structural analysis of manufacturer pricing in the...

MARKETING SCIENCE 2001 INFORMSVol. 20, No. 3, Summer 2001, pp. 244264

0732-2399/01/2003/0244/$05.001526-548X electronic ISSN

Structural Analysis of ManufacturerPricing in the Presence of a

Strategic Retailer

K. SudhirSchool of Management, Yale University, 135 Prospect Street, PO Box 208200, New Haven, CT 06520-8200

[email protected]

AbstractConsumer goods manufacturers usually sell their brands toconsumers through common independent retailers. Theoreticalresearch on such channel structures has analyzed the optimalbehavior of channel members under alternative assumptions ofmanufacturer-retailer interaction (Vertical Strategic Interaction).Research in Empirical Industrial Organization has focused onanalyzing the competitive interactions between manufacturers(Horizontal Strategic Interaction). Decision support systemshave made various assumptions about retailer-pricing rules(e.g., constant markup, category-profit-maximization). The ap-propriateness of such assumptions about strategic behavior forany specific market, however, is an empirical question. Thispaper therefore empirically infers (1) the Vertical Strategic In-teraction (VSI) between manufacturers and retailer, (2) the Hor-izontal Strategic Interaction (HSI) between manufacturers si-multaneously with the VSI, and (3) the pricing rule used by aretailer.

The approach is particularly appealing because it can beused with widely available scanner data, where there is noinformation on wholesale prices. Researchers usually haveno access to wholesale prices. Even manufacturers, whohave access to their own wholesale prices, usually have lim-ited information on competitors wholesale prices. In the ab-sence of wholesale prices, we derive formulae for wholesaleprices using game-theoretic solution techniques under thespecific assumptions of vertical and horizontal strategic in-teraction and retailer-pricing rules. We then embed the for-mulae for wholesale prices into the estimation equations.While our empirical illustration is using scanner data with-out wholesale prices, the model itself can be applied whenwholesale prices are available.

Early research on the inference of HSI among manufac-turers in setting wholesale prices using scanner data (e.g.,Kadiyali et al. 1996, 1999) made the simplifying assumptionthat retailers charge a constant margin. This assumption en-abled them to infer wholesale prices and analyze competi-tive interactions between manufacturers. In this paper, weshow that this model is econometrically identical to a modelthat measures retail-price coordination across brands.Hence, the inferred cooperation among manufacturers couldbe exaggerated by the coordinated pricing (category man-agement) done by the retailer. We find empirical support forthis argument. This highlights the need to properly model

and infer VSI simultaneously to accurately estimate the HSIwhen using data at the retail level.

Functional forms of demand have been evaluated in termsof the fit of the model to sales data. But recent theoreticalresearch on channels (Lee and Staelin 1997, Tyagi 1999) hasshown that the functional form has serious implications forstrategic behavior such as retail passthrough. While the logitand linear model implies equilibrium passthrough of lessthan 100% (Lee and Staelin call this Vertical Strategic Sub-stitute (VSS)), the multiplicative model implies optimalpassthrough of greater than 100% (Vertical Strategic Com-plement (VSC)). Because passthrough rates on promotionshave been found to be below or above 100% (Chevalier andCurhan 1976, Armstrong 1991), we empirically test the ap-propriateness of the logit (VSS) and the multiplicative (VSC)functional form for the data.

We perform our analysis in the yogurt and peanut buttercategories for the two biggest stores in a local market. Wefound that the VSS implications of the logit fit the data betterthan the multiplicative model. We also find that for bothcategories, the best-fitting model is one in which (1) the re-tailer maximizes category profits, (2) the VSI is Manufactur-er-Stackelberg, and (3) manufacturer pricing (HSI) is tacitlycollusive. The fact that the retailer maximizes category prof-its is consistent with theoretical expectations. The inferencethat the VSI is Manufacturer-Stackelberg reflects the insti-tutional reality of the timing of the game. Retailers set theirretail prices after manufacturers set their wholesale prices.Note that in the stores and product categories that we an-alyze, the two manufacturers own the dominant brandswith combined market shares of about 82% in the yogurtmarket and 65% in the peanut butter market. The result isalso consistent with a balance of power argument in theliterature. The finding that manufacturer pricing is tacitlycollusive is consistent with the argument that firms involvedin long-term competition in concentrated markets canachieve tacit collusion.

Managers use decision support systems for promotionplanning that routinely make assumptions about VSI, HSI,and the functional form. The results from our analysis areof substantive import in judging the appropriateness of as-sumptions made in such decision support systems.(Structural Models; Horizontal Strategic Interaction; Vertical Stra-tegic Interaction; Retailer Pricing; Promotional Planning; NewEmpirical Industrial Organization)

STRUCTURAL ANALYSIS OF MANUFACTURER PRICING IN THE PRESENCE OF A STRATEGIC RETAILER

MARKETING SCIENCE/Vol. 20, No. 3, Summer 2001 245

1. IntroductionManufacturers of most consumer goods sell theirbrands to consumers through common independent re-tailers (e.g., supermarkets and convenience stores forgrocery products, department stores, specialty storesfor consumer electronics, sporting goods, etc.). Therehas been substantial theoretical research on such chan-nel structures (e.g., McGuire and Staelin 1983, Choi1991, Lee and Staelin 1997). This stream of research hasanalyzed the optimal behavior of channel members un-der alternative assumptions about vertical strategic in-teractions between manufacturers and retailers. Re-searchers of the new empirical industrial organization(e.g., Kadiyali et al. 1996, 1999) have studied the com-petitive interactions between manufacturers (horizontalstrategic interaction). Decision support systems for pro-motion planning make assumptions about the pricingrules used by retailers (e.g., Silva-Risso et al. 1999 as-sume constant margin, Tellis and Zufryden 1995 as-sume category-profit maximization). The appropriate-ness of such assumptions for any specific market is anempirical question. Our goal in this paper is to empir-ically infer (1) the vertical strategic interaction (VSI) be-tween manufacturers and retailer, (2) the horizontalstrategic interaction (HSI) between manufacturers si-multaneously with the VSI, and (3) the pricing ruleused by a retailer.

The approach in this paper is particularly appeal-ing because it can be used with widely available scan-ner data, where there is no information on wholesaleprices. Researchers usually have no access to whole-sale prices. Manufacturers have access to their ownwholesale prices, but usually have only limited infor-mation on competitors wholesale prices. In the ab-sence of wholesale prices, we derive formulae forwholesale prices using game-theoretic solution tech-niques under the specific assumptions of vertical andhorizontal strategic interaction, demand functionalform, and retailer pricing rules. We then embed theformulae for wholesale prices into the estimationequations.1 While our empirical illustration is using

1It is important to note that the derivation methods used to solvefor wholesale and retail prices in this paper are different from ap-proaches used in theoretical papers. Theoretical models derive theoptimal wholesale and retail prices (and the resulting market

scanner data without wholesale prices, the model it-self is easily applicable to the situation where whole-sale prices are available by using the derived formu-lae for wholesale prices as additional estimationequations in the model.

Relationship with Previous ResearchFor a quick overview of the relative contribution ofthis paper, we compare related papers in the litera-ture in Table 1.

Several papers in the new empirical industrial or-ganization (NEIO) tradition have attempted to infercompetitive interactions underlying pricing behavioramong manufacturers (HSI) using national-level data(for example, see Roy et al. 1994 and Kadiyali 1996).In these papers, retailer behavior is not modeled. Onejustification for this is that the focus is on competitionat the national level. Furthermore, any particular re-tailers strategic behavior will be lost in the data ag-gregation across retailers, and hence, is irrelevant forthe level at which the analysis is done.

Because manufacturers do tailor their marketingmix to local market conditions (Manning et al. 1998,Nichols 1987), NEIO researchers have recentlyshifted their focus to analyzing HSI among manu-facturers in local markets using scanner data. Butat this local level, retailer strategic behavior canhave a significant influence on a manufacturersprice-setting behavior. Therefore, retailers interac-tion with manufacturers (VSI) needs to be account-ed for. A further complication when using scannerdata is that wholesale prices are unavailable to theresearcher. As a result, to analyze manufacturerwholesale-pricing behavior, the wholesale pricesneed to be inferred from the data.

Kadiyali et al. (1996, 1999) infer wholesale pricesby making a simplifying assumption about the VSI.They assume that the retailer is nonstrategic andcharges an exogenous constant margin. This assump-

shares) based on the parameters of the demand model (which areassumed to be completely known with no econometric error). Aneconometric model, however, is used to estimate the parameters ofthe demand model assuming that the observed market shares andretail prices are an outcome of optimal firm behavior conditionalon the underlying parameters of the demand model.

SUDHIRStructural Analysis of Manufacturer Pricing

MARKETING SCIENCE/Vol. 20, No. 3, Summer 2001246

Table 1 Positioning Against Related Research

Manufacturer-Manufacturer Interaction

Manufacturer-RetailerInteraction

Retailer PricingRule

Demand FunctionalForm

WholesalePrice Informa-tion Available

Roy et al. (1994); Kadiyali(1996)

Estimated NA NA Linear NA

Kadiyali et al. (1996, 1999) Estimated Manufacturer Stackelberg Constant margin Linear NoBesanko et al. (1998) Bertrand assumed Vertical Nash Category profit Logit NoCotterill and Putsis (2001) Bertrand assumed Manufacturer Stackelberg,

vertical Nash, and retail-er Stackelberg models(with Bertrand amongmanufacturers)

Category profit Linear, estimates LA-AIDs without struc-tural pricing equa-tions

No

Kadiyali et al. (2000) Cannot separatelyidentify from reac-tion to retailer

1. CV estimated2. Manufacturer Stackel-

berg, vertical nash, andretailer Stackelberg mod-els (but with Bertrandamong manufacturers)

Category profit No Yes

Sudhir (2001; this paper) Estimated Manufacturer Stackelberg,vertical Nash

Category profit, brandprofit, constantmargin

Logit (VSS), Multipli-cative (VSC)

No

tion implies that wholesale prices can be obtained byscaling down retail prices by a constant factor. Theseresearchers have found that manufacturer pricing(HSI) is more cooperative than Bertrand price com-petition. In this paper, we show that these models(with retailer assumed to charge a constant margin)are econometrically indistinguishable from a modelthat simply measures the extent of price coordinationacross brands by a strategic retailer. This observationraises the question as to whether the estimated levelof cooperation among manufacturers could just be co-ordinated pricing (category management) by the re-tailer. It, therefore, highlights the need to properlymodel and infer VSI simultaneously in order to ac-curately estimate the HSI when using data at the re-tail level.

In this paper, we investigate competitive behavioramong manufacturers by allowing for other plausiblemanufacturer-retailer interaction and infer the inter-action that best fits the data. We allow for two typesof VSI between the manufacturers and the retailer: (1)manufacturers as Stackelberg leaders and (2) verticalNash interaction. We also allow for alternative retailerpricing rules: (1) category profit maximization, (2)

brand profit maximization, and (3) constant margins.Using game-theoretic analysis, we infer wholesaleprices conditional on observed retail prices, sales, andother exogenous variables under each of the aboveassumptions. This enables us to analyze competitionamong manufacturers (HSI) under alternative as-sumptions about the VSI.

Besanko et al. (1998) (hereafter referred to as BGJ)focus on the importance of accounting for the endo-geneity of pricing decisions by manufacturers and re-tailers to obtain unbiased estimates for a logit modelusing aggregate data. In contrast to our emphasis oninferring the strategic behavior of market partici-pants, they assume (1) that manufacturers and theretailer make simultaneous pricing decisions, i.e., theyassume that VSI is vertical Nash, (2) that the retailerdoes category management by maximizing total prof-its from the category, and (3) that the HSI amongmanufacturers is Bertrand competition.

Other contemporaneous research has addressedsome of the issues that we discuss in this paper. Ka-diyali et al. (2000) measure the balance of power be-tween manufacturers and retailer by measuring theshare of channel profits. Although they model both



the HSI between manufacturers and the VSI betweenmanufacturers and retailer, their econometric modeldoes not permit one to identify the HSI between man-ufacturers (an issue of key interest in this paper).2

Another key difference is that their technique is ap-plicable only when researchers have access to whole-sale price data.

Cotterill and Putsis (2001) also test for the manu-facturer Stackelberg and vertical Nash VSI betweenmanufacturers and retailers without wholesale pricedata. They also test for constant margin and category-profit-maximizing behavior by the retailer. They an-alyze a number of product categories and find sup-port for both vertical Nash and manufacturerStackelberg interaction. However, they generally re-ject the constant margin assumption. In contrast toour paper, they assume a linear model of demand,assume that HSI between manufacturers is Bertrand,and do not test for brand-profit-maximizing behaviorby the retailer.3

In summary, this is the first paper to simultaneous-ly infer both HSI and VSI in a channel. The techniquecan be applied even in the absence of wholesale pricedata. Methodogically, a key difference with respect toCotterill and Putsis (2001) is that they derive theirsupply-side pricing equations similarly to theoreticalresearchers, by solving for optimal wholesale and re-

2We note that Kadiyali et al. (2000) estimate conjectural variations(CVs) for VSI and, therefore, do not impose the specific restrictionof leader-follower behavior. Estimating CVs, however, does not nec-essarily make the model more flexible, because the CV measuresreactions as a constant across all periods, while the derived optimalreaction in a leader-follower model (that we use here) is flexible toaccommodate changes from period to period based on changes indemand characteristics (a realistic assumption). Further research isneeded on the appropriateness of the two methods. They also testspecific models such as manufacturer Stackelberg, vertical Nash,etc., but, unlike the author of this paper, they assume that the HSIis Bertrand when they test those models. We also note that in theabsence of wholesale price data, a CV cannot be estimated for theVSI. The specific assumption about VSI (leader-follower, verticalNash) is necessary to estimate the model without wholesale pricedata.3They also estimate an LA-AIDS model, but without the structuralpricing equations. Hence it is not possible to choose among thedifferent VSI using the LA-AIDS model.

tail prices in terms of a deterministic demand model.4

In this paper, we recognize that observed marketshares include a demand-side econometric error thatis known to both firms and consumers, and thereforewill affect retail and wholesale passthrough differ-ently under different types of VSI and HSI. By ex-plicitly deriving the equations in terms of observedmarket shares, we account for the impact of demand-side econometric error on retail and wholesalepassthrough in a manner consistent with the theoret-ical structure of the specific model being tested, lead-ing to a more complete structural specification of theeconometric model.

Appropriateness of Demand Functional FormWhile functional forms of demand have been evalu-ated in terms of the fit of the model to sales data,recent game-theoretic research on channels (Lee andStaelin 1997, Tyagi 1999) has shown that the func-tional form of demand has serious implications forstrategic behavior such as retail passthrough. Whilethe logit and linear model implies equilibriumpassthrough of less than 100% (Lee and Staelin callthis vertical strategic substitute (VSS)), the multipli-cative model implies optimal passthrough of greaterthan 100% (vertical strategic complement (VSC)).Since passthrough rates on promotions have beenfound to be below or above 100% (Chevalier and Cur-han 1976, Armstrong 1991), a functional form withthe VSC property may be appropriate for categoriesthat have retail passthrough greater than 100%, whilea functional form with the VSS property may be ap-propriate if the passthrough is less than 100%. In thispaper, we therefore treat the appropriateness of func-tional form of demand as an empirical issue andchoose from the logit (VSS) or multiplicative (VSC)demand models.5

4It should be noted that in contrast to our interest in inferring theVSI and HSI, the primary focus of Cotterill and Putsis was to testspecific models in the theoretical literature on channels. Hence theiruse of deterministic demand models was guided by the theoreticalliterature. Kadiyali et al. (2000) also use the deterministic demandmodel approach when they test specific VSI such as the Stackelbergor Nash interactions.5We thank an anonymous reviewer for suggesting the empiricalanalysis of demand functional forms. A simple explanation for



Figure 1 A Schematic Model of the MarketIn summary, we choose from the following strate-gic interactions and demand models:

(1) Vertical strategic interaction: manufacturerStackelberg and vertical Nash;

(2) Horizontal strategic interaction: Bertrand, tacitcollusion. We also estimate a continuous conjecturalvariation (CV) parameter6;

(3) Retailer pricing rule: category-profit-maximi-zation, brand-profit-maximization, constant markup;

(4) Demand functional form: logit, multiplicative.Section 2 describes the model. Section 3 describes

the data, the estimation procedure, and the results.Section 4 concludes with a discussion of limitationsof the model and suggestions for future research.

2. ModelFigure 1 represents the schematic model of the marketthat we analyze: Two manufacturers sell through acommon retailer to consumers. Consumers maketheir choices after observing the retail prices. In themanufacturer Stackelberg models, the manufacturerschoose wholesale prices first; the retailer chooses re-tail prices after observing the wholesale prices. In thevertical Nash models, the manufacturers and the re-

passthrough greater than 100% in some categories is that retailersmay be using these categories as loss-leaders to drive traffic to thestore.6The CV has been used in previous research in the marketing lit-erature (e.g., Kadiyali et al. 1999, Putsis and Dhar 1999) to measureHSI. As the name suggests, CVs were originally interpreted as mea-sures of a players conjectures about reactions by rivals. This viewhas been discredited in the theoretical literature because such con-jectures cannot be consistent and are not meaningful in a staticanalysis (Tirole 1988, Carlton and Perloff 1994). Empirical research-ers, however, have successfully used CVs as a parameter to measuredeviations from Bertrand behavior, without interpreting them asconjectures about reactions between players. See Bresnahan (1989)for the distinction between the theoretical and empirical interpre-tations of conjectural variations. The menu approach based on the-oretical models does not face these criticisms leveled against the CVapproach. Briefly, for a strategic variable such as price, zero CVindicates Bertrand competition. Positive and negative CVs indicatemore cooperative and more competitive outcomes relative to Ber-trand competition, respectively. See Kadiyali et al. (Forthcoming)for a more detailed discussion.

tailer choose their prices simultaneously. Manufactur-ers choose their wholesale prices simultaneously. Inthe figure, one-sided arrows represent sequential de-cisions and double-sided arrows indicate simulta-neous decisions. The two main assumptions embed-ded in the figure are that (1) there are twomanufacturers in the market and (2) that manufac-turers sell through one retailer. We justify both ofthese assumptions below.

ASSUMPTION 1. There are two manufacturers in the mar-ket.

We focus our empirical analysis on the two largestbrands in the yogurt and peanut butter categories.This is reasonable for our purposes because the twolargest brands have a very large market share (82%for yogurt and 65% for peanut butter). Other brandshave relatively low market share of less than 10% inthis market. Private labels have a minuscule marketshare in these categories in these stores. Hence, theuse of private labels for strategic purposes is not aserious issue as in the studies by Kadiyali et al. (2000)and Putsis and Dhar (1999). While it is possible toextend model development to additional brands,solving for the optimal vertical strategic reactions be-comes computationally cumbersome.

ASSUMPTION 2. Manufacturers sell through one retailer.

The primary effect of this assumption is that we donot model any effect of retail competition. This may



be a serious shortcoming when analyzing categorieswhere retail competition is severe. Slade (1995) andWalters and McKenzie (1988), however, have shownevidence of limited retail competition in some cate-gories. Slade reported, based on her interviews ofgrocery chain managers, that the vast majority ofhouseholds (over 90%) do not engage in comparisonshopping on a week-to-week basis. Most consumersvisit the same store each week, and hence most com-petition seems to take place among brands in thestore rather than across stores. Slade also tested thisinterview-based evidence statistically on the saltinecracker market and found that demand at one storewas unaffected by prices in other chains. Walters andMackenzie examined the impact of loss-leader pricingand other promotions on store sales and profits andconcluded that price specials and double-coupon pro-motions had no significant effect on store traffic. Theyfound that only one of eight loss-leader categories hada significant effect on store traffic. In the structuralmodeling literature, while analyzing the yogurt cat-egory (which is analyzed in this paper), Besanko etal. (1998) and Vilcassim et al. (1999) have also madethe assumption of no cross-store competition.

To address the issue of whether the assumption isappropriate for our analysis, we follow Slade inchecking whether a stores sales are affected by pricesat a competing store. For our analysis we used datafrom two Every Day Low Price (EDLP) stores, whichhappen to be the biggest stores in the market. SeeSection 3 for discussion of the data. We ran a simul-taneous equations regression with two linear demandequations for each store. As the two biggest EDLPstores may also face competition from the promotion-al (High-Low pricing) stores, we also included datafrom a High-Low store. Together these three storesaccounted for 90% of sales in our market. Hence, wehad six equations in our estimation. Each brandssales in a store were regressed against prices of bothbrands at the same store and other stores.7 Whilesame store price coefficients were significant and of

7In addition to prices of our own and competing stores, we useddisplays at the same stores and features at our own and competingstores (to see if they affected store traffic). We also tested otherfunctional forms of demand, such as multiplicative and loglinear.

the right sign, other store prices were insignificant inall six equations. Hence, the assumption seems rea-sonable for the data that we analyze. Essentially, thisimplies that yogurt or peanut butter prices at com-peting stores have only a very minor effect on theconsumers decision to visit a particular store. How-ever, it is important to recognize that previous re-search has shown that detecting store competition re-quires fairly subtle modeling (Bucklin and Lattin1992). For our purposes, it appears that retail com-petition is a second-order effect that is not likely toimpact our results.

DemandAs discussed earlier, we consider two functionalforms: the logit demand model with the VSS prop-erty and the multiplicative demand model with VSCproperty. These functional forms have been usedwidely in the marketing literature: The logit demandmodel has been used both for modeling householdlevel data (for example, Guadagni and Little 1983)and aggregate market share data (for example, Al-lenby 1989). Recently, the logit model has beenshown to provide similar substantive implications,whether one uses the model at either the aggregate(store) or disaggregate (household) level (Allenbyand Rossi 1991, Gupta et al. 1996) under reasonablyrealistic conditions.8 The multiplicative demandmodel is a fairly popular demand model in the lit-erature (for an example, see the SCAN*PRO-basedmodel of Christen et al. 1997).

The Logit Model. The utility for brand i in periodt for consumer j is given by

U f d d p f pijt 0i f it d it dp it it fp it it

p p it it i jti

U i 1, 2, (1)it i jt

where f it, dit, and pit are the features, displays, andretail price associated with brand i in period t. 0i is

8A flexible demand model other than the logit is the LA-AIDSmodel used by Cotterill et al. (2000). Unfortunately, it is not possibleto derive the exact structural supply-side equations for this modelas we do in this paper.



the intrinsic attraction of brand i, and it is the un-observable (to the econometrician, but observable tothe firm and the consumer) component of utility. Uitis the average utility across consumers for brand i inperiod t. We assume that ijt follows an i.i.d. Type-Iextreme value distribution, leading to the logit model.

To allow for the market share of the two insidebrands to expand and contract over different periodswith the choice of the marketing mix, we allow fornonpurchases (through an outside good) denoted byi 0. We normalize the utility of the outside good tozero across periods. That is, we assume U0t 0.9 Themarket share for each brand is given by

exp(U )its , i 0, 1, 2. (2)it 21 exp(U ) kt

k1

Therefore, when both brands reduce prices, the totalmarket share of the two inside brands increases vis-a-vis the outside good and vice versa. Note that whenthe marketing-mix coefficients are the same for bothbrands the above model reduces to a logit model.

It is easy to see that

ln(s /s ) U f d d pit 0t it 0i f it d it dp it it

f p p ,fp it it p it iti

i 1, 2.

Therefore, rewriting the demand equation in termsof quantities,

ln(q ) ln(q ) f d d pit 0t 0i f it d it dp it it

f p p , i 1, 2. (3)fp it it p it iti

Equation (3) is the demand-side estimation equa-tion. The term it serves as the error term in the es-timation equation. As discussed in Besanko et al.(1998) and Villas-Boas and Winer (1999), these errorterms can capture the effects of manufacturer adver-tising and consumer promotions that we do not ex-plicitly model in this paper.

9Modeling the different correlations in ijt between the inside goodsand the outside good using a nested logit model would lead to aricher and more flexible formulation. However, this prevents solvingfor the supply-side estimation equations in closed form.

The first derivatives of market share with respectto prices are

s s 1t 2tp p s 1t 1tt

p s st 1t 2t p p 2t 2t

s (1 s ) s s1t 1t 1t 1t 1t 2t , (4) s s s (1 s )2t 1t 2t 2t 2t 2twhere it dpdit fp f it .pi

The Multiplicative Model. The multiplicative de-mand model was

qit aip p f f d d .bii bij fii fij dii dijit jt it jt it jt

For estimation, we used the log-log model, by tak-ing the logs of the above equation on both sides andadding a normal additive error. The derivatives withrespect to price for the multiplicative model are wellknown.

Retailer ModelWe derive the pricing equations for the retailer underdifferent types of VSI for the logit model. For the mul-tiplicative model, the equations can be derived simi-larly.

For the category-profit-maximizing retailer the ob-jective is to maximize category profits in period t.Since consumers who buy other than the two brandsthat we analyze may contribute to retailer profits, weassume that the outside good gives a constant contri-bution to retailer profit. Denoting the margin from theoutside good as m0, the retailer objective is given by

R [( p w )s ( p w )s m s ]M , (5)t 1t 1t 1t 2t 2t 2t 0 0t t

where p1t and p2t are the retail prices of Products 1and 2, w1t and w2t are the wholesale prices of Prod-ucts 1 and 2 set by the manufacturers, and s1t and s2tare the shares of Products 1 and 2 defined in the de-mand model (note that s0t 1 s1t s2t is the shareof the outside good), and Mt is the size of the market.The subscript t refers to the period t.

For the retailer maximizing brand profits, the ob-jective is to maximize each brand is profits in periodt without considering the impact of the chosen price



on the demand and profits from the other brand. Theobjective is given by

[(pit wit)sit]Mt, i 1, 2.Rit (6)

Because the retailer is a follower in the manufac-turer Stackelberg games, the retailer does not incor-porate manufacturer reactions when choosing retailprices. In the vertical Nash game also, the retailerdoes not incorporate manufacturer reactions, due tothe simultaneous nature of the game. Hence, the first-order conditions and the pricing equations are iden-tical for both the manufacturer Stackelberg modelsand vertical Nash models.

For the retailer maximizing category profits, thefirst-order conditions imply

R st 1t 0 s ( p w m )it 1t 1t 0 [ ]p pit its2t ( p w m ) 0,2t 2t 0 [ ]pit

i 1, 2. (7)

Substituting the price derivatives from (4) and solv-ing the first-order conditions give us the retail-pricingequation

1 s s 1t 2t s s p w 1t 1t 0t 2t 0t1t 1t m . (8) 0 p w 1 s s2t 2t 1t 2t s s 2t 1t 0t 2t 0t

Retail Wholesale

price priceRetail margin

For brand-profit-maximizing case, the first-orderconditions for the retailer are

R st 1t 0 s ( p w ) 0, i 1, 2. (9)it it it [ ]p pit itSubstituting the price derivatives from (4) and solv-

ing the first-order conditions give us the pricingequation

1 (1 s ) p w 1t 1t1t 1t . (10) p w 12t 2t (1 s ) 2t 2t

Retail Wholesale

price priceRetail margin

For the constant retailer margin model, the pricingequation is simply

p w w w1t 1t 1t 1t (1 m) m. p w w w2t 2t 2t 2t (11) Wholesale Retail

price margin

In Pricing Equations (8), (10), and (11) the first termrepresents the input cost (wholesale price) to the retailerand the second term represents the retailer margin.

For the manufacturer Stackelberg model, the retail-ers reactions to manufacturers wholesaler prices areobtained by taking the derivatives of the retail pricesin (8) and (10). It can be shown that (proof in Ap-pendix) for the manufacturer Stackelberg model withthe retailer maximizing category profits, the reactionsare given by

p p 1t 2tw w p 1 s s1t 1tt 1t 1t 10 . (12) w s 1 sp pt 2t 2t1t 2t w w 2t 2t

For the manufacturer Stackelberg model, with theretailer maximizing brand profits, the reactions aregiven by

10As we stated earlier, the logit demand model leads to verticalstrategic substitutability (VSS) since pi/wi 1.

2 2(1 s ) (1 s ) (1 s ) (s s ) 1t 2t 1t 1t 1t 2t2 2(1 s )(1 s ) (s s ) (1 s )(1 s ) (s s ) p 1t 2t 1t 2t 2t 1t 2t 1t 2tt . (13)

2 2w (1 s ) (s s ) (1 s ) (1 s )t 2t 2t 1t 2t 2t 1t 2 2 (1 s )(1 s ) (s s ) (1 s )(1 s ) (s s ) 1t 1t 2t 1t 2t 1t 2t 1t 2t



For the vertical Nash model, both the retailer andthe manufacturers take their decisions simultaneous-ly. Hence, only the direct effect of the change inwholesale price on retail price through the retailerinput cost (wholesale price) is accounted for but notthe indirect effect through its impact on the choice ofretail margin. Hence, for both the category-profit-maximizing case and the brand-profit-maximizingcase the impact on retail price for a change in whole-sale price is given by

p 1 0t . (14) w 0 1tFor the constant margin model, the retailer reaction

to a change in wholesale price is

p p 1t 2tw w p 1 m 01t 1tt . (15) w 0 1 mp pt 1t 2t w w 2t 2t

Manufacturer InteractionsWe now develop the model of manufacturer interac-tions (HSI) and the supply-side estimation equations.We allow for two alternative manufacturer interac-tions: (1) tacit collusion and (2) Bertrand competi-tion.11 The objective function of manufacturer i sellingbrand i in period t is given by

M (w c )s M (w c )s M F ,it it it it t jt jt it t it

i 1, 2; j i, (16)

where wit is the wholesale price for brand i that themanufacturer charges the retailer and cit is the margincost of brand i. Fit is the fixed cost to the manufac-turer (it can include costs that are not related to themarginal sales of the brand; e.g., slotting allowances).Note that 1 for the case of tacit collusion and 0 for the case of Bertrand competition. We definethe marginal cost of brand i as cit i it, wherei is the brand-specific margin cost, and it is the

11After choosing the best-fitting model using Vuongs (1989) test forthese two extreme cases, we also estimate the CVs later. For the CVestimates, refer to the section Implications of the IdentificationProblem.

brand-specific unobservable marginal cost at time t.Note that it is unobservable to the researcher, butobservable to the manufacturers.

The first-order conditions for the manufacturer aregiven by

M s p s pit it 1t it 2t s (w c ) it it it [ ]w p w p wit 1t it 2t its p s pjt 1t jt 2t

(w c ) 0,jt jt [ ]p w p w1t it 2t iti 1, 2; j i,

p st ts (w c ) 0, (17)t t t [ ]w pt twhere

1 1 1 1

for tacit collusion and

1 0 0 1

for Bertrand competition. The operator denotes el-ement-by-element multiplication of a matrix.

We can thus solve for the wholesale prices as1

p st tw c s , (18)t t t [ ]w pt twhere the term

1p st t st [ ]w pt t

is the vector of margins that manufacturers choosefor their brands.

Note that Equation (18) is purely in terms of ob-servable data and model parameters that we will es-timate. In the absence of data on wholesale prices, wecan substitute out the expression for wholesale pricesin (18) into the Retail-Pricing Equation (8), (10), and(11) to get the appropriate supply-side estimationequation that accounts for manufacturer and retailerbehavior,



Table 2 Retail Margins

Model Retailer Margin

Manufacturer StackelbergCategory profit maximization

1 s s 1t 2t s s 1t 1t 0 2t 0t

m 01 s s1t 2t

s s 2t 1t 0t 2t 0t

Manufacturer StackelbergBrand profit maximization

1 (1 s ) 1t 1t

1

(1 s ) 2t 2t

Vertical NashCategory profit maximization

1 s s 1t 2t s s 1t 1t 0t 2t 0t

m 01 s s1t 2t

s s 2t 1t 0t 2t 0t

Vertical NashBrand profit maximization

1 (1 s ) 1t 1t

1

(1 s ) 2t 2t

Constant margin retailer w1t m w2t

Table 3 Retailer Reactions

ModelRetailer Reaction

pt wtManufacturer StackelbergCategory profit maximization

1 s s1t 1t s 1 s2t 2tManufacturer StackelbergBrand profit maximization

2 2(1 s ) (1 s ) (1 s ) (s s ) 1t 2t 1t 1t 1t 2t2 2(1 s )(1 s ) (s s ) (1 s )(1 s ) (s s ) 1t 2t 1t 2t 2t 1t 2t 1t 2t

2 2 (1 s ) (s s ) (1 s ) (1 s )2t 2t 1t 2t 2t 1t

2 2 (1 s )(1 s ) (s s ) (1 s )(1 s ) (s s ) 1t 1t 2t 1t 2t 1t 2t 1t 2t

Vertical NashCategory profit maximization

1 0 0 1Vertical NashBrand profit maximization

1 0 0 1Constant margin retailer 1 m 0 0 1 m

1p st tp c s r . (19)t t t t [ ] w p t t

Manufac- Retailturer cost marginWholesale Margin

Wholesale price (w )t

The actual estimation equations for the five modelscan be obtained by appropriately substituting into theabove model the expression of rt and pt/wt. Wesummarize these in Table 2 and Table 3, respectively,for quick reference. Because these expressions are interms of observed market shares, which include thedemand-side econometric error, we have incorporat-ed demand-side econometric errors into the supply-side estimation equations in a manner consistent withthe theoretical structure of the model. This is a keydifference with respect to Cotterill and Putsis (2001),who use deterministic demand models in derivingtheir supply-side estimation equations, and thereforedo not model the structural effects of demand-sideeconometric error in their supply-side model.

Specifically, denoting the i, j element of matricespt/wt, st/pt, and as pwijt, spijt, and ij, we canwrite the two pricing-estimation equations by doingthe appropriate matrix algebra as follows:



p {[ s ( pw sp pw sp )1t 1 12 2t 11t 12t 12t 22t

s ( pw sp pw sp )]/Det }22 1t 21t 12t 22t 22t t

r ,1t 1t

p {[ s ( pw sp pw sp )2t 2 21 1t 22t 21t 21t 11t

s ( pw sp pw sp )]/Det }11 2t 12t 21t 11t 11t t

r ,2t 2t

where

Det ( pw sp pw sp )t 11 22 11t 11t 12t 21t

( pw sp pw sp )21t 12t 22t 22t

( pw sp pw sp )12 21 11t 12t 12t 22t

( pw sp pw sp ). (20)21t 11t 22t 22t

Therefore, our estimation equations for the logitmodel are the demand equations in (3) and the pric-ing equations in (20). Note, however, that in the cat-egory-profit-maximization case the quantity m0 in re-tailer margin cannot be separately identified from thecost intercept (i). Hence, the intercept estimate in thepricing equation in the category-profit-maximizationmodel is the sum of the brand-specific cost and theper-unit profit from the outside good.

Equivalence of the Constant-Margin RetailerModel and Retailer Coordination Model. In this sec-tion we demonstrate that the constant-margin retailermodel that measures HSI using the CV approach(that has been used in previous studies) is economet-rically identical to an alternative model that ignoresmanufacturers and just measures the degree of co-ordination in pricing across brands by the retailer us-ing the CV approach. To do this, we first show thatthe margin parameter (m) in the estimation equationfor the constant-margin retailer is not identified, and

we therefore derive the actual estimation equationthat is fit on the data. Then we derive the estimationequation for the retailer coordination model andshow that the two equations are equivalent.

Substituting the retailer reaction to wholesale pric-es for the constant-margin model in Equation (15), theestimation equation becomes

11 stp c I s (1 m).t t t [ ]1 m ptHence,

1stp c (1 m) I s . (21)t t t [ ]pt

Therefore, the final estimation equation in this caseis

1stp I s , (22)t 0 t t t [ ]pt

where (1 m) and t(1 m). Of course,tm cannot be identified from this estimation equation.This estimation equation generalizes the equation de-rived in Vilcassim et al. (1999) for their linear demandmodel to a nonlinear demand model.

We now show that the supply-side estimation equa-tion for a model measuring the degree of coordina-tion in pricing across brands using the CV approachis econometrically identical to (22). Here we param-eterize the level of coordination in retail pricingacross brands.

The objective function of a retailer maximizing prof-its from brand i in period t is given by

(pit wit)sitMt, i 1, 2.Rit (23)

The first-order conditions are given by

M s s p it it jtit 0 s ( p w ) 0,it it it [ ]p p p pit it jt iti 1, 2; j i.

Denoting 21 p1t/p2t and 12 p2t/p1t for allt, we can write the above equation in matrix form as

sts I ( p w ) 0, (24)t t t [ ]ptwhere



1 12 121and the operator denotes element-by-element multi-plication of a matrix and I is the identity matrix. Wecan interpret the ij terms as the measure of coordina-tion in pricing across brands by the retailer. Therefore,

1stp w I s . (25)t t t [ ]pt

If we express wt in terms of factor prices and anerror term, then the estimation Equation (25) is econo-metrically identical to (22). Hence, the ambiguity aboutwhat the estimates of the s mean, i.e., whether theymeasure the extent of retail-pricing coordination or thedegree of cooperation among manufacturers when re-tailers are nonstrategic and charge a constant margin.

3. Empirical AnalysisDataWe do our analysis on the yogurt and peanut buttercategories on two EDLP stores from two different re-gional chains in a suburban market.12 These storeshappen to be the two largest in this market. The dataare for a period of 104 weeks during 19911993. Inthe yogurt market, we analyze competition betweenthe two largest brands, Dannon and Yoplait. To-gether, they constitute about 82% of sales in this cat-egory in this market. In the peanut butter market, weanalyze competition between the two largest brandsin the market: Skippy and Jif. Together they con-stitute about 66% of sales in this category. The nextlargest national brand has less than 10% of marketshare in both categories in these stores. Private labelshave a very small market share in these stores.

Because store-level data do not provide any infor-mation on the share of the no purchase alternative,

12These stores claimed to be EDLP. We verified these claims by com-paring the variance of prices between these self-professed EDLPchains and self-professed high-low chains in this market. As ex-pected, the price variance in the EDLP chains is about half of thatof high-low chains. Furthermore, consistent with Bell and Lattin(1998), EDLP chains had a lower average price than the high-lowchains.

we follow BGJ in using information from the house-hold-level data to compute the share of no pur-chase. Assuming that the panel is representative ofthe universe of consumers, BGJ take the share of nopurchase as the proportion of store visits by the pan-elists in the data that did not lead to a purchase inthe category.13

EstimationOur estimation equations are the demand equationsin (3) and the pricing equations in (20). As discussedearlier, details such as consumer promotions and ad-vertising are not available in scanner data and areunobserved by the researcher and therefore capturedby the demand error terms jt. However, manufactur-ers, retailers, and consumers have information onthese, and therefore they affect the manufacturersand retailers choice of prices and the consumers de-cision to buy. Villas-Boas and Winer (1999) and BGJoffer evidence that this is indeed true. We do the samevariation of the Hausman (1978) test that BGJ use andfind price is endogenous. We use lagged price as aninstrument in conducting this test.

Because features and displays are also strategic de-cisions made by the retailer, theoretically they shouldbe considered endogenous. Putsis and Dhar (1999)found that features and displays are indeed endoge-nous. We test for endogeneity of features and displayin two ways. First we follow Villas-Boas and Winer(1999) and look at the correlation between estimatedresiduals (using both three-stage least square (3SLS)and full-information maximum likelihood (FIML),where only price was treated as endogenous and fea-ture and display were treated as exogenous) and fea-ture and display. The correlations were not significant(p values .2), indicating that there would be noendogeneity bias if feature and display were treatedas exogenous. One may note that in our demandmodel, we allow for interaction effects between priceand feature and between price and display. This in-

13Because multiple purchases in a store visit are fairly common inthe yogurt category, in this category we also reweight store visitsby the number of purchases made during the visit in computingthe no purchase share. The results, however, are not very sensitiveto the reweighting.



teraction variable was crucial in eliminating the en-dogeneity bias problem.14 The second test we do is avariation of the Hausman test. We estimate two mod-els with price treated as endogenous using 3SLS: (i)with feature and display as endogenous and usinginstruments (lagged feature and display) and (ii) withfeature and display as exogenous. If feature and dis-play were indeed exogenous, then both models wouldbe consistent, but the first models estimates wouldhave a higher variance because it is an instrumentalvariable method. However if feature and display wereendogenous, only the first model would be consistent.If q denotes the vector of parameters to be estimated,then the test statistic (q1 q2)(V1 V2)1(q1 q2),where V is the estimated covariance matrix, is dis-tributed as 2(#q) distribution, where #q is the num-ber of parameters in the vector q. We find that thenull hypothesis of exogeneity cannot be rejected (p .17).

This endogeneity of prices, however, implies thatwe still need to use an instrumental variables esti-mation procedure. Furthermore, errors across thesupply and estimation equations are correlated dueto price. We therefore need to use a simultaneousequation instrumental variables estimation proceduresuch as FIML or 3SLS. The major advantage of FIMLestimation is that we do not need to provide instru-ments for prices, because the optimal instruments aregenerated within the estimation procedure. To com-pute the optimal instruments in FIML, however, weneed to make the normal distribution assumption onthe error terms. That is, we assume that 1t, 2t, 1t,

2t are assumed multivariate normal. In 3SLS there isno need to make the multivariate normal assumption,but we need to provide instruments. We prefer FIMLin this paper, because formal tests for nonnestedmodels (Vuong 1989) are available using likelihoodestimates.

14We briefly explain the intuition for why modeling the interactioncan help in eliminating the endogeneity bias problem. Let y1 x11 x22 x1x23 be the true model. Suppose x1 is endogenous,but x2 is not. Instrumenting x1 will eliminate the endogeneity bias,but suppose we only fit the model y1 x11 x22 1, then 1 x1x23. In this case we will find that cov(1, x1) 0 andcov(1, x2) 0. Therefore, it will seem that both variables are en-dogenous if we do not include the interaction term.

However, to check whether our results are robustto the choice of estimation procedure, we also esti-mated the model using nonlinear 3SLS, using laggedprices as instruments for prices. The results that wereport are consistent with both types of estimationprocedures. We, however, report only FIML-based es-timates, because we use these to do our tests of modelselection.

ResultsModel Selection: Choice of Functional Form. We

formally test whether the difference in log-likelihoodssignificantly favors one model using the Vuongs(1989) test of model selection for nonnested models.The best-fitting multiplicative model in the yogurtcategory had a log-likelihood of 343.09 for Store 1and 423.9 for Store 2. For the peanut butter category,the best-fitting multiplicative model had a log-likeli-hood of 320.14 for Store 1 and 421.39 for Store 2.Clearly, the logit demand model performed much bet-ter in terms of fit compared with the multiplicativedemand model. This is especially true consideringthat there were three extra parameters in the multi-plicative model compared with the logit model. Weperformed the Vuongs test for this case, and rejectthe multiplicative model at p 0.001. It therefore ap-pears that VSS implication of the logit model fits thedata better than VSC implication of the multiplicativedemand model.

However, an alternative explanation for the poorerfit of the multiplicative model could be that it also fitsthe demand equations rather poorly, compared withthe logit model. We therefore estimated only the de-mand models using both functional forms using3SLS.15 The logit model had a higher sum of squarederrors than the multiplicative model, indicating thatthe multiplicative model with a greater number of pa-rameters fits the data better if we use purely the de-mand equations. Hence, the reduction in fit when weinclude the pricing equations can be attributed to theexplanation that the supply-side implications of thelogit model (VSS) fit the data better than the supply-side implications of the multiplicative model (VSC).

15Note that we cannot use FIML if we do not have the same numberof endogenous parameters and equations.



Table 4 Model Likelihoods and the Vuong Test Statistics

ManufacturerInteraction

Retailer Objective/Manufacturer-Retailer Interaction

Likelihoods for Yogurt(Vuong Test Statistic)

Store 1 Store 2

Likelihoods for Peanut Butter(Vuong Test Statistic)

Store 1 Store 2

Tacit collusion Category profit maximizationManufacturer StackelbergCategory profit maximizationVertical NashBrand profit maximizationManufacturer StackelbergBrand profit maximizationVertical NashConstant marginManufacturer Stackelberg

196.90()

205.19(2.259)

202.38(2.028)

208.25(2.643)

207.29(2.529)

247.27()

298.29(2.101)

292.19(1.972)

321.17(2.529)

309.35(2.318)

240.66()

289.24(2.734)

259.44(1.700)

288.82(2.722)

297.95(2.969)

212.96()

265.47(2.132)

257.41(1.961)

275.28(2.322)

280.95(2.426)

Bertrand competition Category profit maximizationManufacturer StackelbergCategory profit maximizationVertical NashBrand profit maximizationManufacturer StackelbergBrand profit maximizationVertical NashConstant marginManufacturer Stackelberg

203.66(2.040)

208.25(2.643)

266.78(6.558)

204.39(2.147)

211.03(2.949)

249.9(2.030)

309.35(2.318)

318.84(2.489)

310.93(2.347)

325.85(2.608)

271.11(2.164)

288.82(2.722)

266.78(2.005)

291.55(2.798)

303.71(3.114)

269.08(2.204)

275.28(2.322)

277.74(2.368)

301.75(2.772)

307.85(3.821)

Note: The Vuong test statistic is with respect to the best-fitting model (with the highest log-likelihood).

The VSS implication that retail passthrough is lessthan 100% appears to be intuitive for the two cate-gories that we analyze, since yogurt or peanut butterare not usually used as loss-leaders to drive storetraffic. This implication is particularly valid for thisdata set, because our earlier analysis revealed that yo-gurt and peanut butter prices had a very limited im-pact on competitors sales. Hence, these categories areunlikely to have been used to build store traffic.

Model Selection: Results for the Logit Model. Thelikelihoods for the different models of the yogurt andpeanut butter markets for the logit functional formare reported in Table 4. Based on the log-likelihoodsit seems obvious that, for both stores, the manufac-turer Stackelberg model where manufacturers are in-volved in tacit collusion and the retailer maximizescategory profits fits best in both categories. TheVuong statistics for the different models are comput-ed with respect to this best-fitting model. Since theVuong statistic is distributed as a standard normal,

the critical value for rejecting a model at a p value of0.05 is 1.645. Given that all of the Vuong statistics aregreater than 1.645, we can reject the other models infavor of the best-fitting model.

Retailer Objective. The stores that we analyze werepart of large regional chains. Category managementwas becoming an increasingly popular concept at thebeginning of the 1990s. In a survey of retailers, Mc-Laughlin and Hawkes (1994) found that many largeretailers that had the technological infrastructure tocollect and analyze data had adopted the categorymanagement concept. Hence the result that retailer-maximized category profits has face validity. Our re-sults also support the assumption widely made in thetheoretical literature that retailers maximize categoryprofits (Choi 1991, Lee and Staelin 1997).

Manufacturer-Retailer Interaction (VSI). The re-sult that the manufacturer Stackelberg model best fitsthe data is consistent with the institutional practice



Table 5a Estimates for Best-Fitting Model in Yogurt Category

Store 1

Parameter SE t

Store 2

Parameter SE t

Intercept (Dannon)Intercept (Yoplait)FeatureDisplayFeature PriceDisplay PricePriceMarginal cost (Dannon) outside

good retail marginMarginal cost (Yoplait) outside

good retail margin

2.7402.9202.5802.122

4.3780.8006.364

0.337

0.457

0.5630.4730.9392.2271.3563.4470.633

0.042

0.045

4.8706.1702.7500.950

3.2300.230

10.060

8.100

10.250

4.5394.6162.4794.078

3.8836.5077.669

0.281

0.428

0.4950.6170.3491.7830.6393.4450.678

0.050

0.053

9.1807.4907.1102.290

6.0801.890

11.310

5.620

8.060

Table 5b Estimates for Best-Fitting Model in Peanut Butter Category

Store 1

Parameter SE t

Store 2

Parameter SE t

Intercept (Skippy)Intercept (Jif)FeatureDisplayFeature PriceDisplay PricePriceMarginal cost (Skippy) outside

good retail marginMarginal cost (Jif) outside good

retail margin

10.41410.523

3.47014.400

4.94212.54410.539

0.718

0.714

1.5381.5284.3032.3274.9852.2841.326

0.054

0.056

6.7706.8900.8106.190

0.9905.4907.950

13.220

12.870

9.5049.6168.8075.023

8.0662.9449.049

0.798

0.771

2.1622.1422.3762.9702.2212.8951.831

0.082

0.086

4.4004.4903.7101.690

3.6301.0204.940

9.760

9.020

in which manufacturers announce their wholesaleprices and the retailers choose their retail prices as aresponse to these wholesale prices (Quelch and Farris1983). This sequential approach has also been usedin theoretical models of manufacturer-retailer pricinginteractions (McGuire and Staelin 1983, Agrawal1996).

Some theoretical research (e.g., Choi 1991) has putforth the argument that leadership in the manufac-turer-retailer interaction may be a result of power bal-ance between manufacturers and retailers. Using thisargument, BGJ argue that vertical Nash is an appro-priate assumption because increasingly there is bal-ance of power between manufacturers and retailers.Our result that manufacturer Stackelberg leadership

may be a reflection of the fact that the balance ofpower in these categories is in favor of manufacturers.Given the dominance of the two leading brands inthese categories, our result also has substantial facevalidity on the basis of the power argument. In aninterview by Manning et al. (1998), one executive saysit tellingly: We cant walk away from the kind ofshares that they have in some of the categories, so wehave to work with them and we cant afford not topromote these products. 16

16The author notes that Lee and Staelin (1997) show that Stackelbergleadership leads to greater profitability (and therefore implies great-er power) only in the case of demand models characterized by VSS.The power balance argument the author makes holds only because



Manufacturer-Manufacturer Interaction (HSI). Acooperative outcome (relative to Bertrand competi-tion) can be achieved in a noncooperative game byusing appropriate punishment strategies when firmsdeviate from cooperative behavior. Such cooperativebehavior is easier to sustain under certain marketconditions than others. Besanko et al. (1996) providean excellent discussion on how such coordination canbe achieved in a noncooperative setting. A highlyconcentrated market facilitates cooperative behavior.This is because coordination is easier among a smallnumber of firms. Further, detection of deviationsfrom cooperative behavior is relatively easy, makingthe threat of punishment strategies more credible,thus enforcing cooperation. Because Dannon andYoplait have a high concentration in the yogurt mar-ket (82% in our data), it is not surprising that thesefirms behave cooperatively relative to Bertrand com-petition. The same arguments hold for Skippy andJif, who collectively have over 66% market share inthe stores that we analyzed.

Demand and Cost Estimates for the Best-FittingModel. We report the results of our estimation for thebest-fitting models in the yogurt and peanut buttercategory in Table 5a and 5b (see p. 258), respectively.All of the coefficients have the expected signs, givingthe analysis substantial face validity.

As expected, features and display have a positiveeffect on sales in both categories and stores. Price hasa negative effect on sales. In the final estimations wedid not estimate brand-specific price coefficients, be-cause it turned out in the estimation that they werenot significantly different from each other when weincorporate the price-feature and price-display inter-action effects. It is well known that a decrease in pricewhen accompanied by a feature or display has agreater impact on sales than their separate effects.This was confirmed in that the interaction terms be-tween price and display and between price and fea-ture are negative and significant.

The demand intercept for Yoplait is marginally

he has inferred that the VSS logit model is more appropriate thanthe VSC multiplicative model. We thank a reviewer for suggestingthat we highlight this.

higher than for Dannon. However, the estimate ofmanufacturing cost plus retailer margin from outsidegood for Dannon is about 30% lower than that ofYoplait. This implies that Dannon is the low-costleader.17 These results are similar to those of BGJ, eventhough our estimates are on a very different data set.However, the differences in the estimates of manufac-turing cost plus retailer margin from the outsidegood indicates that Store 1 gets a greater margin fromthe outside good in the yogurt category.

In the case of the peanut butter category, the de-mand intercept for Skippy is marginally lower thanfor Jif. The estimate of manufacturing cost plus re-tailer margin from outside good for Skippy is mar-ginally lower than that of Jif. However, the differ-ences in the estimates of manufacturing cost plusretailer margin from the outside good indicate thatStore 2 gets a greater margin from the outside goodin the peanut butter category.

We report estimates of elasticities for the two cat-egories in Table 6a and 6b. Across both stores, wefind that Yoplait has greater price elasticity than Dan-non. Further, Yoplait has greater cross-elasticitywith respect to Dannons prices than vice versa.This indicates a very strong market position for Dan-non, and it is not surprising when we consider thatDannon is usually regarded as synonymous withyogurt.18 In the peanut butter category, across bothstores, Skippy has greater price elasticity than Jif.Further, Skippy has greater cross-elasticity with re-spect to Jifs prices than vice versa. This indicates astronger market position for Jif than for Skippy.Our results in the peanut butter market are consistent

17According to the teaching case YoplaitUSA in the marketing textby Berkowitz et al. (1999, p. 607), some serious concerns forYoplaitUSA in 1993 (the period of our analysis) were (i) RetailPrices: Yoplaits prices for a six ounce cup was higher on some linesthan competitors eight ounce cups. For example, the prices on Yo-plaits 4 pack are about 20% higher per cup than Dannons andKrafts 6 pack. (ii) Low gross margins: Margins have declined, atleast partly because of high production and overhead costs. Theconcern about the relatively high production costs and its impacton prices give face validity to our estimates.18 General Mills Inc.: Yoplait Custard Style Yogurt (A), HarvardBusiness School Case 9-586-087, 1986.



Table 6a Elasticity Estimates for Yogurt Category

Store 1

Elasticity ofDannon

Elasticity ofYoplait

Store 2

Elasticity ofDannon

Elasticity ofYoplait

w.r.t. Dannon pricew.r.t. Yoplait price

4.2930.286

0.6405.420

4.6010.537

1.2896.462

Table 6b Elasticity Estimates for Peanut Butter Category

Store 1

Elasticity ofSkippy

Elasticity ofJif

Store 2

Elasticity ofSkippy

Elasticity ofJif

w.r.t. Skippy pricew.r.t. Jif price

11.0262.488

2.32810.505

8.7552.583

2.1188.370

Table 7 CV Estimates for the Logit Model: Category-Profit-Maximizing Re-tailer and Constant-Margin Retailer

Yogurt

Store 1 Store 2

Peanut Butter

Store 1 Store 2

Category profit max-imizing retailer

Constant margin re-tailer

1212

0.1220.1540.2320.252

0.1260.1490.2620.232

0.1510.3990.2970.454

0.1470.3160.2040.693

with the strength of these brands at the national level(Deveney 1993).

Implications of the Identification Problem. Wehave shown that the constant-margin retailer modelis econometrically identical to a model measuring thedegree of retail coordination. Hence, intuitively weshould expect that CVs estimated for the HSI mightbe exaggerated under the assumption of a constant-margin retailer compared with CV estimates whenthe retailer strategically maximized category profitswith the manufacturer as the Stackelberg leader. Wetest this intuition by comparing the CV estimates forthe two models.19 The CV estimates for the two mod-els in both categories and stores are reported in Table7. CV estimates are consistently higher, exaggeratingthe degree of cooperation among manufacturers forthe constant-margin retailer model. This is consistentwith the intuition we gain from the analytical results.The empirical result further underscores the need toproperly model the VSI in inferring the HSI.

4. ConclusionIn this paper, we empirically inferred the VSI be-tween manufacturers and retailers and the HSI be-

19Since FIML does not converge for the CV models, we use 3SLSfor estimation.

tween manufacturers simultaneously. The approachis particularly appealing because it can be used inthe common situation in which the wholesale priceinformation of all competitors is not available. Weshowed analytically that the simplifying assumptionthat a retailer charges a constant margin (used in ear-lier research) may misinterpret category managementbehavior by the retailer to be cooperative behavior bymanufacturers. Consistent with the intuition from theanalytical result, we find that the estimated cooper-ation among manufacturers is exaggerated for theconstant-margin model, highlighting the need to si-multaneously model and infer the VSI when analyz-ing the HSI.

Since packaged goods manufacturers spend a siz-able share of their marketing-mix budget on tradepromotions (Bucklin and Gupta 1999), several deci-sion support systems (DSSs) have been developed toaid manufacturers in their promotion planning (e.g.,Neslin et al. 1995, Tellis and Zufryden 1995, Midgleyet al. 1997, Silva-Risso et al. 1999). Our results are ofsubstantive import in guiding the assumptions thatgo into such DSSs. For example,

1. DSSs usually assume Bertrand behavior amongmanufacturers (e.g., Midgley et al. 1997). By explicitlytesting for Bertrand behavior as well as cooperativebehavior among manufacturers, we found that man-ufacturers in these markets tend to be more cooper-ative. A DSS that assumes Bertrand pricing behaviorwould have led to more aggressive pricing thanwould be warranted by the actual behavior of themarket participants.

2. Many DSSs assume manufacturer Stackelbergbehavior between manufacturers and retailers (e.g.,



Tellis and Zufryden 1995). However, the theoreticalliterature does not provide clear guidance on whethersuch an assumption is appropriate; it shows that achange in assumption can have substantive implica-tions for pricing behavior of the channel member.Given the apparent shift in power to retailers, thisquestion becomes even more important to managers.We found that for the categories and markets that weanalyzed, the manufacturer Stackelberg assumptionis appropriate.

3. DSSs have used different assumptions about re-tailer-pricing rules. Silva-Risso et al. (1999) assumethat retailers follow a simple passthrough rule andmanufacturers incorporate that assumption when de-ciding their trade deal. Tellis and Zufryden (1995) as-sume that the retailers objective is to maximize cat-egory profits. By testing both these specificassumptions, we found that both retailers objectiveis to maximize category profits.

4. DSSs also make assumptions about the function-al form of demand. While functional forms of de-mand have been evaluated in terms of the fit of themodel to sales data, its ability to accommodate thebehavioral implications of the supply side have notbeen evaluated. We found that the logit model per-formed better than the multiplicative model in itsability to accommodate the strategic behavior of firmsfor the categories that we analyze.

We now discuss some of the limitations in this pa-per and possible avenues for future research. First, itwould be useful to validate the methodology bychecking how well the model predicts actual whole-sale prices by estimating the model on a data set withwholesale prices. Second, the current estimationmethod assumes that the estimation equations can bederived in closed form. To allow for greater flexibilityin the functional forms and also to extend the anal-ysis to a larger number of brands, we need to enableestimation even when closed-form estimation equa-tions cannot be obtained.

Clearly more research in other categories at otherretail stores is needed before we can develop a bodyof evidence that will enable us to understand the im-pact of supply characteristics (for example, degree ofconcentration in market, manufacturer-retailer power

balance, availability of private labels) and demandcharacteristics of category (e.g., high inertia or varietyseeking, stockpiling, average price sensitivity, lossleader) on the inference of strategic interactions. Forexample, Cotterill and Putsis (2001) find that the Ver-tical Strategic Interactions are different across cate-gories, while we found manufacturer Stackelberg be-havior in both categories we analyze. Understandingthe determinants of these differences should be of in-terest in future work.

Putsis and Dhar (1998) have also done a cross-cat-egory analysis of how competitive behavior betweenprivate labels and manufacturers changes as a func-tion of the category and market characteristics. Sudhir(2001) develops hypotheses combining argumentsfrom game-theoretic research and the ability-motiva-tion paradigm (Boulding and Staelin 1995) about howcompetitive behavior in different segments of theauto market will differ, depending on the demand-and-supply characteristics of these markets, and thentests these hypotheses. Such an analysis will helpprovide deeper insights into the determinants of hor-izontal and vertical strategic interactions and appro-priateness of functional forms of demand.

The issue of retail competition was not found tobe particularly important in the yogurt and peanutbutter categories. Future research into categoriessuch as detergents and soda, which are known tohave an impact on store traffic, is needed to studythe role of strategic retail competition on retailer-pricing behavior. Also, retail competition may be atthe basket level across a number of categories (Belland Lattin 1998).

We have limited ourselves to the inference of man-ufacturer-retailer interaction only when the retailer isEDLP. However, accounting for unobserved hetero-geneity among consumers in the demand model canenable us to investigate how loyalty and switchingbehavior, asymmetric responses to lower-price-tierbrands, etc., may cause high-low pricing behavior. Weare investigating how to use household-level data toinfer heterogeneity distributions and how to incor-porate this information into the aggregate model sothat we can extend our analysis to the case of high-low retailers. Horsky and Nelson (1992) and Gold-



berg (1995) provide good starting points for thisstream of research. Recently, there has been interestin recovering heterogeneity from aggregate data (Ber-ry et al. 1995, Kim 1995, Nevo 2001, Sudhir 2001,Chintagunta 1999). In recent work, Villas-Boas andZhao (2000) address many of the issues in modelingchannel behavior with household-level data.

We have not modeled any kind of dynamics thataffect demand or supply. Forward buying by con-sumers, habit persistence, variety seeking, advertis-ing wearout, etc., can have intertemporal demandeffects, which in turn can affect supply-side behav-ior. Forward buying by retailers is another supply-side intertemporal effect. While the use of efficientconsumer response (ECR) has significantly reducedforward buying on the part of retailers, it is still asignificant component of how a retailer reacts to atrade deal. This is an important issue for future re-search. For a more comprehensive set of methodo-logical and substantive questions that await researchin this area, we direct the reader to Kadiyali et al.(2001).

AcknowledgmentsThis paper is based on an essay from the authors1998 Ph.D. dissertation at Cornell University. Hethanks the members of the dissertation committee, es-pecially Vithala R. Rao and Vrinda Kadiyali, for theirextensive comments and suggestions. The author alsothanks Pradeep Chintagunta, Bill Putsis, and RobertShoemaker for their comments, as well as the seminarparticipants at Chicago, Cornell, Dartmouth, Duke,HKUST, INSEAD, NYU, Purdue, Rochester, Stanford,SUNY Buffalo, Toronto, UCLA, and Yale. The authorhas benefited greatly from the review process andthanks the editor, the area editor, and the two anon-ymous reviewers for their input in revising this paper.The usual disclaimer applies.

Appendix

Reactions for Category-Managing RetailerTaking the derivatives of the retail prices in Equation (8) of thepaper,

p 1 1 s p s p1t 1t 1t 1t 2t 1 s 0t2 [w s p w p w1t 0t 1t 1t 1t 2t 1t1 s p s p1t 1t 1t 2t p w p w2t 1t 1t 2t 1t

s s s p s p s p1t 2t 1t 1t 1t 2t 2t 1t p w p w p w1t 2t 1t 1t 2t 1t 1t 1ts p2t 2t .]p w2t 1t

Substituting the share derivatives with respect to prices fromEquation (4), we get

p s p s p1t 1t 1t 2t 2t 1 . (A1)w (1 s s ) w (1 s s ) w1t 1t 2t 1t 1t 2t 1t

Similarly,

p s p s p2t 1t 1t 2t 2t . (A2)w (1 s s ) w (1 s s ) w1t 1t 2t 1t 1t 2t 1t

Solving (A1) and (A2) for p1t/w1t and p2t/w1t, we havep1t/w1t 1 s1t and p2t/w1t s1t. By symmetry, p2t/w2t 1 s2t and p1t/w2t s2t.

These reactions are summarized in Equation (12) of the paper.

Reactions for Brand-Managing RetailerTaking the derivatives of the retail prices in Equation (10) of thepaper,

p 1 s p s p1t 1t 1t 1t 2t 1 ,1t2 2 [ ]w (1 s ) p w p w1t 1t 1t 1t 1t 2t 1tp 1 s p s p2t 2t 1t 2t 2t .2t2 2 [ ]w (1 s ) p w p w1t 2t 2t 1t 1t 2t 1t

Substituting the share derivatives with respect to prices fromEquation (5), we get

p s p s s p1t 1t 1t 2t 1t 2t 2t 1 , (A3)2w (1 s ) w (1 s ) w1t 1t 1t 1t 1t 1t

p s s p s p2t 1t 1t 2t 1t 2t 2t . (A4)2w (1 s ) w (1 s ) w1t 2t 2t 1t 2t 1t

Solving (A3) and (A4) for p1t/w1t and p2t/w1t, we have

2p (1 s ) (1 s )1t 1t 2t and2w (1 s )(1 s ) (s s )1t 1t 2t 1t 2t

2p (1 s ) (s s )2t 1t 1t 1t 2t .2w (1 s )(1 s ) (s s )1t 2t 1t 2t 1t 2t

By symmetry,

2p (1 s ) (1 s )2t 2t 1t and2w (1 s )(1 s ) (s s )2t 1t 2t 1t 2t

2p (1 s ) (s s )1t 2t 2t 1t 2t .2w (1 s )(1 s ) (s s )2t 1t 1t 2t 1t 2t

These reactions are summarized in Equation (13) of the paper.



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