given the important role of temporary price cuts and other promotions in the marketing mix of American and European firms, it is critical that marketing managers and academics have a detailed understanding of the effects of promotions. It is well known that promotions often result in large sales effects for a promoted item. However, this does not mean that the sales increase is truly beneficial. To determine that, we need a model of sales which incorporates the relevant sources of sales increases. These sources differ in attractiveness to the manufacturer and retailer. For example, at the store level the sales increase for a promoted brand could come from other brands (brand switching), from other time periods (stockpiling), from category expansion (category switching and/or increased consumption) and from other stores (store switching). Given the multitude of sources, it is easy to see that the benefit of a sales increase is not the same for manufacturer and retailer. For example, the retailer does not benefit from brand switching within the store, except for differences in margins. Brand switching within the store is relevant to manufacturers, although competitive reactions will reduce the net effect. However, neither retailers nor manufacturers derive benefit if the sales increase borrows from other time periods, unless, say, higher inventories increase consumption levels. Thus, it matters greatly what the sources of sales effects are. Several researchers have decomposed promotion effects using household-level scanner data. They address important aspects, including differences in the nature of decomposition between categories. We use store data to address complementary issues that deserve attention both from scientific and managerial perspectives. Managers often rely on store data for estimating the sales effects of promotions, as Bucklin and Gupta (1999, section 3) indicate in their study on the commercial use of UPC scanner data. However, managers lack the means to decompose these effects (Bucklin and Gupta 1999, p. 268): Research is needed to develop simple, robust models that will provide better estimates of promotional sales that are truly incremental to the manufacturer, not borrowed from the future, from another store, or from a sister brand.. Therefore, we propose a store-level decomposition method that is surprisingly simple to 4

5 implement. It yields a decomposition of the own-brand sales effect into a cross-brand effect, a stockpiling effect, and a category expansion effect. The stockpiling effect includes both postpromotion effects due to purchase acceleration and prepromotion effects that may result from purchase deceleration (anticipatory responses). The category expansion effect is the increase in category sales net of stockpiling effects. These three components comprise the standard decomposition in our model. We also show how the category expansion effect can be decomposed further into a crossstore effect and a market expansion effect. To do this, data on multiple chains in a metropolitan area are required. With SKU data, the cross-sku effect can be decomposed further into a withinbrand and a between-brand effect. This partition allows manufacturers to separate cannibalization effects. Our model accomplishes the decomposition separately for each of four support conditions. That is, temporary price discounts or deals can occur in retail outlets: i) without support, ii) with feature-only support, iii) with display-only support, and iv) with feature-anddisplay support. To allow the decomposition to depend on the support condition, we create four separate price discount variables. Importantly, we allow the decomposition for each support type to depend on the magnitude of a price discount. By using a nonparametric method (local polynomial regression) we obtain decomposition results that allow for flexible main- and interaction effects (the discount effect is estimated nonparametrically for each support type separately). We apply these methods to four store-level scanner data sets. To summarize, our approach includes the following important elements: We use store-level scanner data instead of household-level data to obtain a standard decomposition of the own-brand sales effect into cross-brand effects, stockpiling effects, and category expansion effects. The stockpiling component accommodates effects that are borrowed from the future and from the past. The standard decomposition is applicable to data on brands. 5

6 We further decompose category sales effects into between-store effects and market expansion effects. This extended decomposition is applicable if data exist on brand sales in stores belonging to multiple chains that may compete within a geographic area. We further decompose the cross-sku effect into a within-brand and a between-brand share effect. This approach is applicable for data on SKUs. We allow the decomposition to depend on the type of support offered for a temporary price discount. We let the decomposition depend on the magnitude of the price discount by estimating effects nonparametrically. This paper is organized as follows. In section 2 we briefly review the literature on the decomposition of sales promotion effects at the household level, and we discuss why managers also need decomposition models based on store-level data. In section 3 we propose our storelevel model, and describe how it provides the desired decomposition. We discuss the data in section 4, we provide empirical results for four product categories in section 5, and we present our conclusions in section REVIEW OF HOUSEHOLD LEVEL STUDIES 2.1. Approaches and results Gupta s paper (1988) is a seminal contribution to sales promotion research. His research provides the first decomposition of the elasticity of promotions with respect to when, what, and how much households buy (with data from the coffee category). Gupta (1988) finds that on average, across coffee brands and promotion types, brand choice accounts for 84 percent of the own-brand elasticity, and shorter interpurchase time represents about 14 percent of the own-brand elasticity. In his paper, stockpiling is a negligible phenomenon, accounting for about 2 percent of the own-brand elasticity if the quantity increase represents an increase in household inventory. 6

7 Chiang (1991), Chintagunta (1993), Bucklin, Gupta, and Siddarth (1998), and Bell, Chiang, and Padmanabhan (1999) also provide decomposition models applied to multiple data sets. We focus our review on the average effects by category, and summarize the decomposition results from the five studies in Table 1. Across all categories, the brand-switching component is by far the largest (74 percent), followed by purchase quantity (15 percent), and purchase timing (11 percent). However, the percentages differ substantially across categories. For example, categories for which household inventories tend to be modest, such as margarine and ice cream, show relatively small purchase quantity percentages. For more detail on reasons for differences across categories and brands, see Bell, Chiang, and Padmanabhan (1999). [Insert Table 1 about here] Given these extensive results, why do we need store-level models for the decomposition of sales promotion effects? In theory, household data provide the best opportunities for decomposition. However, store-level data are far more likely to be used by managers for decisions about promotions (Bucklin and Gupta 1999). Store data are also more representative: Gupta (1988) and Bell et al. (1999) report results based on 100 to 250 households whereas store data cover many stores each visited by thousands of households. Also, store data are especially appropriate for low-incidence product categories, for which household data are usually inadequate. It is critical, therefore, for managers and academic researchers to have methods suitable for the decomposition of sales effects based on store-level data. We note that the approach we propose in the next section, is not equivalent to the approaches applied to household data. Since we have data at the store level, it is impossible to recover the individual purchase behaviors that underlie models of household behavior (purchase incidence, brand choice, and purchase quantity decisions). We do argue, however, that our approach is managerially highly useful. For example, our approach provides an unambiguous estimate of the sales increase attributable to stockpiling. 7

8 3. STORE-LEVEL APPROACH FOR DECOMPOSITION We first present a standard decomposition in section 3.1. In sections 3.2 and 3.3 we introduce two extensions of the standard approach. In section 3.4 we present the variable definitions that allow the decomposition to depend on the support type. We discuss estimation methods for constant and varying decompositions in section 3.5. In sections 3.6 and 3.7 we discuss tests of nonlinearity and dynamics. In section 3.8 we provide a discussion of the pros and cons of this approach relative to the household-level approach Standard decomposition The standard decomposition considers three sources for the own-brand sales increase: cross-brand effects, stockpiling effects, and category expansion effects. Cross-brand effects are the losses in other brands sales when the focal brand is promoted. Stockpiling effects are the losses in pre- and postpromotion category sales due to the promotion of the focal brand in a specific week. And category expansion is the increase in category sales in the time window surrounding the promotional week, i.e., the own-brand sales increase that is not borrowed from other brands or other time periods. Category expansion may consist of multiple purchase behaviors such as increased consumption, deal-to-deal purchasing, store switching and category switching. The idea of our decomposition is based on considering unit sales at different levels of linear aggregation. The most disaggregate quantity is S, brand j s sales in store i in week t. The most aggregate quantity is total category sales in store i in some time window surrounding t, [tt*,t+t]: (1) CST it T J st* k 1 S ikts S J k k 1 j S ikt T J S ikts s T k s 0 * 1 OBS CBS CSW it. Equation (1) says that total category sales in the time window is own-brand sales in week t, plus cross-brand sales in week t, plus category sales in the period before and after t. We assume that all sales effects of the promotion occur in the period [t T*, t + T]. We can rewrite (1) as: 8

9 (2) OBS CST CBS CSW. it This equation says that current own-brand sales is total category sales in the time window, minus current cross-brand sales, minus category sales in the same time window excluding week t. The it standard approach consists of estimating linear regression models for OBS, CSTit, CBS, and CSW it as a function of price promotion and other variables. Based on these models we can compute predicted values for these criterion variables, given specific promotion situations. We use a price index variable to represent promotional price. It is defined as the actual price for an item divided by its regular price. This variable equals one in nonpromotional weeks and is lower than one in promotional weeks, when the actual (shelf) price is lower than the regular price. If in a given week the regular price has changed to a new level, the price index is defined relative to the new regular price, and stays one. Thus, this variable captures promotional price fluctuations only. The price index variable is also used in ACNielsen s Scan*Pro model (Wittink et al. 1988). P0 P1 1 P0 Let be the default price index level (=1), and be some price discount level ( P ) in week t. The unit own-brand sales increase equals: (3) OBS OBS P P ) OBS ( P P ) ( P ) ( 1 0 ob 1 P0 where ob is the own-brand effect parameter for P in a linear regression model for OBS (expected to be negative). Using (2), this increase can be written as the sum of three components: (4), ob ob ( P1 P0 ) ce ( P1 P0 ) cb ( P1 P0 ) sp ( P1 P0 ), or ce cb sp where is the category expansion parameter (expected to be negative), the cross-brand ce cb parameter (positive), and sp the stockpiling parameter (positive). These are the parameters for P in the regression models for, respectively, CST CBS, and CSW. Equation (4) says that the it, own-brand sales increase is the sum of total category sales increase ( category expansion effect ), it 9

10 plus the negative of the cross-brand sales loss ( cross-brand effect ), plus the negative of the surrounding period s category sales loss ( stockpiling effect ). We compute the relative contribution for each component as follows: fraction category expansion effect = ce / ob fraction cross-brand effect = cb / ob fraction stockpiling effect = sp / ob. We extend the standard decomposition in (4) in two ways. We decompose the category expansion component into a cross-store component and a market expansion component in section 3.2. Independent of this extension, we decompose the cross-sku component into a within-brand and a between-brand component in section Extended decomposition of the category expansion component The category expansion component may include sales that are borrowed from other stores: cross-store effects. With sales data for competing stores, we can extend the decomposition of (4) and disentangle the category expansion component into a cross-store effect and a market expansion effect. We accomplish this by defining a extended-category-sales-in-time-window variable ECST brand j in competing stores,, which is the sum of CST (total category sales in store i) and the sales of focal SCS i : it ECST CST it SCS T J st* k1 S ikts I h1 hi S hjt, where I is the total number of stores in the market. Rewriting this equation as CST it ECST SCS, we can further decompose the category expansion effect into a market expansion effect ( ) on ECST and a cross-store effect ( ) on SCS, leading to: me (5). ce me cs The market expansion effect is interpretable as the category expansion effect net of within-brand cs cross-store effects. 10

11 3.3.Extended decomposition of the cross-item component Extant decomposition research does not distinguish between cross-item effects within brands (cannibalization) and cross-item effects between brands (competition). These effects can be distinguished in our approach, based on SKU-level data. We define SKU m belonging to brand j which allows us to distinguish between cross-item effects that involve SKU s of the same brand and those of other brands. Note that we can define the sales of SKU m as: S ijmt T J J M T J Sikt s Sikt Sijnt st* k 1 k 1 n1 st* k 1 k j nm s0 S ikts CST it CBb CBw ijmt CSW it This equation states that the sales for one SKU equals the total category sales in the time window, minus current cross-brand sales (CBb, Cross-Brand between), minus current sales of other SKUs belonging to the same brand (CBw, Cross-Brand within), minus the total category sales in a time window excluding t. We can now decompose the cross-brand effect ( ) into a within-brand ( ) and a between-brand effect ( ): cbw (6). cb cbw cbb cbb cb 3.4. Variable definitions to allow the decomposition to depend on sales promotion type Typical sales promotions consist of temporary price discounts which may be communicated to consumers by feature advertising and/or displays or not at all. We allow the magnitudes of decomposition sources to depend on the type of support for a price discount. For example, Van Heerde, Leeflang, and Wittink (2000) find that the stockpiling effect of price discounts differs greatly between support types. It also seems plausible that promotions which are only communicated within a store (e.g., by a display) affect the brand choice decision relatively strongly. If so, unsupported and display-supported price cut effects would consist of relatively high cross-brand effects. On the other hand, discounted items with out-of-store support (i.e. feature) are more likely to enhance stockpiling. 11

12 Extant decomposition research rarely focuses on differences between sales promotion types. Researchers who do, report that the variables (Gupta (1988): feature-and-display, feature-ordisplay, and price cut; Chiang (1991): feature, display) are highly correlated because they are often used simultaneously in practice. We define the variables in such a way that they are by definition uncorrelated. Our perspective is that price promotions have a price reduction as their core, and a communication device with four mutually exclusive options: feature-only, displayonly, feature and display, or neither. Thus, we define four price variables for each brand: deal without support, deal with feature-only support, deal with display-only support, and deal with feature-and-display support. The variables so constructed allow for four separate decompositions, and the results provide a managerially highly relevant interpretation. To avoid confounding regular price and promotional price effects, we use a price index variable. As explained before, the price index variable captures promotional price fluctuations only. Regular price changes occur infrequently. Yet these changes are also highly correlated with the weekly indicator variables we use in our models. We therefore exclude regular price variables from the models. With four price index variables, we obtain a separate decomposition of own-brand sales effects for each of the four different support types, indicated by l 1,,4. However, we first use a pooling test to determine whether it is appropriate to postulate one common model (i.e., with one common effect across the support types). It is meaningful to have separate decompositions for the four different price promotion conditions if the null hypothesis of homogeneity is rejected Estimation methods for constant and flexible decompositions We first introduce the standard method to obtain a decomposition that is constant across price discount depths. We then relax this constraint and allow the decomposition effects to depend on the magnitude of the price discount. To accomplish this, we need models that are mathematically consistent with the decomposition framework in sections Since this framework is based on linearly aggregated sales quantities, we use linear regression models for the constant 12

13 decomposition. ii We note that stores differ in size, and it is inappropriate to assume equal absolute price discount effects on sales across stores. To achieve the more acceptable assumption of equal proportional effects (proportional to category volume) we divide all criterion variables by the across-time average category sales per store ( CS i ). For the basic decomposition (4), we obtain the decomposition effects as follows: ~ S 4 R (7) ˆ ob, l from : OBS ob, l PI ijlt r X ijrt u CSi l1 r1 J S ikt k1 4 R ~ k j (8) ˆ l CBS l PI ijlt r X ijrt u cb, from : cb, CSi l1 r1 T J S ikts s-t* k 1 4 R ~ s0 (9) ˆ l CSWit l PI ijlt r X ijrt u sp, from : sp, CSi l1 r1 T J Sikts 4 R ~ st* k 1 (10) ˆ l CSTit l PI ijlt r X ijrt u ce, from : ce, CS where: S = sales of brand j in store i in week t; i l1 r1 CS i = across-time average category sales in store i; PI ijlt = price index for brand j in store i in week t; l = 1 indicates no support, l = 2: feature-only support, l = 3: display-only support, and l = 4: featureand-display support; X ijrt = covariate r for store i, brand j, week t (see below); u r, u, u, u = disturbance terms for brand j in store i in week t in, respectively, r r r equations (7)-(10);,,, = response parameter for covariate r in, respectively, equations (7)-(10). We note that the covariates are merely included as control variables so as to minimize the X ijrt occurrence of biased parameter estimates due to the omission of relevant predictors. Importantly, 13

14 everything required for the decomposition is contained in the beta parameter estimates. Thus, an advantage of our approach is that all relevant information is contained in a subset of the parameter estimates. We therefore also do not report the parameter estimates for the control variables in the results section. iii These variables include own-brand dummies for features and displays without price cuts, which represent situations that occur rarely. In addition, we have cross-brand instruments: average other-brand price index variables, and average other-brand dummies for features and displays without price cuts. We also include lead and lagged own-brand and cross-brand price index variables. A key assumption in our model is that promotions affect sales variables in the period t T* through t + T. That is, a sales variable in period t is affected by lead variables indexed t + 1,...,t + T* and by lagged variables indexed t 1,...,t T. For a criterion variable, defined as the sum of sales across the period t T* through t + T (for example, CST it ), the lead variables are indexed t + 1,...,t + T + T*, and the lagged variables are indexed t 1,...,t T* T. We include the same set of lead and lagged variables for all criterion variables so as to obtain a logically consistent decomposition. Finally, we include brand dummies and week dummies. The total number of predictor variables is thus high, although not relative to the total number of observations. For the extended decompositions we proceed as follows. To separate the cross-store effect from the market expansion effect, the decomposition proposed in (5), we replace the category sales criterion variable CS ~ T it by the cross-store term S CS ~ and by the extended category sales term E ~ CST. To split between- from within-brand effects as in (6), we replace the cross-sku criterion variable CB ~ S by the between-brand term C Bb ~ and the within-brand term CB ~ w ijmt. The predictor variables are the same as before, except for SKU-level definitions. We estimate the equations by OLS, pooled across brands/skus within a product category. The rationale for pooling across brands is that the goal of our research is not to explore differences between brands. This is consistent with household-level studies. Only Bell, Chiang 14

15 and Padmanabhan (1999) focus on conditional effects in addition to the average decomposition results, and find that category factors have greater influence on variability in promotional response and its decomposition than do brand-specific factors (Bell, Chiang, and Padmanabhan 1999, p. 504). Although the errors from the four equations (7)-(10) may be contemporaneously correlated, estimation by SUR would yield the same parameter estimates since each equation contains the same set of predictor variables (Judge et al. 1985, p. 468). We note that we do allow for contemporaneous correlation between brands within each equation (7)-(10) by the inclusion of the weekly indicator variables. We also note that the use of linear models with the same predictor variables for each equation ensures that the own-brand sales effect estimate equals exactly the estimates of the category expansion effect, minus the cross-brand effect, minus the stockpiling effect, as defined in (4). The same holds for the extended decompositions (5) and (6). Thus, we could refrain from estimating one of the decomposition effects since it can be derived from the other effects. We do not do this, in order to have standard errors for all effects. We emphasize that our use of linear models avoids the possibility of bias inherent in the application of nonlinear models to linearly aggregated data (Christen et al. 1997). We note, however, that the aggregation required to complete the decomposition of promotion effects is restricted to the criterion variables and to some of the control covariates. For example, one criterion variable is the sum of sales for the brands in a time window. There is no aggregation of the predictor variables of interest, so that we can claim that each measure captures what it should. However, one may have reservations about the assumption of linear deal effects, and we now turn to this question. The assumption in the literature is that the decomposition effects are the same across price discount magnitudes. There is some evidence that the relative sizes of the decomposition sources depend on the magnitude of a price discount. For example, Van Heerde, Leeflang, and Wittink (2001) find that the nature of own- and cross-brand effects of a promotion depend on the size of the discount. Analogously, we propose that the size of each decomposition source depends on the 15

16 magnitude of a price discount. For example, households willingness to purchase and consume more of an item may depend on a sufficiently deep price discount. In that case, category expansion effects occur only for some price discounts. Thus, while previous research does not allow the decomposition percentages to differ across discount levels, we relax this constraint. To allow for flexible decomposition we use nonparametric estimation. That is, we use a semiparametric model (partly nonparametric, partly parametric) that allows for flexible main effects for the predictor variables of interest, and assumes fixed parameters for the other variables. For example, for the own-brand effect we replace (7) by the following semiparametric model: 4 R ~ (11) OBS m( PI ) PI X u, ijlt ob, p ijpt p1 r 1 pl where m(.) is a nonparametric function. Thus, we allow one price index variable to have nonparametric effects. We do this separately for each of the four price index variables and separately for all criterion variables that are needed for the decomposition in (4). The nonparametric method we use to estimate m(.) is local polynomial regression (Fan 1992). We use this method because it is free from boundary problems, it is design-adaptive, and it is easy to implement (see section 3.1 in Fan and Gijbels 1996 or the Appendix of this paper for details). An alternative method to accommodate nonlinear effects is (global) polynomial regression. It would require the addition of squares or higher-order powers of the predictors in the regression equations (7)-(10). Fan and Gijbels (1996) argue against this method even though it has been widely used. Among its drawbacks are that polynomial functions are not flexible, that individual observations can have a large influence on remote parts of a curve, and that the polynomial degree cannot be controlled continuously (i.e., it is restricted to integers). In addition, the polynomial terms can be highly correlated, especially when many powers are needed. Fan and Gijbels (1996) argue that local polynomial regression provides the desired flexibility and it overcomes the drawbacks associated with global polynomial modeling. r ijrt 16

17 3.6. Test for nonlinearity To determine the suitability of nonparametric analyses, we use the RESET test for the assumption of constant (decomposition) effects (Stewart 1991, pp ). It is a general procedure, designed to detect the choice of an inappropriate functional form. The argument is that if the functional form is not consistent with the data, one might expect the square or some higher power of one or more of the predictors to improve the explanation of variation in the criterion variable. In practice, one may not have a clear idea as to which powers of a predictor to use. To avoid the use of an arbitrary selection of terms, RESET tests the significance of the square of the estimated criterion variable as an additional variable. The RESET test proceeds as follows: (1) regress y on all predictors and compute ŷ, and (2) regress y on the same predictors augmented with the square of the estimated criterion variable, i.e., 2 ŷ. The RESET test is the two-sided t-test of the parameter estimate for the latter predictor Determination of the time window for dynamic promotion effects We now consider how to specify T for postpromotion and T* for prepromotion effects. This time window should be large enough so that it includes all possible dynamic effects of price promotions. For the proper calculation of the effect size of these dynamic effects it does not matter if the time window is too large, since the estimates beyond those needed are zero by definition. Increasing the time window decreases the number of degrees of freedom very rapidly, however, since the number of predictor variables increases and the sample size decreases as T and T* increase. Thus, we want to use the smallest possible value to capture the dynamic effects. Our choice is T = T* = 6. We base this choice on Van Heerde, Leeflang, and Wittink (2000), Neslin and Macé (2000), and Nijs et al. (2001). Van Heerde, Leeflang and Wittink (2000) studied the lengths of pre- and postpromotion effects for nine brands in two product categories, and they limited their search to the period t 6 and t + 6 (weeks). They found that the maximum possible length occurred in four of eighteen cases (one lead, three lag). Thus 6 weeks sufficed in the vast majority of cases. Neslin and Macé (2000) studied dynamic sales promotion effects for more than 17

18 30,000 SKUs in 83 stores in ten product categories. Their basic model includes dynamic effects for the period t 4 through t + 4. They found similar results for the stockpiling or deceleration effects whether they were calculated based on 4, 5, or 6 period lags (Neslin and Macé, 2000, p. 23). Thus, we might actually be able to justify T = T* = 4. Finally, Nijs et al. (2001) studied dynamic promotion effects at the category level for 560 product categories. Their basic VARX model uses eight lags, but they also use a VARX model with four and six lags. They conclude that the sizes of the elasticity estimates are comparable, and that the impulse response functions for these three alternative lag specifications are highly correlated (Nijs et al, 2001, p. 16). We conclude that a time window choice of [t6,t+6] seems justified. Nevertheless, we also estimate the models with a larger time window [t8,t+8], and find that they yield very similar results (see section 5.3) Comparison with household-level approach Currently, the only published approach to decomposition is based on household data. Household data offer well-known advantages over store data, partly because disaggregate data have higher potential for diagnostics. Yet there are also important strengths in our approach relative to household-level decomposition research. One is that our approach uses a unit sales effect decomposition rather than an elasticity decomposition. Elasticities suffer from the problem that they are not directly comparable (i.e., purchase incidence probability, brand choice probability, and purchase quantity have very different properties). This may seem odd since the elasticity concept is defined in percentage terms which makes it theoretically comparable across a diverse set of conditions. For example, researchers are comfortable with comparisons of, say, own-brand demand elasticities with respect to price. However, this does not imply that it is meaningful to compare incidence, choice and quantity elasticities. In particular, a decomposition of own-brand demand elasticity into these three component elasticities is not equal to a decomposition of ownbrand unit sales effects into unit sales effects attributable to the same three components (Van Heerde, Gupta and Wittink, 2001). Thus, we focus on unit sales effects that are comparable: the 18

19 cross-brand effects are measured in the same units as the stockpiling effects and the category expansion effects. A second strength of our approach is that all the components we use have a straightforward managerial interpretation. The cross-brand component represents the secondary demand effect while the other two components in the standard decomposition capture primary demand effects. And the two primary demand components have a clear function: one captures sales borrowed from other periods (stockpiling), the other provides an estimate of category expansion. We note that in household models, brand choice represents secondary demand, while category choice and quantity together form primary demand. However, both of the latter components can represent stockpiling as well as category expansion. A weakness of our approach is that we do not use data on individual consumers, leading to a potential aggregation bias. Since consumers are exposed to the same marketing mix in a given week and store, the primary source of aggregation bias is absent (Allenby and Rossi 1991; Gupta et al. 1996). Accommodation of heterogeneity at the aggregate level is still in its infancy, and we leave this issue for future research. 4. DATA We apply the models to two American (tuna, tissue) and two Dutch (shampoo, peanut butter) weekly, store-level, scanner data sets. We provide descriptive statistics in Table 2. Tissue has the smallest sample size (about 4,000 observations) and also the smallest number of price discount observations (less than 700). The percent of observations with price discount is higher in the American than in the Dutch data sets, varying from more than 30 percent for tuna to less than 10 percent for peanut butter. In three product categories the largest promotion frequency occurs in the condition without support. For tissue more than half of all deals occur with feature-anddisplay support. [Insert Table 2 about here] The first American data set, from AC Nielsen, contains five national brands in the 6.5 oz. canned tuna fish product category. We have 104 weeks of data for each of the 28 stores of one 19

20 supermarket chain in a metropolitan area. Due to the inclusion of lead and lagged effects indexed ttt*,,t+t+t* = t12,,t+12, we loose 24 observations per store, so that the effective sample size for each item is 28*(10424)=2240. In this sample, brands 2-5 used price promotions while brand 1 did not. Therefore, for the estimation of sales promotion effects we only include the data for brands 2-5, and have 4*2240 = 8,960 observations. We do, however, include the sales data for brand 1 in the following criterion variables relevant to the decomposition: CB ~, C SW ~ it, and STit C ~. Thus, brand 1 may experience a change in sales when other brands are S promoted, and this change is part of the measurement of cross-brand effects via its inclusion in C BS ~. We note that the tuna data set is the only one for which we can use the extended decomposition of the category expansion effect into a cross-store effect and a market expansion effect. We know brand sales in stores of other chains located in the same geographic area. For the estimation of cross-store effects, we assume that within-chain effects are zero. The second data set (52 weeks) pertains to the six largest national brands in the tissue product category in the USA. The data (also from AC Nielsen) are from 24 widely dispersed stores located in the eastern US. For each store the net sample size is 672 observations. All six brands use price promotions so the pooled estimation sample size is 6*672 = 4,032. The first Dutch data set (from AC Nielsen) consists of eleven shampoo brands, of which the five largest engage in promotional activities. For this product category we have 109 weekly observations for almost all 48 stores in a national sample from one large supermarket chain. This provides a net sample size of 4,043 observations for each of the five brands, and 20,215 for pooled estimation. As before, the six other brands are included in relevant criterion variables for the decomposition. The second Dutch data set (AC Nielsen) contains five items of peanut butter. In contrast to the other three data sets, this data set contains multiple SKU s per brand which enables us to separate the secondary demand effect into within-brand and between-brand effects, as in equation (6). Three SKUs used price promotions. For this product category we have 144 weekly 20

21 observations for almost all 49 stores in a national sample from one large supermarket chain. With a net sample size of 5,519 observations for each of these three SKUs, we have a pooled sample of 16,773 observations. The two remaining SKUs are, again, included in the appropriate decomposition criterion variables. We note that since we have a limited number of SKUs we can use a separate intercept for each of them. If we would have had more SKUs we could have replaced those by attribute-specific intercepts as proposed by Fader and Hardie (1996). 5. RESULTS We obtain results through a series of model estimation and validation steps. We first estimate both common and idiosyncratic own-brand sales effects for the four support types to test for homogeneity. We show the results of the pooling tests in section 5.1. The results indicate that the effects differ systematically across the four supports. Thus, it is meaningful to estimate separate parameters for the four supports. In section 5.2 we present the standard decompositions from equation (4), and, where appropriate, the extended decompositions from equations (5) and (6). We validate our time window choice in section 5.3. In section 5.4 we present evidence in favor of flexible decompositions based on RESET test results. Given the rejection of the null hypothesis of constant effects, we show nonconstant decomposition results, based on local polynomial regression, in section Pooling tests For each product category, we test whether it is meaningful to assume one common ownbrand unit sales effect across the four different support conditions. We show in Table 3 that the homogeneity assumption is rejected in all cases. Hence we proceed below by allowing for separate effect sizes for the different support conditions. In each case, the parameter estimate represents the effect of a one unit decrease in the price index (from one to zero) on own-brand sales relative to category sales. The criterion variable is defined in such a manner that the parameter estimates in Table 3 are comparable across product categories (see (7)-(10)). We use a 21

22 20 percent deal to provide a substantively meaningful interpretation. To illustrate, the parameter estimate of 0.68 for the own-brand effect of an unsupported price cut for tuna indicates that a 20 percent price cut leads to an estimated 0.68*0.20 = 0.14 increase in unit sales relative to average category sales in a store. [Insert Table 3 about here] We observe that for every product category the estimated own-brand sales effect is the smallest when there is no support (ranging from 0.41 to 0.68) and the largest with feature and display (ranging from 1.70 to 2.74). The simple average effects (averaged across the categories) are 0.6 without support, 1.4 for feature only, 1.4 for display only, and 2.1 with feature and display. Peanut butter tends to have the highest effects, and shampoo the lowest, except with display where shampoo has the highest effect Constant decomposition We show the standard decomposition of the own-brand sales effect into cross-brand, stockpiling, and category expansion effects in Table 4. Note that the standard decomposition forces the estimated effects to be the same for different price levels (i.e. the proportional effects are assumed to be linear). In the second column of Table 4 we show the results for the own-brand sales equation (7) (also shown in Table 3). The next columns show the results for the cross-brand equation (8), the stockpiling equation (9), and the category expansion equation (10). iv The fit of all standard decomposition models seems reasonable, given that all criterion variables are defined relative to average category sales. The R-square values range from 0.51 to None of the three components of the standard decomposition shows systematically higher R 2 values across the categories. v We expect negative own-brand and category expansion effects (converted here to positive numbers to enhance interpretation) and positive cross-brand and stockpiling effects, and find that all parameter estimates but one have the expected signs vi. We find that all 16 own-brand effects, and 15 out of 16 cross-brand effects, are statistically significant. On the other hand, only 7 stockpiling and 4 category expansion effects are significant. 22

23 This is largely due to the much larger standard errors for these two primary demand effects. This finding is consistent with Neslin, Henderson, and Quelch (1985, Figure 2) who also obtain relatively many insignificant effects in their models for purchase quantity and interpurchase time. A relatively low signal-to-noise ratio for the quantity portion of primary demand effects in the elasticity decomposition based on household data was also identified by Bell, Chiang, and Padmanabhan (1999, p. 513). [Insert Table 4 about here] We show the percentage results for the standard decomposition in Table 5. Perhaps the most intriguing result is that the three standard sources of sales effects on average account for about one third each (last row of Table 5). There is also a fair amount of consistency between the product categories in these percentages. The cross-brand effect captures between 24 percent (peanut butter) and 41 percent (tuna), and the stockpiling effect takes between 26 percent (tissue) and 44 percent (peanut butter). Thus, the secondary demand effect is always less than half of the total sales effect. These results are very different from the elasticity decomposition provided in Table 1, which shows the secondary demand effect to capture 74 percent. To what can this systematic difference can be attributed? Interestingly, Van Heerde, Gupta, and Wittink (2001) show how the elasticity decomposition can be transformed into a unit sales effect decomposition. This transformation shows that the amount attributable to primary demand (unit sales) based on household models is, on average, also about 33 percent. Thus, it appears that a unit sales decomposition differs enormously from an elasticity decomposition, while seemingly quite different models of household and store data generate similar insights with regard to unit sales effects. It is also interesting that the stockpiling effect accounts for about one third of the sales effect. This is noteworthy because until a few years ago researchers experienced great difficulty estimating stockpiling effects in models of store data (Neslin and Schneider Stone, 1996). By accommodating extended periods of lead- and lagged effects, Van Heerde, Leeflang, and Wittink (2000) were able to document that stockpiling accounts for up to 25 percent of the sales increase 23

24 in two product categories. The primary reason for the higher percentage in our results is that we estimate the stockpiling effect at the category level (since C SW ~ it is obtained by aggregating across all brands). Thus, by including cross-brand stockpiling we obtain a higher percent, as would be expected for households who purchase more frequently or larger amounts of multiple discounted brands. We note that a brand manager may want to separate own- from cross-brand stockpiling effects, whereas a retail manager may be indifferent between these two sources of stockpiling. [Insert Table 5 about here] The results in Tables 4 and 5 also show how the decomposition varies across the support types. Recall that the pattern in the own-brand sales effects is as expected: smallest effects for unsupported price discounts, and largest effects for feature-and-display supported price discounts for all product categories (see the second column of Table 4). In relative terms, the differences in the average decomposition percentages across the support types are notable. Perhaps the most useful comparison involves isolating promotions with outside support (feature-only, feature and display). On average, across categories, the stockpiling percent is much higher (45-50 percent) with outside support than without (7-31 percent), as shown in the last panel in Table 5. The latter finding is consistent with the notion that feature advertisements affect households who manage inventories. Related to this, Urbany, Dickson, Sawyer (2000) find that multiple store shoppers read ads and fliers more than mostly-one-store shoppers (89 versus 77 percent), and buy larger quantities on deal (73 versus 67 percent). By contrast, the category expansion percentage is much greater without feature (37 56 percent) than with (18 26 percent). Thus, promotions communicated in-store only may appeal in particular to households that do not plan their purchases as carefully as households that read feature ads. For tuna we further decompose the category expansion effect into a cross-store effect and a market expansion effect. We show the percentages attributable to these two sources in Table 5. Interestingly, for promotions with outside support, the vast majority of the category expansion 24

25 effect is attributable to cross-store effects. For feature-only support, it is more than 90 percent (24/26) while for feature and display it is 67 percent (16/24). Thus, feature advertising appears to be critical to direct store switching, which is the case if households use the advertising content to decide where to shop or they decide which items to purchase in a given store (Bucklin and Lattin 1992). This finding is consistent with Urbany, Dickson, and Sawyer (2000), who report that 89 percent of the multiple store shoppers regularly read ads and flyers. Other households may visit multiple stores and habitually check the shelves and displays for price reductions. According to Dickson and Sawyer (1990), 58% of all households check prices, but only 13% of this subset do this to compare prices between supermarkets. The effects on the choice of store for individual items are referred to as indirect store switching (Bucklin and Lattin 1992). Our results suggest that such indirect store switching effects are less strong than direct store switching effects. The cross-store percentage of the category expansion effect is much smaller in the absence of feature advertising: 6 percent (2/37) without support and 43 percent (9/21) with display-only support. For peanut butter we decompose the cross-sku effect into a within-brand and a betweenbrand effect. On average, we find that the cross-sku effect is mostly explained by the withinbrand effect: 71 percent (17/24). Thus, the vast majority of the effect is attributable to cannibalization. The relative amount of cannibalization is highest without support: 92 percent (22/24), but the absolute amount does increase with more support (Tables 4 and 5). These results are consistent with those of Kalyanam and Putler (1997, Figures 2 and 3), who also find strong effects of the promotion of one brand-size on other sizes within the same brand Validation of the time window The stockpiling and category expansion effects are based on a time window of [t6,t+6] surrounding week t. As we argued before, it does not matter if this window is too large; the decomposition effects stay the same. To find out whether our time window is large enough, we also estimated the decomposition model based on a time window [t8,t+8]. This other time window choice entails three changes in the model: (a) the criterion variables for the stockpiling 25