Sangkil Moon, Gary Russell (2008)
Predicting Product Purchase from Inferred Customer Similarity: An Autologistic Model ApproachManag. Sci., 54
T. Richards, K. Yonezawa, Sophie Winter (2015)
Cross-category effects and private labelsEuropean Review of Agricultural Economics, 42
T. Richards, S. Hamilton (2018)
Retail Market Power in a Shopping Basket Model of Supermarket CompetitionJournal of Retailing
Bart Bronnenberg, C. Sismeiro (2002)
Using Multimarket Data to Predict Brand Performance in Markets for Which No or Poor Data ExistJournal of Marketing Research, 39
Céline Bonnet, Z. Bouamra‐Mechemache (2016)
Organic Label, Bargaining Power, and Profit‐Sharing in the French Fluid Milk MarketERN: Other Econometrics: Applied Econometric Modeling in Agriculture
Jidong Zhou (2014)
Multiproduct Search and the Joint Search EffectThe American Economic Review, 104
Puneet Manchanda, Asim Ansari, Sunil Gupta (1999)
The Shopping Basket: A Model for Multicategory Purchase Incidence DecisionsMarketing Science, 18
Jeremy Bulow, J. Geanakoplos, P. Klemperer (1985)
Multimarket Oligopoly: Strategic Substitutes and ComplementsJournal of Political Economy, 93
J. Besag (1974)
Spatial Interaction and the Statistical Analysis of Lattice SystemsJournal of the royal statistical society series b-methodological, 36
Anthony Dukes, Esther Gal‐Or, K. Srinivasan (2006)
Channel Bargaining with Retailer AsymmetryJournal of Marketing Research, 43
Sergio Meza, K. Sudhir (2010)
Do private labels increase retailer bargaining power?Quantitative Marketing and Economics, 8
Ryan Luchs, Tansev Geylani, Anthony Dukes, K. Srinivasan (2010)
The End of the Robinson-Patman Act? Evidence from Legal Case DataManag. Sci., 56
David Bell, Teck-Hua Ho, Christopher Tang (1998)
Determining Where to Shop: Fixed and Variable Costs of ShoppingJournal of Marketing Research, 35
Tülin Erdem, Baohong Sun (2002)
An Empirical Investigation of the Spillover Effects of Advertising and Sales Promotions in Umbrella BrandingJournal of Marketing Research, 39
D. Staiger, J. Stock (1994)
Instrumental Variables Regression with Weak InstrumentsEconometrics eJournal
Justus Haucap, Ulrich Heimeshoff, Gordon Klein, Dennis Rickert, Christian Wey (2013)
Bargaining power in manufacturer-retailer relationships
Michaela Draganska, Daniel Klapper, S. Villas-Boas (2008)
A Larger Slice or a Larger Pie? An Empirical Investigation of Bargaining Power in the Distribution ChannelStanford Graduate School of Business Research Paper Series
M. Gentzkow (2007)
Valuing New Goods in a Model with Complementarity: Online NewspapersManagerial Marketing
W. Kamakura, Kyuseop Kwak (2012)
Menu-Choice ModelingBehavioral Marketing eJournal
S. Villas-Boas (2004)
Vertical Contracts between Manufacturers and Retailers: Inference with Limited Data
Q. Feng, Lauren Lu (2013)
The Role of Contract Negotiation and Industry Structure in Production OutsourcingERN: Other Microeconomics: Production
K. Binmore, A. Rubinstein, A. Wolinsky (1985)
The Nash bargaining solution in economic modelling
Andrew Rhodes (2012)
Multiproduct Retailing
Eric Anderson, David Bell, A. Mitchell, C. Narasimhan, A. Rao, D. Soberman (2003)
A Bargaining Theory of Distribution ChannelsJournal of Marketing Research, 40
K. Train (2003)
Discrete Choice Methods with Simulation
Marketing Letters, Kusum Ailawadi, Eric Bradlow, Michaela Draganska, V. Nijs, Robert Rooderkerk, K. Sudhir, Kenneth Wilbur, Jie Zhang (2010)
Empirical models of manufacturer-retailer interaction: A review and agenda for future researchMarketing Letters, 21
Gary Russell, A. Petersen (2000)
Analysis of cross category dependence in market basket selectionJournal of Retailing, 76
Mike Rees, N. Cressie (1993)
5. Statistics for Spatial DataJournal of The Royal Statistical Society Series A-statistics in Society, 156
Nitin Mehta (2007)
Investigating Consumers' Purchase Incidence and Brand Choice Decisions Across Multiple Product Categories: A Theoretical and Empirical AnalysisMarketing Science, 26
Q. Feng, Lauren Lu (2013)
Supply Chain Contracting under Competition: Bilateral Bargaining vs. StackelbergSupply Chain Management eJournal
Jean-Pierre Dubé (2004)
Appendix for : Product Di ff erentiation and Mergers in the Carbonated Soft Drink Industry
L. Vogt (2016)
Statistics For Spatial Data
Justin Ho, Kate Ho, J. Mortimer (2008)
The Use of Full-Line Forcing Contracts in the Video Rental IndustryExperimental & Empirical Studies eJournal
Michelle Baggio, J. Chavas (2009)
On the Consumer Value of Complementarity: A Benefit Function ApproachAgricultural & Natural Resource Economics eJournal
Jean-Pierre Dubé (2004)
Multiple Discreteness and Product Differentiation: Demand for Carbonated Soft DrinksMarketing Science, 23
O. Thomassen, Howard Smith, Stephan Seiler, Pasquale Schiraldi (2017)
Multi-Category Competition and Market Power: A Model of Supermarket PricingMicroeconomics: Production
Z. Bouamra‐Mechemache (2015)
Organic label, bargaining power, and prot sharing in
K. Train (2003)
Discrete Choice Methods with Simulation by Kenneth E. Train
Rui Huang, J. Perloff, S. Villas-Boas (2006)
Effects of Sales on Brand LoyaltyJournal of Agricultural & Food Industrial Organization, 4
Inseong Song, Pradeep Chintagunta (2006)
Measuring Cross-Category Price Effects with Aggregate Store DataManag. Sci., 52
David Bell, J. Lattin (1998)
Shopping Behavior and Consumer Preference for Store Price Format: Why Large Basket Shoppers Prefer EdlpMarketing Science, 17
Tülin Erdem, S. Chang (2012)
A cross-category and cross-country analysis of umbrella branding for national and store brandsJournal of the Academy of Marketing Science, 40
S. Misra, S. Mohanty (2004)
Estimating Bargaining Games in Distribution Channels
Howard Smith, Øyvind Thomassen (2012)
Multi-category demand and supermarket pricing☆International Journal of Industrial Organization, 30
T. Richards, M. Gómez, Geoffrey Pofahl (2012)
A Multiple-discrete/Continuous Model of Price PromotionJournal of Retailing, 88
H. Horn, A. Wolinsky (1988)
BILATERAL MONOPOLIES AND INCENTIVES FOR MERGERThe RAND Journal of Economics, 19
Kyuseop Kwak, S. Duvvuri, Gary Russell (2015)
An Analysis of Assortment Choice in Grocery RetailingJournal of Retailing, 91
Ying Zhao, Wei-Lun Fellow, J. Villas-Boas (2005)
Retailer, Manufacturers, and Individual Consumers: Modeling the Supply Side in the Ketchup MarketplaceJournal of Marketing Research, 42
Sha Yang, Yi Zhao, Tülin Erdem, Ying Zhao (2010)
Modeling the Intrahousehold Behavioral InteractionJournal of Marketing Research, 47
Céline Bonnet, P. Dubois (2008)
Inference on Vertical Contracts between Manufacturers and Retailers Allowing for Non Linear Pricing and Resale Price MaintenanceIO: Theory
(1992)
A model of product category competition among grocery retailers
Richard Briesch, Pradeep Chintagunta, Edward Fox (2009)
How Does Assortment Affect Grocery Store Choice?Journal of Marketing Research, 46
Vishal Singh, Karsten Hansen, Sachin Gupta (2005)
Modeling Preferences for Common Attributes in Multicategory Brand ChoiceJournal of Marketing Research, 42
J. Villas-Boas, R. Winer (1999)
Endogeneity in Brand Choice ModelsManagement Science, 45
Amil Petrin, K. Train (2010)
A Control Function Approach to Endogeneity in Consumer Choice ModelsJournal of Marketing Research, 47
Abstract Bargaining power in vertical channels depends critically on the ‘disagreement profit’ or the opportunity cost to each player should negotiations fail. In a multiproduct context, disagreement profit depends on the degree of substitutability among the products offered by the downstream retailer. We develop an empirical framework that is able to estimate the effect of retail complementarity on bargaining power, and margins earned by manufacturers and retailers in the French soft-drink industry. We show that complementarity increases the strength of retailers’ bargaining position, so their share of the total margin increases by almost 28 per cent relative to the no-complementarity case. 1. Introduction Empirical models of vertical bargaining power rely critically on estimates of how consumers respond to changes in prices in the downstream, or consumer, market. Typically, these models address retail purchases from only one category at a time (Villas-Boas and Zhao, 2005; Villas-Boas, 2007), whereas consumers tend to buy products by the shopping basket (Manchanda, Ansari, and Gupta, 1999; Kwak, Duvvuri, and Russell, 2015). Within a single category, the choices – different brands, for example – are plausibly all substitutes for each other. When buying multiple categories at a time, however, the purchase is likely to consist of a mix of substitutes and complements. In a theoretical treatment of this setting, Horn and Wolinksy (1988) show that when wholesale prices are negotiated between suppliers and downstream buyers, differences in how consumers respond to price changes can alter the nature of the bargaining outcome qualitatively for the upstream firms. While the potential for a complex pattern of substitutability and complementarity among items in the shopping basket may be relatively inconsequential if the items are from different manufacturers, the implications for vertical relationships between retailers and manufacturers cannot be ignored. In this research, we use an empirical shopping-basket approach to examine the importance of complementarity among retail grocery products for bargaining power between retailers and manufacturers. With the global consolidation of food production in fewer and fewer hands, some manufacturers may be responsible for items in several categories in a typical shopping basket. We argue that this observation may have important implications for the balance of bargaining power between manufacturers and retailers in the food supply chain. Namely, when downstream firms sell complementary goods, an upstream supplier has less bargaining power than if products downstream are substitutes because the cost of not arriving at an agreement is higher for the supplier. Why? Because retailers are interested in category sales and manufacturers are interested in selling only their brands. When a retailer cannot sell a particular brand, it will sell another, while if a manufacturer selling to multiple retailers loses a distribution contract, the lost sales cannot be replaced as easily. If the manufacturer sells items in substitute categories – Camembert and Brie cheese, for instance – the effect may not be substantial as lost sales can be regained elsewhere. However, if the manufacturer sells complementary goods – Brie cheese and honey, for instance – the effect of losing sales from a dropped brand in one category will be amplified by losses in the other. Therefore, the opportunity cost of arriving at an agreement, which is manifest in the difference between the current and disagreement profits, is higher for the manufacturer than the retailer. Because retail bargaining power is the mirror of manufacturer power, we expect retailer bargaining power to be higher when goods are complements.1 Concerns over bargaining power, on both the retailing and the manufacturing side of the food and beverage industry, are not only curiosities but reflect real changes in industry structure. Food retailing in France is undergoing a rapid process of consolidation, and the use of joint purchasing agreements has become commonplace (Autorité de la Concurrence, 2015). Indeed, the six largest retail groups in the French food retail sector in 2016, with associated market shares, were Groupe Carrefour (21.1 per cent), Groupe Leclerc (20.7 per cent), ITM Entreprises (14.1 per cent), Groupe Casino (11.4 per cent), Groupe Auchan (11.4 per cent) and Groupe Système U (10.1 per cent), implying a four-firm concentration ratio of fully 67.3 per cent (Kantar Worldpanel 2016). Further, retailers continue to expand their use of private labels, not only in France, but throughout the European Union, which increases the bargaining power of retailers relative to manufacturers and producers. On the other side of the table, the soft-drink manufacturing sector is one of the most concentrated in the entire food and beverage industry (European Commission, 2014, p. 306), while the European Commission also notes that ‘the top 50 global brands include 7 food products, mainly beverages’ (European Commission, 2007, p. 34). Although structure does not necessarily imply conduct, these observations suggest that there are conditions on both the buying and selling side of the soft-drink market that may lead to adverse exercise of bargaining power. It is well understood that complementarity affects pricing strategies among retailers downstream. Rhodes (2015) and Smith and Thomassen (2012) argue that internalising cross-product pricing effects on the intra-retailer margin with complementarity leads to lower retail prices as retailers have an incentive to drive volume rather than margin. On the other hand, Richards and Hamilton (2016) show that complementarity on the inter-retailer margin is associated with anti-competitive effects and is a source of market power for retailers. However, none of these studies focus on vertical relationships between multi-product retailers and manufacturers. The increasing prevalence of highly granular data on consumer purchases, whether from frequent shopper cards or from household panel data sets, both highlights the importance of examining shopping-basket purchases, and makes structural models of multi-product purchasing behaviour possible. By observing purchases on each shopping-occasion basis, we have a better understanding of how consumers combine products in a shopping list. Namely, previous research shows that consumers tend to make multiple discrete purchases (Dubé, 2004, 2005; Richards, Pofahl, and Gomez, 2012) and tend to purchase some pairs of products at the same time, for reasons other than traditional price-based complementarity reasons (Song and Chintagunta, 2006; Mehta, 2007).2 In this paper, we use a model of retail demand that explicitly recognises the importance of these two features of consumer-level purchase behaviour. Our demand model is of the multi-variate logit (MVL) class, in which consumers are assumed to make discrete choices among baskets of items. Because each item can reside in one of many different baskets, the choices cannot be described by a traditional logit model. Russell and Peterson (2000) show how the auto-logistic model from spatial econometrics (Besag, 1974) can be used in a shopping-basket model environment to consistently estimate demand elasticities that include a full-range of possibilities, from complementarity to substitutability, and independence in demand. Further, because the estimating model assumes a closed form, Kwak, Duvvuri, and Russell (2015) show that it can be used to inform a wide range of practical issues in structural demand modelling. For this paper, we demonstrate how the implicit assumption of strict substitutability from more usual logit models of demand can impart significant bias to bargaining power estimates in an environment in which demand relationships are likely to be more general. Structural models of vertical relationships between retailers and manufacturers are, by now, reasonably well understood. Assuming Bertrand–Nash rivalry among downstream retailers, the solution to the Nash bargaining problem between retailers and manufacturers yields a single parameter that describes the share of the total margin that is appropriated by either the manufacturer or the retailer, depending on the relative bargaining strength of either party (Draganska, Klapper, and Villas-Boas, 2010).3 While others investigate structural factors that may influence the degree of bargaining power possessed by either side (Meza and Sudhir, 2010; Haucap et al., 2013; Bonnet and Bouamra-Mechemache, 2016), the role of demand interrelationships among downstream retailers is not well understood, despite the clear theoretical importance it plays in the likely outcome of any negotiation (Bulow, Geanakoplos, Klemperer, 1985; Binmore, Rubinstein and Wolinsky, 1986; Horn and Wolinsky, 1988).4 In this paper, we show that the structure of demand, namely whether products are substitutes or complements, can have dramatic effects on estimated bargaining-power parameters.5 We test our hypothesis using data on multi-category soft-drink purchases among households in France. While a discrete-choice model of category incidence would restrict all pairs of categories to be substitutes, we find that complementarity is more common than substitutability at the brand level. When we condition equilibrium wholesale prices on our MVL demand estimates, we find that complementarity is associated with less manufacturer bargaining power and greater retail bargaining power. When products sold by one manufacturer are complements downstream, the disagreement profit, which is the amount earned if the parties fail to agree, is lower with complementarity than under strict substitutability. Lower disagreement profit implies a higher opportunity cost of agreeing. As a result, manufacturers are essentially more keen to arrive at a negotiated solution, so their bargaining power is lower. Our findings have broader implications for vertical relationships in any other industry in which powerful suppliers sell complementary products through oligopoly downstream retailers. Our research contributes to both the theoretical literature on vertical relationships between suppliers and retailers, and the empirical literature on the nature of bargaining power in those relationships. Our primary contribution lies in demonstrating empirically the importance of the theoretical insight of Horn and Wolinsky (1988). Namely, that the downstream demand relationships among items are likely to have significant implications for the exercise of bargaining power between downstream retailers and upstream manufacturers. In terms of the empirical bargaining power literature, we show how the single-category model of Draganska, Klapper, and Villas-Boas (2010) can be extended to a more general, multi-category demand framework, and show that doing so can have dramatic effects on the nature of the equilibrium bargaining solution that results. In the next section, we describe our multi-category demand model, and how it is able to capture complementarity in household-level beverage purchases. The Nash bargaining power model is presented in the third section, where we show how our core hypotheses regarding complementarity and bargaining power are tested. We describe the data from our French soft-drink example in the fourth section, and present some stylised facts that suggest how a shopping-basket approach is both appropriate and necessary in data such as ours. We present and interpret the demand and pricing model results in the fifth section, while the final section concludes, and offers some implications for settings beyond our retail grocery example. 2. Empirical model of multi-category pricing 2.1. Overview We examine the role of complementarity in bargaining power using a structural model of multi-category retail demand, and vertical pricing relationships between beverage manufacturers and retailers in France. Our model is innovative in that the demand component describes relationships among beverages found in a typical shopping-basket, unlike most conventional analyses in this area (Draganska, Klapper, and Villas-Boas, 2010). Our demand model is multi-category in nature in that it recognises the fact that items are purchased through a discrete-choice data generating process, but will nearly as often be complementary as they are substitutes with other items in the basket. When a retailer sells items from the same manufacturer that are likely to be complements, the implications for bargaining power in the vertical channel may be dramatic. Our model is structural in that we estimate equilibrium pricing relationships in the vertical channel, conditional on the structure of retail demand (Villas-Boas, 2007; Bonnet and Dubois, 2010; Bonnet and Bouamra-Mechemache, 2016) across multiple-product categories. 2.2. Model of multi-category demand We develop our empirical model of multi-category choice and local-content demand from a single utility function, in the sense that consumers are assumed to maximise utility in choosing which categories to buy from on each trip to each store, r= 1, 2, …,R. For clarity, we suppress the store subscript until we describe the equilibrium vertical pricing game below. Consumers h= 1, 2, 3,…,H in our model select items from among i= 1, 2, 3,…,I categories, ciht, in assembling a shopping basket, or bundle, bht=(c1ht,c2ht,c3ht,…,cIht) on each trip, t. Define the set of all possible bundles bht∈B and the set of categories i,j∈I. We focus on purchase incidence, or the probability of choosing items from a particular category on each trip to the store, and regard the brand of the chosen item as an attribute of the choice. We assume consumers purchase only one brand within each category in order to remain consistent with the literature. We further assume consumers choose categories in order to maximise utility, Uht, and follow Song and Chintagunta (2006) in writing their utility in terms of a discrete, second-order Taylor series approximation to an arbitrary utility function.6 Utility is written as Uht(bht)=Vht(bht)+εht=∑i∈Iωihtciht+∑i∈I∑j∈Iθijhcihtcjht+εht, (1) where ωiht is the baseline utility for category i earned by household h on shopping trip t, ciht is a discrete indicator that equals 1 when category i is purchased, and is 0 otherwise, εht is an error term that is Gumbel distributed, and iid across households and shopping trips, and θijh is a household-specific parameter that captures the degree of interdependence in demand between categories i and j, such that if θijh< 0, the categories are substitutes, if θijh> 0, the categories are complementary, and if θijh= 0, the pair of categories are independent in demand.7 For example, we would expect to find θijh> 0 for Brie and charcuterie, but θijh< 0 for Brie and Camembert, and θijh= 0 for Brie and laundry detergent. In order to ensure that the model is identified, it is necessary that all θii= 0 and that symmetry be imposed on the matrix of cross-purchase effects such that θijh=θjih,∀i,j,h (Besag, 1974; Cressie, 1993; Russell and Petersen, 2000). The probability that a household purchases in a given category on a purchase occasion, or category incidence, depends on both perceived need, and marketing activities from the brands in the category (Bucklin and Lattin, 1992; Russell and Petersen, 2000). Because we seek to examine demand relationships, and pricing behaviour, at the brand-and-retailer level, however, we extend the usual MVL specification to consider the demand for specific items within each category. We then capture interactions in a parsimonious way through the interaction terms given in equation (1).8 Therefore, we write baseline utility for each brand (k), retailer (r) and category (i) as ωikrht=αikr+βihXikr+γiZh, (2) where αikr are fixed effects that control for the particular brand, k, that is purchased from retailer, r, in category i, Xik is a matrix of category-specific marketing mix elements for each brand, and Zh is a matrix of household attributes. Household attributes affect perceived need, as measured by the rate at which a household consumes products in the category, which when combined with the frequency of category-purchase, determines the amount on hand ( INVh). We infer household inventory using methods that are standard in this literature (Bucklin and Lattin, 1992). Namely, we calculate the category-consumption rate for each household by calculating their total purchases over the sample period, and divide by the total number of days in the data set. We then initialise inventory at the average consumption rate at the start of the time-period for each household, and increment inventory upward with purchases, and downward each day by the average consumption rate. Need is also determined by more fundamental household factors such as the size of the household (HHh), income level ( INCh) and education ( EDUh). Any state dependence in demand is assumed to be captured by the inventory variable as it reflects intertemporal changes in consumption behaviour. Marketing mix elements at the brand-category level include the price of the individual items in each category (pikr), and an indicator of whether the item was on promotion during the purchase occasion at a particular retailer (PRikr).9 Each of the variables entering equation (2) represents sources of observed heterogeneity, whether at the item (brand / category / retailer) ( Xikr) or household ( Zh) levels. However, there is also likely to be substantial unobserved heterogeneity in household preferences and in attributes of the item that may affect incidence. Therefore, we capture unobserved heterogeneity in item preference by allowing for randomly distributed category-interactions ( θijh) and item-level price-response ( βpih). Formally, therefore, we estimate βpih=βpi0+βpi1νih1,vih1∼N(0, 1),∀i,θijh=θij0+θij1νh2,v2h∼N(0, 1), (3) for the price-element of the marketing-mix matrix, and for each of the ij category-interaction parameters. By allowing for a general pattern of correlation among these parameters (Singh, Hansen, and Gupta, 2005), we capture a primary source of coincident demand among categories. In other words, if households tend to be correlated in terms of their price sensitivity, then allowing for co-movements in demand due to price responsiveness will remove some element of randomness from the error term, leaving less variation to be explained by other factors. This extension to the MVL model, by incorporating random parameters into both the marketing-mix and category-interaction parameters is called the random-parameters MVL model, or RP-MVL. With the error assumption in equation (1), the conditional probability of purchasing in each category assumes a relatively simple logit form. Following Kwak, Duvvuri, and Russell (2015), we simplify the expression for the conditional incidence probability by writing the cross-category purchase effect in matrix form, where Θh=[Θ1h,Θ2h,…,ΘNh] and each Θih represents a column vector of the I×I cross-effect Θh matrix which is defined as Θh=[0θ12hθ13h…θ1Ihθ21h0…θ2Ihθ31hθ32h0…θ3Ih...…....….θI1hθI2hθI3h…0], (4) so that the conditional utility of purchasing an item in category i is written as Uht(cikrht|cjkrht)=ωht'bht+Θih'bht+εht, (5) for the items i, k, r in the basket vector bht. Conditional utility functions of this type potentially convey important information, and are more empirically tractable that the full probability distribution of all potential assortments (Moon and Russell, 2008), but are limited in that they cannot describe the entire matrix of substitute relationships in a consistent way, and are not econometrically efficient in that they fail to exploit the cross-equation relationships implied by the utility maximisation problem. To see this more clearly, we derive the estimating equation implied by the Gumbel error-distribution assumption, conditional on the purchases made in all other categories, cjht. With this conditional assumption, the probability of purchasing an item from category i = 1 is written as Pr(c1krht= 1|cjkrht)=[exp(ω1krht+Θ1h'bht)]c1krht1+exp(ω1krht+Θ1h'bht), (6) and bht represents the basket vector. Estimating all I of these equations together in a system is one option, or Besag (1974) describes how the full distribution of bht choices are estimated together. Assuming the Θh matrix is fully symmetric, and the main diagonal consists entirely of zeros, then Besag (1974) shows that the probability of choosing the entire vector bht is written as Pr(bht)=exp(wht'bht+12bht'Θhbht)∑bht∈B[exp(wht'bht+12bht'Θhbht)], (7) where Pr(bht) is interpreted as the joint probability of choosing the observed combination of categories from among the 2I potentially available from I categories.10 Assuming the elements of the main diagonal of Θ is necessary for identification, while the symmetry assumption is required to ensure that equation (7) truly represents a joint distribution, a multi-variate logistic distribution, of the category-purchase events. Essentially, the model in (7) represents the probability of observing the simultaneous occurrence of I discrete events – a shopping basket – at one point in time. And, due to the iid assumption of the logit errors associated with each basket choice, the model in equation (7) implicitly assumes that the baskets are subject to the independence of irrelevant alternatives (IAA), but the categories within the basket are allowed to assume a more general correlation structure (Kwak, Duvvuri, and Russell, 2015). Aggregating equation (7) over households then produces an expression for the probability of purchasing each basket, and each component brand, category, retailer combination captured by each basket. Given the similarity of the choice probabilities to logit-choice probabilities, it is perhaps not surprising that the form of the elasticity matrix is also similar. Given the probability expression above, the marginal effect of a price change in brand k, category i and retailer r, on the own-probability of purchase is written as ∂Pr(cikr)∂pikr=βpihPr(cikr)(1−Pr(cikr)), (8) where βpih is the household-specific marginal utility of income for an item in category i, and Pr(cikr) includes all baskets that contain the specific i, k, r item. Similarly, the marginal effect of a change in the price of an item in a different category (j), of a different brand (l) in the same store on the probability of purchasing an item in category i, when the items are in the same baskets is given by ∂Pr(cikr)∂pjlr=−βpihPr(cikr)Pr(cjlr), (9) and the marginal effect of change in the price of an item that may be in the same category, and of the same brand, but in a different store is ∂Pr(cikr)∂piks=−βpihPr(cikr)Pr(ciks) (10) for all products not in the same store. With these expressions, we can estimate an entire matrix of price responses, for all items with respect to all other items, whether they are from the same brand, category and store, or if they differ entirely. To this point, the development of the MVL model is relatively standard. However, in our application, we are interested not only in the magnitude of each of the Θij parameters (dropping the household subscripts for clarity), but how a consumer’s willingness to substitute (or complement) between categories affects equilibrium prices charged by retailers in each category, and how the resulting margins are divided between retailers and manufacturers. We use the parameter estimates from the RP-MVL model above to condition equilibrium pricing behaviour by retailers, and their bargaining power relative to manufacturers in the vertical channel using the Nash bargaining model developed in the next section. 3. Bargaining power model In this section, we describe the empirical model used to estimate the effect of complementarity on brand-level bargaining power. For this purpose, we use the vertical Nash-in-Nash model developed by Misra and Mohanty (2006) and Draganska, Klapper, and Villas-Boas (2010). Our model differs from either of these studies, however, in that we explicitly account for the effect of complementarity. Horn and Wolinsky (1988) show that complementarity is likely to be critical in influencing the level of bargaining power possessed by either side because downstream-substitution patterns affect the disagreement profit earned by each party should negotiations fail. Disagreement profit, in turn, depends upon how much the market share of each product would rise if the object of the negotiation is dropped from the product line-up. With strict-substitute demand models, the notion that market share will rise if another product is dropped is a given as it is enforced, mathematically. With complementary products, however, the effect is not as straightforward. If I am a retailer, and negotiations fail with my pasta-sauce supplier, I will still sell pasta-sauce from another supplier (substitute product). If I also sell pasta from this same pasta-sauce supplier (a complementary product), then the supplier’s loss in sales is magnified by the complementary relationship between pasta and sauce, but I continue to sell pasta from another supplier. The disagreement profit for the retailer, therefore, is higher in the complementarity case than it is when products are constrained to be strict substitutes, so retailer bargaining power is expected to be higher.11 Ultimately, however, the complexity of the relationships involved in any given shopping basket means that the implications of complementarity for bargaining power is an empirical question. In this section, we describe how the Nash-in-Nash bargaining power model applies to the case of shopping-basket shoppers. We characterise the marketing channel as consisting of several, multi-product retailers, and our several, multiple-product suppliers that sell to each of our sample retailers. We assume retailers arrive at a Nash equilibrium in horizontal competition, pricing as if they were Bertrand–Nash competitors selling differentiated products. Following recent developments in the empirical literature on vertical relationships, we then assume the supplier achieves a Nash bargaining solution (Horn and Wolinsky, 1988) with each of the retailers independently, and estimate the resulting bargaining power parameter that divides the total margin (from marginal production cost to retail price) between the supplier and retailers according to their relative negotiating abilities (Draganska, Klapper, and Villas-Boas, 2010). We begin by solving for the optimal margin values, and then solve for the Nash bargaining solution. Beginning with the retailer decision, and suppressing time-period index (t) for clarity, retailer g sets a price for each item under a maintained assumption of Nash rivalry to solve the following problem: πg=maxpj∑j=1Jg(pj−cjr−wj)Msj,g=1, 2, …,G, where M is the total market demand, wj is the wholesale price, cjr are unit retailing costs, sj is the market share defined above, and retailer g sells a total of Jg products. Marginal retailing costs are assumed to be constant in volume, and a function of input prices, which is plausible given the share of store-sales accounted for by any individual product. The solution to this problem is written in matrix notation as: mg=p−cr−w=−(Wg∗sp)−1s, where mg is a vector of retail margins, p is a J×1 vector of prices, w is a J×1 vector of wholesale prices, cr is a J×1 vector of retailing costs (estimated as a linear function of retailing input prices), s is a J×1 vector of market shares, sp is a J×J matrix of share-derivatives with respect to all retail prices, Ωg is a retail ownership matrix, with each element equal to 1 if the row item and column item are sold by the same retailer, and 0 otherwise, and * indicates element-by-element multiplication.12 Equilibrium retail prices, therefore, are determined by demand interrelationships at the retail level in Bertrand–Nash rivalry. If retail prices are assumed to be determined by the Bertrand–Nash game played among retailers, and marginal production costs determined by the engineering relationships that govern the cost of making each item, then the allocation of the total margin (from retail prices to marginal production costs) depends on how the wholesale price (wj) is determined. Wholesale prices, in turn, are assumed to be determined by a Nash bargaining process (Horn and Wolinsky, 1988; Draganska, Klapper, and Villas-Boas, 2010). In a Nash bargaining solution, the allocation of the total margin between wholesalers and retailers depends on two elements: (i) the disagreement profit that results when negotiations fail and the product is not sold and (ii) the bargaining power parameter, which is a function of the inherent bargaining position of the two players. The disagreement profit term reflects the fact that if a product is not sold, the sales, and profits, of all the other items sold by the retailer, or manufacturer, are affected by the nature of the demand interrelationships each face. Draganska, Klapper, and Villas-Boas (2010) solve for the equilibrium relationship between wholesale and retail prices by maximising the generalised Nash product in wholesale prices for product j: GN=(πjg(wj)−djg(mjg))λj(πjf(wj)−djw(mjw))(1−λj), (11) where wj is the wholesale price, djw(mjw) is the disagreement profit to the supplier for product j, which depends on the supplier’s margin, mjw, and djg(mjg) is the disagreement profit to the retailer for failing to arrive at an agreement to sell the same product. In this expression, λj is the bargaining power parameter, which allocates the share of profit to the retailer ( λj) and the wholesaler ( 1−λj) from the trade of product j. The first-order condition to maximising the Generalised Nash product is (dropping the product subscript and arguments of the disagreement profit): ∂GN∂w=λ(πg−dg)(λ−1)∂πg∂w(πf−df)(1−λ)+(1−λ)(πg−dg)λ(πf−df)−λ∂πf∂w= 0. (12) This expression simplifies to give the equilibrium relationship between retail and wholesale prices as a function of their respective disagreement profits, and the relative bargaining power parameter: λ((πf−df)∂πg∂w)+(1−λ)((πg−dg)∂πf∂w)= 0. (13) Because retail prices are assumed fixed at the BN solution, the derivatives ∂πg∂w=∂πf∂w=Ms so this simplifies to: (πg−dg)= (1−λλ )(πf−df). Stacking over all item-profits provides a simple solution in matrix notation that defines the equilibrium bargaining power parameter, and the margins for each item: mf=(1−λλ)[Ωf∗S]−1[Ωg∗S]mg, (14) where Ωf is the J×J manufacturer ownership matrix (with element = 1 if the manufacturer owns product j and zero otherwise), mf is the manufacturer margin, and S is the matrix that defines the incremental profit between when a product is sold, and when it is not (see Draganska, Klapper, and Villas-Boas, 2010 for details on its construction). Substituting the expression for retail margins ( mg) above, and solving for the total margin gives p−cf−cr=−(1−λλ[Ωf∗S]−1[Ωg∗S]+I)[Ωg∗sp]−1s(p), (15) for the final estimating equation, where cf is a vector of manufacturing costs, estimated as a linear function of manufacturing input prices.13 In our empirical application, we recognise that bargaining power varies by each retailer–manufacturer dyad in the data. Therefore, we allow the λ parameter to be randomly distributed over the entire category-retailer-brand sample ( λj=λj0+λj1ν3,v3∼N(0,σ3)) so that bargaining power reflects any factors that may influence the relative strength of each player’s position, as well as unobserved heterogeneity that, if not accounted for, would bias any inferences drawn about the determinants of λ. Importantly, however, allowing λ to vary randomly also means that we are able to recover a value for the bargaining power parameter for every observation in the data set. With observation-specific measures of λ, we use a supplementary regression to test whether bargaining power is higher or lower for products that are complements for other products. Although our method of recovering λ provides a larger number of λ values to work with compared to the approach taken in Draganska, Klapper, and Villas-Boas (2010), we require a summary measure of complementarity for each item in our data set. Determining whether an item is a complement or substitute is not straightforward because the notion of complementarity is typically defined at the level of each dyad, but our approach assigns a classification to each item as to whether it is more likely to be a complement or a substitute. We use the matrix S to determine whether each product is a net complement or net substitute over all other items in the store. That is, if removing the item from the product line-up reduces the demand for all other products, then it must be primarily a complement, and vice versa. We then define a variable measuring the extent of the impact of removing each item on the demand for all other items ( COMPj) that captures the complementary ( COMPj< 0) or substitute ( COMPj> 0) status of the item in question. Given that the bargaining power estimation routine already controls for the identity of the retailer and other factors, we test our core hypothesis using a straightforward regression model in which bargaining power is estimated as a linear function of the complementarity variable such that λˆj=ϕ0+ϕ1COMPj+μj, (16) where λˆj is the fitted-value from the random-parameter function described above, μ is an iid random variable, and ϕi are parameters to be estimated. In this model, our maintained hypothesis is supported if ϕ1< 0, as this implies that retailers tend to have more bargaining power for complementary products than they do for substitute products (recall that the COMP variable is negative-valued as it is measured as the effect on other product shares if the product is removed), and manufacturers, of course, have less. Based on the theoretical insight of Horn and Wolinsky (1988), we attribute this outcome to the exercise of market power in allocating the transaction surplus between the buyer and the seller due to the fact that goods are complements. When retailers sell complementary goods, and manufacturers are able to internalise the effects of selling their products through multiple retailers, then manufacturers’ bargaining power will be lower for that set of complementary items. Similarly, if ϕ1> 0 then suppliers earn higher margins on complementary products, as the degree of bargaining power shifts to suppliers when products are complements, contrary to the Horn and Wolinsky (1988) model. We also estimate a version of our core bargaining power model in which we allow the manufacturer-share of the total margin to depend on whether the manufacturer offers items for sale in multiple categories or not. Manufacturers may also offer items across categories, whether complementary or not. There are two possible effects on their bargaining power: first, if a manufacturer offers a number of ‘must have’ national brands in key categories, then it may be the case that manufacturer bargaining power rises if it controls brands in a number of categories. Second, a manufacturer may offer a ‘full line forcing’ or bundling arrangement in order to ensure that the retailer provides its brands as wide of coverage as possible. Ho, Ho and Mortimer (2012) find that such an arrangement in the video rental industry is responsible for lower wholesale prices, and, often, lower supplier profits. Therefore, we test a second hypothesis that selling in multiple categories reduces manufacturer relative to retailer bargaining power. 4. Data and estimation In this section, we describe the French soft-drink data and how we identify the parameters of both the demand model, and the bargaining power model. Our data are from a large-scale French consumer panel maintained by Kantar TNS Worldpanel for the year 2013. The panel is designed to be representative of all French households, so contains observations from all regions, urban and rural, and draws households from across all socioeconomic strata.14 Identification with unobserved heterogeneity requires a rich panel data-structure, but the computational complexity of the MVL model (particularly in random-parameters form) limits sample size for practical reasons. Therefore, we drew a random sample of 330 households from the subset of households who purchased at least 50 times in our focal categories, for a total of 29,026 transactions. As a household panel, the Kantar data include information on the specific item that was purchased, the package attributes, how much was paid, where and when it was purchased, and a large set of household socioeconomic and demographic attributes. We infer prices for items not purchased by the household on each occasion by calculating item-specific averages for similar stores and weeks. Due to the dimensionality issues associated with the MVL model described above, we focus on four sub-categories within the soft-drink category: colas, fruit juices, iced teas, and combine all other soft drinks into an ‘other’ category, which generally consist of other sodas, sport and energy drinks and items that were not categorised. In order to ensure that the MVL model is empirically tractable, we also focus on sales through the top four retailers, and four brands in each category that represented both a relatively large amount of volume in the category, and a presence in as many retailers as possible.15 Focusing on as many of the same brands across retailers as possible is desirable for identification as we capture as much cross-sectional variation in margin behaviour as possible.16 Although this 4×4×4 design may seem more restrictive than is normally the case in other shopping-basket demand models, it is necessary in our case because we need to be able to isolate specific retail–manufacturer pairs from the demand model through the bargaining-power estimation process. We identify complementary relationships among items in the four sub-categories by specifically choosing products that are often combined in typical shopping-basket purchases. Whether from a demand for variety, purchasing for multiple use occasions, buying for multiple consumers within the buying household, umbrella branding by manufacturers or some other source, we observe a substantial number of multi-purchase occasions that can be described as evidence of, at least, incidental complementarity if not complete price complementarity.17 In Table 1a, the sample-shares of each item combination are shown in the bottom 15 rows. The data in this table show that purchases of fruit-juice-only are most common (31 per cent), while combinations of juice-and-other (13.4 per cent) and cola-juice-and-other (10.5 per cent) are also common. Importantly, no item combination is null so that each interaction parameter in the MVL model has sufficient choice-variation to be, at least in theory, identified. Table 1a. Summary of sample shares Retailers / brands Baskets Variable Mean SD Variable Mean SD Retailer 1 0.353 0.478 Cola only 0.088 0.284 Retailer 2 0.278 0.448 Fruit juice only 0.310 0.462 Retailer 3 0.190 0.393 Iced tea only 0.014 0.119 Retailer 4 0.179 0.384 Other soft drink only 0.082 0.275 Brand 1, Category 1 0.300 0.458 Cola and juice 0.098 0.297 Brand 2, Category 1 0.031 0.172 Cola and tea 0.005 0.068 Brand 3, Category 1 0.001 0.030 Cola and other 0.055 0.229 Brand 4, Category 1 0.022 0.147 Juice and tea 0.017 0.130 Brand 1, Category 2 0.171 0.377 Juice and other 0.134 0.340 Brand 2, Category 2 0.071 0.257 Tea and other 0.008 0.090 Brand 3, Category 2 0.044 0.204 Cola, juice and tea 0.017 0.130 Brand 4, Category 2 0.004 0.063 Cola, juice and other 0.105 0.307 Brand 1, Category 3 0.074 0.261 Cola, tea and other 0.005 0.073 Brand 2, Category 3 0.013 0.115 Juice, tea and other 0.028 0.164 Brand 3, Category 3 0.003 0.055 Cola, juice, tea and other 0.032 0.177 Brand 4, Category 3 0.065 0.476 Brand 1, Category 4 0.066 0.248 Brand 2, Category 4 0.059 0.237 Brand 3, Category 4 0.046 0.209 Brand 4, Category 4 0.016 0.125 Retailers / brands Baskets Variable Mean SD Variable Mean SD Retailer 1 0.353 0.478 Cola only 0.088 0.284 Retailer 2 0.278 0.448 Fruit juice only 0.310 0.462 Retailer 3 0.190 0.393 Iced tea only 0.014 0.119 Retailer 4 0.179 0.384 Other soft drink only 0.082 0.275 Brand 1, Category 1 0.300 0.458 Cola and juice 0.098 0.297 Brand 2, Category 1 0.031 0.172 Cola and tea 0.005 0.068 Brand 3, Category 1 0.001 0.030 Cola and other 0.055 0.229 Brand 4, Category 1 0.022 0.147 Juice and tea 0.017 0.130 Brand 1, Category 2 0.171 0.377 Juice and other 0.134 0.340 Brand 2, Category 2 0.071 0.257 Tea and other 0.008 0.090 Brand 3, Category 2 0.044 0.204 Cola, juice and tea 0.017 0.130 Brand 4, Category 2 0.004 0.063 Cola, juice and other 0.105 0.307 Brand 1, Category 3 0.074 0.261 Cola, tea and other 0.005 0.073 Brand 2, Category 3 0.013 0.115 Juice, tea and other 0.028 0.164 Brand 3, Category 3 0.003 0.055 Cola, juice, tea and other 0.032 0.177 Brand 4, Category 3 0.065 0.476 Brand 1, Category 4 0.066 0.248 Brand 2, Category 4 0.059 0.237 Brand 3, Category 4 0.046 0.209 Brand 4, Category 4 0.016 0.125 Note: Brand and retailer identities cannot be disclosed. Table 1a. Summary of sample shares Retailers / brands Baskets Variable Mean SD Variable Mean SD Retailer 1 0.353 0.478 Cola only 0.088 0.284 Retailer 2 0.278 0.448 Fruit juice only 0.310 0.462 Retailer 3 0.190 0.393 Iced tea only 0.014 0.119 Retailer 4 0.179 0.384 Other soft drink only 0.082 0.275 Brand 1, Category 1 0.300 0.458 Cola and juice 0.098 0.297 Brand 2, Category 1 0.031 0.172 Cola and tea 0.005 0.068 Brand 3, Category 1 0.001 0.030 Cola and other 0.055 0.229 Brand 4, Category 1 0.022 0.147 Juice and tea 0.017 0.130 Brand 1, Category 2 0.171 0.377 Juice and other 0.134 0.340 Brand 2, Category 2 0.071 0.257 Tea and other 0.008 0.090 Brand 3, Category 2 0.044 0.204 Cola, juice and tea 0.017 0.130 Brand 4, Category 2 0.004 0.063 Cola, juice and other 0.105 0.307 Brand 1, Category 3 0.074 0.261 Cola, tea and other 0.005 0.073 Brand 2, Category 3 0.013 0.115 Juice, tea and other 0.028 0.164 Brand 3, Category 3 0.003 0.055 Cola, juice, tea and other 0.032 0.177 Brand 4, Category 3 0.065 0.476 Brand 1, Category 4 0.066 0.248 Brand 2, Category 4 0.059 0.237 Brand 3, Category 4 0.046 0.209 Brand 4, Category 4 0.016 0.125 Retailers / brands Baskets Variable Mean SD Variable Mean SD Retailer 1 0.353 0.478 Cola only 0.088 0.284 Retailer 2 0.278 0.448 Fruit juice only 0.310 0.462 Retailer 3 0.190 0.393 Iced tea only 0.014 0.119 Retailer 4 0.179 0.384 Other soft drink only 0.082 0.275 Brand 1, Category 1 0.300 0.458 Cola and juice 0.098 0.297 Brand 2, Category 1 0.031 0.172 Cola and tea 0.005 0.068 Brand 3, Category 1 0.001 0.030 Cola and other 0.055 0.229 Brand 4, Category 1 0.022 0.147 Juice and tea 0.017 0.130 Brand 1, Category 2 0.171 0.377 Juice and other 0.134 0.340 Brand 2, Category 2 0.071 0.257 Tea and other 0.008 0.090 Brand 3, Category 2 0.044 0.204 Cola, juice and tea 0.017 0.130 Brand 4, Category 2 0.004 0.063 Cola, juice and other 0.105 0.307 Brand 1, Category 3 0.074 0.261 Cola, tea and other 0.005 0.073 Brand 2, Category 3 0.013 0.115 Juice, tea and other 0.028 0.164 Brand 3, Category 3 0.003 0.055 Cola, juice, tea and other 0.032 0.177 Brand 4, Category 3 0.065 0.476 Brand 1, Category 4 0.066 0.248 Brand 2, Category 4 0.059 0.237 Brand 3, Category 4 0.046 0.209 Brand 4, Category 4 0.016 0.125 Note: Brand and retailer identities cannot be disclosed. In Table 1b, we break down the share of each brand by retailer. The data in this table show that the distribution of sales by brand differs widely across retailers. Although the identity of the four brands differs across our sample of retailers, these data show that the top four brands in each store are likely to be much more important in some retailers than others. Consequently, we expect that each retailer differs in terms of their ability to bargain with the major brand-manufacturers. Table 1b. Category shares by retailer Category Brand Retailer 1 Retailer 2 Retailer 3 Retailer 4 Mean SD Mean SD Mean SD Mean SD 1 1 0.2592 0.4382 0.3451 0.4754 0.3521 0.4777 0.2537 0.4352 1 2 0.0392 0.1940 0.0330 0.1787 0.0291 0.1682 0.0121 0.1094 1 3 0.0007 0.0261 0.0020 0.0445 0.0007 0.0269 0.0181 0.1332 1 4 0.0627 0.2424 0.0335 0.1800 0.0004 0.0190 0.0006 0.0240 2 1 0.4847 0.4998 0.4271 0.4947 0.0559 0.2298 0.0544 0.2268 2 2 0.0551 0.2281 0.1130 0.3167 0.0329 0.1785 0.3593 0.4798 2 3 0.0459 0.2093 0.0654 0.2472 0.0016 0.0403 0.0169 0.1290 2 4 0.0089 0.0939 0.0511 0.2203 0.0042 0.0644 0.0031 0.0554 3 1 0.0548 0.2276 0.1025 0.3033 0.0887 0.2843 0.0500 0.2179 3 2 0.0382 0.1916 0.0235 0.1513 0.0188 0.1359 0.0223 0.1477 3 3 0.0053 0.0724 0.0041 0.0639 0.0007 0.0269 0.0008 0.0277 3 4 0.9018 0.2976 0.0010 0.0315 0.8916 0.3110 0.9262 0.2615 4 1 0.0544 0.2268 0.0777 0.2677 0.0976 0.2968 0.0369 0.1886 4 2 0.0636 0.2440 0.0632 0.2433 0.0666 0.2494 0.0383 0.1918 4 3 0.0369 0.1886 0.0645 0.2457 0.0322 0.1766 0.0484 0.2147 4 4 0.0274 0.1634 0.0923 0.2895 0.0320 0.1761 0.0748 0.2631 Category Brand Retailer 1 Retailer 2 Retailer 3 Retailer 4 Mean SD Mean SD Mean SD Mean SD 1 1 0.2592 0.4382 0.3451 0.4754 0.3521 0.4777 0.2537 0.4352 1 2 0.0392 0.1940 0.0330 0.1787 0.0291 0.1682 0.0121 0.1094 1 3 0.0007 0.0261 0.0020 0.0445 0.0007 0.0269 0.0181 0.1332 1 4 0.0627 0.2424 0.0335 0.1800 0.0004 0.0190 0.0006 0.0240 2 1 0.4847 0.4998 0.4271 0.4947 0.0559 0.2298 0.0544 0.2268 2 2 0.0551 0.2281 0.1130 0.3167 0.0329 0.1785 0.3593 0.4798 2 3 0.0459 0.2093 0.0654 0.2472 0.0016 0.0403 0.0169 0.1290 2 4 0.0089 0.0939 0.0511 0.2203 0.0042 0.0644 0.0031 0.0554 3 1 0.0548 0.2276 0.1025 0.3033 0.0887 0.2843 0.0500 0.2179 3 2 0.0382 0.1916 0.0235 0.1513 0.0188 0.1359 0.0223 0.1477 3 3 0.0053 0.0724 0.0041 0.0639 0.0007 0.0269 0.0008 0.0277 3 4 0.9018 0.2976 0.0010 0.0315 0.8916 0.3110 0.9262 0.2615 4 1 0.0544 0.2268 0.0777 0.2677 0.0976 0.2968 0.0369 0.1886 4 2 0.0636 0.2440 0.0632 0.2433 0.0666 0.2494 0.0383 0.1918 4 3 0.0369 0.1886 0.0645 0.2457 0.0322 0.1766 0.0484 0.2147 4 4 0.0274 0.1634 0.0923 0.2895 0.0320 0.1761 0.0748 0.2631 Note: Brands are not the same across retailers in each category. Table 1b. Category shares by retailer Category Brand Retailer 1 Retailer 2 Retailer 3 Retailer 4 Mean SD Mean SD Mean SD Mean SD 1 1 0.2592 0.4382 0.3451 0.4754 0.3521 0.4777 0.2537 0.4352 1 2 0.0392 0.1940 0.0330 0.1787 0.0291 0.1682 0.0121 0.1094 1 3 0.0007 0.0261 0.0020 0.0445 0.0007 0.0269 0.0181 0.1332 1 4 0.0627 0.2424 0.0335 0.1800 0.0004 0.0190 0.0006 0.0240 2 1 0.4847 0.4998 0.4271 0.4947 0.0559 0.2298 0.0544 0.2268 2 2 0.0551 0.2281 0.1130 0.3167 0.0329 0.1785 0.3593 0.4798 2 3 0.0459 0.2093 0.0654 0.2472 0.0016 0.0403 0.0169 0.1290 2 4 0.0089 0.0939 0.0511 0.2203 0.0042 0.0644 0.0031 0.0554 3 1 0.0548 0.2276 0.1025 0.3033 0.0887 0.2843 0.0500 0.2179 3 2 0.0382 0.1916 0.0235 0.1513 0.0188 0.1359 0.0223 0.1477 3 3 0.0053 0.0724 0.0041 0.0639 0.0007 0.0269 0.0008 0.0277 3 4 0.9018 0.2976 0.0010 0.0315 0.8916 0.3110 0.9262 0.2615 4 1 0.0544 0.2268 0.0777 0.2677 0.0976 0.2968 0.0369 0.1886 4 2 0.0636 0.2440 0.0632 0.2433 0.0666 0.2494 0.0383 0.1918 4 3 0.0369 0.1886 0.0645 0.2457 0.0322 0.1766 0.0484 0.2147 4 4 0.0274 0.1634 0.0923 0.2895 0.0320 0.1761 0.0748 0.2631 Category Brand Retailer 1 Retailer 2 Retailer 3 Retailer 4 Mean SD Mean SD Mean SD Mean SD 1 1 0.2592 0.4382 0.3451 0.4754 0.3521 0.4777 0.2537 0.4352 1 2 0.0392 0.1940 0.0330 0.1787 0.0291 0.1682 0.0121 0.1094 1 3 0.0007 0.0261 0.0020 0.0445 0.0007 0.0269 0.0181 0.1332 1 4 0.0627 0.2424 0.0335 0.1800 0.0004 0.0190 0.0006 0.0240 2 1 0.4847 0.4998 0.4271 0.4947 0.0559 0.2298 0.0544 0.2268 2 2 0.0551 0.2281 0.1130 0.3167 0.0329 0.1785 0.3593 0.4798 2 3 0.0459 0.2093 0.0654 0.2472 0.0016 0.0403 0.0169 0.1290 2 4 0.0089 0.0939 0.0511 0.2203 0.0042 0.0644 0.0031 0.0554 3 1 0.0548 0.2276 0.1025 0.3033 0.0887 0.2843 0.0500 0.2179 3 2 0.0382 0.1916 0.0235 0.1513 0.0188 0.1359 0.0223 0.1477 3 3 0.0053 0.0724 0.0041 0.0639 0.0007 0.0269 0.0008 0.0277 3 4 0.9018 0.2976 0.0010 0.0315 0.8916 0.3110 0.9262 0.2615 4 1 0.0544 0.2268 0.0777 0.2677 0.0976 0.2968 0.0369 0.1886 4 2 0.0636 0.2440 0.0632 0.2433 0.0666 0.2494 0.0383 0.1918 4 3 0.0369 0.1886 0.0645 0.2457 0.0322 0.1766 0.0484 0.2147 4 4 0.0274 0.1634 0.0923 0.2895 0.0320 0.1761 0.0748 0.2631 Note: Brands are not the same across retailers in each category. Soft drinks represent an ideal opportunity to examine our research question as beverages are frequently consumed within the household, consumers tend to exhibit a demand for variety in their soft-drink purchases, and, on the supply side, several manufacturers produce product lines across many of the sub-categories that are the focus of our analysis. For instance, the Coca Cola company not only produces their namesake brand in the cola sub-category but Minute Maid in the juice sub-category, Nestea in the iced tea sub-category and Powerade in the Other category. Further, because of the importance of national brands in the soft-drink category, our data include a number of brands that are offered by the same manufacturer through all four retailers. Because of our focus on bargaining power, variation in pricing and margins for the same brand across retailers is necessary in order to identify differences in bargaining power associated with manufacturer–retailer dyads. Moreover, national brands are a critical element of our model as umbrella branding can be a primary source of purchase complementarity (Erdem and Sun, 2002; Erdem and Chang, 2012; Richards, Yonezawa, and Winter, 2014). If complementarity at the end-user level represents an important source of downstream bargaining power, then it should be manifest in purchases by retailers in this category, if any. The data in Table 1 also summarise the market share of each retailer, and each of our focus brands. Clearly, Retailer 1 is substantially larger than the other three retailers, particularly Retailers 3 and 4. Other than Brand 1 in the cola category, there does not appear to be any dominant brands in either of the four sub-categories, but sufficient variation to identify both the demand model and the disagreement-profit element of the bargaining power model. In terms of the pricing model, we use input price indices from the French National Institute for Statistics and Economic Studies to estimate the marginal cost function. For each category, we first define an index of ‘primary input’ prices, that is, water and sugar or sugar substitutes for cola, water and fruit for fruit juice, water and tea prices for tea, and an average of all content-input prices for the other category. We also create an index of packaging prices by averaging the price indices for aluminium, plastic, and glass. Next, we include an index of wages in the beverage industry to account for the labour content of items in each category. We also calculated an index of energy prices from gasoline, and electricity, but they were found to be statistically insignificant, in any combination, so were excluded from the final model. In the pricing model, we aggregated the data by category, brand and retailer across all household purchases. These averages were weighted by the volume of purchase to arrive at an average price across all participating households. From the data presented in Table 2, the resulting average prices contain sufficient variation to identify any variation in retail pricing over time, and over brands offered by different retailers. We also impute a promotion variable at the household level by measuring the difference in price for the same brand at the same retailer from one week to the next. Any price difference that is larger than −10 per cent, and remains for 1 week, is defined as a temporary price reduction, or a promotion. Table 2 presents the summary statistics for all input prices, item prices and promotional activity. Table 2. Summary of soft-drink pricing data Variable Units Mean SD Minimum Maximum N Aluminium price Index 93.800 4.989 86.700 102.400 3,328 Plastic price Index 106.300 0.332 105.700 106.900 3,328 Glass price Index 104.967 0.661 103.500 105.700 3,328 Sugar price Index 147.106 7.636 134.100 158.500 3,328 Gasoline price Index 113.156 2.265 110.300 118.000 3,328 Electricity price Index 115.331 4.921 107.300 121.300 3,328 Sugar substitute price Index 104.588 0.700 103.510 106.010 3,328 Fruit price Index 2.578 0.115 2.433 2.778 3,328 Tea and coffee price Index 114.602 1.001 112.600 116.000 3,328 Bottled water price Index 110.010 0.533 108.500 110.800 3,328 Beverage industry wage Index 110.650 0.415 110.000 111.100 3,328 Cola price Euros/litre 0.891 0.245 0.295 1.808 3,328 Fruit juice price Euros/litre 1.855 0.538 0.756 3.333 3,328 Iced tea price Euros/litre 0.918 0.221 0.226 2.500 3,328 Other soft-drink price Euros/litre 1.106 0.405 0.212 9.909 3,328 Cola promotion % 0.060 0.238 0.000 1.000 3,328 Fruit juice promotion % 0.052 0.222 0.000 1.000 3,328 Iced tea promotion % 0.064 0.244 0.000 1.000 3,328 Other soft-drink promotion % 0.070 0.255 0.000 1.000 3,328 Variable Units Mean SD Minimum Maximum N Aluminium price Index 93.800 4.989 86.700 102.400 3,328 Plastic price Index 106.300 0.332 105.700 106.900 3,328 Glass price Index 104.967 0.661 103.500 105.700 3,328 Sugar price Index 147.106 7.636 134.100 158.500 3,328 Gasoline price Index 113.156 2.265 110.300 118.000 3,328 Electricity price Index 115.331 4.921 107.300 121.300 3,328 Sugar substitute price Index 104.588 0.700 103.510 106.010 3,328 Fruit price Index 2.578 0.115 2.433 2.778 3,328 Tea and coffee price Index 114.602 1.001 112.600 116.000 3,328 Bottled water price Index 110.010 0.533 108.500 110.800 3,328 Beverage industry wage Index 110.650 0.415 110.000 111.100 3,328 Cola price Euros/litre 0.891 0.245 0.295 1.808 3,328 Fruit juice price Euros/litre 1.855 0.538 0.756 3.333 3,328 Iced tea price Euros/litre 0.918 0.221 0.226 2.500 3,328 Other soft-drink price Euros/litre 1.106 0.405 0.212 9.909 3,328 Cola promotion % 0.060 0.238 0.000 1.000 3,328 Fruit juice promotion % 0.052 0.222 0.000 1.000 3,328 Iced tea promotion % 0.064 0.244 0.000 1.000 3,328 Other soft-drink promotion % 0.070 0.255 0.000 1.000 3,328 Note: Input prices used to form indices in the final estimated model. Promotion indicators calculated using price-reduction threshold of 10%. Table 2. Summary of soft-drink pricing data Variable Units Mean SD Minimum Maximum N Aluminium price Index 93.800 4.989 86.700 102.400 3,328 Plastic price Index 106.300 0.332 105.700 106.900 3,328 Glass price Index 104.967 0.661 103.500 105.700 3,328 Sugar price Index 147.106 7.636 134.100 158.500 3,328 Gasoline price Index 113.156 2.265 110.300 118.000 3,328 Electricity price Index 115.331 4.921 107.300 121.300 3,328 Sugar substitute price Index 104.588 0.700 103.510 106.010 3,328 Fruit price Index 2.578 0.115 2.433 2.778 3,328 Tea and coffee price Index 114.602 1.001 112.600 116.000 3,328 Bottled water price Index 110.010 0.533 108.500 110.800 3,328 Beverage industry wage Index 110.650 0.415 110.000 111.100 3,328 Cola price Euros/litre 0.891 0.245 0.295 1.808 3,328 Fruit juice price Euros/litre 1.855 0.538 0.756 3.333 3,328 Iced tea price Euros/litre 0.918 0.221 0.226 2.500 3,328 Other soft-drink price Euros/litre 1.106 0.405 0.212 9.909 3,328 Cola promotion % 0.060 0.238 0.000 1.000 3,328 Fruit juice promotion % 0.052 0.222 0.000 1.000 3,328 Iced tea promotion % 0.064 0.244 0.000 1.000 3,328 Other soft-drink promotion % 0.070 0.255 0.000 1.000 3,328 Variable Units Mean SD Minimum Maximum N Aluminium price Index 93.800 4.989 86.700 102.400 3,328 Plastic price Index 106.300 0.332 105.700 106.900 3,328 Glass price Index 104.967 0.661 103.500 105.700 3,328 Sugar price Index 147.106 7.636 134.100 158.500 3,328 Gasoline price Index 113.156 2.265 110.300 118.000 3,328 Electricity price Index 115.331 4.921 107.300 121.300 3,328 Sugar substitute price Index 104.588 0.700 103.510 106.010 3,328 Fruit price Index 2.578 0.115 2.433 2.778 3,328 Tea and coffee price Index 114.602 1.001 112.600 116.000 3,328 Bottled water price Index 110.010 0.533 108.500 110.800 3,328 Beverage industry wage Index 110.650 0.415 110.000 111.100 3,328 Cola price Euros/litre 0.891 0.245 0.295 1.808 3,328 Fruit juice price Euros/litre 1.855 0.538 0.756 3.333 3,328 Iced tea price Euros/litre 0.918 0.221 0.226 2.500 3,328 Other soft-drink price Euros/litre 1.106 0.405 0.212 9.909 3,328 Cola promotion % 0.060 0.238 0.000 1.000 3,328 Fruit juice promotion % 0.052 0.222 0.000 1.000 3,328 Iced tea promotion % 0.064 0.244 0.000 1.000 3,328 Other soft-drink promotion % 0.070 0.255 0.000 1.000 3,328 Note: Input prices used to form indices in the final estimated model. Promotion indicators calculated using price-reduction threshold of 10%. We can also draw some stylised facts from our demand data. Our interest in studying the structural effects of complementarity on bargaining power follows from a simple observation: in our soft-drink data, when items from different categories are purchased together, consumers appear to be willing to pay a significant price-premium for either product, relative to their respective category averages (Figure 1). That is, if a consumer purchases only a fruit juice, they would be willing to pay more for the same fruit juice if they also purchased at least one item from another category.18 While there are many factors that may explain this difference, it is suggestive of a pattern that consumers are willing to pay more for items when combined in a shopping basket, than when purchased alone.19 In fact, we find that when multiple soft drinks are purchased together, the multiple purchases tend to be of a higher-priced brand. We interpret this higher willingness to pay as a manifestation of soft-drink consumer preferences. Namely, if a consumer prefers soft drinks enough to purchase several together, their preferences are sufficiently strong to pay for the most expensive variants in the category. Whether this observation means that soft-drinks in different categories are purchase-complements remains to be determined by estimating the MVL model described above. Fig. 1 View largeDownload slide Single vs. basket prices. Fig. 1 View largeDownload slide Single vs. basket prices. In the absence of unobserved heterogeneity, the MVL model is estimated using maximum likelihood in a relatively standard way. However, because we allow a range of parameters to vary across panel observations, the likelihood function no longer has a closed form. Therefore, the model is estimated using simulated maximum likelihood (SML, Train, 2003), using r= 1, 2, 3 …,R simulations. Define a set of indicator variables zk that assume a value of 1 if basket k is chosen and 0 otherwise, so the likelihood function for a panel over h cross-sections and t shopping occasions per household yields a simulated likelihood function written as (Kwak, Duvvuri, and Russel, 2015) ℒ(bht)h=1R∑r=1R∏t∏k(Pr(bht=bhtk)zk, (17) where the joint distribution function for all possible baskets is given in equation (7). We then take the log of equation (17), sum over all households, and maximise with respect to all parameters: LLF(α,β,γ,θ)=∑h=1Hlogℒ(bht)h To increase the efficiency of the SML routine, the simulated draws follow a Halton sequence with 50 draws. The MVL is powerful in its ability to estimate both substitute and complimentary relationships in a relatively parsimonious way, but suffers from the curse of dimensionality. That is, with N products, the number of baskets is N2−1, so the problem quickly becomes intractable for anything more than a highly stylised description of the typical shopping basket. Therefore, we restrict our attention to four categories that are likely to exhibit a pattern of both substitute and complementary relationships. Other methods have been developed in order to explicitly address the problem of dimensionality inherent in shopping-basket demand estimation (Kamakura and Kwak, 2012), but have not yet proven to be as amenable to estimation in panel-scanner data as the RP-MVL. In the demand model, prices are likely to be endogenous (Villas-Boas and Winer, 1999). That is, at the household level, the error term for each demand equation contains some information that the retailer observes in setting equilibrium prices: advertising, in-store displays, preferred shelf-space or a number of other factors that we do not observe in our data. Therefore, we estimate the demand model using the control function method (Petrin and Train, 2010). Essentially, the control function approach consists of using the residuals from a first-stage instrumental variables regression as additional variables on the right-side of the demand model. Because the residuals from the instrumental variables regression contain information on the part of the endogenous price variable that is not explained by the instruments, they have the effect of removing the correlated part from the demand equation. Because input prices are expected to be correlated with retail prices, and yet independent of demand, our first-stage control function regression uses the set of input price variables as instruments. We also include brand and retailer fixed effects in order to account for any endogenous effects that are unique to each item. Although these variables should represent effective instruments, whether they are weak in the sense of Staiger and Stock (1997) is evaluated on the basis of the F-test that results from the first-stage instrumental variables regression.20 In this case, the F-statistic is 65.4, which is much larger than the threshold of 10.0 suggested by Staiger and Stock (1997). Therefore, we conclude that our instruments are not weak. 5. Results and discussion In this section, we first present the results from estimating several versions of the MVL shopping-basket model, and then the estimates from the Nash bargaining-equilibrium model. All bargaining-power estimates are conditioned on the preferred specification for demand, in order to ensure that our estimates are consistent across all of the models used. Because we are able to use these estimates to derive a vector of bargaining-power estimates across each category-retailer-brand observation, we then present the results from a supplementary regression of bargaining power on the extent of complementarity associated with each item. In this way, we are able to test our primary hypothesis regarding the relationship between complementarity and bargaining power. 5.1. Demand-model results Our demand-model estimates are shown in Tables 3 and 4. Table 3 presents the structural estimates for each baseline-utility model, while Table 4 presents the full set of interaction parameters, estimated from the same model. In each case, we compare the estimates from a fixed coefficient version of the MVL model to one that takes unobserved heterogeneity explicitly into account by including random coefficients for both the marginal utility of income, and the category-interaction parameters. A likelihood ratio (LR) test comparing the fixed and random-coefficient versions of the model yields a test-statistic value of 186.2, whereas the critical χ2 value at 5 per cent and 7 degrees of freedom is 14.07, so we interpret the results from the preferred, random-coefficient version of the model. Table 3. MVL demand estimates Category Variable Fixed coefficients Random coefficients Fixed coefficients Random coefficients Estimate t-ratio Estimate t-ratio Estimate t-ratio Estimate t-ratio Price −10.3737* −122.4276 −2.9824* −35.1971 Standard deviation 1.4678 1.7505 Colas Constant −6.0480* −21.6088 −3.6304* −12.9709 Tea Constant 2.2721* 5.1544 −4.0582* −9.2063 Promotion 20.5123* 77.3327 11.0433* 41.6340 Promotion −2.5425* −6.1794 −7.6689* −18.6389 HH size −56.1220* −13.3433 0.8892 0.2114 HH size −65.1401* −13.4826 146.6066* 30.3445 Income −0.9482 −1.8660 7.4980* 14.7560 Income 1.4321 1.6988 2.3930* 2.8387 Education −5.7064* −2.7882 −73.9114* −36.1135 Education −96.3142* −39.4185 −47.4332* −19.4130 Inventory −134.3834* −16.0262 −157.1277* −18.7387 Inventory −165.2920* −17.5644 −212.1655* −22.5453 Retailer 2 −1.6959* −5.4678 −14.9241* −48.1185 Retailer 2 −1.7250* −4.5174 −23.8198* −62.3808 Retailer 3 −4.8390* −11.5203 2.6727* 6.3631 Retailer 3 0.4224 1.1767 0.9384* 2.6144 Retailer 4 −8.4185* −61.4891 2.2564* 16.4810 Retailer 4 −0.0597 −0.3504 7.5996* 44.6397 Brand 1 36.4939* 130.7971 28.5176* 102.2093 Brand 1 39.9710* 53.1157 53.1672* 70.6515 Brand 2 2.3531* 8.0344 5.1927* 17.7297 Brand 3 4.2490* 8.6083 10.1732* 20.6103 Brand 3 −27.6063* −9.3762 −34.8226* −11.8271 Brand 4 −6.6287* −24.8196 −13.7564* −51.5075 Brand 4 58.0533* 177.6811 −2.8304* −8.6630 CF −10.6674* −38.1133 −15.3591* −49.5210 CF −17.0717* −64.3616 −26.4124* −192.9166 Fruit juice Constant −1.9568* −7.9419 −2.0928* −8.4939 Other Constant −4.8275* −17.8587 −3.3627* −12.4400 Promotion 5.0975* 44.2928 15.3943* 133.7640 Promotion 15.6611* 92.7254 11.9560* 70.7881 HH size −164.2370* −45.4800 −102.8920* −28.4925 HH size −104.8114* −24.6190 −71.5824* −16.8139 Income 10.4865* 31.8333 13.0656* 39.6625 Income 3.7661* 11.0882 7.8993* 23.2571 Education −19.4736* −11.0123 −45.6109* −25.7928 Education −8.1430* −4.0154 −43.7277* −21.5625 Inventory 54.4302* 4.5909 122.5980* 10.3404 Inventory 33.1227* 3.2762 −12.7122 −1.2574 Retailer 2 −1.4999* −5.3536 −14.8281* −52.9280 Retailer 2 −2.4039* −8.2860 −15.8365* −54.5862 Retailer 3 −5.7978* −17.5062 1.6649* 5.0270 Retailer 3 −5.7158* −16.9274 1.8109* 5.3630 Retailer 4 −7.3244* −64.0657 2.4833* 21.7211 Retailer 4 −7.3527* −56.1555 2.4551* 18.7506 Brand 2 11.2502 0.2847 34.7106 0.8783 Brand 1 7.1033* 15.8607 7.5656* 16.8928 Brand 3 3.0818* 21.9648 20.7182* 147.6651 Brand 2 184.8058* 126.2629 19.4588* 13.2946 Brand 4 45.1965* 134.4622 2.5195* 7.4958 Brand 3 10.4618* 60.6124 6.0893* 35.2797 CF 8.8679* 104.6567 0.8377* 1.9943 Brand 4 6.5542* 16.5531 5.6731* 14.3279 CF 7.0862 1.6848 −0.0690 −0.2474 LLF / AIC −2324.5900 0.0348 −2231.46 0.0334 Category Variable Fixed coefficients Random coefficients Fixed coefficients Random coefficients Estimate t-ratio Estimate t-ratio Estimate t-ratio Estimate t-ratio Price −10.3737* −122.4276 −2.9824* −35.1971 Standard deviation 1.4678 1.7505 Colas Constant −6.0480* −21.6088 −3.6304* −12.9709 Tea Constant 2.2721* 5.1544 −4.0582* −9.2063 Promotion 20.5123* 77.3327 11.0433* 41.6340 Promotion −2.5425* −6.1794 −7.6689* −18.6389 HH size −56.1220* −13.3433 0.8892 0.2114 HH size −65.1401* −13.4826 146.6066* 30.3445 Income −0.9482 −1.8660 7.4980* 14.7560 Income 1.4321 1.6988 2.3930* 2.8387 Education −5.7064* −2.7882 −73.9114* −36.1135 Education −96.3142* −39.4185 −47.4332* −19.4130 Inventory −134.3834* −16.0262 −157.1277* −18.7387 Inventory −165.2920* −17.5644 −212.1655* −22.5453 Retailer 2 −1.6959* −5.4678 −14.9241* −48.1185 Retailer 2 −1.7250* −4.5174 −23.8198* −62.3808 Retailer 3 −4.8390* −11.5203 2.6727* 6.3631 Retailer 3 0.4224 1.1767 0.9384* 2.6144 Retailer 4 −8.4185* −61.4891 2.2564* 16.4810 Retailer 4 −0.0597 −0.3504 7.5996* 44.6397 Brand 1 36.4939* 130.7971 28.5176* 102.2093 Brand 1 39.9710* 53.1157 53.1672* 70.6515 Brand 2 2.3531* 8.0344 5.1927* 17.7297 Brand 3 4.2490* 8.6083 10.1732* 20.6103 Brand 3 −27.6063* −9.3762 −34.8226* −11.8271 Brand 4 −6.6287* −24.8196 −13.7564* −51.5075 Brand 4 58.0533* 177.6811 −2.8304* −8.6630 CF −10.6674* −38.1133 −15.3591* −49.5210 CF −17.0717* −64.3616 −26.4124* −192.9166 Fruit juice Constant −1.9568* −7.9419 −2.0928* −8.4939 Other Constant −4.8275* −17.8587 −3.3627* −12.4400 Promotion 5.0975* 44.2928 15.3943* 133.7640 Promotion 15.6611* 92.7254 11.9560* 70.7881 HH size −164.2370* −45.4800 −102.8920* −28.4925 HH size −104.8114* −24.6190 −71.5824* −16.8139 Income 10.4865* 31.8333 13.0656* 39.6625 Income 3.7661* 11.0882 7.8993* 23.2571 Education −19.4736* −11.0123 −45.6109* −25.7928 Education −8.1430* −4.0154 −43.7277* −21.5625 Inventory 54.4302* 4.5909 122.5980* 10.3404 Inventory 33.1227* 3.2762 −12.7122 −1.2574 Retailer 2 −1.4999* −5.3536 −14.8281* −52.9280 Retailer 2 −2.4039* −8.2860 −15.8365* −54.5862 Retailer 3 −5.7978* −17.5062 1.6649* 5.0270 Retailer 3 −5.7158* −16.9274 1.8109* 5.3630 Retailer 4 −7.3244* −64.0657 2.4833* 21.7211 Retailer 4 −7.3527* −56.1555 2.4551* 18.7506 Brand 2 11.2502 0.2847 34.7106 0.8783 Brand 1 7.1033* 15.8607 7.5656* 16.8928 Brand 3 3.0818* 21.9648 20.7182* 147.6651 Brand 2 184.8058* 126.2629 19.4588* 13.2946 Brand 4 45.1965* 134.4622 2.5195* 7.4958 Brand 3 10.4618* 60.6124 6.0893* 35.2797 CF 8.8679* 104.6567 0.8377* 1.9943 Brand 4 6.5542* 16.5531 5.6731* 14.3279 CF 7.0862 1.6848 −0.0690 −0.2474 LLF / AIC −2324.5900 0.0348 −2231.46 0.0334 Note: CF is the control function parameter. A single asterisk indicates significance at 5%. Table 3. MVL demand estimates Category Variable Fixed coefficients Random coefficients Fixed coefficients Random coefficients Estimate t-ratio Estimate t-ratio Estimate t-ratio Estimate t-ratio Price −10.3737* −122.4276 −2.9824* −35.1971 Standard deviation 1.4678 1.7505 Colas Constant −6.0480* −21.6088 −3.6304* −12.9709 Tea Constant 2.2721* 5.1544 −4.0582* −9.2063 Promotion 20.5123* 77.3327 11.0433* 41.6340 Promotion −2.5425* −6.1794 −7.6689* −18.6389 HH size −56.1220* −13.3433 0.8892 0.2114 HH size −65.1401* −13.4826 146.6066* 30.3445 Income −0.9482 −1.8660 7.4980* 14.7560 Income 1.4321 1.6988 2.3930* 2.8387 Education −5.7064* −2.7882 −73.9114* −36.1135 Education −96.3142* −39.4185 −47.4332* −19.4130 Inventory −134.3834* −16.0262 −157.1277* −18.7387 Inventory −165.2920* −17.5644 −212.1655* −22.5453 Retailer 2 −1.6959* −5.4678 −14.9241* −48.1185 Retailer 2 −1.7250* −4.5174 −23.8198* −62.3808 Retailer 3 −4.8390* −11.5203 2.6727* 6.3631 Retailer 3 0.4224 1.1767 0.9384* 2.6144 Retailer 4 −8.4185* −61.4891 2.2564* 16.4810 Retailer 4 −0.0597 −0.3504 7.5996* 44.6397 Brand 1 36.4939* 130.7971 28.5176* 102.2093 Brand 1 39.9710* 53.1157 53.1672* 70.6515 Brand 2 2.3531* 8.0344 5.1927* 17.7297 Brand 3 4.2490* 8.6083 10.1732* 20.6103 Brand 3 −27.6063* −9.3762 −34.8226* −11.8271 Brand 4 −6.6287* −24.8196 −13.7564* −51.5075 Brand 4 58.0533* 177.6811 −2.8304* −8.6630 CF −10.6674* −38.1133 −15.3591* −49.5210 CF −17.0717* −64.3616 −26.4124* −192.9166 Fruit juice Constant −1.9568* −7.9419 −2.0928* −8.4939 Other Constant −4.8275* −17.8587 −3.3627* −12.4400 Promotion 5.0975* 44.2928 15.3943* 133.7640 Promotion 15.6611* 92.7254 11.9560* 70.7881 HH size −164.2370* −45.4800 −102.8920* −28.4925 HH size −104.8114* −24.6190 −71.5824* −16.8139 Income 10.4865* 31.8333 13.0656* 39.6625 Income 3.7661* 11.0882 7.8993* 23.2571 Education −19.4736* −11.0123 −45.6109* −25.7928 Education −8.1430* −4.0154 −43.7277* −21.5625 Inventory 54.4302* 4.5909 122.5980* 10.3404 Inventory 33.1227* 3.2762 −12.7122 −1.2574 Retailer 2 −1.4999* −5.3536 −14.8281* −52.9280 Retailer 2 −2.4039* −8.2860 −15.8365* −54.5862 Retailer 3 −5.7978* −17.5062 1.6649* 5.0270 Retailer 3 −5.7158* −16.9274 1.8109* 5.3630 Retailer 4 −7.3244* −64.0657 2.4833* 21.7211 Retailer 4 −7.3527* −56.1555 2.4551* 18.7506 Brand 2 11.2502 0.2847 34.7106 0.8783 Brand 1 7.1033* 15.8607 7.5656* 16.8928 Brand 3 3.0818* 21.9648 20.7182* 147.6651 Brand 2 184.8058* 126.2629 19.4588* 13.2946 Brand 4 45.1965* 134.4622 2.5195* 7.4958 Brand 3 10.4618* 60.6124 6.0893* 35.2797 CF 8.8679* 104.6567 0.8377* 1.9943 Brand 4 6.5542* 16.5531 5.6731* 14.3279 CF 7.0862 1.6848 −0.0690 −0.2474 LLF / AIC −2324.5900 0.0348 −2231.46 0.0334 Category Variable Fixed coefficients Random coefficients Fixed coefficients Random coefficients Estimate t-ratio Estimate t-ratio Estimate t-ratio Estimate t-ratio Price −10.3737* −122.4276 −2.9824* −35.1971 Standard deviation 1.4678 1.7505 Colas Constant −6.0480* −21.6088 −3.6304* −12.9709 Tea Constant 2.2721* 5.1544 −4.0582* −9.2063 Promotion 20.5123* 77.3327 11.0433* 41.6340 Promotion −2.5425* −6.1794 −7.6689* −18.6389 HH size −56.1220* −13.3433 0.8892 0.2114 HH size −65.1401* −13.4826 146.6066* 30.3445 Income −0.9482 −1.8660 7.4980* 14.7560 Income 1.4321 1.6988 2.3930* 2.8387 Education −5.7064* −2.7882 −73.9114* −36.1135 Education −96.3142* −39.4185 −47.4332* −19.4130 Inventory −134.3834* −16.0262 −157.1277* −18.7387 Inventory −165.2920* −17.5644 −212.1655* −22.5453 Retailer 2 −1.6959* −5.4678 −14.9241* −48.1185 Retailer 2 −1.7250* −4.5174 −23.8198* −62.3808 Retailer 3 −4.8390* −11.5203 2.6727* 6.3631 Retailer 3 0.4224 1.1767 0.9384* 2.6144 Retailer 4 −8.4185* −61.4891 2.2564* 16.4810 Retailer 4 −0.0597 −0.3504 7.5996* 44.6397 Brand 1 36.4939* 130.7971 28.5176* 102.2093 Brand 1 39.9710* 53.1157 53.1672* 70.6515 Brand 2 2.3531* 8.0344 5.1927* 17.7297 Brand 3 4.2490* 8.6083 10.1732* 20.6103 Brand 3 −27.6063* −9.3762 −34.8226* −11.8271 Brand 4 −6.6287* −24.8196 −13.7564* −51.5075 Brand 4 58.0533* 177.6811 −2.8304* −8.6630 CF −10.6674* −38.1133 −15.3591* −49.5210 CF −17.0717* −64.3616 −26.4124* −192.9166 Fruit juice Constant −1.9568* −7.9419 −2.0928* −8.4939 Other Constant −4.8275* −17.8587 −3.3627* −12.4400 Promotion 5.0975* 44.2928 15.3943* 133.7640 Promotion 15.6611* 92.7254 11.9560* 70.7881 HH size −164.2370* −45.4800 −102.8920* −28.4925 HH size −104.8114* −24.6190 −71.5824* −16.8139 Income 10.4865* 31.8333 13.0656* 39.6625 Income 3.7661* 11.0882 7.8993* 23.2571 Education −19.4736* −11.0123 −45.6109* −25.7928 Education −8.1430* −4.0154 −43.7277* −21.5625 Inventory 54.4302* 4.5909 122.5980* 10.3404 Inventory 33.1227* 3.2762 −12.7122 −1.2574 Retailer 2 −1.4999* −5.3536 −14.8281* −52.9280 Retailer 2 −2.4039* −8.2860 −15.8365* −54.5862 Retailer 3 −5.7978* −17.5062 1.6649* 5.0270 Retailer 3 −5.7158* −16.9274 1.8109* 5.3630 Retailer 4 −7.3244* −64.0657 2.4833* 21.7211 Retailer 4 −7.3527* −56.1555 2.4551* 18.7506 Brand 2 11.2502 0.2847 34.7106 0.8783 Brand 1 7.1033* 15.8607 7.5656* 16.8928 Brand 3 3.0818* 21.9648 20.7182* 147.6651 Brand 2 184.8058* 126.2629 19.4588* 13.2946 Brand 4 45.1965* 134.4622 2.5195* 7.4958 Brand 3 10.4618* 60.6124 6.0893* 35.2797 CF 8.8679* 104.6567 0.8377* 1.9943 Brand 4 6.5542* 16.5531 5.6731* 14.3279 CF 7.0862 1.6848 −0.0690 −0.2474 LLF / AIC −2324.5900 0.0348 −2231.46 0.0334 Note: CF is the control function parameter. A single asterisk indicates significance at 5%. Table 4. Interaction parameters from MVL Fixed coefficient Random coefficient Estimate t-ratio Estimate t-ratio Cola, fruit juice 48.4471* 78.4467 59.2950* 96.0119 Scale −13.8800* −49.5913 Cola, tea 97.7647* 251.6550 45.9108* 118.1784 Scale −8.4682* −99.9394 Cola, other 76.0721* 177.6280 42.6219* 99.5219 Scale −1.0608* −3.9993 Fruit juice, tea 89.2720* 271.4451 73.5761* 223.7192 Scale 21.6681* 5.1517 Fruit juice, other 63.3418* 165.5473 77.2406* 201.8725 Scale −18.9383* −37.2703 Tea, other 40.8367* 95.1759 36.4701* 84.9990 Scale 3.2041 1.5656 Fixed coefficient Random coefficient Estimate t-ratio Estimate t-ratio Cola, fruit juice 48.4471* 78.4467 59.2950* 96.0119 Scale −13.8800* −49.5913 Cola, tea 97.7647* 251.6550 45.9108* 118.1784 Scale −8.4682* −99.9394 Cola, other 76.0721* 177.6280 42.6219* 99.5219 Scale −1.0608* −3.9993 Fruit juice, tea 89.2720* 271.4451 73.5761* 223.7192 Scale 21.6681* 5.1517 Fruit juice, other 63.3418* 165.5473 77.2406* 201.8725 Scale −18.9383* −37.2703 Tea, other 40.8367* 95.1759 36.4701* 84.9990 Scale 3.2041 1.5656 Note: A single asterisk indicates significance at a 5% level. Table 4. Interaction parameters from MVL Fixed coefficient Random coefficient Estimate t-ratio Estimate t-ratio Cola, fruit juice 48.4471* 78.4467 59.2950* 96.0119 Scale −13.8800* −49.5913 Cola, tea 97.7647* 251.6550 45.9108* 118.1784 Scale −8.4682* −99.9394 Cola, other 76.0721* 177.6280 42.6219* 99.5219 Scale −1.0608* −3.9993 Fruit juice, tea 89.2720* 271.4451 73.5761* 223.7192 Scale 21.6681* 5.1517 Fruit juice, other 63.3418* 165.5473 77.2406* 201.8725 Scale −18.9383* −37.2703 Tea, other 40.8367* 95.1759 36.4701* 84.9990 Scale 3.2041 1.5656 Fixed coefficient Random coefficient Estimate t-ratio Estimate t-ratio Cola, fruit juice 48.4471* 78.4467 59.2950* 96.0119 Scale −13.8800* −49.5913 Cola, tea 97.7647* 251.6550 45.9108* 118.1784 Scale −8.4682* −99.9394 Cola, other 76.0721* 177.6280 42.6219* 99.5219 Scale −1.0608* −3.9993 Fruit juice, tea 89.2720* 271.4451 73.5761* 223.7192 Scale 21.6681* 5.1517 Fruit juice, other 63.3418* 165.5473 77.2406* 201.8725 Scale −18.9383* −37.2703 Tea, other 40.8367* 95.1759 36.4701* 84.9990 Scale 3.2041 1.5656 Note: A single asterisk indicates significance at a 5% level. Comparing the estimates between the two models also shows the extent of bias from not accounting for unobserved heterogeneity, as the marginal utility of income, for example, is nearly one-third as large in the random-coefficient relative to the fixed-coefficient model.21 Among the other parameters of interest in the demand model, note that inventory has a strong, negative effect on the probability that a shopping basket co