Rivalry in Price and Location by Di erentiated Product Manufacturers

Transcription

1 Rivalry in Price and Location by Di erentiated Product Manufacturers Timothy J. Richards, William Allender, and Stephen F. Hamilton Paper presented at 3rd GAEL Conference, June 20-21, Grenoble, FR. May 23, 2013 Abstract In this paper, we estimate a model of strategic rivalry between food manufacturers in product design and pricing. We derive a spatial structural model in which food manufacturers jointly select prices and the optimal attribute composition of their product lines. We nd that manufacturers have an incentive to locate yogurt products nearby others in attribute space and that products with the most similar attribute compositions enjoy the widest price-cost margins. Our ndings explain the obsevation that most consumer package goods tend to be very similar, and yet manufacturers appear to earn above normal pro ts. Running Title: Rivalry in Price and Location JEL Classi cation: L13, C21, M31, Q13. Keywords: di erentiated products, discrete choice, distance metric, yogurt, pricing, product design. Richards is Morrison Professor of Agribusiness, and Allender is Ph.D. student in the Morrison School of Management and Agribusiness, Arizona State University. Hamilton is Professor in the Department of Economics, Orfalea College of Business, California Polytechnic State University, San Luis Obispo. Contact author: Richards, 7231 E. Sonoran Arroyo Mall, San Tan 230B, Mesa, AZ (480) , Fax: (480) , trichards@asu.edu. Support from AFRI-NIFA (USDA) grant no is gratefully acknowledged.

2 Introduction Manufacturers of consumer packaged goods (CPGs) face an important trade-o when pricing and designing food products. When marketing a line of food products, introducing products that have attributes signi cantly di erent from other products in the category increases product di erentiation, which can facilitate wider price-cost margins by softening price competition. On the other hand clustering products more closely around the attributes contained in the top-selling variety can raise total sales volume. In light of this tradeo, Anderson, de Palma and Thisse (ADT, 1992) show that rms do not necessarily have an incentive to di erentiate their products from rivals in settings where individual tastes di er. Rather, if consumers exhibit su cient heterogeneity in their tastes, then...product / taste heterogeneity softens price competition, locating together is no longer ruinous, and central locations allow rms to better serve consumers over the whole market (ADT, 1992, p. 10). Indeed, when multiple manufacturers compete in product lines, collusive strategies may involve segmenting the attribute space served by each manufacturer into distinct submarkets. Understanding the linkages between heterogeneity in consumer tastes for attributes and the attribute space spanned by food manufacturers existing product lines is essential for evaluating both the marketing and welfare implications of product design. Existing empirical research on product design tends to de ne the product space as linear in a single, de ning attribute (Mazzeo, 2002; Seim, 2006; Thomadsen 2007). While reducing the dimensionality of the attribute space has the advantage of simplicity, it may not fully capture the strategic considerations facing food manufacturers in practice. In this paper, we extend the empirical literature on product design and pricing to multi-dimensional attribute space and assess the role of product di erentiation in food manufacturers equilibrium product design and pricing strategies. In so doing, we are able to decompose the manufacturer margins that result from typical mark-up practices from those that come from the nature of the attribute pro le of the product. We frame our study around an explicitly spatial, discrete-choice model of consumer demand and apply it directly to yogurt products. Discrete choice models have become a popular tool for the analysis of complex strategic problems, including retailers strategic choice of geographic location (Mazzeo, 2002; Thomadsen, 2005, 2007; Seim, 2006; Zhu and Singh, 2006; Orhun, 2006), retail pricing format (Ellickson and Misra, 2007) and the design of a product assortment (Draganska, Mazzeo and Seim, 2006). We extend the discrete choice framework here to examine more general forms of strategic interaction among food manufacturers in selecting the relative attribute composition of products in a food category 1

3 where manufacturers are widely known to maintain long product lines. Speci cally, our approach conceives product design in a complex, discrete / continuous attribute space as arising jointly from manufacturers selection of prices and the relative attribute composition of products in their product lines. It is common in spatial models to specify the dependent variable in a cross-section of data as being functionally related to the dependent variable at other locations in space. For example, the prices of homes that are located near each other are likely to be more highly correlated than the prices of homes that are farther away. In our product design application, we similarly consider the utility a consumer receives from one product as being more closely-related to the utility received from consuming a product with a comparable attribute composition than from consuming a product located at a greater distance away in attribute space. Similar to the use of a lagged dependent variable in a time-series model, we account for unobserved factors that explain the utility available from a particular attribute composition in a di erentiated-product market using spatially-lagged values of consumer utility. There are several advantages to de ning consumer utility as coming from a product s attributes in an explicitly spatial framework. First, our spatial model of product di erentiation provides a new interpretation of product variety. Both theoretical models of product variety (ADP, Hamilton, 2009; Hamilton and Richards, 2009) and empirical models of product line decisions (Bayus and Putsis, 1999; Draganska and Jain, 2005) rely on product counts or line-length as a measure of product variety in a category. In contrast, our spatial econometric framework allows us to describe the extent of variety available in a product category in terms of the size of the multi-dimensional attribute space spanned by the set of products sold in the market. From a purely methodological perspective, de ning variety in terms of the size of the attribute space spanned by a collection of objects provides a way of articulating di erences in variety among sets of objects with similar counts, for instance how a rainbow contains greater variety of color than seven shades of blue. Second, our approach provides an analytically rich framework for examining the strategic role of product variety decisions in consumer goods markets. Calculating the distance between each product and all other products in attribute space permits us to examine a broader range of strategic behavior by food manufacturers. For a given domain of consumer preferences, manufacturers that seek to extend their product lines can crowd the attribute space around top-selling products or expand the attribute space by selecting highly di erentiated attribute compositions relative to existing brands, which can serve to attract consumers to the product category who would 2

4 otherwise have fallen into the outside option and not made a purchase at all. We consider product design to be the outcome of a two-stage game in which food manufacturers rst select the attribute composition of their product lines and then select prices. To limit the number of strategic variables involved in de ning the rst-stage choice of attribute location over a large number of products, we conceive manufacturers choice of attribute composition in terms of selecting the relative distance between each product and other products in the category to maximize pro t resulting from the second-stage pricing decision. This approach results in a stylized choice problem where manufacturers select the entire constellation of products based on the relative distance between the location of each product and the location of all other products in attribute space. Our resulting measure of equilibrium product design, which responds to the willingness-to-pay of consumers at the category level for product variety, can be interpreted as the optimal degree of attribute clustering among manufacturer s o erings in the product category. We apply our model to a data set that combines detailed data on product attributes with retail scanner data on sales volume, shelf prices and promotional activity for a large number of US yogurt brands. 1 Similar to Feenstra and Levinsohn (1995) and Seim (2006), our econometric model is structural in nature as it includes components for di erentiated product demand, and strategic choice of product location and pricing; however, we depart from these studies by using a distance metric / multinomial logit (DM-MNL) approach for the demand model. Conditional on this spatial demand model, the rst-order-conditions for rm pro t maximization convey this spatial structure into yogurt manufacturer s price and product location choices. Our major ndings for product design and pricing in the yogurt category are as follows. First, in the demand-side model we nd that consumer preferences for yogurt attributes exhibit a positive spatial lag in the utility structure, which suggests consumers prefer to consume yogurt products with a similar attribute composition. That is, when switching between one yogurt product and another, utility rises with greater proximity between the products in attribute space. Second, after accounting for the e ect of product di erentiation on softening price competition, we nd that yogurt manufacturers have an incentive to locate products nearby others in attribute space. Third, we nd that yogurt products with the most similar attribute compositions enjoy the widest price-cost margins, suggesting that yogurt manufacturers are able to raise prices by introducing products in the most congested portions of the attribute space. This raises the interesting possibility that co-locating products in attribute space can crowd out the products of rival manufacturers, 3

5 thereby providing a measure of local market power as rms enjoy hegemony over consumers on each side of a Hotelling beach. Our results in this sense are broadly consistent with the observation that food manufacturers exert considerable research and development e ort to identify the most popular product formulation as opposed to the most unique product design. The remainder of the paper is organized as follows. In the next section, we present the econometric model used to estimate yogurt manufacturers strategic behavior in price and product design. Section 3 provides a brief overview and description of the U.S. yogurt market. Section 4 describes the data and estimation methods used to implement our econometric approach. In Section 5 we present and interpret our estimation results and provide a numerical simulation to demonstrate the role of spatial trends in consumer attribute preferences on product design, pricing, and welfare. We conclude in Section 6 by identifying implications of our results for product design and highlighting some general directions for further study on strategic behavior by manufacturers in the attribute composition and pricing of product lines. Econometric Model of Product Pricing and Design We model demand using a random utility model of choices among di erentiated products (Berry, 1994; Nevo, 2001). Within this general modeling structure, we account for consumer heterogeneity and product di erentiation by directly measuring the distance between choices made by individuals in attribute space and we estimate the resulting model of product di erentiation using spatial econometric methods following Pinkse and Slade (2004) and Slade (2004). The supply-side of the model consists of a set of food manufacturers who choose the degree of product di erentiation between a new product and existing products when designing and pricing new products. The rms anticipate rivals optimal design choices and choose attribute distances between products in a continuous, spatial framework. The econometric model therefore consists of demand, pricing and product design components that are grounded in theoretical frameworks of consumer behavior. We discuss each element of the model in detail below and then simulate our equilibrium results in the nal section of the paper to highlight the importance of key parameters on predicting the price and product design choices of food manufacturers. Consumer Demand When making a purchasing decision in the yogurt category, we model each consumer as making a discrete choice of a single brand and avor. In our discrete choice framework, 4

6 consumers choose the one product from all alternatives that provides the highest level of utility, where utility is assumed to be made up of the utility the consumer gets from consuming the product as well as a random term that re ects heterogeneity among consumer tastes. Yogurt products in the choice set are di erentiated by brand, nutrient and marketing attributes, where the composition of attributes in a particular product e ects utility by de ning a product s location relative to others. Our spatial modeling structure allows us to account for di erences in the perceived location of each yogurt in attribute space, which allows the extent to which a particular brand of yogurt is di erentiated from others (based on its distance in attribute space) to enter consumer utility. We model the distance between products in attribute space as a primitive of the consumer choice process. Slade (2004) applies a similar notion of product di erentiation to the discrete choice model by assuming the price-coe cient to be a function of attributes; however, a disadvantage of this approach is that a consumer s price-response in a discrete-choice model of demand is determined by the marginal utility of income, which is a characteristic of the individual that cannot logically vary over choices. To circumvent this problem, we introduce the attribute distance between products directly into the utility function in a parsimonious manner that re ects the role of product di erentiation in determining the relative utility level available from each product. To understand our framework of consumer demand, suppose the relative utility level available to consumer i from choosing product j depends on how di erent the set of attributes contained in the product is from the attributes contained in other products. For example, the utility from consuming a product such as mocha Greek yogurt relative to the utility from consuming another yogurt product would be di erent if all other yogurts are traditional, vanilla avors than if all other yogurts are cappuccino avors. In aggregate data, our conceptual interpretation of spatial dependent utility is that utility of the representative consumer is context-dependent, and this need only be true for the representative consumer. For example, consider a convenience store that o ers only skim milk and whole milk and a supermarket that o ers 2% milk, skim milk, whole milk (4%), and 1% milk (set goat s milk and soy milk aside for the moment). If half the consumers in the convenience store purchase whole milk and half purchase skim milk, then we can think of a representative consumer in the convenience store that prefers 2% milkfat. But there is no reason why the utility level of this representative consumer must be the same as the utility level of a representative consumer in a supermarket where 20% of the customers purchase skim milk, 20% purchase 1% milk, 30% purchase 2% milk and 30% purchase whole milk, even 5

7 though the average product purchased in the latter case is also 2% milkfat. Utility from the choice of the representative consumer is inherently state-dependent, where the state characterizes the amount of product variety as measured by the span of the attribute space. Our approach re ects a similar mechanism to that described by the address models developed by ADT (1992) and Feenstra and Levinsohn (1995). Speci cally, the utility from each choice depends upon the distance between the attributes contained in that choice and the consumer s ideal set of product attributes, where the ideal product reduces, in this case, to the product chosen by a representative consumer. We account for the utility-loss associated with distance in by introducing a spatial autoregression parameter to measure the extent to which di erentiation from other products raises (or lowers) the utility from choosing product j according to the relative distances between products and the ideal attribute mix of a given consumer. In this way, we model the spatial state-dependence of demand. 2 The resulting estimation framework nests a general model of di erentiation in the utility structure that is grounded in theory and capable of accommodating di erentiation in multiple attributes. 3 We begin by developing a model of mean utility and then incorporate unobserved heterogeneity to motivate the empirical model. We follow ADT (1992) and Feenstra and Levinsohn (1995) by adopting a non-linear utility-loss function, where mean utility from product j falls (or rises) in the distance from all other products, measured by the distance matrix W. Each element of W measures the distance between each pair of product, so the element w jl measures the distance between product j and product l in the multi-attribute space described below. Our approach di ers from previous studies in that we project the utility-loss from product matches into utility space using a spatial auto-regressive framework instead of measuring it directly in attribute space. We write the mean utility for product j = 1; 2; :::; J in week t = 1; 2; :::; T in vector notation (with bold notation indicating a vector) as: = 0 x + W p + ; (1) where is a JT 1 vector of mean utility, x is a JT K matrix of demand shifters (brand indicators, discount and discount-price interaction), p is a JT 1 vector of prices, and is a random error unobserved by the econometrician that re ects variables known to the manufacturer to in uence price, for instance the quality of ingredients, marketing inputs, and anticipated surpluses (shortages). The vector and scalar parameters and are to be 6

8 estimated. The matrix W measures the e ect of product di erentiation on utility according to attribute distance, which de nes as a spatial autoregression parameter (Anselin, 2002). 4 The interpretation of is the marginal impact on mean utility from the observed choice according to the attribute distance between the product and all other products in the choice set. This re ects the notion that consumers evaluate the utility attainable from each product relative to the utility that can be attained from consuming other available products in the choice set. We follow convention in de ning W as a measure of inverse-distance, or proximity, so that greater product di erentiation in the yogurt category reduces utility when > 0 (i.e., utility rises with attribute proximity) and increases utility when < 0. Solving equation (1) for mean utility gives = (I W) 1 ( 0 x p + ); (2) where (I W) 1 is the Leontief inverse, or spatial multiplier matrix (Anselin, 2002) describes the utility of each choice relative to the utility available from all other choices in the product category. We measure proximity in terms of the inverse Euclidean distance between products in terms of nutritional and avor attributes. Inverse Euclidean distance is represented continuously using a general spatial weight matrix, W, with typical element w jl between the nutritional pro le of item j and item l de ned as 0 v 1 ux w jl + 2t M (n jk n lk ) 2 A k=1 1 ; (3) where n jk is the value of attribute k associated with product j and similarly for item l. For our application to yogurt products, the set of nutrient attributes contains fat, protein, sugar, sodium and total calories. Recall that equation (3) is de ned it terms of inverse-distance, so that larger values of w jl represent items that are closer together in attribute space. 5 We then de ne the J J spatial weight matrix that includes all of the w jl as elements and thus describes the distance between all pairs of products that are compared in the sample. The distance between each product and itself is normalized to 0, which in terms of equation (3) implies that own-proximity is normalized to 1. Notice by construction that W is symmetric, that is the distance between items j and l is the same as the distance between items l and j; however, recall that mean utility in equation (2) re ects only observed heterogeneity and not unobserved heterogeneity. Assuming utility varies among consumers in a random way, we write utility as 7

9 u i = + " i ; (4) where " i is an iid random error that accounts for unobserved consumer heterogeneity. This leads to our description of behavior - consumer i chooses item j if the utility from this choice is greater than the utility from all other alternatives: Pr(j = 1) = Pr[ j l " il " ij ] where j is the jth element of. The probability that consumer i chooses product j over all others is governed by the distribution of " ij. As in the non-spatial case, if " ij is extreme value distributed, then the random utility model in (4) implies a market share expression for item j given by: JX S j = exp( j )=(1 + exp( l )); (5) where S j is the volume-share of product j. Thus, our model is closely-related to the distancemetric multinomial logit (DM-MNL) model of discrete choice among di erentiated products developed by Slade (2004). Given the evident non-linearity of the system, we follow Berry (1994) and Cardell (1997) and linearize equation (5) by taking logs of both sides and write the resulting expression in vector notation as l=1 ln S ln S 0 = (I W) 1 ( 0 x p + ); (6) where is the error term described in equation (3). By explicitly recognizing the extent of di erentiation among the products in our yogurt sample, the resulting demand model is more exible than simple discrete-choice models in that the cross-price elasticities of demand are not restricted to be equal for all products. Our approach is similar to Slade (2004) and Pinkse and Slade (2004) in that we explicitly incorporate a distance-metric component in the demand model; however, attribute distance enters in a structural way in equation (6) through the utility function. Given that yogurt manufacturers price and locate products to maximize pro ts for a given demand structure, the parameters from the demand system condition the pricing and positioning (attribute) decisions made by food manufacturers. When a rm considers introducing a new yogurt product, the optimal product design takes into account the set of consumers who prefer a given combination of attributes, for instance the demand for vanilla- avored yogurt with standard fat, sugar and sodium content relative to the demand for low-sodium, non-fat, key lime- avored yogurt. The manufacturer can produce a highly di erentiated line of yogurt products or cluster yogurt products more closely around a 8

10 popular attribute composition, and the strategy the rm pursues in equilibrium depends on the expected price-cost margins and sales volumes that can be attained under various product compositions. We derive the equilibrium choice of price and location in attribute space in the next section. Pricing and Product Location Now consider the supply side of the model. Each manufacturer sells multiple brands and avors j 2 M and engages in Bertrand-Nash competition with rivals in prices and product location. To simplify the interpretation of our model, we assume cooperative vertical relationships exist between manufacturers and retailers, so that manufacturers choice of optimal price and location is conditioned directly by retail demand conditions. 6 Following Thomadsen (2007) and Stavins (1997), manufacturers play a two-stage game in selecting attribute locations and prices for their products. Firms choose location in the rst stage, and then compete in prices in a second stage. We solve the game by backward induction, solving the pricing sub-game rst and then the location game. 7 When designing a new product, manufacturers must choose a speci c location for the product. In the product-design literature, Stavins (1997), and Draganska, Mazzeo and Seim (2009) take the direct approach of de ning the location of all products in attribute space, much like one would consider the position of individual retailers in geographic space (Thomadsen, 2007); however, such an approach is only practical when the attribute space is highly simpli ed. In our model, we accommodate the multidimensional attribute space of yogurt products by looking at the entire constellation of products in terms of the relative di erence in attribute composition between individual products in the category. This provides a measure of the degree of product di erentiation in the category that is embodied implicitly in a scaled, perceptual, Euclidean-distance sense of the relationship between all products sold in the category. Put di erently, product designers span the attribute space with an equilibrium composition of products, and the resulting pricing and market share implications of locating products at particular locations in attribute space depend on the entire composition of the product line in terms of the relative distance between products in equilibrium. It is helpful to consider the analogy between product design and the choice of geographic location. When retailers contemplate store location, they typically apply algorithms that involve drawing concentric circles of one mile and 1.5 miles in radius and then analyze the trading area therein (Berman and Evans, 2009). Selecting a location at the center of this two-dimensional circle amounts to choosing an average distance between the store and 9

11 all other stores that lie within the two circles. 8 We adopt a similar heuristic to simplify the description of equilibrium attribute location in multi-dimensional space by measuring market share and prices in terms of the average distance between a product and all other products in the category. Each element of the spatial weight matrix, W, above describes how far each product j lies from each other product l in a multi-dimensional attribute space. To assume that the manufacturer chooses each row-element of this matrix uniquely is neither tractable nor interesting, and we consequently follow Feenstra and Levinsohn (1995) and Stavins (1995, 1997) in assuming manufacturers consider the pro t implications of locating products at di erent average-distances from all other products using an arithmetic-mean de nition of distance. 9 To operationalize our measure, we de ne a J J matrix b with each element [b jk ] = 1=J and post-multiply the spatial weight matrix to create a diagonal matrix of average distances, w = Wb I, with typical element w j where indicates element-byelement multiplication and I is a J J identity matrix. We write the pro t maximization problem for a yogurt manufacturer as j = max p j ; w j X j2j Q(p j c j )S j ( w j ) F j g( w j ); (7) where c j is the marginal cost of production, Q is the size of the total market, F j is the xed cost of manufacturer j, and g( w j ) is a cost function that re ects the cost of producing items that are either similar to, or di erentiated from, others in the market and is assumed to be separable from c j. 10 We specify the marginal cost of production as arising from a normalized quadratic cost function, C j, so that marginal cost is c j j =@q j = ' j0 + P ' k v k ; where v k k are input prices in the manufacturing process and q j is the quantity of product j purchased. Finally, for expedience, we subsume both production and marketing inputs, which consist of the price of class III milk, sweeteners, packaging, and dairy-product manufacturing labor, utilities and transportation costs, into the marginal cost function. j is The rst order necessary condition for the rm s optimal choice of price for j = QS j ( w j ) + Q(p j c j j( w j ) + j l6=j Q(p l c l l( w l j = 0: (8) Solving equation (8) for the optimal price-cost markup provides an expression for the rela- 10

12 tionship between the margin and degree of di erentiation for product j; namely, ( w j ) (p j c j ) = S j ( w j ) + X! (p l c l l( w l ) : j Equation (9) allows us to form hypotheses on the expected e ect of greater distance among products on pricing behavior. To see this more clearly, rewrite equation (9) in matrix notation and de ne S p as the logit share-derivative matrix in prices so that the rst-ordercondition for all products becomes: l6=j p c = (I (Wb I))(S 1 p )S = (S p 1 )S+(Wb I)(S 1 p )S: (10) The second expression on the right decomposes the markup term into the conventional markup (S 1 p )S and the part due to spatial di erentiation (Wb I)(S 1 p. )S Notice that the markup term in equation (10) di ers from the markup in the nondi erentiated case according to the value of the spatial auto-regressive parameter,. > 0, consumers prefer products that are more like existing products in the market, so that rival rms can be expected to raise prices if the manufacturer selects a more similar composition of products. The collusive or minimum di erentiation e ect of ADT (1992) dominates product design decisions, leading rms to increase w j, thereby gravitating products toward the center of the attribute space to obtain local monopoly power over consumers who prefer the attribute composition of their products and higher margins. If Conversely, if < 0, consumers prefer products that are more di erentiated, and a maximum di erentiation (d Aspremont, Gabszewicz and Thisse, 1979) e ect dominates product design decisions, leading rms to reduce w j to increase margins. If utility does indeed rise in the extent to which a product is di erentiated from others, then the softening price competition outcome prevails and rms reduce margins on mass-market products in order to compensate for low margins through high volume. di erentiated yogurt brands. In this study, we test which e ect prevails in a sample of Following Villas-Boas and Zhao (2005), Draganska and Klapper (2007), and others, we recognize that manufacturers are unlikely to adhere to the Bertrand-Nash solution concept exactly. Therefore, we parameterize deviations from the maintained solution by adding a parameter,, to the markup term in (10) that measures any deviation from the hypothesized Bertrand-Nash outcome: p c = (I (Wb I))(S 1 p )S = (S p 1 )S+(Wb I)(S 1 p )S: (11) 11

13 In empirical studies of market power, is commonly referred to as a conduct parameter. The conduct parameter measures the exercise of market power either below or above that implied by the elasticity of product demand. 11 Speci cally, a value of = 1 implies pricing behavior consistent with Bertrand-Nash rivalry, while < 1 implies pricing that is more competitive than Bertrand, and > 1 suggests behavior that is less competitive. In the pricing model, two parameters ( and ) describe possible sources of valueadded for new yogurts. To asses the pricing power of a yogurt at a particular point in attribute space we test the null hypothesis H 0 : = 0. If this parameter is not signi cantly di erent from zero, then the rm sets competitive prices for attributes; however, if > 0 the manufacturer earns positive margins between the retail price and production costs, so the new product is value-adding. If > 1, the yogurt adds more value than one priced in a manner consistent with Bertrand-Nash rivalry, and if < 1, then it is more competitive than Bertrand. We now turn to the rst-stage problem of choosing a product s location in attribute space. This problem is conceptually more di cult than price choices, because the decision is potentially multi-valued. The typical strategy among market researchers is to reduce this problem to a tractable form by either assuming a simple one-dimensional location problem (Seim, 2006) or by assuming consumers always value more of each attribute (Horsky and Nelson, 1992), where the problem is reduced by the later approach to one of nding how to incorporate the most of each attribute at the lowest cost. Our spatial framework de ned over relative distances is a relatively parsimonious solution. Rather than choosing the speci c attributes of each product, we follow Stavins (1995, 1997) in modeling rms as choosing the relative distance between each product and all other products in the category. As in the pricing decision, we assume the location decision is a Nash equilibrium among manufacturers, in the average distance of their product from all others. For simplicity, we again assume one product per manufacturer, but it is a simple matter to accommodate multiple-item production through the addition of an ownership matrix (Nevo, 2001). We do so in the empirical model below. Using scalar notation for clarity, the rst order condition with respect to distance is given j = Q(p j c j j( w j ) + w w j l6=j Q(p l c l l( w j w w j w j = 0: (12) where g( w j ) = 0 + 1=2 1 w 2 j is the cost of di erentiation function, so the marginal cost is g w = 1 w j. Again focusing on the solution for product j, the share derivatives are given by 12

14 j ( w j w j = (1 w j ) 2 (S j (1 S j )); (13) for the cross-location term. the estimating l ( w j w j = (1 w j ) 2 (S j S l ); (14) Substituting these expressions into (12) and simplifying yields Q(p j c j )S j (1 S j ) + Q X (p l c l )S j S l = (1=)( 1 w j )(1 w j ) 2 ; (15) l6=j which is then estimated along with equation (11) after substituting in the share expressions, adding an error term, allowing for a set of brand-speci c indicator variables to identify the cost parameters, j0, and de ning the marginal cost function, c l ; as a linear function of input prices as de ned above. Our model is therefore completely speci ed by equations (8), (11), and (15), which we estimate simultaneously to incorporate the cross-equation restrictions implied by the spatial demand model. We compare this fully spatial model to a non-spatial alternative to assess the relative t of each model and discuss the pricing implications of ignoring the endogeneity of product location. Several testable hypotheses on the relationship between pricing and product location arise from equation (15). Applying the implicit function theorem to (15), we nd that the conventional result from Hotelling (1929), namely that the optimal distance from other products rises in the price of product j is a special case in this model. w j =@p j > 0 holds only under the condition that < 1= w j ; which is immediately satis ed if < 0 (consumers prefer di erentiated products), or if > 0 and products are su ciently highly di erentiated (i.e., w j is su ciently large). 12 Note that this hypothesis is qualitatively similar to Thomadsen (2007), although our framework is more general. We test these hypotheses using the spatial empirical model described below. We then simulate the resulting equilibrium to show in a more concrete way the e ect of varying on equilibrium price and location choices. Data Description Our data describe weekly sales of all adult brands of yogurt in 18 U.S. markets during 2005 from the two major national manufacturers: Dannon and Yoplait. The data are from IRI and are widely available to academic researchers (Bronnenberg, Kruger and Mela, 2008). As a category, yogurt represents an excellent opportunity to explain strategic product 13

15 location. First, the two major manufacturers constitute a near duopoly in most markets so each must necessarily consider the position of rival products in designing their own. Private labels represent a considerable share of many markets (see table 1), but retailers tend to locate store brands near to existing national brands in attribute space (Mills, 1995) so do not represent unique spatial in uences. Moreover, detailed nutritional data are not available for the private labels used during the sample period, so form part of the outside option, which includes all other brands not represented in our model. For example, other, relatively minor brands such as Stoney eld Farms and YoFarm are also assumed to represent choices in the outside option. Second, yogurts are di erentiated in a number of dimensions, from brand identity and nutritional pro le to avor and package size. Therefore, we are con dent that we observe su cient variation among the items in our data set to identify the incentive to locate at di erent points in attribute space, and to set prices accordingly. Third, yogurt input prices also exhibit signi cant variation over time, input proportions vary according to the brand and product type, and retailers in di erent geographic markets follow markedly di erent pricing strategies so there is easily enough exogenous variation in the market to identify demand. The data presented in table 1, which summarizes the brand / avor data for the top 10 yogurt brands in our data set for ve representative markets, documents the extent of inter-brand and inter-market price variability. The contribution to the variability of not only prices, but volume sales and promotion activity are documented in table 2. Clearly, variation in product attributes explains much of the di erence in promotion activity between products, but market-driven variation in demand explains more of the variation in volume sales. [table 1 in here] [table 2 in here] In any multi-dimensional, distance-based model, the units of measure for each element of the distance calculation are clearly important. For example, we measure the protein content of yogurt in terms of grams per ounce and energy content in calories per 100 grams, so the relative weight of each attribute in the distance metric will re ect the absolute value of each measure. We need a method of determining weights for each attribute that re ect their underlying economic importance. For this purpose, we use a hedonic pricing model (Rosen, 1974) in which the market price of a product is interpreted as a weighted sum of the marginal values of each attribute. We estimate the marginal value, or willingness-to-pay, for each attribute by estimating a linear-hedonic regression model over all markets and spec- 14

16 ifying price per ounce as a function of yogurt attributes: total calories per ounce, grams of protein, fat and sugars per ounce, milligrams of sodium per ounce, and a set of brand-speci c dummy variables. The units of measure are thus standardized in monetary terms, meaning that distance is expressed in terms of dollars per 100 grams of yogurt. We estimate this model with a random-e ects approach using simulated maximum likelihood. Measured this way, our yogurt brands are arrayed across a relatively large attribute space. For example, the fourth brand, Dannon La Creme, is only $0:76 away from the other brands, on average, while Yoplait Thick & Creamy is fully $1.66 apart from the others. Estimation Method We estimate the entire structural model in one stage because the spatial lag parameter appears in all three equations. We consider both prices and product attributes to be endogenous and accordingly estimate the entire system using generalized method of moments (GMM) by applying an identi cation strategy similar to Pinkse, Slade and Brett (2002) and Kelejian and Prucha (1998, 1999). 13 For the demand model, we construct two sets of instruments, one for prices and another for product attributes. The rst set consists of yogurt manufacturing prices (raw milk, sweetener, plastic for packaging, milk manufacturing wages, transport costs and utilities) interacted with individual brand indicator variables. This is a standard approach in estimating structural models of di erentiated product demand (Berto Villas Boas, 2007) in which retail prices are likely to be endogenous. Input prices vary over time, and inputcontents vary by brand, so the interaction between the two exhibits su cient variation to identify the demand parameters. Further, because the demand model includes brand xede ects, the instruments will not be correlated with the unobservable errors for each demand equation because the brand-e ects have been removed (Berto Villas-Boas, 2007). Our second set of demand-instruments accounts for the attributes of brands and avors sold in other markets. Speci cally, we apply spatially-weighted averages of the nutritional attributes of all other products in other markets, which are calculated by multiplying each variable by the inverse Euclidean distance weight matrix described above. This procedure is used by Pinkse and Slade (2004) and Slade (2004) and is also suggested by Kelejian and Prucha (1998) who include non-linear spatial-interaction terms in developing their spatial GMM estimator. Weighted average yogurt attributes from other brands and markets are likely to be valid instruments because the remaining unobservables in the demand equation include such things as shelf-placement, in-store advertising and display activity all of which are independent of either pricing or design decisions. Moreover, rival product at- 15

17 tributes vary due to di erences in the portfolio of products sold by retailers in each market (Berry, Levinsohn and Pakes, 1995; Draganska, Mazzeo and Seim, 2009). Regressing this set of instruments the weighted attributes of other yogurts and the input-price / brand interactions on the endogenous prices produces an F-statistic of Each of the spatial-interaction terms are highly signi cant so, combined with this F-statistic, we are con dent that our instruments are not weak in the sense of Staiger and Stock (1997). 14 In the pricing and product design equations, we seek a set of instruments that are correlated with share and location measures that appear on the right-side of those equations, but are mean independent of the speci c price and location of each product. For this purpose, we again use two sets of instruments: one consistent with well-accepted practices taken in the extant literature and the other exploiting the spatial nature of the model and data. Intuitively, we seek a set of instruments that shift demand and, hence, markup terms in a way that is exogenous to the pricing and location decisions of the two manufacturers considered here. Factors that are pre-determined to the pricing and design decisions in a panel data set, and vary both over time and across markets, include demographic measures unique to each market. Income, age, education and racial composition are all valid instruments in this regard. We interact these variables with binary brand indicators to separately measure the variation in demand for each brand. Our second set of supply-instruments includes spatially-weighted values of demand shifters in other markets. While others use the attributes of rival products as instruments, the attributes of rival products are not valid instruments in our framework of endogenous product design. Consequently, we rely only on exogenous variation in demand and supply to identify the conduct parameters in our model. The summary statistics in Tables 1 and 2 document the inherent time-series and cross sectional variation in both the observed retail price and share data. This variation is more than su cient to identify di erences in pricing and design behavior among manufacturers. F-statistics from regressing average distance and price on this set of instruments are and 92.01, respectively, suggesting that these instruments are suitable for the purpose at hand. In each of the demand, pricing and location models we also test for spatial autocorrelation in the data. Analogous to serial correlation in time-series data, if spatial autocorrelation is present and not explicitly taken into account, the resulting parameter estimates remain unbiased and consistent, but are ine cient. To the extent that neighboring product characteristics are important omitted variables, we expect some bias in the non-spatial estimates. LeSage (1998) presents a number of tests for spatial autocorrelation, the most 16

18 straightforward of which involves a Wald test for the signi cance of the spatial autocorrelation parameter,. Because a non-spatial model is nested within a spatial alternative, we also use a quasi-likelihood ratio (QLR) test to determine whether a spatial speci cation is necessary. Results and Discussion In this section, we rst present the results from a series of speci cation tests for the spatial model, relative to non-spatial alternatives, and then tests of the central hypotheses of the paper. We begin with the demand model and then move to the pricing and spatial location models, which are the focus of this study. Although the demand, pricing and location equations are estimated as a system, we present the demand estimates in tables 3 and 4 and the pricing and location estimates in table 5. The results from the simulation exercise are shown in table 6. In table 3, we present the results for three di erent demand models: (1) a nonspatial model estimated with instrumental variables, (2) a spatial model estimated with least squares, and (3) a spatial model estimated with instrumental variables. 15 Both IV models are estimated with GMM, but we include the non-iv estimates in this table in order to show the extent of bias present if endogeneity is not properly accounted for. Comparing the spatial and non-spatial models using a quasi-likelihood ratio test, we nd a chi-square test statistic value of 582.2, rejecting the restricted, non-spatial model in favor of the spatial alternative. Similarly, applying t-test to the spatial lag coe cient also indicates rejection of the null hypothesis that there is no spatial autocorrelation in the data. The implication of this nding is that the demand for a product at one location in attribute space depends on the demand for products at other locations. Because the di erence in location is measured as inverse Euclidean distance, a higher value indicates greater proximity between products. A positive spatial lag parameter therefore suggests that two yogurt products that are located near each other have reinforcing, or complementary e ects on demand. Consumers who prefer a certain product design are more likely to try similar products than they are entirely dissimilar ones, much like a BMW driver is more likely to test drive an Audi convertable than a minivan. Our nding of a positive e ect of proximity suggests that the Hotelling s minimum di erentiation result is an important element of new product design in the yogurt category. [table 3 in here] The extent of the omitted-variables bias inherent in the non-spatial estimator is also apparent from the results in Table 3. While the average own-price elasticity implied by the 17

19 spatial estimates is , the same measure for the non-spatial estimates is nearly three times as large. Clearly, inferences made regarding the price sensitivity of brands from the non-spatial model will lead to dramatically incorrect pricing decisions. Spatial estimates of promotion sensitivity, however, are stronger than the non-spatial alternatives. Finding that demand shifts inward during promotional periods is likely due to the fact that we control for both shift- and rotation of the demand curve. Accounting for these interaction e ects, we nd that demand rotates clockwise, or becomes more inelastic while promoted, a nding that is consistent with previous research in the retail price-promotion literature (Chintagunta, 2002). One of the primary advantages of estimating a DM-MNL model of demand is that we avoid the IIA property inherent in the simple logit model in a straightforward, intuitive way (Richards, Hamilton and Patterson 2010). With this approach, we allow cross-product substitution e ects to depend on the relative distance in attribute space directly, rather than through correlation with unobserved components of consumer utility as in a mixed logit model (see, e.g. Nevo, 2001). The elasticity matrix in Table 4 illustrates the exibility of the DM-MNL model. 16 In a simple logit model, the cross-product elasticities would be the same in each column, but with the DM-MNL approach, they depend on the relative distance in attribute space. Low-fat yogurts, in general, substitute more readily for other low-fat yogurts, and less so with more indulgent brands. This feature is critically important in the optimal price and attribute location choice decision considered next. [table 4 in here] We estimate the demand, pricing and location models jointly to recognize their fundamental interdependence, particularly in a model of strategic interaction. We also allow for a departure from the maintained Bertrand-Nash assumption in order to allow for market power e ects to vary by distance. The results from estimating the nal two components of the joint model appear in table 5 below. In terms of the pricing model, we compare two alternative models to our maintained spatial / GMM: (1) one that ignores the endogeneity of the markup and di erentiation terms (OLS), and (2) another that ignores the spatial element of demand and rivalry in the pricing equation. In terms of the GMM / OLS comparison, we nd that the results are not qualitatively di erent between models, but the extent of the bias in the OLS estimates is apparent. Table 5 compares our spatial and non-spatial parameter estimates. Notice from the entries in Table 5, it is clear that the non-spatial model does not t the data as well as the spatial model, although it does produce similar brand-level margin estimates. The key 18