Supermarket Pricing Strategies

Vol. 27, No. 5, September–October 2008, pp. 811–828issn 0732-2399 �eissn 1526-548X �08 �2705 �0811

informs ®

doi 10.1287/mksc.1080.0398©2008 INFORMS

Supermarket Pricing Strategies

Paul B. EllicksonDepartment of Economics, Duke University, Durham, North Carolina 27708,

[email protected]

Sanjog MisraWilliam E. Simon School of Business Administration, University of Rochester,

Rochester, New York 14627, [email protected]

Most supermarket firms choose to position themselves by offering either everyday low prices (EDLP) acrossseveral items or offering temporary price reductions (promotions) on a limited range of items. While

this choice has been addressed from a theoretical perspective in both the marketing and economic literature,relatively little is known about how these decisions are made in practice, especially within a competitive envi-ronment. This paper exploits a unique store level data set consisting of every supermarket operating in theUnited States in 1998. For each of these stores, we observe the pricing strategy the firm has chosen to follow,as reported by the firm itself. Using a system of simultaneous discrete choice models, we estimate each store’schoice of pricing strategy as a static discrete game of incomplete information. In contrast to the predictions ofthe theoretical literature, we find strong evidence that firms cluster by strategy by choosing actions that agreewith those of its rivals. We also find a significant impact of various demographic and store/chain characteristics,providing some qualified support for several specific predictions from marketing theory.

Key words : EDLP; promotional pricing; positioning strategies; supermarkets; discrete gamesHistory : Received: March 22, 2006; accepted: February 27, 2008; processed by David Bell.

1. IntroductionWhile firms compete along many dimensions, pricingstrategy is clearly one of the most important. In manyretail industries, pricing strategy can be characterizedas a choice between offering relatively stable pricesacross a wide range of products (often called every-day low pricing) or emphasizing deep and frequentdiscounts on a smaller set of goods (referred to aspromotional or PROMO pricing). Although Wal-Martdid not invent the concept of everyday low pricing,the successful use of everyday low pricing (EDLP)was a primary factor in their rapid rise to the topof the Fortune 500, spawning a legion of followersselling everything from toys (Toys RUs) to buildingsupplies (Home Depot). In the 1980s, it appeared thatthe success and rapid diffusion of the EDLP strategycould spell the end of promotions throughout muchof retail. However, by the late 1990s, the penetrationof EDLP had slowed, leaving a healthy mix of firmsfollowing both strategies, and several others employ-ing a mixture of the two.Not surprisingly, pricing strategy has proven to be

a fruitful area of research for marketers. Marketingscientists have provided both theoretical predictionsand empirical evidence concerning the types of con-sumers that different pricing policies are likely toattract (e.g. Lal and Rao 1997, Bell and Lattin 1998).While we now know quite a bit about where a person

is likely to shop, we know relatively little about howpricing strategies are chosen by retailers. There aretwo primary reasons for this. First, these decisionsare quite complex: managers must balance the pref-erences of their customers and their firm’s own capa-bilities against the expected actions of their rivals.Empirically modeling these actions (and reactions)requires formulating and then estimating a complexdiscrete game, an exercise which has only recentlybecome computationally feasible. The second is thelack of appropriate data. While scanner data setshave proven useful for analyzing consumer behavior,they typically lack the breadth necessary for tack-ling the complex mechanics of inter-store competi-tion.1 The goal of this paper is to combine newlydeveloped methods for estimating static games witha rich, national data set on store level pricing poli-cies to identify the primary factors that drive pricingbehavior in the supermarket industry.Exploiting the game theoretic structure of our

approach, we aim to answer three questions thathave not been fully addressed in the existing liter-ature. First, to what extent do supermarket chainstailor their pricing strategies to local market condi-tions? Second, do certain types of chains or stores

1 Typical scanner data usually reflect decisions made by only a fewstores in a limited number of markets.

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Ellickson and Misra: Supermarket Pricing Strategies812 Marketing Science 27(5), pp. 811–828, © 2008 INFORMS

have advantages when it comes to particular pricingstrategies? Finally, how do firms react to the expectedactions of their rivals? We address each of these ques-tions in detail.The first question naturally invites a market pull

driven explanation in which consumer demographicsplay a key role in determining which pricing strategyfirms choose. In answering this question, we alsoaim to provide additional empirical evidence that willinform the growing theoretical literature on pricingrelated games. Since we are able to assess the impactof local demographics at a much broader level thanprevious studies, our results provide more conclusiveevidence regarding their empirical relevance.The second question concerns the match between

a firm’s strategy and its chain-specific capabilities.In particular, we examine whether particular pricingstrategies (e.g., EDLP) are more profitable when firmsmake complementary investments (e.g. larger storesand more sophisticated distribution systems). Theempirical evidence on this matter is scant—this is thefirst paper to address this issue on a broad scale. Fur-thermore, because our data set includes all existingsupermarkets, we are able to exploit variation bothwithin and across chains to assess the impact of storeand chain level differences on the choice of pricingstrategy.Finally, we address the role of competition posed

in our third question by analyzing firms’ reactionsto the expected choices of their rivals. In particular,we ask whether firms face incentives to distinguishthemselves from their competitors (as in most modelsof product differentiation) or instead face pressuresto conform (as in network or switching cost mod-els)? This question is the primary focus of our paperand the feature that most distinguishes it from earlierwork.Our results shed light on all three questions. First,

we find that consumer demographics play a signifi-cant role in the choice of local pricing strategies: firmschoose the policy that their consumers demand. Fur-thermore, the impact of these demographic factorsis consistent with both the existing marketing liter-ature and conventional wisdom. For example, EDLPis favored in low income, racially diverse markets,while PROMO clearly targets the rich. However, a keyimplication of our analysis is that these demographicfactors act as a coordinating device for rival firms,helping shape the pricing landscape by defining anequilibrium correspondence. Second, we find thatcomplementary investments are key: larger storesand vertically integrated chains are significantly morelikely to adopt EDLP. Finally, and most surprisingly,we find that stores competing in a given market haveincentives to coordinate their actions. Rather thanchoosing a pricing strategy that distinguishes them

from their rivals, stores choose strategies that match.This finding is in direct contrast to existing theoreticalmodels that view pricing strategy as a form of dif-ferentiation, providing a clear comparative static thatfuture pricing models must address.Our paper makes both substantive and method-

ological contributions to the marketing literature. Onthe substantive front, our results offer an in-depthlook at the supermarket industry’s pricing practices,delineating the role of three key factors (demand,supply, and competition) on the choice of pricingstrategy. We provide novel, producer-side empiri-cal evidence that complements various consumer-sidemodels of pricing strategy. In particular, we find qual-ified support for several claims from the literatureon pricing demographics, including Bell and Lattin’s(1998) model of basket size and Lal and Rao’s (1997)positioning framework, while at the same time high-lighting the advantages of chain level investment.Our focus on competition also provides a structuralcomplement to Shankar and Bolton’s (2004) descrip-tive study of price variation in supermarket scannerdata, which emphasized the role of rival actions. Ourmost significant contribution, however, is demonstrat-ing that stores in a particular market do not use pric-ing strategy as a differentiation device but insteadcoordinate their actions. This result provides a directchallenge to the conventional view of retail compe-tition, opening up new and intriguing avenues forfuture theoretical research. Our econometric imple-mentation also contributes to the growing literature inmarketing and economics on the estimation of staticdiscrete games, as well as the growing literature onsocial interactions.2 In particular, our incorporation ofmultiple sources of private information and our con-struction of competitive beliefs are novel additions tothese emerging literatures.The rest of the paper is organized as follows. Sec-

tion 2 provides an overview of the pricing landscape,explicitly defining each strategy and illustrating theimportance of local factors in determining store leveldecisions. Section 3 introduces our formal model ofpricing strategy and briefly outlines our estimationapproach. Section 4 describes the data set. Section 5provides the details of how we implement the model,including the construction of distinct geographic mar-kets, the selection of covariates, our two-step estima-tion method, and our identification strategy. Section 6

2 Recent applications of static games include technology adop-tion by internet service providers (Augereau et al. 2006), prod-uct variety in retail eyewear (Watson 2005), location of ATMbranches (Gowrisankaran and Krainer 2004), and spatial differenti-ation among supermarkets (Orhun 2005), discount stores (Zhu et al.2005), and video stores (Seim 2006). Structural estimation of socialinteractions is the focus of papers by Brock and Durlauf (2002),Bayer and Timmins (2006), and Bajari et al. (2005).

Ellickson and Misra: Supermarket Pricing StrategiesMarketing Science 27(5), pp. 811–828, © 2008 INFORMS 813

provides our main empirical results and discussestheir implications. Section 7 concludes with directionsfor future research.

2. The Supermarket PricingLandscape

2.1. Pricing Strategy ChoicesCompetition in the supermarket industry is a complexphenomenon. Firms compete across the entire retailand marketing mix, enticing customers with an attrac-tive set of products, competitive prices, convenientlocations, and a host of other services, features, andpromotional activities. In equilibrium, firms choosethe bundle of services and features that maximizeprofits, conditional on the types of consumers theyexpect to serve and their beliefs about the actions oftheir rivals. A supermarket’s pricing strategy is a keyelement in this multidimensional bundle.The majority of both marketers and practitioners

frame a store’s pricing decision as a choice betweenoffering everyday low prices or deep but tempo-rary discounts, labeling the first strategy EDLP andthe second PROMO (Table 1).3� 4 Not surprisingly,the simple EDLP-PROMO dichotomy is too narrowto adequately capture the full range of firm behav-ior. In practice, firms can choose a mixture of EDLPand PROMO, varying either the number of categoriesthey put on sale or changing the frequency of salesacross some or all categories of products. Practitionershave coined a term for these practices—hybrid pric-ing. What constitutes HYBRID pricing is necessarilysubjective, depending on an individual’s own beliefsregarding how much price variation constitutes adeparture from pure EDLP. Both the data and defini-tions used in this paper are based on a specific storelevel survey conducted by Trade Dimensions in 1998,

3 This is clearly a simplification—a supermarket’s pricing policyis closely tied to its overall positioning strategy. Pricing strategiesare typically chosen to leverage particular operational advantagesand often have implications for other aspects of the retail mix. Forexample, successful implementation of EDLP may involve offeringa deeper and narrower product line than PROMO, allowing firmsto exploit scale economies (in particular categories), reduce theirinventory carrying costs, and lower their advertising expenses. Onthe other hand, PROMO pricing gives firms greater flexibility inclearing overstock, allows them to quickly capitalize on deep man-ufacturer discounts, and facilitates the use of consumer loyalty pro-grams (e.g. frequent shopper cards). In other words, the choice ofpricing strategy is more than just how prices are set: it reflects theoverall positioning of the store. This paper focuses on the pricingdimension alone, taking the other aspects of the retail mix as given.While this is limiting, modeling the entire retail mix is beyond thescope of this paper.4 Note that we focus on the choice of pricing strategy and abstractaway from issues related to more tactical decisions about how pricesare (or should be) set (see e.g., Kumar and Rao 2006).

Table 1 Descriptive Statistics

Variable Obs Mean Std. dev. Min. Max

StrategyEDLP 17�388 0�28 0�45 0 1HYBRID 17�388 0�38 0�48 0 1PROMO 17�388 0�34 0�47 0 1

MSA characteristicsSize (sq. miles) 333 1�868�31 1�943�99 46�40 11�229�6Density (pop ’000 333 10�42 9�62 0�91 49�06per sq. mile)

Avg. food expenditure 333 663�64 1�201�37 16�04 9�582�09($ ’000)

Market variablesMedian household size 8�000 2�66 0�35 1�32 5�69Median HH income 8�000 35�255�59 9�753�95 18�109�60 81�954�60Proportion Black 8�000 0�08 0�14 0�00 0�97Proportion Hispanic 8�000 0�06 0�13 0�00 0�98Median vehicles in HH 8�000 2�12 0�33 0�56 3�37

Chain/store characteristicsVertically integrated 17�388 0�51 0�50 0�00 1�00Store size (sqft ’000) 17�388 28�99 16�34 2�00 250�00Independent store 17�388 0�23 0�42 0�00 1�00Number of stores 804 390�15 478�45 1�00 1�399�00in chain

which asked individual store managers to choosewhich of the following categories best described theirstore’s pricing policy:• Everyday Low Price (EDLP): Little reliance on

promotional pricing strategies such as temporaryprice cuts. Prices are consistently low across theboard, throughout all packaged food departments.• Promotional (Hi-Lo) Pricing: Heavy use of spe-

cials, usually through manufacturer price breaks orspecial deals.• Hybrid EDLP/Hi-Lo: Combination of EDLP and

Hi-Lo pricing strategies.According to Trade Dimensions, the survey was

designed to allow for a broad interpretation of theHYBRID strategy, as they wanted it to capture devia-tions along either the temporal (i.e., number of salesper year) or category based dimensions (i.e., numberof categories on deal). We believe that pricing strat-egy is best viewed as a continuum, with pure EDLP(i.e., constant margins across all categories) on oneend and pure PROMO (i.e. frequent sales on all cate-gories) at the other. This data set represents a coarsediscretization of that continuum.

2.2. Supermarket Pricing: A Closer LookWithout observing data on individual stores, it mightbe tempting to conclude that all pricing strategies aredetermined at the level of the chain. While there arecertainly incentives to choose a consistent policy, thedata reveals a remarkable degree of local heterogene-ity. To examine the issue more closely, we focus in ona single chain in a single market: the Pathmark chainin New Jersey. Figure 1 shows the spatial locations of


Figure 1 Pathmark Stores in New Jersey

41.0

40.5

39.5

39.0

–75.5 –75.0 –74.5 –74.0

EDLPHYBRIDPROMO

40.0

every Pathmark store in New Jersey, along with itspricing strategy. Two features of the data are worthemphasizing. We address them in sequence.First, Pathmark does not follow a single strategy

across its stores: 42% of the stores use PROMO pric-ing, 33% follow EDLP, and the remaining 25% useHYBRID. The heterogeneity in pricing strategyobserved in the Pathmark case is not specific to thisparticular chain. Table 2 shows the store level strate-gies chosen by the top 15 U.S. supermarkets (bytotal volume) along with their total store counts. Aswith Pathmark, the major chains are also surprisinglyheterogeneous. While some firms do have a clearfocus (e.g. Wal-Mart, H.E. Butt, Stop & Shop), oth-ers are more evenly split (e.g. Lucky, Cub Foods).This pattern extends to the full set of firms. Table 3shows the pricing strategies chosen by large and

Table 2 Pricing Strategies of the Top 15 Supermarkets

Firm Stores % PROMO % HYBRID % EDLP

Kroger 1�399 47 40 13Safeway 1�165 52 43 5Albertson’s 922 11 41 48Winn-Dixie 1�174 3 30 67Lucky 813 35 38 27Giant 711 29 60 11Fred Meyer 821 22 60 18Wal-Mart 487 1 26 73Publix 581 13 71 16Food Lion 1�186 2 12 86A&P 698 55 30 15H.E. Butt 250 1 3 96Stop & Shop 189 50 43 7Cub foods 375 26 34 40Pathmark 135 42 25 33

Table 3 Pricing Strategy by Firm Type

% EDLP % HYBRID % PROMO

“Large” firms:Chain 33 37 30Vertically integrated 35 36 29Large store size 32 38 30Many checkouts 31 39 30

“Small” firms:Independent 22 28 50Not vertically integrated 21 32 47Small store size 23 26 52Few checkouts 22 26 52

small chains, using four alternative definitions of“large” and small.5 While large chains seem evenlydistributed across the strategies and “small” chainsseem to favor PROMO, firm size is not the primarydeterminant of pricing strategy.The second noteworthy feature of the Pathmark

data is that even geographically proximate storesadopt quite different pricing strategies. While there issome clustering at the broader spatial level (e.g. northversus south New Jersey), the extent to which thesestrategies are interlaced is striking. Again, lookingbeyond Pathmark and New Jersey confirms that thiswithin-chain spatial heterogeneity is not unique tothis particular example: while some chains clearlyfavor a consistent strategy, others appear quiteresponsive to local factors. Broadly speaking, thedata reveal only a weak relationship between geog-raphy and pricing strategy. While southern chainssuch as Food Lion are widely perceived to favorEDLP and Northeastern chains like Stop & Shop arethought to prefer PROMO, regional variation doesnot capture the full story. Table 4 shows the per-cent of stores that choose either EDLP, HYBRID, orPROMO pricing in eight geographic regions of theUnited States. While PROMO pricing is most popularin the Northeast, Great Lakes, and central Southernregions, it is far from dominant, as both the EDLP andHYBRID strategies enjoy healthy shares there as well.EDLP is certainly favored in the South and Southeast,but PROMO still draws double digit shares in bothregions. This heterogeneity in pricing strategy canbe illustrated using the spatial structure of our dataset. Figure 2 plots the geographic location of everystore in the United States, along with their pricing

5 The four definitions of firm size are: chain/independent, verticallyintegrated and not, large/small store, and many/few checkouts.A chain is defined as having 11 or more stores, while an indepen-dent has 10 of fewer. Vertically integrated means the firm operatesits own distribution centers. Large versus small store size and manyversus few checkouts are defined by the upper and lower quartilesof the full store level census.


Table 4 Pricing Strategies by Region

Region % PROMO % HYBRID % EDLP

West Coast 39 39 22Northwest 32 51 17South West 20 48 32South 32 25 43Southern Central 45 27 28Great Lakes 54 29 17North East 40 37 23South East 23 37 40

strategy. As is clear from the three panels correspond-ing to each pricing strategy, there is no obvious pat-tern: all three strategies exhibit quite uniform cover-age. Taken together, these observations suggest look-ing elsewhere for the primary determinants of pricing

Figure 2 Spatial Distribution of Store Pricing Strategy

HYBRID stores

EDLP stores

PROMO stores

Table 5 Local Factors

EDLP HYBRID PROMO

Local demographicsMedian household 2�84 (0.331) 2�81 (0.337) 2�80 (0.329)size

Median household 34,247 (14,121) 36,194 (15,121) 36,560 (16,401)income

Median vehicles 2�12 (0.302) 2�13 (0.303) 2�09 (0.373)in HH

Median age 35�4 (4.59) 35�8 (4.98) 35�7 (4.25)Proportion Black 0�128 (0.182) 0�092 (0.158) 0�110 (0.185)Proportion Hispanic 0�078 (0.159) 0�073 (0.137) 0�070 (0.135)

Strategies of rivalsPercent of rivals using 49 (31) 49 (25) 52 (23)same strategy

Note. The main numbers in each cell are means, standard deviations are inparentheses.

strategy. We turn next to the role of market demo-graphics and then to the nature and degree of com-petition.Table 5 contains the average demographic char-

acteristics of the local market served by stores ofeach type.6 PROMO pricing is associated with smallerhouseholds, higher income, fewer automobiles percapita, and less racial diversity, providing some ini-tial support for Bell and Lattin’s (1998) influen-tial model of basket size.7 However, the differencesin demography, while intuitive, are not especiallystrong. This does not mean that demographics areirrelevant, but rather that the aggregate level patternslinking pricing strategy and demographics are notoverwhelming. Isolating the pure impact of demo-graphic factors will require a formal model, which weprovide below.The final row of Table 5 contains the share of rival

stores in the competing market that employ the samestrategy as the store being analyzed. Here we find astriking result: 50% of a store’s rivals in a given loca-tion employ the same pricing strategy as the focalstore. Competitor factors also played a lead role inthe work of Shankar and Bolton (2004), which ana-lyzed pricing variability in supermarket scanner data.In particular, they note that “what is most striking,however, is that the competitor factors are the mostdominant determinants of retailer pricing in a broadframework that included several other factors” (p. 43).Even at this rather coarse level of analysis, the data

6 Roughly corresponding to areas the size of a ZipCode, these “localmarkets” are defined explicitly in §5.2.7 Bell and Lattin (1998) find that the most important features ofshopping behavior can be captured by two interrelated choices:basket size (how much you buy) and shopping frequency (howoften you go). They suggest that large or fixed basket shoppers(i.e. those who buy more and shop less) will more sensitive tothe overall basket price than those who shop frequently and willtherefore prefer EDLP pricing to PROMO. They present empiricalevidence that is consistent with this prediction.


reveal that most stores choose similar pricing strate-gies to their rivals. This pattern clearly warrants amore detailed investigation and is the focus of ourstructural model.Stepping back, three key findings emerge. First, su-

permarket chains often adopt heterogeneous pricingstrategies, suggesting that demand related forces cansometimes outweigh the advantages of chain levelspecialization. Second, local market factors play a keyrole in shaping demand characteristics. Finally, anyempirical analysis of pricing strategy must addressthe role of competition. While investigating the roleof market demographics and firm characteristics isnot conceptually difficult, quantifying the structuralimpact of rival pricing strategies on firm behaviorrequires a formal game theoretic model of pricingbehavior that accounts for the simultaneity of choices.In the following section, we embed pricing strategyin a discrete game that accommodates both localdemographics and the strategies of rival firms. Wethen estimate this model using the two-step approachdeveloped by Bajari et al. (2005).

3. A Strategic Model ofSupermarket Pricing

A supermarket’s choice of pricing strategy is natu-rally framed as a discrete game between a finite setof players. Each firm’s optimal choice is determinedby the underlying market conditions, its own charac-teristics and relative strengths, as well as its expecta-tions regarding the actions of its rivals. Ignoring strate-gic expectations, pricing strategy could be modeled asa straightforward discrete choice problem. However,since firms condition their strategies on their beliefsregarding rivals’ actions, this discrete choice must bemodeled as a system of simultaneous equations. Inour framework, firms (i.e., supermarket chains8) makea discrete choice of pricing strategy, selecting amongthree alternatives: everyday low pricing, promotionalpricing, and a hybrid strategy. While there is clearlya role for dynamics in determining an optimal pric-ing policy, we assume that firms act simultaneously ina static environment, taking entry decisions as given.This static treatment of competition is not altogetherunrealistic since these pricing strategies involve sub-stantial store level investments in communication andpositioning related costs that are not easily reversed.9

We assume that competition takes place in “local”markets, each contained in a global market (here, an

8 Henceforth, we will use chains and firms interchangeably.9 As discussed above, pricing decisions are relatively sunk, due tothe positioning costs associated with conveying a consistent store-level message to a group of repeat customers. Furthermore, sincethis is not an entry game, we are not particularly concerned aboutthe possibility of ex post regret that can sometimes arise in staticgames (Einav 2003).

MSA). Before proceeding further, we must introducesome additional notation. Stores belonging to a givenchain c = 1� � � � �C, that are located in a local mar-ket lm = 1� � � � �Lm, in an MSA m = 1� � � � �M , will beindexed using i

lmc = 1� � � � �N lm

c . The total numberof stores in a particular chain in a given MSA isNmc = ∑Lm

lm=1Nlmc , while the total number of stores

in that chain across all MSAs is Nc =∑M

m=1Nmc . In

each local market, chains select a pricing strategy(action) a from the three element set K = E�H�P�,where E ≡ EDLP, H ≡ HYBRID, and P ≡ PROMO.If we observe a market lm containing N lm = ∑C

c=1Nlmc

players for example, the set of possible action pro-files is then Alm

= E�H�P�Nlmc with generic element

alm = �a1� a2� � � � � ailmc � � � � � aN lmc�. The vector of actions of

store ilmc ’s competitors is denoted a−ilmc = �a1� � � � � ailmc −1�ailmc +1� � � � � aN lm

c�.

In a given market, a particular chain’s state vec-tor is denoted smc ∈ Smc , while the state vector for themarket as a whole is sm = �sm1 � � � � � s

mNc� ∈∏Nm

cc=1 S

mc . The

state vector sm is known to all firms and observed bythe econometrician. It describes features of the mar-ket and characteristics of the firms that we assumeare determined exogenously. For each firm, there arealso three unobserved state variables (correspondingto the three pricing strategies) that are treated asprivate information of the firm. These unobservedstate variables are denoted �

ilmc�a

ilmc�, or more com-

pactly �ilmc, and represent firm specific shocks to the

profitability of each strategy. The private informa-tion assumption makes this a game of incompleteor asymmetric information (e.g. Harsanyi 1973) andthe appropriate equilibrium concept one of BayesianNash Equilibrium (BNE). For any given market, the�ilmc’s are assumed to be i.i.d. across firms and actions,

and drawn from a distribution f ��ilmc� that is known

to everyone, including the econometrician.Firms maximize store-level profits, choose pricing

strategies independently across stores. In market lm,the profit earned by store ic is given by

�ilmc=�

ilmc

(sm� a

ilmc� a−ilmc

)+ �ilmc� (1)

where �ilmcis a known and deterministic function of

states and actions (both own and rival’s). Since the�’s are private information, each firm’s decision ruleailmc= d

ilmc�sm� �

ilmc� is a function of the common state

vector and its own �, but not the private informationof its rivals. From the perspective of both its rivalsand the econometrician, the probability that a givenfirm chooses action k conditional on the common statevector is then given by

Pilmc

(ailmc= k

)= ∫1{dilmc

(sm� �

ilmc

)= k}f(�ilmc

)d�

ilmc� (2)

where 1 dilmc�s� �

ilmc�= k� is an indicator function equal

to 1 if store ilmc chooses action k and 0 otherwise.


We let Plm denote the set of these probabilities for agiven local market. Since the firm does not observe itscompetitors actions prior to choosing its own action,it makes decisions based on its expectations. Theexpected profit for firm i

lmc from choosing action a

ilmc

is then

��ilmc

(ailmc� sm� �i�Plm

)= ��

ilmc

(ailmc� sm

)+ �ilmc

(3)

= ∑a−ilmc

�ilmc

(sm� a

ilmc� a−ilmc

)P−ilmc + �

ilmc� (4)

where P−ilmc = ∏j �=ilmc Pj �aj � sm�. Given these expected

profits, the optimal action for a store is then

�ilmc

= Pr{��

ilmc

(ailmc� sm

)+ �ilmc

(ailmc

)> ��

ilmc

(a′ilmc� sm

)+ �ilmc

(a′ilmc

) ∀a′ilmc�= a

ilmc

}� (5)

which is the system of equations that define the (purestrategy) BNE of the game. Because a firm’s optimalaction is unique by construction, there is no need toconsider mixed strategies.If the �’s are drawn from a Type I Extreme Value

distribution, this BNE must satisfy a system of logitequations (i.e. best response probability functions).The general framework described above has beenapplied in several economic settings and its propertiesare well understood. Existence of equilibrium followsdirectly from Brouwer’s fixed point theorem.To proceed further, we need to choose a particular

specification for the expected profit functions. We willassume that the profit that accrues to store ilmc fromchoosing strategy k in location lm is given by

��ilmc

(ailmc=k�sm��i�Plm

) = sm′ k+!E−ilmc "k1+!P

−ilmc"k2

+#mc �k�+$c�k�+%ilmc �k� (6)

where sm is the common state vector of both market(local and MSA) and firm characteristics (chain andstore level). The !E−ilmc

and !P−ilmcterms represent the

expected proportion of a store’s competitors in mar-ket lm that choose EDLP and PROMO strategies,respectively

!�k�

−ilmc= 1N lm

∑j �=ilmc

Pj �aj = k��

Note that we have assumed that payoffs are a lin-ear function of the share of stores that choose EDLPand PROMO, which simplifies the estimation prob-lem and eliminates the need to consider the sharewho choose HYBRID �H�. We further normalize theaverage profit from the PROMO strategy to zero, one

of three assumptions required for identification (wediscuss our identification strategy in detail in §5.7).In addition, we have assumed that the private infor-mation available to store ilmc (i.e. �

ilmc) can be decom-

posed into three additive stochastic components

�ilmc�k�= #mc �k�+ $c�k�+ %

ilmc�k�� (7)

where %ilmc�k� represents local market level private

information, #mc �k� is the private information thata chain possesses about a particular global market(MSA), and $c�k� is a nonspatial component of pri-vate information that is chain specific. Following ourearlier discussion, we assume that %

ilmc�k� is an i.i.d.

Gumbel error. We further assume that the two remain-ing components are jointly distributed with distribu-tion function F �#mc �k�� $c�k�'(�, where ( is a set ofparameters associated with F . Denoting the parametervector )= �"�(� and letting *

ilmc�k� be an indicator

function such that

*ilmc�k�=

1 if a

ilmc= k�

0 if ailmc�= k�

(8)

the optimal choice probabilities (conditional on#mc �k�� $c�k�) for a given store can be written as

�ilmc

(ailmc=k ��Plm�X�#mc �k��$c�k�

)

=exp

(sm′ k+!E−ilmc "k1+!

P

−ilmc"k2+#mc �k�+$c�k�

)∑

k′∈ E�H�P�exp(sm′ k′ +!E−ilmc "k′1+!

P

−ilmc"k′2+#mc �k′�+$c�k′�

)(9)

while the likelihood can be constructed as

∏c∈C

∫$c�k�

∏m∈M

∫#mc �k�

{ ∏lm∈Lm

∏ilmc ∈Nlm

c

[�ilmc

(ailmc= k ��Plm� s�

#mc �k�� $c�k�)]*

ilmc�k�}dF �#mc �k�� $c�k�'(�

s.t. Plm =� #� $�

[�lm

(��Plm� s� #

mc �k�� $c�k�

)]� (10)

Note that the construction of the likelihood involvesa system of discrete choice equations that must sat-isfy a fixed point constraint �Plm =�lm

�. There are twomain approaches for dealing with the recursive struc-ture of this system, both based on methods originallyapplied to dynamic discrete choice problems. The first,based on Rust’s (1987) Nested Fixed Point (NFXP)algorithm, involves solving for the fixed point of thesystem at every candidate parameter vector and thenusing these fixed point probabilities to evaluate thelikelihood. However, the NFXP approach is both com-putationally demanding and straightforward to apply


only when the equilibrium of the system is unique.10

An alternate method, based on Hotz and Miller’s(1993) Conditional Choice Probability (CCP) estimator,involves using a two-step approach that is both com-putationally light and more robust to multiplicity.11

The first step of this procedure involves obtaining con-sistent estimates of each firm’s beliefs regarding thestrategic actions of its rivals. These “expectations” arethen used in a second stage optimization procedure toobtain the structural parameters of interest. Given thecomplexity of our problem, we chose to adopt a two-step approach based on Bajari et al. (2005), who werethe first to apply these methods to static games.

4. Data SetThe data for the supermarket industry are drawnfrom Trade Dimension’s 1998 Supermarkets PlusDatabase, while corresponding consumer demograph-ics are taken from the decennial Census of the UnitedStates. Descriptive statistics are presented in Table 1.Trade Dimensions collects store level data from everysupermarket operating in the United States for use intheir Marketing Guidebook and Market Scope publica-tions, as well as selected issues of Progressive Grocermagazine. The data are also sold to marketing firmsand food manufacturers for marketing purposes. The(establishment level) definition of a supermarket usedby Trade Dimensions is the government and industrystandard: a store selling a full line of food productsand generating at least $2 million in yearly revenues.Foodstores with less than $2 million in revenues areclassified as convenience stores and are not includedin the data set.12

Information on pricing strategy, average weeklyvolume, store size, number of checkouts, and addi-tional store and chain level characteristics was gath-ered using a survey of each store manager, conductedby their principal food broker. With regard to pric-ing strategy, managers are asked to choose the strat-egy that is closest to what their store practices on

10 It is relatively simple to construct the likelihood function whenthere is a unique equilibrium, although solving for the fixed pointat each iteration can be computationally taxing. However, con-structing a proper likelihood (for the NFXP) is generally intractablein the event of multiplicity, since it involves both solving for allthe equilibria and specifying an appropriate selection mechanism.Simply using the first equilibrium you find will result in mispec-ification. A version of the NFXP that is robust to multiplicity hasyet to be developed.11 Instead of requiring a unique equilibrium to the whole game,two-step estimators simply require a unique equilibrium be playedin the data. Futhermore, if the data can be partioned into distinctmarkets with sufficient observations (as is the case in our applica-tion), this requirement can be weakened further.12 Firms in this segment operate very small stores and compete onlywith the smallest supermarkets (Ellickson 2006, Smith 2006).

a general basis: either EDLP, PROMO or HYBRID.The HYBRID strategy is included to account for thefact that many practitioners and marketing theoristsview the spectrum of pricing strategies as more acontinuum than a simple EDLP-PROMO dichotomy(Shankar and Bolton 2004). The fact that just over athird of the respondents chose the HYBRID option isconsistent with this perception.

5. Empirical ImplementationThe empirical implementation of our frameworkrequires three primary inputs. First, we need tochoose an appropriate set of state variables. Thesewill be the market, store and chain characteristicsthat are most relevant to pricing strategy. To deter-mine which specific variables to include, we drawheavily on the existing marketing literature. Second,we will need to define what we mean by a “mar-ket.” Finally, we need to estimate beliefs and con-struct the empirical likelihood. We outline each ofthese steps in the following subsections, concludingwith a discussion of unobserved heterogeneity andour strategy for identification.

5.1. Determinants of Pricing StrategyThe focus of this paper is the impact of rival pricingpolicies on a firm’s own pricing strategy. However,there are clearly many other factors that influencepricing behavior. Researchers in both marketing andeconomics have identified several, including con-sumer demographics, rival pricing behavior, and mar-ket, chain, and store characteristics (Shankar andBolton 2004). Since we have already discussed the roleof rival firms, we now focus on the additional deter-minants of pricing strategy.Several marketing papers highlight the impact of

demographics on pricing strategy (Ortmeyer et al.1991, Hoch et al. 1994, Lal and Rao 1997, Bell andLattin 1998). Of particular importance are consumerfactors such as income, family size, age, and accessto automobiles. In most strategic pricing models, thePROMO strategy is motivated by some form of spa-tial or temporal price discrimination. In the spatialmodels (e.g. Lal and Rao 1997, Varian 1980), PROMOpricing is aimed at consumers who are either will-ing or able to visit more than one store (i.e. thosewith low travel costs) or, more generally, those whoare more informed about prices. The EDLP strategyinstead targets consumers who have higher travelcosts or are less informed (perhaps due to hetero-geneity in the cost of acquiring price information). Inthe case of temporal discrimination (Bell and Lattin1998, Bliss 1988), PROMO pricing targets customerswho are willing to either delay purchase or stockpileproducts, while EDLP targets customers that preferto purchase their entire basket in a single trip or at a


single store. Clearly, the ability to substitute over timeor across stores will depend on consumer characteris-tics. To account for these factors, we include measuresof family size, household income, median vehicleownership, and racial composition in our empiricalanalysis.Since alternative pricing strategies will require dif-

fering levels of fixed investment (Lattin and Ortmeyer1991), it is important to control for both store andchain level characteristics. For example, large andsmall chains may differ in their ability to effi-ciently implement particular pricing strategies (Dharand Hoch 1997). Store level factors also play arole (Messinger and Narasimhan 1997). For example,EDLP stores may need to carry a larger inventory (tosatisfy large basket shoppers), while PROMO storesmight need to advertise more heavily. Therefore, weinclude a measure of store size and an indicatorvariable for whether the store is part of a verticallyintegrated chain. Finally, since the effectiveness ofpricing strategies might vary by market size (e.g.urban versus rural), we include measures of geo-graphic size, population density, and average expen-ditures on food.

5.2. Market DefinitionThe supermarket industry is composed of a largenumber of firms operating anywhere from 1 to1,200 outlets. We focus on the choice of pricing strat-egy at an individual store, abstracting away from themore complex issue of how decisions are made atthe level of the chain. This requires identifying theprimary trading area from which each store drawspotential customers. Without disaggregate, consumer-level information, the task of defining local marketsrequires some simplifying assumptions. In particular,we assume markets can be defined by spatial prox-imity alone, a strong assumption in some circum-stances (Bell et al. 1998). However, absent detailedconsumer level purchase information, we cannot relaxthis assumption further. Therefore, we will try to beas flexible as possible in defining spatial markets.Although there are many ways to group firms

using existing geographic boundaries (e.g. ZipCodesor Counties), these pre-specified regions all share thesame drawback: they increase dramatically in sizefrom east to west, reflecting established patterns ofpopulation density.13 Rather than imposing this struc-ture exogenously, we allow the data to sort itself byusing cluster analysis. In particular, we assume thata market is a contiguous geographic area, measur-able by geodesic distance and containing a set of

13 One exception is Census block groups, which are about half thesize of a typical ZipCode. However, we feel that these areas are toosmall to constitute reasonably distinct supermarket trading areas.

competing stores. Intuitively, markets are groups ofstores that are located close to one another. To con-struct these markets, we used a statistical clusteringmethod (K-means) based on latitude, longitude, andZipCode information.14 Our clustering approach pro-duced a large set of distinct clusters that we believeto be a good approximation of the actual markets inwhich supermarkets compete. These store clusters aresomewhat larger than a typical ZipCode, but signifi-cantly smaller than the average county. As robustnesschecks, we experimented with the number of clus-ters, broader and narrower definitions of the market(e.g. ZipCodes and MSAs), as well as nearest neigh-bor methods and found qualitatively similar results(see Appendix B.1).

5.3. Estimation StrategyAs noted above, the system of discrete choice equa-tions presents a challenge for estimation. We adopt atwo stage approach based on Bajari et al. (2005). Thefirst step is to obtain a consistent estimate of Plm , theprobabilities that appear (implicitly) on the right handside of Equation (9).15 These estimates ��Plm � are usedto construct the !−ilmc ’s, which are then plugged intothe likelihood function. Maximization of this (pseudo)likelihood constitutes the second stage of the proce-dure. Consistency and asymptotic normality has beenestablished for a broad class of two-step estimatorsby Newey and McFadden (1994), while Bajari et al.(2005) provide formal results for the model estimatedhere. We note in passing that consistency of the esti-mator is maintained even with the inclusion of thetwo random effect terms �$ and #�, since these vari-ables are treated as private information of each store.A final comment relates to the construction of stan-dard errors. Because the two-step approach precludesusing the inverse information matrix, we use a boot-strap approach instead.16

5.4. The LikelihoodIn our econometric implementation, we will assumethat $ and # are independent, mean zero normalerrors, so that

F �#mc �k�� $c�k�'(�

= F#�#mc �k�'(#�k��× F$�$c�k�'($�k�� (11)

14 ZipCodes are required to ensure contiguity: without ZipCodeinformation, stores in Manhattan would be included in the samemarket as stores in New Jersey.15 The !−ilmc

’s are functions of Plm .16 In particular, we bootstrapped across markets (not individ-ual stores) and held the pseudorandom draws in the simulatedlikelihood fixed across bootstrap iterations. To save time we usedthe full data estimates as starting values in each bootstrap iteration.


where both F# and F$ are mean zero normal dis-tribution functions with finite covariance matrices.For simplicity, we also assume that the covariancematrices are diagonal with elements +2$ �k� and +2# �k�.For identification, consistent with our earlier inde-pendence and normalization assumptions, we assumethat #mc �P� = $c�P� = 0 ∀ c ∈ C�m ∈ M . We can thenuse a simulated maximum likelihood procedure thatreplaces (10) with its sample analog

��)� = ∏c∈CR−1$

R$∑r$=1

∏m∈M

[R−1#

R#∑r#=1

{ ∏lm∈Lm

∏ilmc ∈Nlm

c

[�ilmc

(ailmc=k ��

�Plm�s�#mc �k��$c�k�)]*

ilmc�k�}]� (12)

In the simulation procedure, .#mc �k�/r# and .$c�k�/r$are drawn from mean zero normal densities with vari-ances +2# �k� and +2$ �k� respectively. We use R# = R$ =500 and maximize (12) to obtain estimates of the struc-tural parameters. Note that the fixed point restriction,Plm =�lm

, no longer appears since we have replacedPlm with �Plm in the formulae for !E−ilmc and !P−ilmc

, whichare used in constructing �

ilmc(see (9)). We now turn

to estimating beliefs.

5.5. Estimating BeliefsIn an ideal setting, we could recover estimates ofeach store’s beliefs regarding the conditional choiceprobabilities of its competitors using fully flexiblenonparametric methods (e.g. kernel regressions orsieves). Unfortunately, our large state vector makesthis infeasible. Instead, we employ a parametricapproach for estimating !̂−ilmc , using a mixed multi-nomial logit (MNL) specification to recover these firststage choice probabilities (Appendix B.4 provides asemi-parametric robustness analysis). This is essen-tially the same specification employed in the sec-ond stage procedure (outlined above), only the store’sbeliefs regarding rivals’ actions are excluded from thisreduced form. Note that we do not require an explicitexclusion restriction, since our specification alreadycontains natural exclusion restrictions due to the pres-ence of state variables that vary across stores andchains.We implement an estimator similar to (12), but with

the coefficients on the !−ilmc ’s (i.e. "’s) set to zero.Let the parameters in the first stage be denoted by01 = 1�(1�

17 and the first stage likelihood for agiven store be denoted by �

ilmc�0�#mc �k�� $c�k��. Using

a simulated maximum likelihood (SML) approach, we

17 The subscript 1 indicates that these are first stage estimates.

obtain 0̂1, the SML estimate of 01. Given these esti-mates, and applying Bayes’ rule, the posterior expec-tation of P�a

ilmc= k � s� #mc �k�� $c�k�� can be obtained via

the following computation(∫

$

∫#�ilmc

(ailmc=k �0̂�#mc �k��$c�k�

·�ilmc�0̂�#mc �k��$c�k��dF �#

mc �k��$c�k�' �(1�k��

)

·(∫

$

∫#�ilmc�0̂�#mc �k��$c�k��dF �#

mc �k��$c�k�' �(1�k��

)−1�

(13)

While this expression is difficult to evaluate analyt-ically, the vector of beliefs defined by

�Pilmc

(ailmc=k)=� $�#�

[�ilmc

(ailmc=k �0̂�#mc �k��$c�k�

)](14)

can be approximated by its simulation analog

�Pilmc

(ailmc=k)

�∑R

r=1�ilmc

(ailmc=k �0̂�.#mc �k��$c�k�/r

)�ilmc�0̂�.#mc �k��$c�k�/r �∑R

r=1�ilmc�0̂�.#mc �k��$c�k�/r �

(15)

in which .#mc �k�� $c�k�/r are draws from a distributionF �#mc �k�� $c�k�' �(� with similar properties to those de-scribed in §5.4. Again, we use R = 500 simulationdraws. Recalling that k ∈ K = E�H�P�, we can nowdefine a consistent estimator of !�k�−ilmc

as

!̂�k�

−ilmc=(∑v �=c

N lmv

)−1 ∑j �=ilmc

�Pj(ailmc= k

)� (16)

5.6. Common UnobservablesWhile our data set is rich enough to include a largenumber of covariates upon which firms may condi-tion their actions, the strong emphasis we have placedon strategic interaction may raise concerns regardingthe role of unobserved heterogeneity. In particular,how can we be sure that firms are actually reacting tothe actions of their rivals, rather than simply optimiz-ing over some common features of the local marketthat we do not observe? Manski (1993) frames this asthe problem of distinguishing between endogenousand correlated effects. Although the presence of botheffects yields collinearity in the linear in means modelthat Manski analyzes (i.e. the reflection problem), thenonlinearity of the discrete choice framework elimi-nates this stark nonidentification result in our setting.However, the presence of correlated unobservablesremains a concern. In what follows, we outline twostrategies for handling this problem. The first incorpo-rates a fixed effect at the MSA level, while the second


incorporates a random effect at the level of the cluster.Our main results are robust to either alternative.The most direct solution is to add a common unob-

servable, denoted 2lm , to the strategy specific profitfunction of each store. Using the notation defined ear-lier, this can be written

��ilmc

(ailmc= k� sm� �i�Plm

)= sm′ k+!E−ilmc

"k1+!P−ilmc"k2+2lm + �

ilmc�k�� (17)

Ideally, one would estimate each 2lm as a clusterspecific fixed effect. However, this would require esti-mating 8,000 additional parameters with less than18,000 observations, which is clearly infeasible. A fea-sible alternative is to model the common unobserv-able at the level of the MSA (i.e. include 2m insteadof 2lm�. In practice, this simply requires running thefirst stage separately for each MSA and then addingan MSA level fixed effect to the second stage proce-dure. This has the added benefit of relaxing the equi-librium restriction: we need now only assume that aunique equilibrium is played in every MSA, insteadof across all MSAs. We implement this strategy below.However, given the local nature of the strategicinteraction documented here, an MSA level commonunobservable may not be sufficient to account for therelevant correlated effects.A second alternative is to use a cluster level ran-

dom effect (i.e. assume the unobservables come froma pre-specified density g�2lm�) and simply integrateout over 2lm in the second stage estimation procedure,maximizing the resulting marginalized sample like-lihood. However, there is an additional impedimentto implementing this strategy: the fact that 2lm isa common unobservable prevents the econometricianfrom obtaining a consistent first stage estimate of Plm ,a requirement of the two-stage procedure employedabove. (Note that this is not a problem if the firststage can be estimated separately for each market, aswas the case with the MSA level unobservable.) Toaccommodate cluster level random effects, we adoptan approach based on Aguirregabiria and Mira (2007)that is tailored to our particular setting (the details ofour algorithm are provided in Appendix C).

5.7. IdentificationBajari et al. (2005) establish identification of the struc-tural parameters of a broad class of discrete games ofincomplete information, of which ours is a subcase.Their identification argument rests on three assump-tions. The first two have already been (implicitly)stated, but will be repeated here more formally. Thefirst assumption is that the error terms � are dis-tributed i.i.d. across players and actions in any given

local market (i.e., cluster)18 and are drawn from a dis-tribution of known parametric form. This is clearlysatisfied by the assumptions imposed above. The sec-ond assumption normalizes the expected profit asso-ciated with one strategy to zero. This is a standardidentification condition of any multinomial choicemodel. We normalize the mean profit of the PROMOstrategy to zero. The final assumption is an exclusionrestriction.The need for an exclusion restriction can be illus-

trated using Equation (9). Our two-step approachinvolves estimating the shares (!−ilmc ’s) on the righthand side of (9) in a first stage. These shares, whichare simple functions of each firm’s beliefs regard-ing the conditional choice probabilities of its rival’s,depend on the same state vector �sm� as the firstterm of the profit function �sm′ k�, creating a potentialcollinearity problem. Of course, identification can betrivially preserved by the inherent nonlinearity of thediscrete choice problem, but this follows directly fromfunctional form. An alternative strategy (suggested byBajari et al. 2005) involves identifying one or morecontinuous covariates that enter firm i’s payoffs, butnot the payoffs of any of its rivals. Note that eachfirm’s private shock ��

ilmc� has already been assumed

to satisfy this restriction, creating at least one set of“natural” exclusion restrictions. The characteristics ofrival firms constitute an additional exclusion. How-ever, a more subtle identification issue concerns thesource of exogenous variation in the data that canpin down the form of strategic interaction. For this,we exploit the specific structure of the private infor-mation term and the presence of large multi-marketchains. The two random effect terms in (7) captureeach firm’s tendency to employ a consistent strategywithin an MSA �#mc �k�� and/or across all stores �$c�k��in the chain. These firm level tendencies vary acrosschains and markets, providing a source of variationfor the local interactions that take place in any givencluster. The key assumption is that we sometimessee firms that follow a consistent strategy (EDLP, forexample) at the market level deviate in a local clus-ter by playing either PROMO or HYBRID when thedemographics of the local market or its beliefs regard-ing rival strategies outweigh its desire to follow aconsistent (chain or MSA-wide) strategy. This has theflavor of an instrumental variable approach, wherethe instruments are measures of the overall strat-egy a chain adopts outside the local market or MSA.In order to maintain the static, local, simultaneousmove structure of the game, we have restricted these

18 Note that the i.i.d. requirement need only hold at the cluster level.In particular, it’s fine to include random effects in the error term, solong as they are treated as private information. This is the approachwe adopt in our main specification.


firm level tendencies to be privately observed ran-dom effects. However, an alternative specification inwhich we conditioned directly on the average strate-gies that firms follow outside a given MSA yieldedsimilar results.

6. Results and DiscussionAs noted earlier, choosing an optimal pricing strat-egy is a complex task, forcing firms to balance thepreferences of their customers against the strategicactions of their rivals. A major advantage of ourtwo-step estimation approach is that, by estimatingbest response probability functions rather than equi-librium correspondences, we can separately identifystrategic interactions, reactions to local and marketlevel demographics, and operational advantages asso-ciated with larger stores and proprietary distributionsystems. The Bayesian structure of the game allowsus to account for different equilibria with the samecovariates, due to the presence of unobserved types.More importantly, it allows us to model all 8,000 mar-kets as variations in the play of a game with thesame structure, but different conditioning variables.As the conditioning variables vary, we are able totrace out the equilibrium correspondence and iden-tify the impact of several distinct factors. First, wefind that firms choose strategies that are tailored to

Table 6 Estimation Results

EDLP HYBRID

Estimate Std. err T -stat Estimate Std. err T -stat

EffectIntercept −1�5483 0�2426 −6�3821 2�1344 0�2192 9�7372

Strategy variables�̂EDLP−i

lmc

4�4279 0�1646 26�9010 −2�0924 0�1595 −13�1185�̂PROMO−i

lmc

−3�7733 0�1501 −25�1386 −6�3518 0�1351 −47�0155

MSA characteristicsSize (’000 sq. miles) 0�0394 0�0848 0�4645 −0�0566 0�0804 −0�7039Density (pop 10,000 per sq. mile) −0�0001 0�0002 −0�4587 0�0006 0�0002 2�9552Avg. food expenditure ($ ’000) −0�0375 0�0155 −2�4225 −0�0013 0�0141 −0�0904

Market variablesMedian household size 0�5566 0�1989 2�7983 0�2150 0�0900 2�3889Median HH income −0�0067 0�0019 −3�5385 0�0056 0�0017 3�2309Proportion Black 0�6833 0�1528 4�4719 0�0139 0�1443 0�0963Proportion Hispanic 0�5666 0�2184 2�5943 −0�0754 0�2033 −0�3708Median vehicles in HH −0�1610 0�0840 −1�9167 0�2263 0�1173 1�9292

Store characteristicsStore size (sqft ’000) 0�0109 0�0015 7�2485 0�0123 0�0014 8�8512Vertically integrated 0�1528 0�0614 2�4898 0�0239 0�0550 0�4343

Chain characteristicsNumber of stores in chain −0�0002 0�0001 −2�7692 0�0002 0�0001 3�5000Chain effect 1�7278 0�0998 17�3176 2�8169 0�0820 34�3531Chain/MSA effect 0�7992 0�0363 22�0408 0�9968 0�0278 35�8046

the demographics of the market they serve. More-over, the impact of demographics corresponds closelyto existing empirical studies of consumer preferencesand conventional wisdom regarding search behavior.Second, we find that EDLP is favored by firms thatoperate larger stores and are vertically integrated intodistribution. Again, this accords with conventionalwisdom regarding the main operational advantagesof EDLP. Finally, with regard to strategic interaction,we find that firms coordinate their actions, choosingpricing strategies that match their rivals. This iden-tifies an aspect of firm behavior that has not beenaddressed in the existing literature: exactly how firmsreact to rival strategies.Our main empirical results are presented in Table 6.

The coefficients, which represent the parametersof the profit function represented in Equation (6),have the same interpretation as those of a stan-dard MNL model: positive values indicate a positiveimpact on profitability, increasing the probability thatthe strategy is selected relative to the outside option(in this case, PROMO).

6.1. The Role of DemographicsThe coefficients on consumer demographics are pre-sented in the second and third sections of Table 6.With the exception of two MSA-level covariates, everydemographic factor plays a significant role in the


choice of EDLP as a pricing strategy. This is importantfrom an econometric standpoint, since we use thesevery same factors to construct expectations in the firststage. In particular, the significance of the estimatesmeans that we do not have to worry about collinear-ity. The statistical significance of the parameters isalso substantively important. It suggests that the evenafter accounting for competitive and supply side (e.g.store/chain) characteristics, consumer demand playsa strong role in determining pricing strategy.Focusing more closely on the demand related

parameters, we find that (relative to PROMO), EDLPis the preferred strategy for geographic markets thathave larger households � HH = 0�5566�, more racialdiversity in terms of African-American � BL = 0�6833�and Hispanic � HI = 0�5666� populations, lowerincome � INC = −0�0067�, and fewer vehicles perhousehold � VH =−0�1610�. These results suggest thatEDLP is mostly aimed at lower income consumerswith larger families (i.e. more urbanized areas). Ourfindings are clearly consistent with the consumer seg-ments that firms like Wal-Mart and Food Lion arewidely perceived to target. It also accords quite wellwith the “fixed basket” model of shopping behav-ior (Bliss 1988, Bell and Lattin 1998), in which con-sumers who are more sensitive to the price of an over-all basket of goods prefer EDLP. In particular, ourresults suggest that the consumers who are unableto substitute inter-temporally are disproportionatelypoor, nonwhite, and from larger families. On the otherhand, we find that consumers who are most able todefer or stockpile purchases (wealthy suburbaniteswith greater access to transportation) tend to preferPROMO or HYBRID pricing.

6.2. Firm and Store Level CharacteristicsTurning next to chain and store level characteris-tics, we again find that most parameter estimatesare statistically significant. These effects, which are inline with both theory and broad intuition, providean additional empirical validation of our structuralframework.The last two sections of Table 6 reveal that stores

choosing EDLP are both significantly larger � SS =0�0109� and far more likely to be vertically integratedinto distribution � VI = 0�1528�. This is consistentwith the view that EDLP requires substantial firmlevel investment, careful inventory management, anda deeper selection of products in each store in orderto satisfy the demands of one-stop shoppers. It isalso consistent with the logic of Lal and Rao (1997),whereby pricing strategy involves developing anoverall positioning strategy, requiring complementaryinvestments in store quality and product selection.Surprisingly, the total number of stores in the chain isnegatively related to EDLP � ST =−0�0002�, although

this is difficult to interpret since almost all the largechains are vertically integrated into distribution (i.e.there are almost no large, nonvertically integratedfirms). Finally, both the chain specific and chain/MSArandom effects are highly significant, which is not sur-prising given the geographic patterns shown earlier.19

6.3. The Role of Competition:Differentiation or Coordination

By constructing a formal model of strategic interac-tion, we are able to address the central question posedin this paper—what is impact of competitive expec-tations on the choice of pricing strategy? Our conclu-sions are quite surprising. The first section of Table 6reveals that firms facing competition from a high(expected) share of EDLP stores are far more likely tochoose EDLP than either HYBRID or PROMO � �"k1 =4�4279� �"k2 = −3�7733�. The HYBRID case behavesanalogously; when facing a high proportion of eitherEDLP or PROMO rivals, a store is least likely tochoose HYBRID � �"k1 = −2�0924� �"k2 = −6�3518�. Inother words, we find no evidence that firms differenti-ate themselves with regard to pricing strategy. To thecontrary, we find that rather than isolating themselvesin strategy space, firms prefer to coordinate on asingle pricing policy. Pricing strategies are strategiccomplements.This coordination result stands in sharp contrast

to most formal models of pricing behavior, which(at least implicitly) assume that these strategies arevehicles for differentiation. Pricing strategy is typi-cally framed as a method for segmenting a hetero-geneous market—firms soften price competition bymoving further away from their rivals in strategyspace. This is not the case for supermarkets. Insteadof finding the anti-correlation predicted by these spa-tial models, we find evidence of associative matching,which usually occurs in settings with network effectsor complementarities. This suggests that firms areable to increase the overall level of demand by match-ing their rivals’ strategies, a possibility we discuss inmore detail below. However, before discussing ourcoordination result in greater detail, we must addressthe issue of correlated unobservables.

19 An earlier version of this paper also included the share ofeach firm’s stores outside the local MSA that employ EDLP andPROMO pricing as additional regressors. Not surprisingly, a firm’spropensity to follow a particular strategy at the level of the chainhad a large and significant impact on its strategy in a particularstore (and soaked up a lot of variance). While this suggests thepresence of significant scale economies in implementing pricingstrategies, as suggested by both Lattin and Ortmeyer (1991) andHoch et al. (1994), we omitted it from the current draft to maintainthe internal coherency of the underlying model (i.e. the simultane-ity of actions). However, these results are available from the authorsupon request.


Table 7 Robustness

Specification Strategy Strategy �̂ EDLP−i

lmc

Variables �̂PROMO−i

lmc

Baseline EDLP 4�4279 (0.1646) −3�7733 (0.1501)HYBRID −2�0924 (0.1595) −6�3518 (0.1351)

MSA by MSA EDLP 3�1867 (0.2522) −3�2823 (0.1771)HYBRID −3�4418 (0.2603) −6�2746 (0.1701)

NPL EDLP 1�7464 (0.1743) −2�5699 (0.1723)HYBRID −0�7365 (0.1770) −4�9899 (0.1739)

The surprising nature of our coordination resultdemands careful consideration. Again, how can we besure that firms are actually reacting to the actions oftheir rivals, rather than simply optimizing over somecommon but unobserved feature of the local market?Section 5.6 described two alternative strategies fordealing with the potential presence of common unob-servables. The first method involved adding an MSAlevel fixed effect to the baseline specification. In prac-tice, this requires estimating the first stage separatelyfor each MSA (to ensure a consistent first stage) andthen expanding the second stage likelihood to includean MSA fixed effect. The main coordination resultsare presented in the section of Table 7 titled MSAby MSA (the demographic and chain level covariateshave been suppressed for brevity, but are availablefrom the authors upon request). While the coefficientshave changed slightly in magnitude, the main coor-dination result remains strong. The second methodinvolved adding a cluster level random effect, and re-estimating the model using Aguirregabiria and Mira’s(2006) NPL algorithm. These results are presented inthe section titled NPL. Here we find that the magni-tudes of the coefficients fall relative to both the base-line and MSA by MSA specifications, as one mightexpect if firms are indeed reacting to a common unob-servable. However, the coordination effects are stilllarge and significant: pricing strategies are indeedstrategic complements.But how important are these strategic effects? The

parameter estimates from our baseline model canbe used to gauge the relative influence that strate-gic interactions have on profits. Because individualcovariates can influence profits either negatively orpositively, a simple additive decomposition of prof-its by strategic and nonstrategic factors is inappropri-ate. To adjust for this, we adopted the method pro-posed in Silber et al. (1995), using the average squaredcontributions of each factor to construct a measureof the share of variance explained. This decomposi-tion reveals that, on average, strategic factors explainabout 20.3% of the variation in EDLP profits and13.2% of the variation in HYBRID profits, quite sub-stantial fractions. The remaining variance is explained

by nonstrategic factors, including market characteris-tics, store and firm-level covariates, and the randomeffects that we have treated as private information.In addition to this decomposition of profits, we also

conducted a policy experiment aimed at highlight-ing the mechanism by which strategic effects influ-ence pricing strategy. To do so, we simply shut off thestrategic effects and compared the odds of choosingPROMO relative to EDLP under this counterfactualscenario to what we see in the data.20 The results arestriking. At the aggregate level, the true odds ratiowas around 1.31, implying that PROMO is roughly31% more likely to be chosen than EDLP. However, inthe counterfactual scenario (without strategic effects)this drops to 4.1% (odds ratio= 1�041). This finding isnotable since it offers an explanation for why EDLPdid not become the dominant paradigm in supermar-ket pricing. To see why, notice first that even with-out strategic effects, the odds ratio was greater thanone. This implies that there are market factors that,on average, lead a market to lean towards one strat-egy. With the same set of characteristics, the strate-gic effects induce a feedback effect that can causethe market to tip more significantly in that direction.While these are clearly aggregate trends, we observedsimilar phenomena in individual markets as well.Broadly speaking, strategic effects strengthen coordi-nation in markets where one strategy is weakly dom-inant (under the counterfactual).

6.4. Discussion of ResultsThe Bayesian structure of our game allows us torepresent a quite complex game using a relativelysimple structure. By tracing out the equilibrium corre-spondence, we have found that firms favor particularstrategies in certain markets, in ways that are con-sistent with existing theory. We have also found thatcertain types of firms favor particular strategies, alsoconsistent with existing theory. Finally, we have foundthat firms are more likely to choose a particular strat-egy if they expect their rivals to do the same. Thisis a sharp departure from existing theory. It is worthemphasizing that reactions to market demographicsand firm characteristics help explain how firms areable to coordinate on consistent strategies. However,they do not explain why they choose to do so. Coordi-nation implies that firm’s conditional choice probabil-ities act as strategic complements, meaning that theirbest response probability functions (9) are upwardsloping. To support such complementarity, coordina-tion must somehow increase the overall size of theperceived market. In most cases, this means drawingexpenditures away from the outside good.

20 Note that � �PPROMO/ �PEDLP� is now our object of interest.


In the context of supermarket pricing, this suggeststhat coordination may actually increase the amountconsumers are willing to spend on groceries, perhapsby drawing them away from substitutes like restau-rants, convenience stores, and discount clubs. Oneway this might occur in practice is if consumers aremore likely to trust retailers that provide a messagethat is consistent with those of their rivals. In otherwords, if one firm tells you that providing the high-est value involves high price variation while anothertouts stable prices, you may be unwilling to trusteither, shifting your business to a discount club oranother retail substitute. While this intuition has yetto be formalized, it is consistent with the empha-sis that Ortmeyer et al. (1991) place on maintainingpricing credibility. Another possibility, consistent withLal and Rao (1997), is that price positioning ismulti-dimensional and by coordinating their strate-gies stores can mitigate the costs of competing alongseveral dimensions at once. Without a formal modelof consumer behavior and detailed purchase data,we are unable to pin down the exact source of thecomplementarities we have documented here. How-ever, we have provided strong empirical evidenceregarding how firms actually behave. Understand-ing why firms find it profitable to coordinate theiractions remains a promising area for future theoreticalresearch.The results presented above provide definitive

answers to the three questions posed in the intro-duction of this paper. We have found that demandrelated factors (i.e. demographics) are important fordetermining the choice of pricing strategy in a market;store and firm level characteristics also play a centralrole. Both of these results are in line with the extantliterature. However, our results concerning competi-tive expectations are in sharp contrast to prevailingtheory in both economics and marketing and warrantfurther attention. The final section outlines a researchagenda for extending the results found in this paper.

7. Conclusions and Directions forFuture Research

This paper analyzes supermarket pricing strategiesas discrete game. Using a system of simultaneousdiscrete choice models, we estimate a firm’s optimalchoice conditional on the underlying features of themarket, as well as each firm’s beliefs regarding itscompetitor’s actions. We find evidence that firmscluster by strategy, rather than isolating themselvesin product space. We also find that demographicsand firm characteristics are strong determinants ofpricing strategy. From a theoretical perspective, itis clear that we have yet to fully understand what

drives consumer demand. The fact that firms coor-dinate with their rivals suggests that consumers pre-fer to receive a consistent message. While our resultspertain most directly to supermarkets, it seems likelythat other industries could behave similarly. Futureresearch could examine the robustness of our findingsby analyzing other retail industries, such as depart-ment stores or consumer electronics outlets.In this paper, our primary focus was the construc-

tion and econometric implementation of a frameworkfor analyzing best responses to rival pricing strate-gies. Our analysis describes the nature of strategicinteractions, but does not delve into the details ofwhy these strategies are dominant. Decomposing thewhy element of strategic coordination seems a fruitfularea for research. We hasten to add that such researchis needed not only on the empirical side but alsoon the theoretical front. Building theoretical modelsthat allow for the possibility of both differentiationand coordination is a challenging but undoubtedlyrewarding path for future research.The tendency to coordinate raises the possibility

that games such as this might support multiple equi-libria. While this is not a concern in our current study,it could play a central role when conducting pol-icy experiments or when analyzing settings in whichdemographics (or other covariates) cannot effectivelyfacilitate coordination. Developing methods that arerobust to such possibilities remains an important areafor future research.On the methodological front, our research also cen-

ters its attention on the discrete choice aspect of strat-egy. There are a number of issues that emerge oncesuch strategic choices have been made such as thereaction of consumers (see e.g. Singh et al. 2006) andthe overall demand faced by stores. Research thataims at incorporating such postgame outcome datainto the analysis promises to offer newer and crisperinsights into the nature of competition in the market.Finally, in building our model of strategic interac-

tion, we have assumed that firms interact in a staticsetting, making independent decisions in each store.A more involved model would allow chains to makejoint decisions across all of their outlets and accountfor richer (dynamic) aspects of investment. Develop-ing such a model is the focus of our current research.

AcknowledgmentsThe authors thank participants at the Supermarket Retail-ing Conference at the University of Buffalo, the 2006BCRST Conference at the University of Toronto, the2005 QME Conference at the University of Chicago, andthe Supermarket Conference held at IFS London, as wellas seminar participants at Duke, UCLA, Stanford, UTDallas, and Yale. The authors also thank Victor Aguirrega-biria, Pat Bajari, J. P. Dubé, Han Hong, Paul Nelson, and


Chris Timmins for their comments. All remaining errors arethe authors’ responsibility.

Appendix A. Survey ValidityAll of the variables in the Trade Dimensions data, includ-ing the information on pricing strategy, are self-reported.This may raise some concerns regarding accuracy, especiallygiven the high degree of local variation we observe in thedata. Two questions naturally arise. First, are firms actuallywilling and able to set prices at such local levels? Second,do these self-reported strategies reflect actual differences inpricing behavior? We will address both issues in turn.First, with regard to local pricing, we should note that

supermarket firms clearly have the technological resourcesto set prices (and therefore pricing strategy) at a verylocal level. Indeed, Montgomery (1997) provides a novelmethod for profitably customizing prices at the store level,using widely available scanner data.21 We contacted pricingmanagers at several major chains and other industry pro-fessionals regarding their ability to engage in such micro-marketing. Even on the condition of anonymity, they wereextremely reluctant to discuss the details of their actualpricing strategies, but did acknowledge that they “certainlyhave the data and resources to do it.” Furthermore, a con-sultant who was involved in several recent supermarketmergers confirmed that the extent of local pricing was a keyfactor in the approval process.22

A related issue is whether firms face significant pressureto maintain a consistent (pricing) image across stores. Wesuspect not. Unlike many other types of retail food services(e.g., fast food establishments), supermarket customers dothe majority of their shopping in a single store.23 There-fore, while consumers undoubtedly have strong preferencesover the pricing strategy of their chosen store, they have lit-tle reason to care directly about the overall strategy of thechain. Of course, chains may have strong operational incen-tives (e.g. scale economies in distribution and advertising)to maintain a consistent strategy across several (not neces-sarily proximate) stores, which might lead them to adopt acommon strategy in multiple outlets. Indeed, we are rely-ing on just such incentives to provide the variation neededto identify the effect of strategic interactions (see §5.7). Thepoint is that firms may indeed have both strong incentivesand the ability to tailor pricing to the local environment.The second question concerns the validity of the survey

instrument itself. We note first that the survey was of storemanagers but administered by brokers (who explained thequestions), providing an additional level of cross-validation.It is unlikely that the results reported below could be the

21 While the emphasis there is on maintaining a consistent image,Montgomery argues that the potential gains to micro-marketingare quite significant. Setting different sales frequencies in differentstores is simply an alternative method of micro-marketing.22 While detailed information on the degree of micro-marketing inthe supermarket industry is not publicly available, explicit evidenceof local pricing was a major issue in the proposed merger betweenStaples and Office Depot (Ashenfelter et al. 2006).23 According to the Food Marketing Institute, consumers allocate78% of their overall budget to their primary store. Moreover, theirsecondary store is almost always part of a different chain.

product of systematic reporting error, as this would requirecoordination between tens of thousands of managers andhundreds of brokers to willfully and consistently mis-reporttheir practices (for no obvious personal gain). However, tofurther allay such fears, we cross-verified the data ourselvesusing publicly available data from the Dominick’s FinerFoods (DFF) supermarket chain in Chicago. In particular,we extracted store level prices from four major product cate-gories for every store in the DFF data set and matched themup to the pricing classifications reported by Trade Dimen-sions. The vast majority of the Dominick’s stores are iden-tified as PROMO (93%), while the remainder are HYBRID,which is itself encouraging since Dominick’s is known to bea PROMO chain. We then checked whether the incidenceof promotions (i.e. whether a UPC was “on sale”) variedacross PROMO and HYBRID stores. In all four categoriesthat we examined (Soft Drinks, Oatmeal, Paper Towels, andFrozen Juice), we found a significantly lower incidence ofpromotions at the HYBRID stores. The differences rangedfrom 8.1% in Soft Drinks (a very heavily promoted cate-gory) to 23.4% in Oatmeal. All differences were significantat the 1% level.In addition, we also compared the HYBRID and PROMO

stores for equality in the variance of the prices using stan-dard folded—F tests. One would expect PROMO storesto have higher variances. For three of the four categories(Oatmeal, Paper Towels, and Frozen Juice) the variance inprices was indeed higher in the PROMO stores, validatingthe survey data. The difference was not significant for SoftDrinks category. We also repeated each analysis for onlythe highest selling UPC in each category and found qual-itatively similar results. While these tests use only a fewproduct categories from a single chain in a single market,the sharpness of the results should provide additional con-fidence in the integrity of our data.

Appendix B. Robustness Checks

B.1. Market Delineation and DefinitionAs noted earlier, our empirical analysis uses specific marketdefinitions based on spatial cluster analysis. We verified therobustness of our results to alternative market definitionsby repeating the analysis using ZipCodes, Counties, andMSAs. In all cases, the results were qualitatively similar. Wealso varied the number of clusters and did not find signifi-cant differences from the results reported above. Finally, weexperimented with n-nearest neighbor methods (we tried 3and 5 nearest neighbors of a focal store) and again foundsimilar results.

B.2. MultiplicityAs we noted in the main text, consistent estimation of astatic (or dynamic) game requires some form of uniquenessof equilibrium, either in the model or in the data.24 Con-sistency of our baseline model requires that only one equi-librium be played in the data which, in our context, means

24 Uniqueness may fail to hold in many settings. Brock and Durlauf(2001) and Sweeting (2004) provide two such examples. Non-uniqueness can complicate policy experiments, which typicallyinvolve solving for a new equilibrium.


every location in every MSA. It is possible to relax this byestimating the first stage separately for each MSA, so therequirement becomes that a unique equilibrium be playedin each MSA (we do not have enough data to estimate thefirst stage separately for each cluster, which would elim-inate the problem entirely). The results of this procedurewere very close to the baseline model. For brevity, we reportonly the coefficients on the strategy variables (see Table 7).

B.3. Format CharacterizationIn our baseline model, we assumed that firms care onlyabout the share of their rivals that choose each strategy.An alternative, similar to what is done in the entry litera-ture, is to assume that firms care instead about the numberof rivals. We reestimated the baseline model using countsinstead of shares and found qualitatively similar results.

B.4. Nonparametric Estimation of !−iAs noted above, the ideal approach for estimating beliefsis nonparametric. However, the number of covariates weuse precludes us from adopting such a strategy. To assessthe robustness of our results, we used a bivariate thin-platespline to model pricing strategies as nonparametric func-tions of the strategies chosen outside the MSA. Again, themain results were qualitatively similar to those presentedabove.

B.5. Nonlinearity of f �!−i�To examine the potentially nonlinear relationship betweenpayoffs (�) and strategies (!−i), we adopted a smoothingsplines approach to modeling f �!−il�. In particular, we re-estimated our model using a bivariate thin-plate spline,treating the functional relationship as

fj(a−ilmc

)= f(!E−ilmc

� !P−ilmc�9)

� (18)

The qualitative results obtained using the linear specifica-tion continue to hold. For example, the probability of firmschoosing EDLP increases with the proportion of competi-tors that also choose EDLP.

B.6. Error StructureIn our analysis we assumed that firm types (the �i’s) weredistributed Gumbel (Type I Extreme Value), allowing us tospecify set of simultaneous multinomial logit choice prob-abilities for determining pricing policies. As an alternativespecification, similar to the empirical application in Bajariet al. (2005), we also tested ordered logit/probit models inwhich the strategies were ranked ordered EDLP to PROMO.While qualitative findings were similar, these ordered spec-ifications force a particular ranking of strategies that maynot be warranted.

Appendix C. Nested Pseudo Likelihood (NPL)AlgorithmWe assume that the common unobservables are jointly dis-tributed with distribution function F ��lm

�(�, where ( is aset of parameters associated with F . To start the algorithm,let Plm be the set of strategy choice probabilities across play-ers in a given local market lm. Finally, let �P0lm be some (notnecessarily consistent) estimator for Plm .

In the rth iteration implement the following steps:Step 1. Given �Pr−1 update �

��r = argmax�

∑m∈M

∑c∈Cln

∫ [ ∏lm∈Lm

∏ilmc ∈Nlm

c

∏k∈K

[�ilmc

(ailmc= k ��

Plm � s��lm�k�

)]*ilmc�k�]dF

(�lm

�()

Step 2. Update Plm using�)r , setting

�Prilmc�a

ilmc= k� =

∫�ilmc

(ailmc= k � �)r��Pr−1lm

�X�2lm�k�)

·0(2 � �)r��Pr−1lm� s��lm

�k�� ailmc

)dF

(�lm

� ��r)�

where

0�2 � ···�=( ∏lm∈Lm

∏ilmc ∈Nlm

c

∏k∈K

[�ilmc

(ailmc=k � �)r��Pr−1lm

�s�2lm�k�)]*

ilmc�k�)

·(∫ ∏

lm∈Lm

∏ilmc ∈Nlm

c

∏k∈K

[�ilmc

(ailmc=k � �)r�

�Pr−1lm�s��lm

�k�)]*

ilmc�k�dF

(�lm

� ��r))−1

Step 3. If �Prlm − Pr−1lm� is smaller than a predetermined

value, stop and choose �)NPL = )r . If not, increment r andreturn to Step 1.Note that there are a few key differences between our

approach and the Nested Pseudo Likelihood (NPL) algo-rithm proposed by Aguirregabiria and Mira (2007) (hence-forth AM). First, unlike AM, our game is static. This doesnot alter the main econometric properties of the NPL esti-mator, since a static game is simply a one-period subcaseof a dynamic one. However, a natural consequence of thestatic setting is that the state variables do not transition overtime, allowing us to extend the NPL approach to includecontinuous states. A more significant point of departurebetween our algorithm and the NPL is the inclusion of con-tinuous heterogeneity. Since the evolution of the observedstate variables naturally depends on the unobserved statevariables, AM restricted their estimator to a finite support.In our case, the static nature of the problem, coupled withan independence assumption (2lm is orthogonal to s), allowsus to simply integrate out over a continuous heterogeneitydistribution. An attractive feature of the NPL algorithm isthat it works even in the presence of inconsistent or poorlyestimated initial probabilities. As long as the algorithm con-verges, it will do so to the root of the likelihood equations.In our experience, the procedure converged very quickly tothe same fixed point for several different starting values.

ReferencesAguirregabiria, V., P. Mira. 2007. Sequential estimation of dynamic

discrete games. Econometrica 75(1) 1–53.Ashenfelter, O., D. Ashmore, J. B. Baker, S. Gleason, D. S. Hosken.

2006. Econometric methods in merger analysis: Econometricanalysis of pricing in FTC v. staples. Internat. J. Econom. Bus.13(2) 265–279.


Augereau, A., S. Greenstein, M. Rysman. 2006. Coordination ver-sus differentiation in a standards war: 56K modems. RAND J.Econom. 37(4) 887–909.

Bajari, P., C. L. Benkard, J. Levin. 2007. Estimating dynamic modelsof imperfect competition. Econometrica 75(5) 1331–1370.

Bajari, P., H. Hong, J. Krainer, D. Nekipelov. 2005. Estimating staticmodels of strategic interactions. Working paper, University ofMichigan.

Bayer, P., C. Timmins. 2007. Estimating equilibrium models of sort-ing across locations. Econom. J. 117(518) 353–374.

Bell, D., J. Lattin. 1998. Shopping behavior and consumer prefer-ence for store price format: Why “large basket” shoppers preferEDLP. Marketing Sci. 17(1) 66–88.

Bell, D., T. Ho, C. S. Tang. 1998. Determining where to shop:Fixed and variable costs of shopping. J. Marketing Res. 35(3)352–369.

Bliss, C. 1988. A theory of retail pricing. J. Indust. Econom. 36(4)375–391.

Brock, W., S. Durlauf. 2001. Discrete choice with social interactions.Rev. Econom. Stud. 62(2) 235–260.

Dhar, S. K., S. J. Hoch. 1997. Why store brand penetration varies byretailer. Marketing Sci. 16(3) 208–227.

Einav, L. 2003. Not all rivals look alike: Estimating an equilib-rium model of the release date timing game. Working paper,Stanford University.

Ellickson, P. 2006. Quality competition in retailing: A structuralanalysis. Internat. J. Indust. Organ. 24(3) 521–540.

Gowrisankaran, G., J. Krainer. 2004. The welfare consequencesof ATM surcharges: Evidence from a structural entry model.Working paper, Washington University.

Harsanyi, J. 1973. Games with randomly disturbed payoffs: A newrationale for mixed-strategy equilibrium points. Internat. J.Game Theory 2(1) 1–23.

Hoch, S., X. Dreze, M. Purk. 1994. EDLP, Hi-Lo, and margin arith-metic. J. Marketing 58(4) 16–27.

Hotz, J., R. Miller. 1993. Conditional choice probabilities andthe estimation of dynamic models. Rev. Econom. Stud. 60(3)497–531.

Kumar, N., R. Rao. 2006. Using basket composition data for intelli-gent supermarket pricing. Marketing Sci. 25(2) 188–199.

Lal, R., R. Rao. 1997. Supermarket competition: The case of every-day low pricing. Marketing Sci. 16(1) 60–81.

Lattin, J., G. Ortmeyer. 1991. A theoretical rationale for everydaylow pricing by grocery retailers. Working paper.

Manski, C. 1993. Identification of endogenous social effects: Thereflection problem. Rev. Econom. Stud. 60(3) 531–42.

Messinger, P., C. Narasimhan. 1997. A model of retail formats basedon consumers’ economizing on shopping time. Marketing Sci.16(1) 1–23.

Montgomery, A. L. 1997. Creating micro-marketing pricing strate-gies using supermarket scanner data. Marketing Sci. 16(4)315–337.

Newey, W. K., D. McFadden. 1999. Large sample estimation andhypothesis testing. D. McFadden, R. Engle, eds. Handbookof Econometrics, Vol. 4, Chap. 36. Elsevier, North-Holland,Amsterdam, The Netherlands, 2113–2245.

Orhun, A. Y. 2005. Spatial differentiation in the supermarket indus-try. Working paper, University of California.

Ortmeyer, G., J. Quelch, W. Salmon. 1991. Restoring credibility toretail pricing. Sloan Management Rev. 33(1) 55–66.

Rust, J. 1987. Optimal replacement of GMC bus engines: An empir-ical model of Harold Zurcher. Econometrica 55(5) 999–1033.

Seim, K. 2006. An empirical model of firm entry with endogenousproduct-type choices. RAND J. Econom. Forthcoming.

Shankar, V., R. Bolton. 2004. An empirical analysis of determinantsof retailer pricing strategy. Marketing Sci. 23(1) 28–49.

Silber J., P. Rosenbaum, R. Ross. 1995. Comparing the contributionsof groups of predictors: Which outcomes vary with hospitalrather than patient characteristics. J. Amer. Statist. Assoc. 90(429)7–18.

Singh V., K. Hansen, R. Blattberg. 2006. Market entry and consumerbehavior: An investigation of a wal-mart supercenter. Market-ing Sci. 25(5) 457–476.

Smith, H. 2006. Supermarket choice and supermarket competitionin market equilibrium. Rev. Econom. Stud. Forthcoming.

Sweeting, A. 2004. Coordination games, multiple equilibria, andthe timing of radio commercials. Working paper, NorthwesternUniversity.

Varian, H. 1980. A model of sales. Amer. Econom. Rev. 70(4) 651–659.Watson, R. 2005. Product variety and competition in the retail mar-

ket for eyeglasses. Working paper, University of Texas.Zhu, T., V. Singh, M. Manuszak. 2005. Market structure and compe-

tition in the retail discount industry. Working paper, CarnegieMellon University, Pittsburgh.

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