Competitive Package Size Decisions

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Competitive Package Size Decisions夽 Koichi Yonezawa a,b,∗ , Timothy J. Richards c a

TUM School of Management, Technische Universität München, Alte Akademie 16, 85354 Freising, Germany Charles H. Dyson School of Applied Economics and Management, Cornell University, Ithaca, NY 14850, USA c Morrison School of Agribusiness, W. P. Carey School of Business, Arizona State University, 7231 E. Sonoran Arroyo Mall, Mesa, AZ 85212, USA b

Abstract In the consumer packaged goods (CPGs) industry, consumers base their purchase decisions in part on package size because different package sizes offer different levels of convenience. The heterogeneous preference for package size allows manufacturers to use package size as a competitive tool in order to raise margins in the face of higher production costs. By competing in package sizes, manufacturers may be able to soften the degree of price competition in the downstream market, and raise margins accordingly. In order to test this hypothesis, we develop a structural model of consumer demand, and manufacturers’ joint decisions regarding package size and price applied to supermarket chain-level scanner data for the ready-to-eat breakfast cereal category. While others have argued that manufacturers reduce package sizes as a means of raising unit prices in a hidden way, we show that package size and price are strategic complements – downsizing intensifies price competition, which does not allow manufacturers to raise unit prices through package downsizing. Therefore, package downsizing does not yield a desirable outcome for manufactures. On the other hand, retailers benefit from package downsizing, as it leads to lower wholesale prices, and higher category profits. © 2016 New York University. Published by Elsevier Inc. All rights reserved. Keywords: Differentiated products; Discrete choice; Package size; Pricing; Product design

1. Introduction Consumer packaged goods (CPGs) face very public scrutiny when they reduce package sizes, yet keep shelf prices constant (Poulter 2013). According to McIntyre (2011), Heinz reduced the size of some of its ketchup products by an average of 11 percent, Kraft reduced the amount of crackers in its Nabisco Premium saltines and Honey Maid graham crackers boxes by 15 percent, and PepsiCo reduced the size of its half-gallon cartons of Tropicana by 8 percent, all while either keeping the package-price the same, or increasing it (in the PepsiCo case by 5–8 percent). Reducing package sizes as a means of raising retail unit-prices may be a rational response by manufacturers to

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The authors thank the reviewers and editor, Murali K. Mantrala for their valuable comments and suggestions throughout the review process. The authors also ¸ akır, Carola Grebitus and Sungho Park wish to thank Joseph V. Balagtas, Metin C for their helpful comments. Funding from the Agriculture and Food Research Initiative (AFRI) – National Institute for Food and Agriculture (NIFA), USDA is gratefully acknowledged. ∗ Corresponding author. Tel.: +1 607 255 5024. E-mail address: [email protected] (K. Yonezawa).

the expectation that consumers tend to respond more sharply to package-prices than unit-prices (C¸akır and Balagtas 2014), but ignores the strategic nature of changing package sizes. Rather, it is more likely that oligopolistic manufacturers take into account not only consumer responses to a change in package size, but responses by rivals. In this study, we examine package-size changes from a strategic perspective, and show that the implications can be dramatic. Other researchers consider demand-side motivations for changing package sizes, but not cost or strategic reasons. Because few consumers have perfect recall of package sizes or unit prices, they tend not to compare unit prices over time or among products (Binkley and Bejnarowicz 2003; Granger and Billson 1972; Raghubir and Krishna 1999; Russo 1977). Accordingly, manufacturers may change package sizes, and hence unit prices, without changing the shelf price as a means of passing along higher costs. C¸akır and Balagtas (2014) find that manufacturers change package sizes, rather than price, because consumers tend to ignore changes in unit-prices. However, they do not account for the fact that package size decisions are endogenous, and strategic. Ignoring the endogeneity of packagesize changes is not trivial, because, if prices and package

http://dx.doi.org/10.1016/j.jretai.2016.06.001 0022-4359/© 2016 New York University. Published by Elsevier Inc. All rights reserved.

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size are strategic complements, then package-size reductions by one firm are no longer simply price increases that are likely to be ignored. Rather, other firms may reduce prices, leading to sharper price competition, and perhaps even lower prices. If consumer demand depends at least in part on package size, and products sold by different manufacturers are substitutable, then manufacturers are likely to use package size as a strategic variable. Consumers exhibit heterogeneous preferences for package size depending on their consumption rate, storage cost, transaction cost, and marginal utility from increased consumption (Gerstner and Hess 1987; Subramaniam and Gal-Or 2009). Therefore, manufacturers often differentiate on the basis of package size in order to attract particular market segments. For example, Kelloggs offers Special K in some 11 different package sizes, while General Mills sells Cheerios in 24 others. By offering different package sizes, they attempt to avoid direct price comparison with substitute products (Anderson, De Palma, and Thisse 1992). Empirical evidence shows that if firms in oligopolistic markets have multiple decision variables – price and non-price variables – they tend to compete in non-price variables, but collude in price. This is true for a range of variables, from investment in R&D and capacity (Brod and Shivakumar 1999; Davidson and Deneckere 1990; Fershtman and Gandal 1994), advertisement (Dixit and Norman 1978; Slade 1995), promotion (Richards 2007), line extension (Kadiyali, Vilcassim, and Chintagunta 1998), product-line length (Draganska and Jain 2005), product assortment (Draganska, Mazzeo, and Seim 2009), location in geographic space (Friedman and Thisse 1993; Thomadsen 2007), and location in attribute space (Jehiel 1992; Seim 2006). In each case, non-price variables can serve as strategic tools that change the nature of price competition. Despite its prominence in product design, and salience to consumers, competitive package sizing has received little attention in the literature. We frame our hypothesis regarding manufacturers’ choices of price and package size in a structural model of consumer demand, production cost, and manufacturers’ optimal response to package-preferences. On the demand-side, we explicitly account for package-size preferences. By conditioning manufacturer decisions on consumer preferences for different package sizes, we ensure that manufacturer decisions are optimal responses with respect to their expectations on how consumers will react. On the supply-side, oligopolistic manufacturers jointly set package size and wholesale prices and retailers set retail prices taking into account consumer demand, manufacturer and retailer costs, and competition in package size and price. Retailers are assumed to pass-through manufacturers’ package size decisions and set retail prices. Following Slade (1995), Besanko, Gupta, and Jain (1998) and Sudhir (2001), we assume that retailers act as local monopolists once consumers have chosen a particular store. Estimating a structural model is not only necessary to avoid bias and inconsistency in our econometric estimates (Villas-Boas and Zhao

2005), but by doing so we are able to estimate the extent of strategic interaction among manufacturers in the upstream market. We apply our empirical framework to supermarket chainlevel scanner data for the ready-to-eat breakfast cereal category for a major US metropolitan market. We find that package size decisions by manufacturers reflect both consumer preferences, and competition in both price and package size. Manufacturers tend to reduce package sizes in response to higher costs as a means of mitigating the potential negative impact on profits. However, shrinking packages to pass along higher costs is only part of the story. Rather, changing package sizes is costly, and changing in package sizes incites strong price competition. Therefore, the incentive to change packages is much more constrained than previously thought, and often not in manufacturers’ interests at all. We contribute to the empirical marketing literature by endogenizing joint package size and price decisions. We show that strategic considerations are as important to manufacturers as consumers’ responses to smaller package sizes. On a substantive level, we show that when manufacturers change package sizes, they respond not only to consumer preferences, but to the structure of packaging costs, and the nature of rivalry in their industry. As a consequence of the destructive price-competition they incite, package changes are infrequent. Our findings have practical implications for both manufacturers and retailers. For manufacturers, the observation that package size and price are strategic complements means that downsizing can be expected to lead to lower competitor prices, more intense price competition, and lower margins. For retailers, lower wholesale prices, if passed through to consumers, may lead to more aggressive price competition and lower margins downstream as well. On a practical level, retailers that have adopted rigorous pricing algorithms will have to reoptimize pricing and promotion schedules following a downsizing. Further, if more intense rivalry among manufacturers results in lower profits, then they will be less likely to fund trade promotions or other allowances – off-invoice items that traditionally form a substantial part of total retail profits. The remainder of this paper is organized as follows. In the second section, we provide a brief review of the relevant literature on package size choices, packaging costs, and the strategic nature of package-size decisions. In the third section, we describe a structural econometric model designed to test our hypotheses regarding the strategic role of package sizes in consumer-good pricing, and how the model is estimated. In the fourth section, we describe the data, and present some stylized facts drawn from our sample that motivates this study. In the fifth section, we present the estimation and simulation results and discuss how package size affects consumer demand, production costs, and competition in the market and the equilibrium relationship between package size and price. We draw conclusions, explain some fundamental implications for firms and regulators in the CPGs industry, and describe potential extensions in the final section.

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2. Background on Package Size Research Both package size and price have a direct impact on manufacturers’ profitability, but consumers perceive them differently. Package prices are relatively clear and transparent, whereas changes in package size are rarely announced, and often hidden. As a result, consumers are less sensitive to change in package size than in price, which implies that package downsizing can serve as a more effective means of increasing profit than a change in shelf-price (C ¸ akır and Balagtas 2014). Further, package downsizing makes the direct comparison of unit price particularly difficult, which may lead to rise in profits (Ellison and Ellison 2009). However, changes in package size are likely to involve costly changes in production and distribution systems. More importantly, competitors are likely to be more aware of packagesize changes than consumers, and respond by attempting to re-gain lost market share. Therefore, it is critical to consider not only consumer responses to package-size changes, but also cost and competitor reactions. There are two types of cost associated with making packages. One is variable, and the other fixed. For example, the cost of packaging materials increases if manufacturers produce larger packages. Manufacturers also incur some costs that are independent of volume, such as set-up costs, inventory costs, and distribution costs. Manufacturers may be able to increase unit prices by selling in smaller packages, but it is possible that the costs of producing a new package outweigh the higher price. In this study, we explicitly account for both types of packaging cost in estimating the effect of changing package size on profitability. Packaging costs are clearly important in explaining packagesize decisions. In an equilibrium framework, Koenigsberg, Kohli, and Montoya (2010) consider the costs of producing a particular package size, as well as the consumption rate, consumption utility, and marginal value of consumption. They show that the equilibrium package size depends on the curvature of the cost function in package size, as well as the effect of package size on demand. However, they do not take into account product differentiation, or competition among firms. Package size is an often-overlooked attribute in models of differentiated-product demand. In fact, consumers may differ in their package-size preferences for (at least) three reasons. First, consumers with different consumption rates tend to choose different package sizes (Gerstner and Hess 1987). Second, consumers are generally risk-averse (Erdem, Imai, and Keane 2003; Erdem and Keane 1996; Kahneman and Tversky 1979; Meyer and Sathi 1985; Roberts and Urban 1988). When consumers purchase an unfamiliar product, they face the risk that it does not meet their prior expectations, so tend to choose a smaller package because doing so can minimize their exposure to uncertainty of buying a large amount of a product they don’t like (Shoemaker and Shoaf 1975). Third, smaller packages are often regarded as more convenient as they allow consumers to match their purchase and consumption rates (Koenigsberg, Kohli, and Montoya 2010). By using smaller packages, consumers can flexibility accommodate any preference for variety or deviation from planned consumption that may arise after purchase. Package

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size is therefore a critical decision variable for packaged-good manufacturers. Despite this observation, researchers tend to ignore the importance of package size decisions. Allenby et al. (2004) develop a model of package-choice, but assume price is exogenously given so they do not address firm pricing behavior. On the other hand, Khan and Jain (2005), Cohen (2008), and Gu and Yang (2010) endogenize retailer, manufacturer, or retailer and manufacturer behaviors and investigate pricing strategies for different package sizes. They find that firms use package size as a price discrimination tool, and can earn super-normal profits by charging higher unit prices for smaller packages. But, these authors focus on pricing different, exogenously given package sizes so are silent on how manufacturers determine package sizes as strategic variables. We develop a structural model of consumer demand, retailer pricing decisions, and manufacturers’ joint decisions regarding package size and price to address this gap in the literature.

3. Model 3.1. Overview In this section, we describe a structural model of consumer, retailer, and manufacturer behavior. On the demand side, we employ a random utility model of consumer choice among differentiated products (Berry 1994; Berry, Levinsohn, and Pakes 1995; Nevo 2001). On the supply side, we assume that manufacturers set package sizes and wholesale prices, and retailers set retail prices taking into account consumer demand and manufacturer and retailer costs. We model the vertical relationship between manufacturers and retailers using a three-stage game: In the first stage, manufacturers propose a contract to retailers that specifies the wholesale price of each product for each package. In the second stage, retailers set retail prices conditional on retailers’ acceptance of that contract. Consumer demand is realized in the third stage. We estimate this three-stage game using backward induction. Namely, we first estimate consumer demand, and then estimate the retailer profit maximization problem, and the manufacturer package-size and pricing decisions conditional on consumer, retailer, and competitor behaviors. We discuss each stage of the model in the following subsections.

3.2. Demand-Side Model In this subsection, we describe a model of consumer demand that is appropriate for studying preferences at the SKU-level. We follow the recent structural modeling literature and use a random utility model in which consumers are assumed to make a discrete choice among differentiated products. Products are differentiated by SKU, or a specific brand, flavor, and size. Different package sizes under the same brand are treated as different products because: (1) consumers may vary in the amount of convenience they derive from each package size, and (2) manufacturers and retailers use different pricing strategies for

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different package sizes.1 Consumers make hierarchical purchase decisions, first deciding whether to purchase a product from a retailer in our data, or another retailer, and then deciding on a specific product, conditional on retailer choice. Consequently, we employ a generalized extreme value (GEV) model of consumer demand (McFadden 1978). Formally, the utility from household h purchasing product i ∈ I (under brand name b ∈ B) from retailer j ∈ J at time t is represented by:

polynomial form. That is, to arrive at a closed form formula for f(qit ), we approximate it by a second-order Taylor series expansion (TSE) to obtain:

uhijt = αhb + βht pijt + f (qit ) + ψdijt + ω(pijt × dijt )

where γ 1h (= f (0)) and γ 2 (= f  (0)/2) are parameters to be estimated.3 In weekly, store-level data, γ 1h and γ 2 capture variation in household consumption rates.4 Specifically, if consumers have a low consumption rate, they are likely to choose a small pack, and γ 1h and γ 2 tend to be small. If consumers have a high consumption rate, they choose a large pack, and γ 1h and γ 2 tend to be large. However, household-level variation in consumption rates is less likely to lead to a non-linear relationship between package size and discrete purchase decisions than other factors. Namely, the desire to minimize risk or to maximize convenience are more likely to generate non-linearities. One reason why consumers prefer a small pack is because it allows consumers to minimize the loss in utility associated with the risk of purchasing a product they may find unsatisfactory in subsequent usage occasions (Shoemaker and Shoaf 1975). Considerations of risk are well-understood to have non-linear effects on utility (Kahneman and Tversky 1979). Smaller packages are also more convenient in the sense that they allow consumers to match their purchase and consumption plans (Koenigsberg, Kohli, and Montoya 2010). Convenience, therefore, is defined as the ability to purchase an amount close to intended consumption over the purchase cycle, without accumulating inventory or excessive waste. By choosing a small package, consumers can flexibility accommodate any deviation from planned consumption that may arise after purchase without accumulating inventory, or wasting perishable food (Kahn 1998; Kahneman and Snell 1992; McAlister and Pessemier 1982; Simonson 1990). Packages that are too small increase purchase frequency and raise transactions costs prohibitively, while

+ ξijt + τhijt + (1 − σ)εhijt ,

(1)

where αhb , βht , ψ, ω and σ are parameters to be estimated, pijt is the shelf price, f(·) is the utility derived from purchasing packages of different sizes, qit , dijt is a binary discount variable that takes a value of one if the product’s price is reduced by at least 10 percent from one week to the next and then returned to its previous value in the following week, zero otherwise, pijt × dijt is an interaction term between the price and the discount variable, ξ ijt is an iid error term that reflects product attributes that are relevant, but unobserved to the econometrician, such as brand loyalty, advertising, and display, εhijt is a household-product-, store-, and time-specific iid error term that reflects unobserved consumer heterogeneity, and τ hijt is an error term such that the entire error term, τ hijt + (1 − σ)εhijt is extreme-value distributed (Cardell 1997). The GEV scale parameter σ is bounded between zero and one and measures the correlation among retailers. As σ approaches one, the correlation of utility among retailers goes to one and retailers are regarded as perfect substitutes. As σ approaches zero, on the other hand, the correlation among retailers goes to zero. Package size may have a significant impact on utility. Because consumers choose a particular package size depending on their consumption rate, perception of risk (Shoemaker and Shoaf 1975) and convenience (Koenigsberg, Kohli, and Montoya 2010), we explicitly account for the utility of purchasing a particular package size by including f(qit ). Allowing utility to vary with package size is well established in the empirical marketing and industrial organization literatures (Allenby et al. 2004; C ¸ akır and Balagtas 2014; Cohen 2008; Gu and Yang 2010; Khan and Jain 2005).2 Because the precise way in which package size enters utility is unknown, we approximate it using a general

1 Using a discrete choice model implicitly assumes consumers purchase a single box both before and after any downsizing event. We test this assumption by comparing the number of boxes sold before and after General Mills reduced the size of many packages in week 13. We find that the number of boxes purchased did not change (p = 0.409), and confirm this result using Kelloggs and Post downsizings. Further, Wansink (1996) finds that package size and consumption volume are positively correlated as consumers perceive larger packages to contain less expensive products. 2 Erdem, Imai, and Keane (2003), Sun (2005), Hendel and Nevo (2006), and Osborne (2011) assume forward-looking consumers and examine their dynamic choice of purchase quantity or package sizes depending on the knowledge of product quality and retailers’ temporary price discounts. But, those demand models are empirically intractable in a structural model of demand and supply such ours. Given that our focus is firms’ joint decision of package size and price

f  (0) 2 (2) qit . 2 We assume contribution to utility is zero if quantity is zero, so f(0) = 0 and Eq. (2) is then written as:

f (qit ) = f (0) + f  (0)qit +

f (qit ) = γ1h qit + γ2 qit2 ,

(3)

in the supply side, we use a static model as in Allenby et al. (2004), Khan and ¸ akır and Balagtas (2014). Jain (2005), Cohen (2008), Gu and Yang (2010), and C 3 Draganska and Jain (2005) use a similar approach to derive the functional form of the relationship between utility and product-line length. In each case, there is no theoretical prior, so approximating a general polynomial form is a reasonable way to proceed. 4 Total purchase quantity over a period of time is a product of three variables: purchase frequency, the number of units purchased, and the quantity per unit. In store-level data, we do not observe purchase frequency, and our discrete choice assumption means that we restrict attention to only purchases of single packages. Logically, therefore, variation in consumption rate must be captured by variation in package size. If we had access to household-level data for this project (which is less relevant for estimating market-level rivalry), we could directly measure consumption rate and variation in household inventory. However, in store-level data the implicit assumption is always that households do not intend to accumulate inventory without bound, or draw it down to zero over the sample period. Based on the assumption of stable inventories, therefore, package size should be highly correlated with consumption rate.

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packages that are too large are difficult to store, and increase the likelihood of spoilage. Therefore, it is reasonable to expect that γ 1h ≥ 0 and γ 2 ≤ 0.5 Although the GEV model captures different degrees of substitution among products across groups, it still suffers from the independent of irrelevant alternatives (IIA) property within each group, which generates an unrealistic substitution pattern. To overcome this problem, we allow the brand-specific intercept, the marginal utility of income, and the marginal utility of package size to vary across households in a random way (Berry, Levinsohn, and Pakes 1995; Nevo 2001). This assumption also captures unobserved heterogeneity in brand preference, price responsiveness, and preference for different package sizes. Formally, the brand-specific intercept is assumed to be normally distributed across households, so that: αhb = α0b + σα ιbh ,

ιbh ∼N(0, 1),

(4)

where α0b , α1b and σ α are parameters to be estimated, and ιbh is a household-specific random component capturing brand preference. Similarly, the marginal utility of income is assumed to be normally distributed across households, so that: βht = β0 +

K 

βk ykt + σβ κh ,

κh ∼N(0, 1),

(5)

k=1

where βk ’s and σ β are parameters to be estimated, ykt ’s are mean household demographic attributes at time t, and κh is a term capturing household-specific random variation in price response. Finally, we assume the marginal utility of package size differs across households, so that: γ1h = γ0 + σγ λh ,

λh ∼N(0, 1),

(6)

where γ 0 and σ γ are parameters to be estimated and λh is a household-specific term that captures random variation in package size. In this specification, γ 1h tends to be large if a consumer is risk-loving, or has a high consumption rate, preferring large to small packages. Eqs. (4)–(6) capture unobserved consumer heterogeneity, which is typically important in explaining consumers’ choices among differentiated products. Further, by allowing for random coefficients, the elasticities are the function of the attributes of all the choices rather than the one in question and the one changed, which generates a more realistic substitution pattern. The utility associated with the outside option is specified as follows: uh00t = εh00t .

(7)

When a household chooses the outside option, it implies that they do not purchase any of the products i ∈ I sold at retailer j ∈ J. With an outside good, households are allowed to substitute 5

Our approximation of f(qit ) allows a consumer to respond to each packagesize change differently. For example, if package size has a concave effect on utility, and the package size of a given product is less than consumer’s optimal size, he or she responds negatively to a package downsizing. If the package size is above the optimal size, on the other hand, he or she responds positively.

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to other goods, while in the absence of an outside good, a simultaneous change in the price of all products leads to no change in aggregate consumption. Following Berry, Levinsohn, and Pakes (1995) and Nevo (2001), we decompose Eq. (1) into the mean part that varies over products and stores, but not households, and the idiosyncratic part that varies over products, stores and households, or: uhijt = δijt (xb , ykt , pijt , qit , dijt , ξijt ; α, β, γ) + φhijt (ιh , κh , λh ; σ) + εhijt ,

(8)

where δijt (·) is the mean part and φhijt (·) is the idiosyncratic part. We define the density of ιh , κh and λh as g1 (ι), g2 (κ) and g3 (λ) respectively. By integrating over the distributions of g1 (ι), g2 (κ) and g3 (λ), we derive the probability that consumer h purchases product i offered by retailer j at time t as:  exp(δijt +φhijt )/(1−σ)   g1 (ι)g2 (κ)g3 (λ) dι dκ dλ, shijt = 1−σ DJσ j ∈ J DJ (9)  where DJ = i ∈ I exp(δijt + φhijt )/(1 − σ). In Eq. (1), ξ ijt are unobservable to the econometrician, but known to consumers, retailers, and manufacturers. The retail prices and package sizes determined by the interactions among them are potentially correlated with unobserved demand shocks, which yield biased estimates. To address this issue, we estimate Eq. (9) via simulated maximum likelihood (SML) method combined with the control function approach (Park and Gupta 2009; Petrin and Train 2010; Train 2009). The detailed estimation method is described in the Estimation and Identification section below. 3.3. Supply-Side Model Pricing and package-size decisions by manufacturers depend critically on consumer response, and cost considerations. In modeling supply decisions, manufacturers set package sizes and wholesale prices taking into account the structure of their own costs, and retailer responses, while retailers pass-through manufacturers’ package size decisions and set prices to consumers taking into account their costs and the nature of consumer demand.6 Manufacturers are assumed to compete horizontally among themselves in both package sizes and wholesale prices.7

6 In our supply model, retailers are not allowed to decide which sizes to carry. This approach is justified because our primary interest is manufacturers’ joint decision regarding package size and price. 7 A reviewer suggests that a dynamic model would be more appropriate than the static one used here. Besides the fixed costs of changing packages, there are few other reasons to suspect that dynamics would be an overriding concern in the cereal market. Cereals are not durable assets, purchasing a box of cereal is not a substantial investment for most households, and cereal is of too low volume-to-value to represent an item that would subject to long-term storage. With our focus on interaction among multiple-dimensions, the dynamic model we would have to write down would be exceedingly complicated, but would likely arrive at the same conclusions that we do here.

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Others find that consumers base their store selection decisions not only on prices charged for a single product category, but also on their basket price and store’s non-price attributes such as store location, service quality, and product variety (Arnold, Oum, and Tigert 1983; Bawa and Ghosh 1999; Bell, Ho, and Tang 1998; Bell and Lattin 1998; Briesch, Chintagunta, and Fox 2009). Therefore, in our model, we assume that retailers behave as local monopolists once consumers have chosen a particular store.8 Manufacturers and retailers interact vertically according to a manufacturer-Stackelberg assumption (Sudhir 2001).9 We solve the model using backward induction by first estimating the second-stage retail pricing decision, and then the first-stage package size and wholesale price equations. In the remainder of this section, we derive the subgame perfect Nash equilibrium in package sizes and prices to this channel game. To simplify notation, we drop time subscript t in the subsequent discussion. Consider first the pricing decision facing retailer j . Following Slade (1995), Besanko, Gupta, and Jain (1998) and Sudhir (2001), we assume that retailers behave as local monopolists once consumers have chosen a particular store. That is, retailer j carrying I products chooses the optimal retail prices pi that maximize its category profit. Accordingly, the profit maximization problem for retailer j is written as: πj = maxQ pi

I 

(pi − ri )si − Fj ,

∀j,

(10)

r

Qr i =

+ ν1r wi

I

+

L 

νlr zrli ,

(11)

l=2

where νlr ’s are parameters to be estimated, wi is the wholesale price for product i paid by retailer j, zrli ’s are other retailing input prices for selling product i.10 Because retailer j passes-through manufacturers’ package size decisions and chooses retail price pi to maximize its category profit, retailer j’s first order condition for product i is obtained by differentiating Eq. (10) with respect to pi , so that:

8 This assumption is well-supported by empirical evidence (Besanko, Gupta, and Jain 1998; Slade 1995; Sudhir 2001). 9 Assuming manufacturers are able to set prices and package sizes first is wellsupported by the empirical literature on vertical supply relationships (Besanko, Dubé and Gupta 2003; Draganska and Klapper 2007; Villas-Boas and Zhao 2005; Villas-Boas 2007). 10 The normalized quadratic unit cost function for product i is C = μT z + i 1 μ2 yi + (1/2)(zT μ3 z + zT μ4 yi ) where yi is the output of product i and z is the vector of normalized input prices. So, the marginal cost for product i, ∂Ci /∂yi is written by the linear combination of normalized prices, which supports our linear specification of marginal costs.

∀i, j.

(12)

i=1

Eq. (12) is then solved for retailer j’s margin, which gives, in matrix notation: p − r = −()−1 s,

(13)

where p = (p1 , . . ., pI )T , r = (r1 , . . ., rI )T , s = (s1 , . . ., sI )T and  is an I × I matrix of share derivatives with respect to all retail prices where the (i, j) element is given by ∂sj /∂pi . Eq. (13) indicates that retail margins are inverse functions of the share derivatives with respect to retail prices weighted by market  share. Manufacturer m offers products Im (i.e., M m=1 Im = I) and is assumed to compete in package sizes and wholesale prices in Bertrand–Nash fashion. Following Koenigsberg, Kohli, and Montoya (2010), we assume that manufacturers make simultaneous decisions regarding package size and price. Setting package prices and sizes together is both reasonable and descriptive of business practice as manufacturers target a specific price per unit of measure for each SKU – a policy that is only possible if prices and package sizes are determined together. Consequently, the profit maximization problem facing manufacturer m is written as: π = maxQ m

wi ,qi

i=1

where Q is the size of the total market, si is the market share of product i, ri is the retailing marginal costs for product i, and Fj is the fixed cost for retailer j. We assume the retailing costs are captured by a normalized quadratic unit cost function (Diewert and Wales 1987), so the marginal cost is given by the following linear combination of retailing input prices: ν0r

 ∂πj ∂si = si + (pi − ri ) = 0, ∂pi ∂pi

Im 

(wi − ci )si − Fm −

i=1

Im 

h(qi ),

(14)

i=1

where ci is the marginal cost of product i, Fm is the fixed cost of manufacturer m, and h(qi ) is the per-period fixed cost of making a package of size qi , such as set-up costs, inventory costs, distribution costs and marketing costs. In this equation, the per-period fixed cost associated with each package is assumed to be separable between ci and Fm , and independent of production volume, but is nonetheless a weekly decision variable.11 Marginal production costs may vary with package size, but these costs are not separately identified from the costs associated with varying package sizes over time. We capture any variation in production costs associated with package size by including item-specific fixed effects in the cost equation. While it would seem reasonable to expect marginal production costs vary with package size, but the content of a box of cereal represents a very small proportion of its cost (Hannah 2014) so the cost associated with periodically changing the size of the package is more important to manufacturers. As in the retailers’ profit maximization problem, we assume the marginal cost for product i is arisen from a normalized quadratic unit cost function (Diewert and Wales 1987). So, the marginal cost for product i is written as: m

Qci =

ν0m

+

L 

νlm zm li ,

(15)

l=1

11

The function h(qi ) is assumed to capture only the cost of changing package sizes, which includes re-configuring production lines, adjusting templates, and other costs that are likely to be convex in the magnitude of the change.

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where νlm ’s are parameters to be estimated, zm li ’s are input prices for selling product i. Again, the exact form of packaging costs is not known, a priori, but they can be approximated by a TSE. Applying a TSE to an arbitrary function of package size implies: h(qi ) = h(0) + h (0)qi +

h (0) 2 q , 2 i

(16)

or h(qi ) = θ0 + θ1 qi + θ2 qi2 ,

(17)

where θ 0 (= h(0)), θ 1 (= h (0)), and θ 2 (= h (0)/2) are parameters to be estimated. The fixed cost associated with producing and distributing packages may be either increasing or decreasing as packages that are too small or too large may require special packaging technology, excessive costs associated with setting up the production line, or special handling in the distribution system and shelf display. Consequently, we expect that the fixed packaging cost function is convex, or θ 2 > 0. With this objective function, we then consider manufacturer m’s pricing problem. Differentiating Eq. (14) with respect to wi , manufacturer m’s first order condition for product i is written as:   Im I   ∂si ∂pl (wi − ci ) si + (18) = 0, ∀i. ∂pl ∂wk k=1

l=1

In Eq. (18), wi − ci represents manufacturer margin for product i and (∂si /∂pl ) (∂pl /∂wk ) represents the change in the market share of product i in response to the change in the wholesale price of product k. The change in wholesale price affects all retail prices, which in turn influences the market share of the product in question. Notice that Eq. (18) includes the retail–wholesale passthrough term, ∂pl /∂wk that is not observable in the data set.12 Following Sudhir (2001), Villas-Boas and Zhao (2005) and Villas-Boas (2007), we recover the retail–wholesale passthrough term by totally differentiating Eq. (12) to yield (in matrix notation):  = G−1 ,

(19)

where  is an I × I matrix with (i, j) element given by ∂pi /∂wj and G is an I × I matrix with (i, j) element given by:   I  ∂sk2 ∂sj ∂si + gij = + (pk − rk ) , ∀i, j. (20) ∂pj ∂pi ∂pj ∂pi k=1

In Eq. (20), ∂si /∂pj represents the change in the market share of product i in response to the change in the retail price of product j, pk − rk is the retail margin of product k, and ∂sk2 /∂pi ∂pj is the change in ∂sk /∂pi in response to the change in the retail price 12 We assume that a retailer does not know the terms of the contract between manufacturers and other retailers. This implies that ∂pl /∂wk = 0 if pl is the retail price in one retailer and wk is the wholesale price offered to other retailers. The derivatives are not necessarily equal to zero if pl is the retail price in one retailer and wk is the wholesale price offered to the same retailer. We describe how this is revealed in the subsequent discussion.

7

of product j. As shown in Eq. (19), the retail–wholesale passthrough matrix,  is obtained by the product of the inverse of the matrix, G and the matrix of share derivatives with respect to all retail prices. Eq. (18) is then solved for manufacturer m’s margin using the matrix  to find (in matrix notation): −1

w − c = −((G−1 ) ∗ IN )

(21)

s,

where IN is an I × I identity matrix and * is an elementby-element multiplication. Eq. (21) implies that manufacturer margins depend on the inverse functions of the share derivatives with respect to wholesale prices weighted by market share. As discussed above, the share derivatives with respect to wholesale prices are the function of the G matrix and the share derivatives with respect to all retail prices. Retailers and manufacturers are assumed to know the structure of the game and set retail prices and wholesale prices according to Eqs. (13) and (21), respectively. As Villas-Boas and Zhao (2005) and Draganska and Klapper (2007) note, however, it is possible that the actual outcome of this game differs from theoretical predictions due to asymmetric market information, regulations, and supply constraints. Accordingly, we allow for deviations from either profit-maximizing retail prices, or Bertrand–Nash wholesale prices by using “conduct parameters.” Specifically, Eqs. (13) and (21) are written as: −1 1 p−r =− s  ρ

(22)

and −1

w − c = −ϕ((G−1 ) ∗ IN )

(23)

s,

where ρ and ϕ are conduct parameters to be estimated. In this context, conduct parameters capture the extent of deviation from the maintained solution concept for the retail and manufacturer games, respectively. If ρ = ϕ = 0, then both retailers and manufactures set prices competitively. If ρ = ϕ = 1, then retailers set prices as perfect local monopolists, and manufacturers as perfect Bertrand–Nash competitors. In each case, ρ > 1 and ϕ > 1 imply retailers and manufactures exercise greater market power.13 The latter case is likely to happen if retailers or manufacturers compete in non-price attributes such as service quality, advertisement, and product assortment, and set price collusively. Finally, we consider the package-size decisions of manufacturer m. Differentiating Eq. (14) with respect to qi , manufacturer m’s first order condition for product i is given by: Q

Im  k=1

(wk − ck )

∂sk − θ1 − 2θ2 qi = 0, ∂qi

∀i.

(24)

13 Corts (1999) points out the conduct parameters are biased because the estimation based on the static conjectural variations approach cannot be independent of any dynamic oligopolistic behaviors. We acknowledge this issue, but note that this method of estimating market power is well-accepted in the quantitative marketing literature, and is a parsimonious way to examine the competitiveness of price and package size decisions.

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In Eq. (24), wk − ck represents manufacturer margin for product k and ∂sk /∂qi represents the change in the market share of product k in response to the change in the package size of product i. Eq. (24) is then solved for manufacturer m’s optimal package size to find: q = η0 + η1 Q(w − c),

(25)

where q = (q1 , . . ., qI )T , η0 (=− θ 1 /2θ 2 ) and η1 (= 1/2θ 2 ) are parameters to be estimated,14  is an I × I matrix of share derivatives with respect to package sizes with (i, j) element given by ∂sj /∂qi . Because (w − c) is the product of the share derivatives with respect to package size and the estimates of manufacturer competitive response to changes in demand conditions expressed in price elasticity terms, η1 measures the effect of competition and package size substitutability on equilibrium package sizes, and can be interpreted as conduct parameter in package size space. In summary, the retailer and manufacturer decisions are characterized by Eqs. (22), (23), and (25), respectively. Our intent is to reveal how manufacturers use package size and price as complementary tools in strategic competition. The interaction between the equilibrium wholesale prices determined by Eq. (23) and the equilibrium package sizes determined by Eq. (25) is our primary concern. Because explicitly including crossresponse parameters between package-size and price makes the model econometrically intractable, we conduct a simulation to determine their joint equilibrium realizations. The simulation, therefore, allows us to examine how manufacturers respond to a change in their competitive environment caused by package downsizing. 3.4. Estimation and Identification The equilibrium model is estimated in two stages. In the first stage, we estimate the demand model (Eq. (9)), and in the second stage, conditional on the demand estimates, the supply model (Eqs. (22), (23), and (25)) is estimated. While fully simultaneous estimation may be more efficient, our two-stage approach provides consistent demand estimates regardless of the assumptions made regarding the supply-side model (Yang, Chen, and Allenby 2003). On a practical level, two-stage estimation also renders a highly complex model of consumer, retailer, and manufacturer interactions tractable to estimate. In this subsection, we describe the estimation methods used for both the demand and supply models. Identification of retailer and manufacturer conduct in structural models such as this can never be proven conclusively, but rests on the logic of the identification strategy, and the quality of the estimation results. For the current model, market share and retail price vary across product, retailer, and time, which easily identify price-response parameters (Table 1). Manufacturers offer a variety of package sizes. The average

14

θ 0 is not identified in our econometric model. But, it does not have any impacts on the subsequent discussion.

package size is 16.1 oz and the standard deviation is 3.6 oz, which provides sufficient cross-sectional variation in package size. We also observe several package-downsizing events. Specifically, 15 out of 35 products changed the package size once over the sample period. Although package size changes less often over time, time-series variation in package size is at least conceptually identified, and both time-series and cross-sectional variation in package size is enough to identify the package-sizeresponse parameters. With respect to wholesale prices, others rely on implicitly estimated wholesale price variation (Draganska and Klapper 2007; Villas-Boas and Zhao 2005; Villas-Boas 2007), but our data contains wholesale prices paid by non-selfdistributing retailers (we describe these prices in more detail below). Our wholesale prices vary substantially over time and across products (Table 1), so identifying manufacturer behavior is, at least conceptually, much easier than if we were to impute wholesale prices (Nakamura and Zerom 2010). Moreover, input prices for both retailers and manufacturers are highly volatile over the sample period (Table 3), so variation in input costs enable us to identify key parameters of the demand and supply models. Variation, however, does not solve the problem that retail prices and package sizes on the demand side, and manufacturer and retailer margins on the supply side are likely to be endogenous. Specifically, retail prices are likely to be endogenous in any demand model estimated with store-level retail scanner data. Because unobserved (to the econometrician) factors such as advertisement, in-store promotion, and shelf placement are known to consumers, retailers, and manufacturers, observed prices are likely to be correlated with unobserved demand shocks, which may yield inconsistent estimates. There are two approaches to address this endogeneity issue. One is to use a simulated generalized method of moments (SGMM) approach (Berry, Levinsohn, and Pakes 1995), and the other is the control function approach (Park and Gupta 2009; Petrin and Train 2010). We employ the control function approach, because SGMM tends to be sensitive to sampling error and, as a result, requires to use brand as a fundamental unit of analysis, and the data that consists of multiple markets and multiple stores in each market (Berry, Linton, and Pakes 2004; Park and Gupta 2009). Further, the control function approach has been shown to be useful in contexts similar to ours (Park and Gupta 2009). The control function approach is intended to introduce a proxy variable that accounts for the unobserved factors, ξ ijt affecting retail prices, such that the remaining variation in retail prices, pijt , is independent of the error term, εhijt so standard estimation approaches are then consistent. For illustration purposes, we rewrite Eq. (8) as:

uhijt = V (xb , ykt , pijt , qit , dijt , ιh , κh , λh ; α, β, γ, σ) + ξijt + εhijt .

(26)

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Table 1 Conditional share, retail price, and wholesale price across product and retailer. Manufacturer

General Mills

Kelloggs

Post

Quaker Oats

Product

Honey Nut Cheerios 14/12.25 oz Honey Nut Cheerios 20/17 oz Cheerios 10/8.9 oz Cheerios 15/14 oz Frosted Flakes 14 oz Frosted Flakes 17 oz Rice Krispies 12 oz Rice Krispies 18 oz Froot Loops 15/12.2 oz Froot Loops 19.7/17 oz Frosted Mini-Wheats 18 oz Frosted Mini-Wheats 24 oz Special K Red Berries 12 oz Special K Red Berries 16.7 oz Special K Original 12 oz Special K Original 18 oz Cocoa Krispies 17.5/16.5 oz Apple Jacks 15/12.2 oz Apple Jacks 19.1/17 oz Raisin Bran 20 oz Raisin Bran 25.5 oz Raisin Bran Crunch 18.2 oz Corn Flakes 12 oz Corn Flakes 18 oz Crispix 12 oz Honey Bunches of Oats 16/14.5 oz Honey Bunches of Oats 21/19/18 oz Honey Bunches of Oats Almonds 16/14.5 oz Honey Bunches of Oats Almonds 21/19/18 oz Fruity Pebbles 13/11 oz Cocoa Pebbles 13/11 oz Oatmeal Squares 16 oz Cap’N Crunch Crunch Berries 15 oz Cap’N Crunch 16 oz Cap’N Crunch 22 oz

Retailer 1

Retailer 2

Conditional market share (percent)

Retail price per oz ($)

Wholesale price per oz ($)

Conditional market share (percent)

Retail price per oz ($)

Wholesale price per oz ($)

Mean

Std. dev.

Mean

Std. dev.

Mean

Std. dev.

Mean

Std. dev.

Mean

Std. dev.

Mean

Std. dev.

1.722

1.495

0.253

0.049

0.253

0.023

5.103

5.774

0.274

0.063

0.253

0.023

1.022

0.764

0.254

0.046

0.223

0.011

2.624

2.410

0.276

0.054

0.224

0.011

1.688 1.558

1.945 1.431

0.337 0.250

0.078 0.049

0.298 0.235

0.018 0.015

4.428 4.867

4.970 6.152

0.370 0.248

0.077 0.056

0.299 0.235

0.018 0.015

0.903 0.601 0.930 0.441 0.759

0.771 0.507 0.589 0.269 0.626

0.216 0.226 0.260 0.229 0.235

0.046 0.042 0.053 0.038 0.051

0.222 0.204 0.255 0.211 0.235

0.008 0.007 0.012 0.007 0.031

4.238 3.074 2.473 1.599 2.308

6.068 3.790 2.430 1.490 3.102

0.221 0.216 0.299 0.256 0.269

0.067 0.064 0.079 0.059 0.080

0.222 0.204 0.255 0.211 0.234

0.008 0.007 0.012 0.007 0.030

0.342

0.263

0.224

0.036

0.194

0.020

1.210

1.827

0.240

0.059

0.194

0.020

0.993

0.669

0.181

0.037

0.173

0.007

2.329

1.972

0.191

0.048

0.173

0.007

0.706

0.645

0.172

0.032

0.145

0.005

2.358

1.955

0.164

0.038

0.145

0.005

0.805

0.447

0.280

0.041

0.261

0.008

2.290

2.567

0.301

0.068

0.261

0.008

0.486

0.208

0.269

0.035

0.241

0.003

2.145

1.956

0.273

0.053

0.241

0.003

0.626 0.351

0.309 0.154

0.281 0.253

0.039 0.035

0.262 0.223

0.008 0.003

1.953 1.595

1.732 1.218

0.302 0.253

0.067 0.050

0.262 0.223

0.008 0.003

0.627

0.453

0.186

0.039

0.182

0.011

2.251

2.263

0.203

0.057

0.182

0.011

0.580 0.263 1.135 0.663 0.573

0.465 0.175 0.849 0.618 0.274

0.233 0.225 0.155 0.157 0.218

0.050 0.033 0.034 0.029 0.034

0.237 0.197 0.151 0.129 0.177

0.029 0.018 0.005 0.004 0.004

2.083 1.118 2.617 1.846 1.550

2.876 1.595 3.153 1.990 1.628

0.268 0.245 0.167 0.154 0.197

0.079 0.057 0.042 0.034 0.046

0.236 0.197 0.151 0.129 0.177

0.028 0.018 0.005 0.004 0.004

0.445 0.565 0.539

0.508 0.313 0.253

0.278 0.186 0.282

0.040 0.037 0.055

0.206 0.173 0.252

0.009 0.005 0.009

1.769 1.349 1.302

1.276 1.118 1.356

0.274 0.211 0.319

0.055 0.052 0.072

0.206 0.173 0.252

0.009 0.005 0.009

0.888

0.803

0.210

0.053

0.197

0.024

2.195

1.855

0.213

0.055

0.197

0.025

0.618

0.362

0.207

0.043

0.177

0.023

1.267

0.802

0.220

0.039

0.177

0.023

0.844

0.806

0.208

0.053

0.198

0.024

2.078

1.938

0.212

0.055

0.198

0.024

0.553

0.403

0.204

0.044

0.177

0.022

1.090

0.754

0.219

0.040

0.178

0.022

0.664 0.593

0.680 0.621

0.241 0.239

0.059 0.061

0.226 0.226

0.031 0.031

1.416 1.211

1.570 1.344

0.234 0.234

0.067 0.067

0.226 0.227

0.030 0.031

0.965

0.522

0.219

0.049

0.193

0.028

0.985

1.266

0.279

0.049

0.193

0.028

0.354

0.367

0.236

0.066

0.201

0.030

1.492

2.283

0.256

0.071

0.201

0.030

0.420 0.288

0.441 0.216

0.221 0.198

0.062 0.039

0.189 0.153

0.028 0.019

1.400 0.877

2.274 0.828

0.241 0.195

0.066 0.044

0.189 0.153

0.028 0.019

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Suppose the endogenous price variable, pijt is expressed as a linear combination of n observed instruments, vijtn and an unobservable factor, πijt , so that: pijt =

N 

χn vijtn + πijt ,

(27)

n=1

where χn ’s are parameters to be estimated and εhijt and πijt are independent of pijt , but εhijt and πijt are correlated. The correlation between εhijt and πijt reflects the price endogeneity problem. We decompose εhijt into the mean part conditional on πijt and the deviation part that is independent of πijt : εhijt = E(εhijt |πijt ) + ε˜ hijt . The conditional expectation is a function of πijt , and is called the control function, denoted by CF(πijt ). With the conditional expectation term, or control function, and the deviation part, Eq. (26) is written as: uhijt = V (xb , ykt , pijt , qit , dijt , ιh , κh , λh ; α, β, γ, σ) + ξijt + CF (πijt ) + ε˜ hijt .

(28)

Because ε˜ hijt is independent of pijt , standard simulated maximum likelihood (SML) is applicable. For the control function (CF(πijt )), we use the residuals from Eq. (27) that is πˆ ijt =  pijt − N ˆ n vijtn . n=1 χ Package sizes are also likely to be endogenous in the demand model because they are a decision variable for manufacturers. Factors such as loyalty, advertisement and shelf placement are known to consumers and manufacturers, and may influence package sizes, but unknown to the econometricians, so observed package sizes are likely to correlated with unobserved demand shocks. To address this issue, we again use the control function approach. The control function approach is a two-step process. In the first step, the endogenous price and package-size variables are regressed on exogenous instruments, each of which generates vector of residuals. In the second step, the demand model is estimated using the residual vectors as explanatory variables. Because the IV residuals account for unobservable factors in prices and package sizes that may be correlated with errors in the demand equation, this method controls for the potential implied bias, and provides consistent demand estimates. We then use SML to estimate the full model, including the control functions (Petrin and Train 2010; Train 2009). SML uses random draws from the distributions that reflect consumer heterogeneity so, to aid in the computational speed and efficiency of estimation, we use 100 Halton draws (Bhat 2003). Instruments for retail prices must be correlated with the observed price series, but independent of any unobservable factors. As suggested by Villas-Boas (2007) and Draganska and Klapper (2007), the set of instrumental variables includes a variety of cost, brand, and dynamic variables. First, manufacturer and retail level input prices such as grain prices, sugar prices, wholesale prices, gas prices, diesel prices, and wages are used because input prices are likely to be correlated with retail prices, but not the unobservable demand factors. Second, brand specific intercepts account for unobservable supply factors that influence retail prices. Third, lagged share values are likely

to be correlated with current-period prices, but only weakly correlated with current-period demand shocks (Villas-Boas and Winer 1999). In order to instrument for package sizes, we apply the same logic, and use grain prices, sugar prices, wholesale prices, lagged share values, product specific intercepts, wages in the food manufacturing industry, gas prices and diesel prices as instruments. The grain prices, sugar prices, wholesale prices and lagged share values capture variation in the variable costs of making packages, while product specific intercepts, wages in the food manufacturing industry, gas prices and diesel prices account for the variation in the per-period fixed costs. None of these variables is likely to be correlated with the unobservable demand shocks. From the first-stage instrumental-variables regressions, the set of instruments explains 36.3 percent of the total variation in the endogenous retail price and 98.5 percent of the endogenous package size. The F statistics are 186 for the first-stage endogenous price regression, and 17,524 for the first-stage endogenous package-size regression, which implies that the instruments are not weak (Staiger and Stock 1997). Instruments for the supply model are also necessary because retailer and manufacturer margins in the price and package-size equations are likely to be endogenous. Factors such as supply contracts, supply constraints, and retailer marketing strategies are known to retailers and manufacturers, and so influence margins at both levels, but are unobservable to the econometrician. The control function approach is used again, as in the demand model. In order to exploit the gains in estimation efficiency from contemporaneous correlation among the supply-side equations, seemingly unrelated regressions (SUR) is used to estimate the supply-side model, with the control function included. In the supply model, the instruments must be correlated with margins, but not correlated with the unobservable factors in the price and package-size equations. On an intuitive level, supply instruments are variables that shift the demand curve and, hence, identify equilibrium points on the supply curve. We use the set of instruments well-accepted in the literature (Draganska and Klapper 2007; Villas-Boas 2007) for this purpose. For the manufacturer margin, demographic variables such as household income and educational attainment are used to capture variation in demand. Second, retailer fixed-effects capture variation in retailer-specific costs that are likely to influence the derived-demand for breakfast cereals. Third, lagged wholesale prices are used because they are likely to be correlated with current margins, but not with the unobservable factors. Fourth, manufacturer-specific binary variables capture idiosyncratic supply factors that are unobservable to the econometrician, but are known to retailers and manufacturers. Finally, binary variables accounting for seasonal effects are included to account for temporal variation that may be important in determining manufacturers’ margins. For the retailer margin, demographic variables, lagged margins, and store- and product-specific binary variables are used, following the same general logic as with the manufacturermargin equation. This set of instruments explains 1.4 percent of the total variation in the endogenous manufacturer margin,

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and 92.7 percent of the retailer margin. The F statistics are 15 for the first-stage IV regression for the manufacturer margin, and 3,395 for the retailer margin, respectively. Because each of these F statistics is greater than 10, we again conclude that the instruments are not weak in the sense of Staiger and Stock (1997). 4. Data Description We estimate the empirical model using supermarket chainlevel retail scanner data (IRI Infoscan) from the ready-to-eat breakfast cereal category for a major US metropolitan market.15 The data set includes 156 weeks (April 2007–March 2010) of supermarket chain-level unit and dollar sales of ready-to-eat breakfast cereal products in UPC level, sold in two major supermarket chains: retailer 1 and retailer 2. Each product-alternative is defined as an SKU. For tractability, we focus on 35 major SKUs, subject to the restriction that each product is sold in both stores. All other SKUs are assumed to be in the outside option. The outside option is defined as the difference between total market sales and the sales captured by the data, where the total market is defined as the population of the given market multiplied by per capita consumption. Per capita consumption is calculated by assuming each consumer in the market has an average serving-size per day as in Nevo (2001). Defining the outside option this way means that the model captures not only the IRI-products excluded from the analysis, but also those sold in stores that do not provide their sales data to IRI. The breakfast cereal category represents an ideal case-study of package size and pricing strategy. First, breakfast cereals are frequently purchased and consumed by a wide variety of consumers, so the distribution of preferences helps to identify the demand parameters. Second, there are two major manufacturers, General Mills and Kelloggs, which are well-understood to compete strategically using multiple tools – an observation that also helps identify competitive interactions at the manufacturer level. Finally, manufacturers offer a variety of package sizes and often change the size of their packages relative to manufacturers who sell products in cans or bottles, and cross-sectional and time-series variation in package size is necessary to identify the core parameters of interest. The manufacturer pricing data is provided by Promodata, Inc., and includes the price charged by manufacturers before allowances are applied, markups charged by wholesalers to retailers, the effective date of new case prices, “deal allowances,” or off-invoice items offered to retailers by the wholesaler, the type of promotion suggested by the wholesaler to the retailer, and the allowance date. For the analysis, we define the wholesale price as the price charged to the retailer net of any allowances. One limitation of this data set is that it captures prices charged by wholesalers to non-self-distributing retailers. While some

15 Chain-level data are preferred to store-level data, because retailers typically use chain-wide (or at least regional) pricing strategies (Bolton, Shankar, and Montoya 2006) and manufacturers sell products to retail chains, not individual stores.

Fig. 1. Conditional share, retail price, and wholesale price before and after the change in Honey Nut Cheerios 14/12.25-oz box.

retailers do indeed self-distribute, we assume that the wholesale price is likely to be highly correlated with that charged to selfdistributing retailers. There are two reasons why this is a valid assumption. First, the Robinson–Patman Act requires any deals offered in a market to be offered to all (Richards and Hamilton 2015). Second, manufacturers typically do not want to build illwill among their retail customers by offering deals that differ sharply between competitors. At the very least, compared with existing methods of imputing wholesale prices (Villas-Boas and Zhao 2005; Villas-Boas 2007), the resulting error is likely to be minimal. Variation in wholesale prices, market shares, and retail prices is critical to identify the parameters of interest in the empirical model. Table 1 shows the conditional market share defined by the percentage of boxes sold, retail price per ounce, and wholesale price per ounce of the 35 products in each retailer. Taken together, the 35 focal-products in our data account for 15 percent of the total market sales. The data in Table 1 reveals that the market shares vary across package size and retailer, and that manufacturers set different prices for different package sizes even within the same product line. The data also show that retailers and manufacturers generally charge higher unit prices for smaller packages, which is consistent with the finding by Gerstner and Hess (1987). The data summary also reveals that fully 15 out of 35 products changed package size once during the sample period,16 so covariations in package size and price are at least conceptually identified in the data. In fact, the discrete nature of package-size changes helps make this case more clearly. Table 2 compares the conditional market share, retail price, and wholesale price before and after changes in package size. Overall, most retail prices and wholesale prices rise when manufacturers downsize packages. We present a typical example in Fig. 1. In this figure, the dashed lines represent the actual values of the conditional market shares, retail prices and wholesale prices of Honey Nut Cheerios 14/12.25-oz box, while the solid lines show these time trends before and after the changes in package size. This figure shows that the retail price increased when General Mills reduced the

16

Honey Bunches of Oats changed its package size twice.

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Table 2 Conditional share, retail price, and wholesale price before and after changes in package size. Manufacturer

General Mills

Product

Honey Nut Cheerios 14/12.25 oz

Honey Nut Cheerios 20/17 oz

Cheerios 10/8.9 oz

Cheerios 15/14 oz

Kelloggs

Froot Loops 15/12.2 oz

Froot Loops 19.7/17 oz

Cocoa Krispies 17.5/16.5 oz

Apple Jacks 15/12.2 oz

Apple Jacks 19.1/17 oz

Post

Honey Bunches of Oats 16/14.5 oz

Honey Bunches of Oats 21/19/18 oz

Honey Bunches of Oats Almonds 16/14.5 oz

Honey Bunches of Oats Almonds 21/19/18 oz

Fruity Pebbles 13/11 oz

Cocoa Pebbles 13/11 oz

Variable

Retailer 1

Retailer 2

Before

After

Before

After

Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($)

1.137 0.277 0.219 0.884 0.240 0.194 3.197 0.289 0.273 1.642 0.237 0.220

1.771 0.252 0.256 1.034 0.256 0.226 1.551 0.341 0.301 1.551 0.252 0.236

4.175 0.250 0.219 2.164 0.251 0.194 3.910 0.351 0.273 2.878 0.250 0.220

5.181 0.276 0.256 2.662 0.278 0.226 4.471 0.372 0.301 5.003 0.248 0.236

Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($)

0.595 0.224 0.198 0.384 0.211 0.171 0.589 0.192 0.171 0.514 0.219 0.203 0.301 0.217 0.177

0.867 0.243 0.258 0.314 0.233 0.209 0.652 0.182 0.189 0.624 0.242 0.259 0.238 0.230 0.210

2.106 0.226 0.198 1.226 0.207 0.171 2.678 0.186 0.171 1.895 0.229 0.202 1.094 0.221 0.177

2.434 0.295 0.257 1.199 0.261 0.209 1.968 0.214 0.189 2.205 0.292 0.258 1.133 0.261 0.210

Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($) Conditional market share (percent) Retail price per oz ($) Wholesale price per oz ($)

0.749 0.203 0.170 0.633 0.204 0.168 0.691 0.202 0.170 0.572 0.203 0.170 0.647 0.245 0.215 0.567 0.244 0.215

0.924 0.212 0.204 0.584 0.212 0.196 0.882 0.209 0.205 0.506 0.206 0.196 0.728 0.228 0.266 0.685 0.225 0.266

1.948 0.204 0.170 1.181 0.231 0.167 1.912 0.200 0.170 1.006 0.231 0.169 1.333 0.247 0.213 1.150 0.247 0.213

2.258 0.216 0.204 1.446 0.197 0.197 2.120 0.215 0.205 1.268 0.194 0.196 1.647 0.199 0.259 1.382 0.201 0.263

package size from 14 oz to 12.25 oz in week 13. Retailers clearly do not intend to hold unit prices constant after the change in package size. Further, General Mills raised the wholesale price at the same time. This simple comparison shows that manufacturers apparently use changes in package size to, effectively, raise wholesale prices. Despite higher retail prices, more consumers choose the smaller-sized product, perhaps because the new size is closer to their consumption rate than the next-smallest size. If this example holds more generally, however, then it begs the question as to why manufacturers do not downsize more often. Figs. 2 and 3 provide other examples, describing the effects associated with downsizing Froot Loops 15/12.2-oz box and

Honey Bunches of Oats with Almonds 16/14.5-oz box, respectively. These figures provide further evidence that manufacturers tend to raise the wholesale price following a package-size reduction. But, these figures beg the question of why, if package downsizing is an effective marketing strategy, why it doesn’t occur more often? Figs. 4 and 5 provide part of the answer as the wholesale prices of General Mills’ brands tend to rise in response to downsizing by Kellogss. Kelloggs reduced the package size of Froot Loops from 15 oz to 12.2 oz in week 61, while Post reduced Honey Bunches of Oats with Almonds from 16 oz to 14.5 oz in week 30. In response to the former change, General Mills

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Table 3 Input costs.

Fig. 2. Wholesale price and package size of Froot Loops 15/12.2-oz box.

Fig. 3. Wholesale price and package size of Honey Bunches of Oats with Almonds 16/14.5-oz box.

Fig. 4. Reactions of General Mills’ wholesale prices to package downsizing of Froot Loops 15-oz box.

Variable

Mean

Std. dev.

Gas price for retailers Gas price for manufacturers Diesel price for retailers and manufacturers Grain price for manufacturers Sugar price for manufacturers Wage in the food manufacturing industry Wage in the retail industry

103.506 96.981 107.387

27.090 23.948 24.701

123.944 136.903 103.516

25.156 32.775 3.135

104.210

3.425

Note: Grain price is the weighted average of main grain prices. Week 1’s value of the input costs is normalized to 100 in each series.

reduced the price of Honey Nut Cheerios 14/12.25-oz box from $0.259 to $0.153, Cheerios 10/8.9-oz box from $0.304 to $0.281 and Cheerios 15/14-oz box from $0.240 to $0.225 (Fig. 4). In response to the latter change, General Mills reduced the price of Honey Nut Cheerios 14/12.25-oz box from $0.216 to $0.160 and Cheerios 15/14-oz box from $0.240 to $0.225 (Fig. 5). Although not definitive, these figures suggest that manufacturers may indeed reduce wholesale prices in response to a rival’s downsizing.17 Clearly, strategic responses like the one shown here reduce the incentive to downsize in the first place as doing so is likely to initiate a destructive reduce-discount-reduce war of attrition. Estimating costs requires detailed data on input prices that comprise retailer and manufacturer costs. Both retailer and manufacturer costs are functions of a number of input prices specific to their production processes. Retailers’ costs consist of average weekly commercial gas prices, average weekly diesel prices, average weekly wages in the retail industry, as well as the wholesale prices described above. Manufacturers’ costs include average weekly industrial gas prices, average weekly wages in the food manufacturing industry, and average weekly prices of agricultural commodity inputs such as corn, wheat, oats, rice, malt, and sugar. Manufacturers use some of these grains for producing each product, so we use volume-shares as weights in creating an index of grain prices. Energy prices are from the U.S. Department of Energy (2011), and wages are from the U.S. Bureau of Labor Statistics (2011), and are smoothed to produce weekly series from the native monthly series, while agricultural commodity prices are from the U.S. Department of Agriculture (Economic Research Service, 2011). Table 3 reports the mean and the standard deviation of the input prices. Note that the value of week one is normalized to 100 in each series of costs. This table reveals substantial variation in input prices over time, and the fact that some important input prices rose over the sample period.

17

Fig. 5. Reactions of General Mills’ wholesale prices to package downsizing of Honey Bunches of Oats with Almonds 16-oz box.

Another possible explanation is the hike in commodity prices in 2008. But, even during that period, manufacturers did not change the size of their products as frequent as the wholesale prices (Figs. 2 and 3). This implies that commodity prices may be one factor, but there may be something more important that explains why a change in package size is less frequent.

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Table 4 Demographics. Variable

Mean

Std. dev.

Household income ($,000) Household size Age Educational attainment of a householder

67.934

1.107

2.606 42.007 0.322

0.004 0.264 0.012

Demand also depends on observed heterogeneity, or variation in household demographic and socioeconomic attributes. For the demand model and the first-stage IV regressions in the supplyside model, we include mean household income, household size, age, and educational attainment, which takes the value of one if a householder is college-graduate or more, zero otherwise. Each is smoothed to produce a weekly series from the native yearly observations obtained from the U.S. Census Bureau (2011). Table 4 presents the mean and the standard deviation of each demographic variable. Each of these variables capture variation in demand-shifting demographic attributes over time, which is useful in estimating the demand-side model and constructing instruments for retailer and wholesaler margins.18 5. Results and Discussion In this section, we present the results obtained from estimating the structural models described in the previous section. Among the parameters presented in this section, our primary interest lies in consumers’ response to changes in package size, and how their response conditions competitive interactions among manufacturers. Our hypothesis is that consumers prefer smaller packages, and that preference for package size is heterogeneous among consumers. The key parameters in the supply model, on the other hand, are retailer pricing conduct, and manufacturer conduct with respect to both prices and package size. We first present the estimates obtained from the demand model, and then the estimates from the supply-side of the model, and explain how the costs of changing package size present practical limitations to manufacturers’ ability to respond to consumers’ demand for variety in package sizes. Finally, we discuss the strategic implications of changing package sizes, and draw some more general findings for manufacturers and retailers of CPGs. 5.1. Demand Results Our demand model has three important components: (1) consumers’ hierarchical choices among retailers, (2) unobserved heterogeneity in terms of brand preference, price-response, and preference for package sizes, and (3) the importance of endogeneity, as measured by the control function parameters (Park

18

The sample period includes the economic downturn mainly triggered by the bankruptcy of Lehman Brothers in 2008. So, it is important to account for the time series variation of demographics.

and Gupta 2009; Petrin and Train 2010). We first establish the validity of the maintained demand model by conducting a series of specification tests. Table 5 reports the estimation results from the random-coefficient nested logit model without the control function, and with the control function respectively. We begin by conducting a t-test on the GEV scale parameter. If the scale parameter is not significantly different from zero, then consumers do not regard retailers as different sources of cereal, and a simple logit model would suffice. The result of the t-test on the GEV scale parameter shows that it is statistically different from zero, which suggests that the nested logit specification is superior to the simple logit. Next, we investigate the validity of the random-coefficient specification. The standard deviations of the random parameters in the random-coefficient nested logit model are all significantly different from zero, and the LR test statistic in which the random-coefficient logit model is the alternative, and the fixed-coefficient nested logit model is the null specification, is 28,832 with 3 degrees of freedom, so the null is rejected in favor of the alternative specification at the 5 percent level 2 (df = 3) = 7.815). Both results conclude of significance (χcrit that the random-coefficient specification outperforms the fixedcoefficient version. Finally, we investigate the extent of the endogeneity problem arising from retail price and package size, and examine whether the control function is able to adequately address the issue. As shown in Table 5, the estimates obtained without the control function are evidently different from those with control function. Further, the t-test for the IV regression residuals indicates that both of the control parameters are statistically different from zero, suggesting that the control functions effectively correct for the endogeneity bias that would otherwise be present (Wooldridge 2010). In summary, therefore, these specification tests support the validity of the random-coefficient nested logit model with the control function included. Therefore, we use this model to calculate demand elasticities, which form key inputs to the manufacturer and retail supply equations estimated in the second-stage. Most relevant to our objectives, we find that the coefficient on the square of the package size variable is negative and the package size variable is positive, suggesting that package size has a non-linear and concave effect on utility. This result implies that consumers are reluctant to buy a very small packages, nor do they prefer large packages. The optimal package size implied by these estimates is 11.5 oz, on average. Given that our data includes box sizes ranging from 8.0 oz to 25.5 oz, the optimal package size of 11.5 oz indicates that consumers prefer smaller packages in general. This finding is consistent with the empirical results by Khan and Jain (2005) and Cohen (2008). Consumers prefer smaller packages because their consumption rate is low on average, because they are risk-averse (Shoemaker and Shoaf 1975), or because they are better able to match purchase volumes more closely to consumption rates (Koenigsberg, Kohli, and Montoya 2010). The standard deviation of the random package-size coefficient is statistically significant, which implies that package-size preferences are heterogeneous among cereal shoppers, as

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Table 5 Estimation results of demand model. Variable

Brand preference

Constant Honey Nut Cheerios Cheerios Frosted Flakes Rice Krispies Froot Loops Frosted Mini-Wheats Special K Red Berries Special K Original Cocoa Krispies Apple Jacks Raisin Bran Raisin Bran Crunch Corn Flakes Crispix Honey Bunches of Oats Honey Bunches of Oats Almonds Fruity Pebbles Cocoa Pebbles Oatmeal Squares Cap’N Crunch Crunch Berries

Random-coefficient nested logit model without control function

Random-coefficient nested logit model with control function

Estimate

Std. error

Estimate

Std. error

0.7330* 1.1038* 0.5219* 0.3401* 0.6213* 0.3712* 1.0429* 0.5943* 0.2941* 0.2799* 0.2619* 0.4101* 0.5396* 0.6635* 0.6335* 0.2809*

0.0281 0.0078 0.0097 0.0074 0.0068 0.0070 0.0081 0.0084 0.0093 0.0083 0.0068 0.0097 0.0233 0.0111 0.0330 0.0098 0.0091

−2.6290* 0.7560* 1.1368* 0.5214* 0.3603* 0.6535* 0.3566* 1.0698* 0.6177* 0.2847* 0.2915* 0.2384* 0.4007* 0.5458* 0.6951* 0.6342* 0.2822*

0.0597 0.0095 0.0133 0.0081 0.0085 0.0133 0.0097 0.0115 0.0118 0.0102 0.0076 0.0123 0.0169 0.0123 0.1009 0.0127 0.0102

0.0239* 0.1905* 0.5852* 0.6923*

0.0088 0.0229 0.0136 0.0235

0.0307* 0.1936* 0.5989* 0.7015*

0.0100 0.0419 0.0174 0.0236

−2.7781*

Marketing mix

Price Discount Package size Package size squared

−0.0749* 0.1617* 0.0434* −0.0018*

0.0034 0.0135 0.0031 0.0001

−0.0909* 0.1637* 0.0385* −0.0017*

0.0050 0.0140 0.0036 0.0001

Interaction terms

Price × discount Price × household income

−0.0058* 0.0883*

0.0005 0.0048

−0.0059* 0.1049*

0.0005 0.0058

Std. dev. of random parameters

Constant

0.3852*

0.0015

0.3877*

0.0020

Price Package size

0.0116* 0.0198*

0.0001 0.0001

0.0114* 0.0197*

0.0001 0.0001

Residuals from the 1st-stage retail price regression Residuals from the 1st-stage package size regression

−

−

0.0048*

0.0015

−

−

−0.0245*

0.0023

0.8762*

0.0023

0.8755*

0.0024

0.1594*

0.0015

0.1590*

0.0015

Control function

GEV scale parameter Estimate of std. dev. Simulated log likelihood at convergence *

4227.8059

4259.2704

Significance at a 5 percent level.

expected. If consumers differ in their demand for packages of different sizes, then this finding may explain manufacturers’ and retailers’ motivation for offering different package sizes within the same product line. Manufacturers and retailers typically use indirect price discrimination by offering quantity discounts (Table 1), or lower unit prices for larger packages (Gerstner and Hess 1987). Consumers who purchase larger packages likely understand this unit price difference, and tend to consume greater amounts with larger packages (Wansink 1996), leading to an increase in sales. Manufacturers may offer

different packages as a means of strategic obfuscation (Ellison and Ellison 2009) as offering many packages with differing unit price is likely to prevent consumers from making direct price comparisons. Whether each package-size is priced optimally depends on the own-price and cross-price elasticities with other brands and other SKUs within the same brand. Table 6 shows the matrix of own- and cross-price elasticities for some of the products in the sample offered by General Mills and Kelloggs in retailer 1. Substitution across products is stronger for products with

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Table 6 Price and package-size elasticities of demand in retailer 1. With respect to

Response of 1

1: Honey Nut Cheerios 14/12.25 oz 2: Honey Nut Cheerios 20/17 oz 3: Cheerios 10/8.9 oz 4: Cheerios 15/14 oz

−3.372

2

3

4

5

6

7

8

9

10

11

12

13

14

0.166

0.188

0.211

0.229

0.195

0.215

0.176

0.217

0.178

0.201

0.142

0.208

0.169

Package size −0.913 0.023 0.093 −3.114 Price

0.123 0.063

0.067 0.101

0.070 0.114

0.030 0.115

0.093 0.092

0.017 0.123

0.075 0.103

0.017 0.124

0.020 0.133

−0.021 0.135

0.092 0.090

0.029 0.100

Package size Price

0.094 −2.110 0.100 0.417 0.259 −2.933

0.088 0.345

0.089 0.361

0.070 0.278

0.096 0.431

0.065 0.249

0.090 0.392

0.063 0.250

0.062 0.245

0.013 0.131

0.100 0.427

0.071 0.283

Package size Price

0.057 −0.019 −0.176 0.025 0.179 0.153 0.122 −3.398

0.066 −0.019 0.166 0.161

0.042 0.177

−0.018 0.163

−0.011 0.187

−0.030 0.142

0.065 0.163

−0.015 0.148

0.049 0.088

0.105 0.095

0.037 0.085

0.090 0.101

0.034 0.085

0.041 0.111

−0.012 0.078

0.106 0.083

0.048 0.076

0.060 0.045

0.020 0.060

0.053 0.052

0.019 0.060

0.026 0.067

−0.007 0.072

0.055 0.044

0.025 0.050

0.032 0.106

0.045 0.152

0.032 0.105

0.033 0.118

0.010 0.076

0.049 0.134

0.035 0.105

0.047 0.042

0.008 0.058

0.010 0.060

−0.012 0.064

0.052 0.036

0.014 0.045

Price

Package size 5: Frosted Price Flakes 14 oz Package size Price 6: Frosted Flakes 17 oz Package size 7: Rice Price Krispies 12 oz Package size 8: Rice Price Krispies 18 oz Package size 9: Froot Loops Price 15/12.2 oz Package size Price 10: Froot Loops 19.7/17 oz Package size 11: Frosted Price MiniWheats 18 oz Package size 12: Frosted Price MiniWheats 24 oz Package size 13: Special K Price Red Berries 12 oz Package size 14: Special K Price Red Berries 16.7 oz Package size 15: Special K Price Original 12 oz Package size 16: Special K Price Original 18 oz

0.032 −0.009 0.189 0.167

0.106 0.091

0.043 0.080

0.117 −1.273 0.087 0.068 0.091 −3.470

0.056 0.051

0.023 0.052

0.062 0.032

0.045 −1.343 0.026 0.053 0.056 −3.290

0.050 0.135

0.033 0.104

0.048 0.128

0.046 0.126

0.045 −2.103 0.047 0.142 0.112 −3.756

0.049 0.039

0.011 0.047

0.073 0.026

0.034 0.043

0.038 0.047

0.014 −0.874 0.008 0.051 0.037 −3.497

0.041 0.087

0.033 0.074

0.041 0.074

0.040 0.084

0.039 0.100

0.034 0.080

0.041 −2.395 0.039 0.103 0.076 −3.635

0.032 0.079

0.031 0.092

0.009 0.065

0.042 0.084

0.034 0.071

0.041 0.030

0.014 0.037

0.052 0.020

0.032 0.034

0.035 0.036

0.016 0.040

0.050 0.028

0.011 −1.201 0.046 0.034

0.012 −3.566

0.014 0.048

−0.008 0.052

0.042 0.028

0.016 0.034

0.032 0.078

0.027 0.094

0.031 0.044

0.033 0.089

0.032 0.113

0.028 0.102

0.032 0.080

0.030 0.109

0.033 0.095

−2.468 0.111

0.028 −3.373

0.011 0.142

0.033 0.069

0.028 0.086

0.087 0.056

0.066 0.092

0.072 0.023

0.087 0.067

0.102 0.075

0.071 0.114

0.092 0.048

0.068 0.115

0.094 0.064

0.067 0.119

−2.369 0.135

0.020 −2.923

0.083 0.045

0.067 0.080

0.137 0.134

0.177 0.105

0.083 0.133

0.153 0.125

0.157 0.132

0.211 0.111

0.123 0.136

0.197 0.106

0.144 0.131

0.198 0.104

0.208 0.108

−4.449 0.071

0.123 −3.831

0.168 0.104

0.045 0.047

0.010 0.050

0.071 0.034

0.032 0.050

0.033 0.052

0.013 0.054

0.049 0.046

0.007 0.055

0.037 0.049

0.006 0.055

0.008 0.058

−0.011 0.057

−0.852 0.043

0.013 −3.111

0.044 0.104

0.029 0.081

0.053 0.103

0.040 0.098

0.038 0.102

0.029 0.086

0.045 0.106

0.026 0.082

0.040 0.102

0.025 0.081

0.024 0.083

0.003 0.055

0.046 0.111

−1.962 0.081

0.036 0.031

0.008 0.037

0.057 0.021

0.025 0.034

0.026 0.037

0.010 0.039

0.039 0.030

0.006 0.041

0.029 0.034

0.005 0.042

0.007 0.045

−0.008 0.048

0.042 0.028

0.010 0.037

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Table 6 (Continued) With respect to

Response of 1

Package size 17: Cocoa Price Krispies 17.5/16.5 oz Package size 18: Apple Price Jacks 15/12.2 oz Package size 19: Apple Price Jacks 19.1/17 oz Package size Price 20: Raisin Bran 20 oz Package size 21: Raisin Price Bran 25.5 oz Package size 22: Raisin Price Bran Crunch 18.2 oz Package size Price 23: Corn Flakes 12 oz Package size Price 24: Corn Flakes 18 oz Package size

2

3

4

5

6

7

8

9

10

11

12

13

14

0.035 0.051

0.027 0.055

0.038 0.033

0.034 0.053

0.032 0.065

0.027 0.063

0.036 0.058

0.025 0.064

0.033 0.067

0.024 0.065

0.023 0.082

0.007 0.080

0.036 0.046

0.031 0.051

0.048 0.066

0.031 0.056

0.045 0.056

0.043 0.064

0.050 0.075

0.035 0.061

0.056 0.078

0.031 0.058

0.055 0.084

0.031 0.060

0.036 0.071

0.005 0.050

0.046 0.064

0.032 0.054

0.032 0.023

0.011 0.028

0.040 0.015

0.025 0.026

0.028 0.028

0.013 0.031

0.038 0.022

0.009 0.034

0.034 0.026

0.009 0.036

0.011 0.036

−0.005 0.039

0.033 0.022

0.013 0.026

0.024 0.080

0.020 0.111

0.023 0.041

0.024 0.096

0.024 0.135

0.021 0.121

0.024 0.082

0.021 0.132

0.024 0.103

0.020 0.137

0.020 0.191

0.007 0.216

0.025 0.068

0.020 0.097

0.125 0.057

0.119 0.104

0.090 0.022

0.132 0.071

0.174 0.081

0.129 0.128

0.131 0.049

0.127 0.133

0.144 0.068

0.127 0.139

0.165 0.161

0.074 0.347

0.115 0.045

0.115 0.088

0.164 0.046

0.237 0.053

0.089 0.028

0.192 0.050

0.200 0.054

0.282 0.065

0.145 0.043

0.272 0.061

0.180 0.050

0.277 0.062

0.297 0.069

0.407 0.080

0.144 0.041

0.220 0.050

0.054 0.060

0.041 0.047

0.050 0.053

0.051 0.053

0.051 0.060

0.049 0.049

0.052 0.060

0.041 0.047

0.051 0.061

0.041 0.047

0.041 0.051

0.017 0.034

0.053 0.058

0.043 0.045

0.024 0.045

0.005 0.053

0.035 0.027

0.016 0.049

0.017 0.063

0.006 0.060

0.025 0.045

0.004 0.062

0.021 0.052

0.004 0.062

0.004 0.078

−0.006 0.081

0.025 0.040

0.006 0.048

0.049

0.038

0.044

0.048

0.057

0.042

0.051

0.038

0.052

0.038

0.044

0.012

0.048

0.038

Note: Each entry represents the percentage change in the share of column product with respect to a percentage change in the price or package size of row product. The elasticity estimates in retailer 2 show a similar pattern, but are not shown here due to space limitations. The full matrix and the standard error for each element are available from the contact author.

similar package sizes relative to those with different package sizes, which is consistent with the finding of Cohen (2008). For example, the first row of Table 6 shows that a price change for Honey Nut Cheerios 14/12.25-oz box has a greater impact on the share of Cheerios 15/14-oz box than Cheerios 10/8.9-oz box, Frosted Flakes 14-oz box than Frosted Flakes 17-oz box and so on. If prices and package sizes are determined simultaneously, package-size elasticities are also of practical importance to manufacturers and retailers alike. Table 6 also presents the matrix of own- and cross-package-size elasticities in retailer 1. The package size elasticities are smaller than price elasticities, which ¸ akır and Balagtas (2014). is consistent with the finding of C This finding implies that consumers are relatively insensitive to changes in package size and likely pay more attention to changes in price. Own-package-size elasticities tend to be negative and cross-package-size elasticities be positive. The negative own package-size elasticities confirm the finding that consumers prefer smaller package sizes, in general, while the positive cross effects suggest that larger package sizes for one SKU cause the utility from another SKU to rise, as expected if consumers prefer smaller packages.

While these demand results are of considerable interest themselves, the objective of this analysis is to determine how consumer preferences for package size condition manufacturer decisions to offer SKUs that differ in terms of their package size, how they are to be priced, and how retailers pass-through manufacturer price changes to the consumer level.

5.2. Supply Results We use the demand estimates reported in Table 5 to calculate market shares and share derivatives with respect to all retail prices, wholesale prices, and package sizes. These variables are then substituted into the supply model, which is then estimated by SUR with the control function approach. First, an LR test is used to compare the supply-side model against a naïve model that consists of only constants. The LR statistic is 16,904, which is chi-square distributed with 54 degrees of freedom, so we reject the naïve model in favor of the maintained supply-side specification at the 5 percent level of significance 2 (df = 54) = 72.153), and we conclude that the supply(χcrit side model fits the data better than no model at all.

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Table 7 Estimation results of retail price equation. Variable

Retail cost

Conduct parameter Control function R-squared *

Without control function

With control function

Estimate

Std. error

Estimate

Std. error

0.583 0.013 0.040 0.139 0.378 0.169 0.201 0.154

−23.277*

1.409 0.013 0.042 0.138 1.121 0.167 0.205 0.152

0.002 –

0.145* −12.750* 0.323

−3.333*

Constant Wholesale price Gas price Diesel price Retailer 1 First quarter Second quarter Third quarter

0.858* 0.362* −0.068 3.213* −0.728* −1.140* −0.079 0.031* – 0.307

Changes in demand condition Residuals from the 1st-stage retail-margin regression

0.795* 0.097* 0.068 19.572* −0.543* −0.314 −0.077

0.007 0.787

Significance at a 5 percent level.

Second, we compare the results of the model with and without instrumental variables to show the extent of bias present if endogeneity is not properly accounted for. In Tables 7–9, we present the estimation results from the supply model without control function and with control function respectively. In the noninstrumented model, the estimated Wu–Hausman test statistic value is 9, 942 with 3 degrees of freedom, so the null hypothesis of no endogeneity of retailer or manufacturer margin is rejected 2 (df = 3) = 7.815), at the 5 percent level of significance (χcrit and we conclude that the margins are endogenous and the instrumental variables are necessary. In general, the supply-model estimates provide reasonable results in terms of goodness of fit and statistical significance. First, recall that the retail price equation examines the relationship between retail prices and retail costs and demand conditions expressed in elasticity terms. Table 7 shows the estimates obtained for the retail pricing equation. In terms of goodness-of-fit, the results in this table show that the variables used in this equation explain 32.3 percent of the total variation in retail price. Further, a t-test on the IV regression residuals indicates that the residual parameter is statistically different from zero, suggesting that the control function approach again addresses the endogeneity of retail margins as expected. Retail cost variables such as wholesale-price and gas-price variables are all positively related to retail prices, suggesting that retailers tend to charge higher prices as costs increase. The extent of strategic behavior is estimated through the conduct parameter. The conduct parameter is statistically different from, but close to zero, which suggests that the retail market is relatively competitive. Nonetheless, retailers still have non-zero margins. Next, we interpret the estimates from the manufacturer price equation (Table 8). With this equation, we investigate whether variation in wholesale prices is explained by variation in manufacturer costs such as grain, sugar and gas prices, wage, seasonaland product-specific costs, and the demand conditions facing manufacturers. The estimated goodness-of-fit statistics again suggest our model provides a relatively good fit to the data as variation in the explanatory variables explains fully 92.6 percent of the total variation in wholesale prices. A t-test on the IV regression residuals implies that the control function

approach appropriately accounts for any endogeneity of the implied margin term. Therefore, the conduct parameter is estimated consistently, and is positive and significant, but close to zero. This implies that competition among manufacturers is relatively strong in the wholesale market. Finally, we examine the results of manufacturer packagesize equation (Table 9). The estimates reveal how manufacturers choose package size in response to the estimate of competitive response and pack-size elasticities.19 The package-size “conduct” parameter, which captures the competitive response of manufacturers to changes in rivals’ decisions, is also positive and significant. A positive package-size conduct parameter implies that package sizes are strategic complements.20 Recall that the own-package-size elasticities of demand are negative and the manufacturer conduct parameter is positive. So, the positive conduct parameter means that a reduction in package size is associated with a higher own-wholesale price (which explains why manufacturers reduce package sizes), but lower wholesale price by the rival firm. The intuition of this finding is straightforward. When one package is reduced in size, the wholesale price of that product increases because there is a negative relationship between price and package size of the same product. Also, according to the demand results, the cross-package-size elasticities of demand are positive. Taken together, a decrease in one package size then leads to an increase in its wholesale price, and so the appropriate competitive response to that product, ceteris paribus, is an increase in competitors’ package sizes and decrease in competitors’ wholesale prices. In sum, a package downsizing for one product causes a decline in competitors’ wholesale prices and intensifies competition among manufacturers, which is the reason why manufacturers are reluctant to reduce the package size 19

The variation in the market size is negligible small. For the purpose of illustration, we ignore the effect of the market size variable and consider manufacturer package-size equation with two prod ∂s1 ∂s2 + (w2 − c2 ) ∂q and q2 = η0 + ucts, so that: q1 = η0 + η1 (w1 − c1 ) ∂q 20





1

1

∂s1 ∂s2 + (w2 − c2 ) ∂q where η1 is positive, ∂s1 /∂q1 and ∂s2 /∂q2 η1 (w1 − c1 ) ∂q 2 2 are negative, and ∂s2 /∂q1 and ∂s1 /∂q2 are positive. This simplification helps to understand the discussion in this paragraph.

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Table 8 Estimation results of manufacturer price equation. Variable

Manufacturer cost

Conduct parameter Control function R-squared *

Constant Grain price index Sugar price Gas price Wage Honey Nut Cheerios 14/12.25 oz Honey Nut Cheerios 20/17 oz Cheerios 10/8.9 oz Cheerios 15/14 oz Frosted Flakes 14 oz Frosted Flakes 17 oz Rice Krispies 12 oz Rice Krispies 18 oz Froot Loops 15/12.2 oz Froot Loops 19.7/17 oz Frosted Mini-Wheats 18 oz Frosted Mini-Wheats 24 oz Special K Red Berries 12 oz Special K Red Berries 16.7 oz Special K Original 12 oz Special K Original 18 oz Cocoa Krispies 17.5/16.5 oz Apple Jacks 15/12.2 oz Apple Jacks 19.1/17 oz Raisin Bran 20 oz Raisin Bran 25.5 oz Raisin Bran Crunch 18.2 oz Corn Flakes 12 oz Corn Flakes 18 oz Crispix 12 oz Honey Bunches of Oats 16/14.5 oz Honey Bunches of Oats 21/19/18 oz Honey Bunches of Oats Almonds 16/14.5 oz Honey Bunches of Oats Almonds 21/19/18 oz Fruity Pebbles 13/11 oz Cocoa Pebbles 13/11 oz Oatmeal Squares 16 oz Cap’N Crunch Crunch Berries 15 oz Cap’N Crunch 16 oz First quarter Second quarter Third quarter Changes in demand condition Residuals from the 1st-stage manufacturer-margin regression

Without control function

With control function

Estimate

Std. error

Estimate

Std. error

1.075 0.001 0.004 0.012 0.067 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.124 0.046 0.046 0.044

−3.815*

0.784 0.001 0.003 0.008 0.050 0.092 0.090 0.102 0.090 0.108 0.103 0.121 0.105 0.113 0.100 0.095 0.090 0.124 0.116 0.124 0.109 0.097 0.114 0.100 0.091 0.090 0.095 0.103 0.095 0.120 0.091 0.090 0.091 0.090 0.096 0.096 0.093 0.094 0.092 0.142 0.229 0.128

−14.563* 0.004* 0.003 0.005 1.757* 9.545* 6.905* 14.233* 7.807* 6.389* 4.861* 9.821* 5.652* 7.782* 3.967* 1.726* −0.852* 10.462* 8.576* 10.492* 6.825* 2.587* 7.965* 4.247* −0.431* −2.363* 2.157* 5.041* 1.807* 9.614* 4.069* 2.262* 4.138* 2.335* 6.878* 6.921* 3.882* 4.586* 3.351* 0.160* 0.405* 0.453* 0.000 – 0.856

0.000 –

0.002* 0.062* −0.130* 0.430* 7.716* 6.769* 9.545* 7.076* 0.461* −0.089 1.790* 0.230* 1.015* −0.375* −1.281* −2.232* 2.034* 1.327* 2.046* 0.668* −0.950* 1.092* −0.267* −2.099* −2.796* −1.096* 0.041 −1.232* 1.737* 2.460* 1.828* 2.485* 1.871* 3.536* 3.578* 1.474* 1.723* 1.255* 14.061* 23.165* 12.883* 0.091* −9.090* 0.926

0.001 0.090

Significance at a 5 percent level.

Table 9 Estimation results of manufacturer package-size equation. Variable

Conduct parameter Control function R-squared *

Constant Package-size elasticities × changes in demand condition Residuals from the 1st-stage manufacturer-margin regression

Without control function

With control function

Estimate

Std. error

Estimate

16.042* 1.374* – 0.002

0.035 0.295 –

16.042* 1.399* −0.001 0.002

Std. error 0.035 0.296 0.004

Significance at a 5 percent level.

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of their products. The opposite case occurs when package size rises – a rise in package size softens price competition among manufacturers. Packaging costs are important determinants of the incentive to change package size as well. The estimates of the packagesize equation describe the shape of the cost function in package size, and permit the derivation of an optimal package. Package size has a non-linear and convex effect on production costs. The costs decrease until the optimal package size of 16.0 oz, and then increase afterward. Evidently, packages that are too small may require special packaging technology, excessive costs associated with adjusting the production line, or special handling in the distribution system and shelf display. For similar reasons, manufacturers incur higher costs if packages are too large. Recall that the optimal size based on demand estimates alone was 11.5 oz on average. Due to competition among manufactures and packaging costs, the optimal package size is more likely greater than the size that consumers prefer. This result suggests that brand managers must consider both the demand and supply effects associated with package-size decisions. For example, Kelloggs reduced the size of its cereal boxes of Apple Jacks from 19.1 oz to 17.0 oz and 15.0 oz to 12.2 oz, respectively. Based on the costs associated with the larger size, Kelloggs can expect both an increase in share and a reduction in cost. In the latter case, on the other hand, Kelloggs can expect an increase in share, but must incur the cost of switching to the new packages. This result suggests that package downsizing is not always effective, both due to competition among manufacturers, that reduces the marginal benefit of changing package size, and higher costs associated with producing larger packages. A counterfactual, numerical simulation that includes both strategic interactions and the cost of changing package sizes provides a more concrete demonstration of this effect. For this simulation, we shock the size of a particular package by 10 percent, and then use the estimates from structural model to calculate the implied effect on demand, margins, prices and package sizes. For example, suppose Kelloggs reduced the size of Special K Red Berries 16.7-oz box by 10 percent. Using the estimated demand and supply parameters, we calculated market shares, margins and equilibrium prices at both the retailer and manufacturer levels under this scenario. Table 10 reports the change in equilibrium retail prices, retail price-cost margins, equilibrium wholesale prices, equilibrium package sizes, and manufacturer price-cost margins relative to their original values. This table shows that the wholesale price of other competing products would be generally reduced in response to the package downsizing of the given product. For example, the wholesale price of Frosted Flakes 14-oz box would be reduced by $0.042 per oz, Rice Krispies 12-oz box by $0.025 per oz, and Rice Krispies 18-oz box by $0.039 per oz.21 Package size and wholesale price are, therefore, strategic

21 Because the effect of package size on utility is non-linear and concave, the size reduction in extra-large box has an substantial positive impact on market share, which allows manufacturers offering such boxes to raise their prices and margins. In response to the downsizing of Special K Red Berries 16.7-oz box,

complements. Recall that consumers prefer smaller packages. The smaller package of Special K Red Berries attracts more consumers, which results in a increase in manufacturer margin (+$0.002 per oz). Kelloggs would expect to charge a higher price on the new package of Special K Red Berries, however, end up with raising the wholesale price by only $0.002 per oz due to the price competition. Downsizing sharpens price competition and does not allow manufacturers to increase unit price, which dramatically reduces the incentives for manufacturers to reduce package size.22 Manufacturers are expected to change the size of their packages in response to rivals’ action. However, this effect is small. Table 10 shows the package size would change by only tiny amount. Because equilibrium package size is a function of the estimates of the competitive response and the response in market share with respect to package size, and the product of these components is small, competitors may recognize that price is more effective tool for covering cost increases in this case. Package downsizing has two distinct effects on the retail price and margin of the downsized product. First, it allows retailers to charge a higher price because consumers tend to prefer smaller packages. The other effect lies in the change in retail cost. Due to the interdependency between package size and price, manufacturers respond to the package downsizing by changing wholesale prices – one of the primary elements of retail cost – which provides retailers an incentive to pass the change in wholesale price onto consumers. Retailers set the prices, taking into account these effects. In the simulation, we find that Kelloggs takes advantage of consumers’ preference for the smaller Special K Red Berries box to charge a $0.002 higher price per oz to retailers, and retailers raise their price by $0.001 per oz. Nevertheless, retailers still benefit from package downsizing as downsizing intensifies price competition among manufacturers, and the wholesale price of other products falls more generally. As a result, the retail cost of the category overall falls by $0.081 per oz, which is beneficial to retailers.23 Consumers are likely to benefit when manufacturers reduce the size of a product. Empirically, the net benefit to consumers is easily found by calculating the consumer surplus, which, in a logit framework, is the difference in the log-sum of item-level utility before and after package downsizing (Train 2009). We find that reducing the size of a particular product promotes price competition among manufacturers, and reduces wholesale prices of other products, which leads to lower retail prices. Moreover, consumers generally prefer smaller packages, so benefit

Kelloggs would reduce the size of extra-large boxes such as Frosted Mini-Wheats 24-oz box, Raisin Bran 20-oz box, and Raisin Bran 25.5-oz box, which leads to the increase in the market share and margin. This is the reason why the price of these products would increase in the simulation. 22 In order to demonstrate the robustness of our simulation results, we conducted downsizing simulations using Cheerios 15/14-oz and Raisin Bran 20-oz boxes. We find results that are similar to those reported in Table 10, so these alternate simulations provide general support for our main findings. The results are available in Web Appendix. 23 Recall retailers’ objective is to maximize not a brand profit but a category profit.

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Table 10 Change in retail price, retail margin, wholesale price, package size, and manufacturer margin if the size of Special K Red Berries 16.7-oz box was reduced by 10 percent. Product

Honey Nut Cheerios 14/12.25 oz Honey Nut Cheerios 20/17 oz Cheerios 10/8.9 oz Cheerios 15/14 oz Frosted Flakes 14 oz Frosted Flakes 17 oz Rice Krispies 12 oz Rice Krispies 18 oz Froot Loops 15/12.2 oz Froot Loops 19.7/17 oz Frosted Mini-Wheats 18 oz Frosted Mini-Wheats 24 oz Special K Red Berries 12 oz Special K Red Berries 16.7 oz Special K Original 12 oz Special K Original 18 oz Cocoa Krispies 17.5/16.5 oz Apple Jacks 15/12.2 oz Apple Jacks 19.1/17 oz Raisin Bran 20 oz Raisin Bran 25.5 oz Raisin Bran Crunch 18.2 oz Corn Flakes 12 oz Corn Flakes 18 oz Crispix 12 oz Honey Bunches of Oats 16/14.5 oz Honey Bunches of Oats 21/19/18 oz Honey Bunches of Oats with Almonds 16/14.5 oz Honey Bunches of Oats with Almonds 21/19/18 oz Fruity Pebbles 13/11 oz Cocoa Pebbles 13/11 oz Oatmeal Squares 16 oz Cap’N Crunch Crunch Berries 15 oz Cap’N Crunch 16 oz Cap’N Crunch 22 oz

Retailer

Manufacturer

Change in retail price ($/oz)

Change in retail margin ($/oz)

Change in wholesale price ($/oz)

Change in package size (oz)

Change in manufacturer margin ($/oz)

0.001 0.001 0.001 0.001 −0.033 0.014 −0.020 −0.031 −0.028 −0.032 −0.007 0.052 −0.033 0.001 −0.033 0.004 −0.035 −0.029 0.003 0.036 0.056 0.034 −0.016 0.012 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

−0.009 0.014 0.037 −0.008 −0.027 −0.011 0.004 0.004 −0.005 0.008 −0.019 −0.014 0.010 0.007 0.010 0.004 −0.018 −0.009 0.008 −0.025 −0.013 −0.002 0.040 −0.007 0.025 −0.015 0.003 −0.017 0.001 −0.014 −0.015 0.024 0.014 0.010 0.006

0.001 0.001 0.002 0.002 −0.042 0.018 −0.025 −0.039 −0.036 −0.041 −0.009 0.066 −0.041 0.002 −0.041 0.004 −0.045 −0.037 0.004 0.045 0.070 0.043 −0.020 0.015 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.001 0.000 0.000 0.000 0.000 −0.007 0.001 0.002 0.000 0.001 −0.001 −0.031 −0.007 −0.008 −0.005 −0.005 0.001 0.000 −0.003 −0.043 −0.024 −0.010 −0.002 −0.005 −0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.001 0.001 0.002 0.002 −0.042 0.018 −0.025 −0.039 −0.036 −0.041 −0.009 0.066 −0.041 0.002 −0.041 0.004 −0.045 −0.037 0.004 0.045 0.070 0.043 −0.020 0.015 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

from smaller packages in two ways. Both of these effects raise consumer surplus. Conventional wisdom argues that manufacturers would prefer to cover higher manufacturing costs in a hidden way, by reducing package sizes and keeping the package price same. However, we find that the optimal reaction from competitors to package downsizing is to lower wholesale prices. In other words, package size and price are strategic complements. The interdependence between package size and price does not allow manufacturers to easily raise unit price. Therefore, package downsizing may not be in manufacturers’ best interests when strategic interactions are taken into account. Because manufacturers implicitly understand the equilibrium response to downsizing, this finding may explain why package downsizing is relatively rare. Manufacturers recognize the deeper consequences associated with package downsizing, so tend to rely on raising wholesale prices instead.

6. Conclusions and Implications In this paper, we investigate how manufacturers of CPGs choose package size and unit-price, or the price per unit volume. Package size and price are important elements of the marketing mix because consumers observe both package size and package price directly, but must infer the unit price. Whereas others regard this disconnect between package prices and unit-prices, or “actual” prices as an opportunity for manufacturers to pass hidden price increases on to consumers, the reality of the situation is not as simple. Indeed, when cost and strategic considerations are taken into account, actual manufacturer behavior is likely to be exactly the opposite. Our primary concern is how manufacturers make package size and pricing decisions in consideration of consumer preferences, production and distribution costs, and strategic interactions among manufacturers. To that end, we develop a structural model of interactions among consumers, retailers, and

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manufacturers when both package size and price are supplierdecision variables. Consumers make discrete choices among differentiated products, while manufacturers jointly set package sizes and wholesale prices, and retailers pass-through manufacturers’ package size decisions and set retail prices taking into account consumer demand and manufacturer and retailer costs. In this way, we model the process of product design and pricing as a simultaneous decision of how large a package to offer, and what unit-price to charge. As a structural model of market equilibrium, our model reveals the interdependence of manufacturer package-size and pricing decisions, with optimal responses from competitors in both dimensions. We apply this model to supermarket chain-level retail scanner data from the ready-to-eat breakfast cereal category from two major retailers in the US metropolitan market. We find that package size is an important attribute in a consumer’s choice among cereal SKUs. Specifically, consumers prefer small packages, in part, due to their perception of risk and convenience, but their preference for package size is heterogeneous. So, that explains why manufacturers offer multiple packages within the same product line. When manufacturers offer a particular package size, they consider consumer demand, the costs associated with making packages, and potential competitive responses from rivals. Consequently, equilibrium package size outcomes result not only from consumer preferences, but from more complex responses from manufacturers to their perceived incentives. Our results are in sharp contrast to findings that have become received wisdom in the literature, namely that downsizing is an effective means of passing along cost increases to consumers. The fact that consumers tend to over- or under-estimate package size allows manufacturers to use changes in package size as an obfuscation strategy (Binkley and Bejnarowicz 2003; Ellison and Ellison 2009; Granger and Billson 1972; Raghubir and Krishna 1999; Russo 1977). Moreover, others find package downsizing is an effective way for manufacturers to maintain margins in the face of cost increases, because consumers are less responsive to changes in package size than to changes in price (C ¸ akır and Balagtas 2014). However, we show that manufacturers may be better off raising prices, and leaving package sizes alone. On the surface, package downsizing may mitigate the effect of an input-price increase, but also generates a strategic reaction from competitors. If a package is downsized, competitors tend to reduce their wholesale prices in response. Price competition in the wholesale market is intensified, and manufacturers’ ability to raise unit prices through changes in package size is constrained by competition. This dynamic explains why downsizing is a relatively rare event, and not a common occurrence as the consumer-response literature would lead us to believe. We also find that a change in package size affects retailers’ pricing decisions. Retailers can charge consumers a higher price for the downsized product because consumers prefer smaller packages. In addition, the wholesale-price competition caused by package downsizing allows retailers to reduce their retail costs. Our results imply that if manufacturers increase the size of their packages, on the other hand, competitors are likely to raise

their wholesale prices, and wholesale margins rise at the expense of retailers. Raising a package size is not a common business practice. However, if we consider the brand rather than the UPC as a fundamental unit of analysis, launching a new large package can be regarded as increase in package size. In response to the introduction of large packages as additions to an existing product line, competitors may raise their wholesale prices, which softens price competition among manufacturers and raises manufacturer margins. As a consequence, introducing line-extensions with larger packages allows manufacturers to potentially collude in setting prices. Our findings are consistent with the more general literature on semi-collusion in components of the marketing mix. Advertising, capacity investment, and product-line length are all ways suppliers can soften price competition – essentially drawing competitor attention away from prices, and toward some other means of competing. As another example of this more general line of research, we show that package size is a facilitating practice that has the potential to enhance manufacturer market power. Our findings have a number of practical implications. First, retailers and manufacturers should recognize that both package size and price have substantial effects on manufacturers’ profitability – effects that are not independent, but inextricably linked through the cost of production and the way these changes alter the competitive environment among manufacturers. Second, manufacturers would be well-advised to launch at least one small-pack product, and multiple package sizes to meet consumers’ diverse tastes regarding package size, particularly during the introduction phase. The reason comes from the fact that consumers prefer small packages, but their preference is subject to a considerable amount of heterogeneity. Third, manufacturers should base their package-size decisions not only on the derived demand from retailers, but on responses from rivals, and the costs associated with making different packages. In the face of higher production costs, manufacturers may have an incentive to downsize packages according to consumers’ demand for package size, but doing so may not always yield the desired outcome. Package size decisions are also of importance to retailers. First, we provides insight into retailers’ product assortment decisions. Given that there is a proliferation of products in the CPGs industry, and only limited shelf-space, retailers need to understand the structure of package-size preferences, and the strategic nature of stocking decisions (Mantrala et al. 2009). Consumers prefer variety (Kahn and Lehmann 1991). But, consumers do not benefit from too-many-choice because it increases their cognitive burdens (Chernev 2003). In fact, Broniarczyk, Hoyer, and McAlister (1998) finds reduction of irrelevant items does not worsen store patronage. Taken together with our finding, too small and too large packages can be removed from their product assortment. Second, our study provides insight into the effect of package downsizing on retailing costs as well as consumer behavior. Consumers generally prefer smaller packages, so package downsizing itself does not have a negative impact on their choice decisions. Manufacturers are likely to increase unit price along with package downsizing, leading to an increase in a retailing cost. But, we show that price competition is intensified

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as a result of package downsizing. Given retailers’ objective is not to maximize brand profit but to maximize category profit, retailers can expect the lower costs when manufacturers reduce the package size of their products. Finally, our findings provide policy makers new insight into the recent food price inflation. Regulators have concerned about cost-pass through to consumers as it determines the rate of food price inflation. If manufacturers pass through cost increases easily through raising unit prices by package downsizing, then the pass-through is quicker. However, our results do not support that outcome. The interdependence of package size and price does not allow manufacturers to easily pass-through cost increases through package downsizing. As a result, retail prices increases slower than once thought. Manufacturers are not to blame for consumer food price inflation in this respect. A potential direction for future research in this area is to consider other industries in which products and services are offered as packages, and the size of these packages serve as points of competition among suppliers. Interdependence between price and package size may exist in markets beyond the CPGs industry. For example, when consumers choose a restaurant meal, they consider many factors. Especially, for health-conscious consumers, caloric content is one of the important choice attributes for the entire meal package. Such consumers are likely to choose a meal by considering both price and caloric content, so if restaurants choose to offer lower-calorie meal choices, they may charge a higher price, and earn a larger margin. In this case, which is common practice, particularly among fast-casual, chain-restaurants, restaurants may compete in caloric content, and collude in price. It would be interesting to examine such a mechanism with a broader set of markets, services, and products. Another direction is to examine consumers’ and firms’ dynamic package size decisions. Consumers in our model are assumed to be myopic. However, it is possible that consumers are forwardlooking and choose a particular package size depending on their knowledge and expectation of product quality (Erdem, Imai, and Keane 2003; Hendel and Nevo 2006; Osborne 2011). Consumers may prefer a small package of a product if they are uncertain about its quality, and then switch to a large pack as they become familiar with the product. Manufacturers may launch smaller packs and charge higher prices on them, and at a later stage of product life cycle, they may offer large packs in response to consumers’ dynamic package choice behaviors. Dynamic package size decisions will be a fruitful area of study. We leave these questions for future research. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.jretai.2016.06.001. References Allenby, Greg M., Thomas S. Shively, Sha Yang and Mark J. Garratt (2004), “A Choice Model for Packaged Goods: Dealing with Discrete Quantities and Quantity Discounts,” Marketing Science, 23 (1), 95–108.

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