مدلسازی وابستگی ها در نتایج انتخاب نام تجاری (برند) در سراسر طبقه بندی های مکمل

We build an econometric model of a household's contemporaneous brand choice outcomes in complementary product categories. This model explicitly captures cross-category dependencies in brand choice outcomes of a household. Such dependencies have not been modeled in existing multi-category demand models. Our model accommodates cross-category dependencies that arise on account of three component effects: (1) complementarity due to the additional utility that a household derives from the joint purchase of brands in complementary categories, (2) marketing spillovers due to the effects of brands’ prices in one category affecting the households’ latent utilities for brands in the complementary category, (3) unobserved dependencies due to correlations in households’ latent utilities for brands across categories. We estimate our proposed multi-category brand choice model using scanner panel data on cake mix and frosting categories. We find that complementarity accounts for the vast majority of the estimated cross-category effects in demand. We also find that as much as 55 percent of the total retail profit impact of price promotions arise on account of brand-level (focus of our study), as opposed to category-level (focus of previous studies), dependencies in household demand. Finally, we propose an easily interpretable visual representation – Largess and Free-Ride Plot – of cross-category price elasticities that summarizes the differential abilities of brands to influence, or be influenced by, brands in the complementary category.

Many consumer packaged goods categories are dominated – in terms of the number of available products, as well as their relative market shares – by a few national brands. Some of these national brand manufacturers have long product lines in multiple categories. For example, General Mills manufactures a wide range of product categories, including bottled juice, cake mix, cereal, dinner kits, fruit snacks, salad dressing, frosting, pasta, pasta sauce, and popcorn. Similarly Kraft produces bacon, cake mix, cheese, coffee, cookies, dinner kits, frozen pizza, and many more. Both manufacturers use umbrella brand names across these categories. Table 1a and Table 1b list the popular umbrella brands of both companies. For example, Betty Crocker and Pillsbury are popular umbrella names used by General Mills across a large number of product categories, while Kraft and Oscar Mayer are popular umbrella names used by Kraft Foods across many categories. Within a manufacturer's product mix, it is not necessary that demands for its products – even products that bear the same umbrella brand name – are correlated. For example, weekly demand for Betty Crocker brownies may be independent of weekly demand for Betty Crocker mashed potatoes. However, to the extent that cake mix and frosting are complements in consumption (i.e., together provide greater utility to consumers than the sum of the individual utilities), the weekly demand for Betty Crocker cake mix may be positively correlated with the weekly demand for Betty Crocker frosting. In other words, lowering the price of Betty Crocker cake mix may not only increase its own sales, but also increase the sales of Betty Crocker frosting at the same time. As the manufacturer of a wide product mix, with umbrella brand names sometimes straddling seemingly related product categories (such as cake mix and frosting), General Mills has, therefore, a strategic need to understand correlations in market demand for its product offerings across product categories. Such an understanding will assist General Mills in better coordinating its pricing and promotion decisions for its product lines in related categories.While understanding demand inter-relationships between its product offerings (bearing the same umbrella brand name) in related product categories, it is also necessary for General Mills to understand its brands’ demand inter-relationships with other brands in those categories. For example, the Pillsbury brand competes with the Betty Crocker brand in both categories. However, the Pillsbury brand is also owned by General Mills. On the other hand, Aurora Foods, the main competitor of General Mills in the cake mix and frosting categories, markets products under the umbrella brand name of Duncan Hines in both categories. This means that on the one hand, while General Mills may want to prevent the cannibalization of Betty Crocker sales by Pillsbury sales (since both are company-owned brands), on the other hand, General Mills may want to steal sales from the competing Duncan Hines brand in one or both categories. The strategy space for General Mills's marketing mix, therefore, expands in an interesting manner on account of not only owning multiple brand names (i.e., Betty Crocker and Pillsbury), but also being present in two related product categories. In order to facilitate strategic decision-making of firms in such situations, multi-category brand choice models must be estimated using customers’ longitudinal brand choices in complementary product categories. There exist two research streams in the marketing literature that propose and estimate multi-category brand choice models (see Russell et al. (1999) and Seetharaman et al. (2005) for thorough reviews of multi-category models). The first stream – Ainslie and Rossi (1998), Kim, Srinivasan, and Wilcox (1999), Seetharaman, Ainslie, and Chintagunta (1999), Iyengar, Ansari, and Gupta (2003), and Duvvuri, Ansari, and Gupta (2007) – deals with the estimation of multi-category brand choice models to study whether households have similar marketing mix sensitivities across categories. The second stream – Russell and Kamakura (1997), Erdem (1998), Erdem and Winer (1999), Singh, Hansen, and Gupta (2005), and Hansen, Singh, and Chintagunta (2006) – deals with the estimation of multi-category brand choice models that allow a household's brand preferences to be correlated across categories. In models under both streams, conditional on a household's preference parameters (i.e., marketing mix sensitivities and brand preferences) in the product categories, the household's contemporaneous brand choice outcomes in the categories are assumed to be uncorrelated. Such models ignore contemporaneous cross-category dependencies that would arise on account of product categories being consumption complements. Our focus in this paper is to propose and estimate a multi-category brand choice model that is appropriate for modeling households’ contemporaneous brand choices in complementary categories, and to demonstrate its application. There exists a literature on modeling cross-category dependencies in households’ category-level buying behavior in complementary product categories. For example, Manchanda, Ansari, and Gupta (1999) and MAG (1999) henceforth, estimate a multivariate probit (MVP) model to explain household-level contemporaneous incidence outcomes in the cake mix and frosting categories. They allow for two types of cross-category dependencies in their multi-category incidence model: (1) marketing spillovers due to the effects of one category's price affecting the household's latent utility for the complementary category and (2) unobserved dependencies due to correlations in households’ latent utilities for the two categories. Niraj, Padmanabhan, and Seetharaman (2008) and NPS (2008) henceforth, estimate a bivariate logit (BVL) model, first used in Marketing by Russell and Peterson (2000), to explain household-level contemporaneous incidence outcomes in the bacon and egg categories. They allow for two types of cross-category dependencies in their multi-category incidence model: (1) marketing spillovers, as in MAG (1999), and (2) complementarity due to the additional utility that a household derives from the joint purchase of the complementary categories. From MAG (1999) and NPS (2008) emerge three underlying components of cross-category dependencies in households’ incidence outcomes: (1) complementarity, (2) marketing spillovers, and (3) unobserved dependencies. While they document strong cross-category dependencies in households’ incidence outcomes, both MAG (1999) and NPS (2008) ignore brand choice outcomes in their analyses. Two recent papers – Mehta (2007) and Song and Chintagunta (2007) – address this issue by deriving multi-category models of households’ incidence and brand choice outcomes. However, neither of these models accommodates cross-category dependencies in households’ brand choice outcomes. Cross-category demand dependencies are modeled only in incidence outcomes (as in MAG (1999) and NPS (2008)). Our study, for the first time, addresses this issue. We propose and estimate a multi-category brand choice model which accommodates cross-category dependencies in households’ brand choice outcomes (in addition to incidence outcomes) in complementary product categories. Our model explicitly allows for three components to underlie such cross-category dependencies in brand choice outcomes, i.e., (1) complementarity, (2) marketing spillovers, and (3) unobserved dependencies. We methodologically extend the incidence models of MAG (1999) and NPS (2008) to appropriately represent these three cross-category components at the brand-level. We estimate our proposed multi-category brand choice model using scanner panel data on cake mix and frosting categories. In doing so, we not only estimate correlations in brand choice outcomes across categories (for the first time in the literature on multi-category demand models), but also decompose such correlations into (1) category-level versus brand-level dependencies and (2) dependencies arising from complementarity versus marketing spillovers versus unobserved dependencies. Using the estimation results, we propose an easily interpretable visual representation – Largess and Free-Ride Map – of cross-category price elasticities that summarizes the differential abilities of brands to influence, or be influenced by, brands in the complementarity category. The rest of the paper is organized as follows. In the next section, we develop our proposed multi-category model of demand. Next, we lay out the estimation details. Following this, we discuss the data and estimation results. Finally, we present some managerial implications of our estimation results, and conclude by summarizing the contributions of this study, as well as proposing suggestions for future research.

Consumers derive more satisfaction when they consume a pair of complementary products together than when they consume these products separately. Such consumption complementarity should manifest itself as positive associations in observed purchase incidence and brand choice outcomes of households across the complementarity product categories. We build an econometric model to capture such complementarity-based associations and estimate the proposed model using scanner panel data on two obviously complementarity categories, cake mix and frosting. Complementarity is modeled as the additional utility that consumers derive from the joint consumption of brands in the two categories. Our proposed multi-category brand choice model also accommodates the effects of marketing spillovers (through cross-category effects of prices) and unobserved dependencies in demand across categories (through correlated error terms in households’ utility functions). We estimate our proposed model using households’ contemporaneous brand choice outcomes in the cake mix and frosting categories. We correct for the effects of possible price endogeneity. We find that our proposed multi-category brand choice model fits (in sample) and validates (out of sample) households’ incidence and brand choice outcomes better than multi-category brand choice models (such as those previously proposed in the literature) that model cross-category dependencies in incidence outcomes only. The estimated complementarities for all major brand-pairs across the two categories are found to be positive and significant. Betty Crocker and Duncan Hines brands show their largest cross-category brand-level complementarity with respect to the same umbrella brand in the other category. This suggests that households may be more likely to match a cake mix brand with its own umbrella brand of frosting, than with a different brand of frosting. Brand complementarity effects alone account for 77.21 percent of the deterioration in model fit from ignoring cross-category dependencies in our brand choice model. Cross-category price effects account for 16.51 percent, while unobserved dependencies account for the remaining 6.28 percent. We summarize our estimated price elasticities using two brand-level measures: (1) largess, which captures how much a complementary brand's demand gains from a focal brand's price cut and (2) free-ride, which captures how much a focal brand gains from a price cut on complementary brands. We present two-dimensional plots of estimated Largess and Free-Ride measures across brands. Such plots will assist retailers in understanding relationships between complementary brands across categories. Using a promotional simulation, we show that if the retailer wants to offer a 10 percent price cut on one of the available cake mix and frosting brands, promoting Betty Crocker cake mix is optimal, in terms of producing the largest increase in total retail profit (increasing profits from both cake mix and frosting categories). We also find that a price cut of 10 percent on Betty Crocker frosting produces a significantly lower increase in total retail profit. By performing a decomposition of the (magnitude of) the estimated retail profit impact of a 10 percent price cut on each brand into incidence and brand choice components, we find that the percentage that is accounted for by brand-level effects is 42 percent within the promoted category and 55 percent within the complementary category. Previously proposed multi-category demand models have estimated cross-category effects in incidence outcomes only. We show here that at least an equally, if not more, significant component of cross-category linkages in demand arises on account of brand-level effects. This is a new and important finding in the literature on multi-category demand models, as well as the literature on retail promotional effects on demand. We recognize some caveats and limitations here. First, to the extent that there are other product categories that are complements to cake mix and frosting (our focal categories), excluding such categories from the analyses would lead to biases in our parameter estimates. Our endogeneity correction procedure for price and feature may also not apply.12 Two, extending our model to a larger number of product categories will increase the computational burden of estimation since we have to account for all brands’ pair-wise demand dependencies across all categories. Employing a structural, as opposed to (our) reduced-form, model of cross-category demand (as in, e.g., Mehta (2007)) is one solution to this parameter explosion problem. It may also render moot some types of endogeneity correction for marketing variables since the variables’ effects can be explicitly accounted for within the postulated behavioral structure of the model. Similarly, variants of Berry (1994) method, such as the one used in Song and Chintagunta (2006), can account for price endogeneity without making assumptions about supply-side behavior. Third, our specification of unobserved heterogeneity in model parameters using a latent class approach is less flexible than a mixture of normals specification (which nests the latent class specification as a special case). As mentioned earlier, we use a latent class approach for the sake of interpretability and computational convenience. Finally, while our model indeed accounts for category-level complementarity, it is difficult to explicitly disentangle the relative contribution of category-level complementarity within the estimated brand-level complementarity parameters. For example, when all brand-level complementarity parameters are estimated to be equal, one may interpret them as representing either (1) category-level complementarity only, with no residual brand-level complementarity or (2) brand-level complementarity only (with all brands complementing each other equally), without any residual category-level complementarity. Imposing additional structure on our model may render such decomposition feasible, but our model is agnostic on this issue. We note this as a limitation of our model. Here are some useful directions for future research. First, it would be useful to extend our modeling framework to a large number of categories, particularly paying attention to picking categories that are substitutable (as opposed to complementary) to the chosen categories. Even categories that appear to be independent to the chosen categories from a consumption standpoint may be inter-related to them on account of the household's budget constraint. Therefore, including seemingly independent categories (over and above obviously substitutable categories) in the analysis will be a useful extension. Second, it would be useful to extend our proposed model to handle purchase quantity outcomes (as in Song and Chintagunta (2007) and Niraj, Padmanabhan, and Seetharaman (2008)). Third, it will be interesting to model supply-side implications of the estimated cross-category effects in demand, for example, studying whether retailers engage in product mix pricing by accounting for cross-category effects of the chosen retail prices in each category. Executive summary Many national brand manufacturers in the CPG industry sell products in complimentary categories through retailers. Both the manufacturers of these products and the retailers that sell them to the end consumers have to make complex decisions on the pricing and promotional strategies for these brands. For example, a manufacturer supplying complimentary product lines must decide on the wholesale prices and when, whether and how to promote complimentary products. A retailer in turn has to set retail prices and promotional strategies for multiple brands across complimentary product lines. While each is driven by different profit considerations, it is clear that understanding the drivers of demand for each brand, and the inter and intra category demand relationship among these brands is crucial. To accomplish this we need models and measurements that quantify such demand interdependencies within and across categories. Past research has primarily addressed this by modeling interdependencies in purchase incidences across categories but not in brand choices. The authors attempt to fulfill this gap in the literature and highlight how their model and the implications of their results can be potentially useful to decision makers. The authors propose a multi-category brand choice model which accommodates cross-category dependencies in households’ brand choice outcomes (in addition to incidence outcomes) in complementary product categories. This model explicitly allows for three components to underlie such cross-category dependencies in brand choice outcomes, i.e., (1) complementarity, (2) marketing spillovers, and (3) unobserved dependencies. The authors estimate the proposed model using scanner panel data on cake mix and frosting categories, and they find that complementarity explains the vast majority of the estimated cross-category effects in demand. As much as 55 percent of the total retail profit impact of price promotions arise on account of brand-level, as opposed to category-level, dependencies in household demand. The findings offer managers new perspectives for brand management. First, since there are significant asymmetries in how different brand pairs complement each other, when manufacturers make merger and acquisition decisions, they must correctly account for these asymmetries in order to best exploit inter-brand synergies, while avoiding cannibalization among one's own brands. Second, since half of the retail profit impact of price promotions can be attributed to brand-level dependencies, retailers can benefit significantly from better coordinated pricing and promotion decisions across brands in complementary categories. Last, but not least, the authors provide a simple and intuitive tool, Largess and Free-Ride Plots, to visually represent the estimated cross-category pricing effects. These plots can help managers understand the differential ability of brands to influence, or be influenced by, brands in complementary categories, and assist brand management decisions accordingly.