SupermarketPricingStrategies

Transcription

1 SupermarketPriingStrategies PaulB.Ellikson Duke University SanjogMisra University of Rohester November 13, 2006 Abstrat Most supermarket firms hoose to position themselves by offering either Every Day Low Pries (EDLP) aross several items or offering temporary prie redutions(promotions) on a limited range of items. While this hoie has been addressed from a theoretial perspetive in both the marketing and eonomi literature, relatively little is known about how these deisions are made in pratie, espeially within a ompetitive environment. This paper exploits a unique store level dataset onsisting of every supermarket operating in the United States in For eah of these stores, we observe thepriingstrategythefirmhashosentofollow,asreportedbythefirmitself. Usinga system of simultaneous disrete hoie models, we estimate eah store s hoie of priing strategy as a disrete game of inomplete information. In ontrast to the preditions of the theoretial literature, we find strong evidene that firms luster by strategy by hoosingationsthatagreewiththoseofitsrivals. Wealsofindasignifiantimpatof various demographi and store/hain harateristis, providing some qualified support for several speifi preditions from marketing theory. Keywords: EDLP, promotional priing, positioning strategies, supermarkets, disrete games. JEL Classifiation Codes: M31, L11, L81 TheauthorswouldliketothankpartiipantsattheSupermarketRetailingConfereneattheUniversity of Buffalo and the 2005 QME onferene at the University of Chiago. The authors have benefitted from onversations with Pat Bajari, Han Hong, Chris Timmins, J.P. Dube, Vitor Aguirregabiria, and Paul Nelson. All remaining errors are our own. DepartmentofEonomis,DukeUniversity,DurhamNC paul.ellikson@duke.edu. Corresponding author. William E. Simon Shool of Business Administration, University of Rohester, Rohester, NY misra@simon.rohester.edu. 1

2 1 Introdution While firms ompete along many dimensions, priing strategy is learly one of the most important. In many retail industries, priing strategy an be haraterized as a hoie between offering relatively stable pries aross a wide range of produts(often alled every day low priing ) or emphasizing deep and frequent disounts on a smaller set of goods (referred to as promotional or PROMO priing). Although Wal-Mart did not invent the oneptofeverydaylowpriing(edlp),thesuessfuluseofedlpwasaprimaryfator in their rapid rise to the top of the Fortune 500, spawning a legion of followers selling everything from toys (Toys R Us) to building supplies (Home Depot). In the 1980s, it appeared that the suess and rapid diffusion of the EDLP strategy ould spell the end of promotions throughout muh of retail. However, by the late 1990s, the penetration of EDLP had slowed, leaving a healthy mix of firms following both strategies, and several otherswhousedamixtureofthetwo. Not surprisingly, priing strategy has proven to be a fruitful area of researh for marketers. Marketing sientists have provided both theoretial preditions and empirial evidene onerning the types of onsumers that different priing poliies are likely to attrat (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 how priing strategies are hosen by retailers. There are two primary reasons for this. First, these deisions are quite omplex: managers must balane the preferenes of their ustomers and their firm s own apabilities against the expeted ations of their rivals. Empirially modeling these ations (and reations) requires formulating and then estimating a omplex disrete game, an exerise whih has only reently beome omputationally feasible. The seond is the lak of appropriate data. While sanner data sets have proven useful for analyzing onsumer behavior, they typially lak the breadth neessary for takling the omplex mehanis of inter-storeompetition. 1 Thegoalofthispaperistoombinenewlydevelopedmethodsfor estimating stati games with a rih, nation-wide dataset on store level priing poliies to identify the primary fators that drive priing behavior in the supermarket industry. Exploiting the game theoreti struture of our approah, we aim to answer three ques- 1 Typialsannerdatausuallyrefletdeisionsmadebyonlyafewstoresinalimitednumberofmarkets. 3

3 tions that have not been fully addressed in the existing literature. First, to what extent do supermarket hains tailor their priing strategies to loal market onditions? Seond, do ertain types of hains or stores have advantages when it omes to partiular priing strategies? Finally, how do firms reat to the expeted ations of their rivals? We address eah of these questions in detail. The first question naturally invites a market pull driven explanation in whih onsumer demographis play a key role in determining whih priing strategy firms hoose. In answering this question, we also aim to provide additional empirial evidene that will inform the growing theoretial literature on priing related games. Sine we are able to assess the impat of loal demographis at a muh broader level than previous studies, our results provide more onlusive evidene regarding their empirial relevane. The seond question posed above addresses the math between a firm s strategy and its hain-speifi apabilities. In partiular, we examine whether partiular priing strategies (e.g. EDLP) are more profitable when firms make omplementary investments(e.g. larger stores and more sophistiated distribution systems). The empirial evidene on this matter issare-thisisthefirstpapertoaddressthisissueonabroadsale. Furthermore,beause our dataset inludes every existing supermarket, we are able to exploit variation both within andarosshainstoassesstheimpatofstoreandhainleveldifferenesonthehoieof priing strategy. Finally, we address the role of ompetition posed in our third question by analyzing firms reations to the expeted hoies of their rivals. In partiular, we ask whether firms fae inentives to distinguish themselves from their ompetitors(as in most models of produt differentiation) or instead fae pressures to onform (as in network or swithing ost models)? Thisquestionistheprimaryfousofourpaperandthefeaturethatmostdistinguishes it from earlier work. Our results shed light on all three questions. First, we find that onsumer demographis play a signifiant role in the hoie of loal priing strategies: firms hoose the poliy that their onsumers demand. Furthermore, the impat of these demographi fators is onsistent with both the existing marketing literature and onventional wisdom. For example, EDLP is favored in low inome, raially diverse markets, while PROMO learly targets the rih. However, a key impliation of our analysis is that these demographi fators at 4

4 as a oordinating devie for rival firms, helping shape the priing landsape by defining an equilibrium orrespondene. Seond, we find that omplementary investments are key: larger stores and vertially integrated hains are signifiantly more likely to adopt EDLP. Finally, and most surprisingly, we find that stores ompeting in a given market have inentives to oordinate their ations. Rather than hoosing a strategy that distinguishes them from their rivals, stores hoose strategies that math. This finding is in diret ontrast to existing theoretial models that view priing strategy as a form of differentiation. While we donotaimtotestapartiulartheoryofstrategipriingbehavior,wehopeadeeperexamination of these ompetitive interations will address important issues that have remained unanswered. Our paper makes both substantive and methodologial ontributions to the marketing literature. On the substantive front, our results offer an in-depth look at the supermarket industry s priing praties, delineating the role of three key fators(demand, supply and ompetition) on the hoie of priing strategy. We provide novel, produer-side empirial evidene that omplements various onsumer-side models of priing strategy. In partiular, we find qualified support for several laims from the literature on priing demographis, inluding Bell and Lattin s(1998) model of basket size and Lal and Rao s(1997) positioning framework, while at the same time highlighting the advantages of hain level investment. Our fous on ompetition also provides a strutural omplement to Shankar and Bolton s (2004) desriptive study of prie variation in supermarket sanner data, whih emphasized the role of rival ations. Our most signifiant ontribution, however, relates to the finding that stores in a partiular market do not use priing strategy as a differentiation devie but instead oordinate their ations. This result provides a diret hallenge to the onventional view of retail ompetition, opening up new and intriguing avenues for future theoretial researh. Our eonometri implementation also ontributes to the growing literature in marketing and eonomis on the estimation of stati disrete games, as well as the growing literatureonpeereffets 2. Inpartiular,ourinorporationofmultiplesouresofprivate 2 Reentappliationsofstatigamesinludetehnologyadoptionbyinternetservieproviders(Augereau et al. 2006), produt variety in retail eyewear (Watson, 2005), loation of ATM branhes (Gowrisankaran and Krainer, 2004), and spatial differentiation among supermarkets(orhun, 2005), disount stores(zhu et al., 2005), and video stores (Seim, 2006). Strutural estimation of peer effets is the fous of papers by Brok and Durlauf(2002), Bayer and Timmins(2006), and Bajari et al. (2005). 5

5 information and our onstrution of ompetitive beliefs are novel additions to these emerging literatures. The rest of the paper is organized as follows. Setion 2 provides an overview of the priing landsape, illustrating the importane of loal fators in determining store level strategies. Setion 3 introdues our formal model of priing strategy and briefly outlines our estimation method and identifiation strategy. Setion 4 desribes the dataset. Setion 5 provides the details of how we implement the model, inluding the onstrution of distint geographi markets, the seletion of ovariates, and our two-step estimation strategy. Setion 6 provides our main empirial results and disusses their impliations. Setion 7 onludes with diretions for future researh. 2 The Supermarket Priing Landsape Supermarket firms ompete along many dimensions, entiing ustomers with an attrative mix of produts, ompetitive pries, onvenient loations, and a host of other servies, features, and marketing programs. In equilibrium, firms hoose the bundle of servies and features that maximize profits, onditional on the types of onsumers they expet to serve and their beliefs regarding the ations of their rivals. Building a formal model of a hain s overall positioning strategy is an intratably omplex problem, involving an extremely high dimensional multiple disrete/ontinuous hoie problem that is well beyond the urrent frontier. Our fous is more modest, emphasizing only a single aspet of a firms positioning strategy: their priing poliy. The vast majority of both marketers and pratitioners frame the priing deision as hoie between offering every day low pries aross a wide ategoryofprodutsordeepbuttemporarydisountsononlyafew,labelingthefirststrategy EDLP and the seond Hi-Lo or PROMO. This is, of ourse, a simplifiation. Atual priing deisions are made in onjuntion with an overall positioning strategy and tailored to partiular operational advantages. For example, suessful implementation of EDLP typially involves offering a deeper and narrower produt line than PROMO, allowing these firms to leverage greater sale eonomies(in partiular ategories), redue their inventory arrying osts, and lower their advertising expenses. On the other hand, PROMO priing gives firms greater flexibility in learing overstok, allows them to quikly apitalize on deep 6

6 manufaturer disounts, and failitates the use of onsumer loyalty programs(e.g. frequent shopper ards). Given the information in our dataset, we have hosen to fous squarely on the priing dimension, although we will aount for some of the operational motives by onditioning on observable features of eah hain. Even abstrating from an overall positioning strategy, the EDLP-PROMO dihotomy istoonarrowtoadequatelyapturethefullrangeoffirmbehavior. Inpratie,firmsan hooseamixtureofedlpandpromo,varyingeitherthenumber ofategoriestheyput on sale or hanging the frequeny of sales aross some or all ategories of produts. Not surprisingly, pratitioners have oined a term for these praties, hybrid priing. What onstitutes HYBRID priing is neessarily subjetive, depending on an individual s own beliefs regarding how muh prie variation onstitutes a departure from pure EDLP. Boththedataanddefinitionsusedinthispaperarebasedonaspeifistorelevelsurvey onduted by Trade Dimensions in 1998, whih asked individual store managers to hoose whih of the following ategories best desribed their store s priing poliy Everyday Low Prie (EDLP): Little reliane on promotional priing strategies suh as temporary prie uts. Pries are onsistently low aross the board, throughout all pakaged food departments. Promotional(Hi-Lo) Priing: Heavy use of speials, usually through manufaturer prie breaks or speial deals. Hybrid EDLP/Hi-Lo: Combination of EDLP and Hi-Lo priing strategies. Aording to Trade Dimensions, the survey was designed to allow for a broad interpretation of the HYBRID strategy, as they wanted it to apture deviations along either the temporal(i.e. number of sales per year) or ategory based dimensions(i.e. number of ategories on deal). Sine the survey was of store managers but administered by brokers (whoexplainedthequestions),itwasultimatelyuptobothofthemtodeidethebestfit. Webelievethatpriingstrategyisbestviewedasaontinuum,withpureEDLP(i.e. onstantmarginsarossallategories)ononeendandpurepromo(i.e. frequentsalesonall ategories) at the other. This dataset represents a oarse disretization of that ontinuum. 7

7 Without this data on individual stores, it is tempting to onlude that all priing strategiesaredeterminedatthelevelofthehain. Toexaminetheissuemorelosely,wefous inonasinglehaininasinglemarket: thepathmarkhaininnewjersey. Figure1shows the spatial loations of every Pathmark store in New Jersey, along with its priing strategy. Two features of the data are worth emphasizing. We address them in sequene. First, Pathmark does not follow a single strategy aross its stores: 42% of the stores use PROMO priing, 33% follow EDLP, and the remaining 25% use HYBRID. The heterogeneity in priing strategy observed in the Pathmark ase is not speifi to this partiular hain. Table3showsthestorelevelstrategieshosenbythetop15U.S.supermarkets(by total volume) along with their total store ounts. As with Pathmark, the major hains are also surprisingly heterogeneous. While some firms appear to have a lear fous (e.g. Wal-Mart, H.E. Butt, Stop& Shop), others are more evenly split(e.g. Luky, Cub Foods). This pattern extends to the full set of firms. Table 4 shows the priing strategies hosen bylargeandsmallhains,usingfouralternativedefinitionsof large and small. 3 While large hains seem evenly distributed aross the strategies and small hains seem to favor PROMO, firm size is not the primary determinant of priing strategy. The seond noteworthy feature of the Pathmark data is that even geographially proximate stores adopt quite different priing strategies. While there is some lustering at the broader spatial level (north vs. south New Jersey), the extent to whih these strategies are interlaed is striking. Again, looking beyond Pathmark and New Jersey onfirms that this within-hain spatial heterogeneity is not unique to this partiular example. Broadly speaking, the data reveal only a weak relationship between geography and priing strategy. While southern hains suh as Food Lion are widely pereived to favor EDLP and Northeastern hains like Stop& Shop are thought to prefer promotional(promo) priing, regional variation does not apture the full story. Table 2 shows the perent of stores that hoose either EDLP, HYBRID, or PROMO priing in eight geographi regions of the U.S. While PROMO priing is most popular in the Northeast, Great Lakes and entral Southern regions, it is far from dominant, as both the EDLP and HYBRID strategies enjoy healthy 3 Thefourdefinitionsoffirmsizeare: hain/independent,vertiallyintegratedandnot,large/smallstore, and many/few hekouts. A hain is defined as having 11 or more stores, while an independent has 10 of fewer. Vertially integrated means the firm operates its own distribution enters. Large versus small store sizeandmanyversusfewhekoutsaredefinedbytheupperandlowerquartilesofthefullstorelevelensus. 8

8 shares there as well. EDLP is ertainly popular in the South and Southeast, but PROMO still draws double digit shares in both regions. This heterogeneity in priing strategy is easily illustrated using the spatial struture of our dataset. Figure 2 plots the geographi loationofeverystoreintheu.s.,alongwiththeirpriingstrategy. Asislearfromthe panels orresponding to eah priing strategy, there is no obvious pattern at this level of aggregation. Taken together, these observations suggest looking elsewhere for the primary determinants of priing strategy. We turn next to the role of market demographis and then to the nature and degree of ompetition. Table 5 ontains the average demographi harateristis of markets served by stores of eah type. PROMO priing is assoiated with smaller households, higher inome, fewer automobiles per apita, and less raial diversity, providing some support for Bell and Lattin s (1998)influentialmodelof basketsize 4. However,thedifferenesarenotoverwhelming and, in many ases, statistially insignifiant. We note that this does not imply that demographis are irrelevant, but rather that the aggregate level patterns linking priing strategy and demographis are not overwhelming. We will demonstrate below that loal variation in demographis helps explain why hains tend to adopt heterogeneous priing strategies aross stores. The final row of Table 5 ontains the share of rival stores in the ompeting market thatemploythe samestrategyas thestorebeinganalyzed. Herewefindastrongresult: 50% of a store s rivals in a given loation employ the same priing strategy as the store being analyzed. Competitor fators were also the most important explanatory fator in Shankar and Bolton s(2004) analysis of priing variability in supermarket sanner data. In partiular, they note that what is most striking, however, is that the ompetitor fators are the most dominant determinants of retailer priing in a broad framework that inluded several other fators. Even at this rather oarse level of analysis, the data reveal that most stores hoose similar priing strategies. This pattern learly warrants a more detailed investigation and is the fous of our strutural model. 4 BellandLattin(1998)find thatthemostimportantfeaturesofshoppingbehavioranbeapturedby two interrelated hoies: basket size(how muh you buy) and shopping frequeny(how often you go). They suggest that large or fixed basket shoppers (i.e. those who buy more and shop less) will more sensitive to the overall basket prie than those who shop frequently and will therefore prefer EDLP priing to PROMO. They present empirial evidene that is onsistent with this predition. 9

9 Three entral features of supermarket priing strategy emerge from this disussion. First, supermarket hains adopt heterogeneous priing strategies, suggesting that demand related fores may outweigh any advantages aruing from hain level speialization. Seond, loal market fators play a key role in shaping demand harateristis. Finally, any empirial analysis of priing strategy must inlude the role of ompetition. While investigating the role of market demographis and firm harateristis is not oneptually diffiult, quantifying the strutural impat of rival priing strategies on firm behavior requires a formal game theoreti model of priing behavior that aounts for the simultaneity of hoies. In the following setion, we embed priing strategy in a disrete game that aommodates both loal demographis and the strategies of rival firms. We then estimate this model using a two-step approah developed by Bajari et al. (2005). 3 Theoretial Framework A supermarket s hoie of priing strategy is naturally framed as a disrete game between a finite set of players. Eah firm s optimal hoie is determined by the underlying market onditions, its own harateristis and individual strengths, and its expetations regarding theationsofitsrivals. Notably,thestrategihoieofeahfirmisafuntionoftheantiipated hoies of its ompetitors, and vie versa. If strategi expetations were ignored, a firm s hoie of priing strategy would be a straightforward disrete hoie problem. However, sine firms will ondition their strategies on their beliefs regarding rivals ations, this disrete hoie must be modeled using a system of simultaneous equations. In what follows, we outline our model in detail. 3.1 A Strategi Model of Supermarket Priing Inourframework,firms(i.e. supermarkethains 5 )makeadisretehoieofpriingstrategy, seleting among three alternatives: everyday low priing, promotional priing, and a hybrid strategy. While there is learly a role for dynamis in determining an optimal priing poliy, we assume that firms at simultaneously in a stati environment, taking entry deisions as 5 Heneforth,wewilluse hains and firms interhangeably. 10

10 given. 6 Astatitreatmentofompetitionis notaltogetherunrealisti sinethesepriing investments involve substantial investments in ommuniation and positioning related osts thatarenoteasilyreversible. 7 Inwhatfollows,weassumethatompetitiontakesplaein loal markets, 8 eahontained in a global market(here, an MSA). Before proeeding further, we must introdue someadditionalnotation. Storesbelongingtoagivenhain=1,..,C,thatareloatedin aloalmarketl m =1,..,L m,inanmsam=1,..,m,willbeindexedusingi l m =1,..,N l m ThetotalnumberofstoresinapartiularhaininagivenMSAisN m = thetotalnumberofstoresinthathainarossallmsasisn = L m l m=1. N lm,while M N m. Ineahloalmarket,hainsseletapriingstrategy(ation)afromthethreeelementsetK={E,H,P}, where E EDLP, H HYBRID,and P PROMO.If weobserve amarket l m ontaining N l m C = N l m players for example, the vetor of possible ation profiles is then =1 A lm ={E,H,P} Nl m with generi element a lm =(a 1,a 2,...,a i,...,a N ). The vetor of ationsofi l m sompetitorsisdenoteda i =(a 1,..,a i 1,a i lm +1,..a N lm ). In a given market, a partiular hain s state vetor is denoted s m S m, while the N m state vetor for the market as a whole is s m = (s m 1,...,sm N ) S m. The state vetor s m isknowntoallfirmsandobservedbytheeonometriian. Itdesribesfeaturesofthe market and harateristis of the firms that are assumed to be determined exogenously. For eah firm, there are also three unobserved state variables (orresponding to the three 6 Ideally, entry and priing deisions would be modeled jointly, allowing for firms that favor EDLP, for example, to prefer ertain types of markets. Unfortunately, even modeling supermarket loation hoie alone would be intratable, as it would require estimating a oordinated hoie of up to 1200 store loations by eah of hundreds of firms (the urrent state of the art (Jia, 2006) an handle two firms). Nonetheless, we believe that ignoring entry will not yield signifiant bias in our setting, sine logistial issues far outweigh priing strategy in determining entry deisions. In partiular, supermarket hains hoose store loations to maximize supply side density eonomies, designing hub and spoke networks to minimize transportation osts. The spatial distribution of stores traks population very losely; the gaps that one would expet if firms were herry piking priing-friendly markets simply do not exist. Ellikson (2006) presents empirial evidene onsistent with these laims. 7 Sine this is not an entry game (and priing deisions are relatively sunk), we are not partiularly onerned about the possibility of ex post regret that an sometimes our in stati games(einav, 2003). 8 Inourappliation,aloalmarketisasmallgeographitradingarea,roughlythesizeofazipode. The proedure we used to onstrut these markets is desribed in Setion 5.2. m=1 =1 11

11 priing strategies) that are treated as private information of the firm. These unobserved statevariablesaredenotedɛ i (a i lm,ormoreompatlyɛ i,andrepresentfirmspeifi shoks to the profitability of eah strategy. The private information assumption makes this ) a game of inomplete or asymmetri information(e.g. Harsanyi, 1973) and the appropriate equilibriumoneptoneofbayesiannashequilibrium(bne). 9 Foranygivenmarket,the ( ) ɛ i sareassumedtobeiidarossfirmsandations,anddrawnfromadistributionf ɛ i that is known to everyone, inluding the eonometriian. Firms hoose priing strategies in eah store independently, with the objetive of maximizingexpetedprofitsineahstore. Inmarketl m,theprofitearnedbystorei isgiven by π i =Π i (s m,a i,a i )+ɛ i (1) where Π i is a known and deterministi funtion of states and ations (both own and rival s). This extends the standard disrete hoie framework by allowing the ations of a firm s rivals to enter its payoff funtion. Sine the ɛ are treated as private information, afirm sdeisionrulea i =d i (s m,ɛ i lm isafuntionoftheommonstatevetorand itsownɛ, butnot theprivateinformationof itsrivals. Theprobabilitythatagivenfirm hoosesationkonditionalontheommonstatevetoristhengivenby P i (a i lm ) =k } = ) { ) } ( 1 d i (s m,ɛ i =k f ɛ i )dɛ i, (2) { where 1 d i (s,ɛ i lm =k isanindiatorfuntionequalto1ifstorei lm hooses ation k and 0 otherwise. These probabilities represent the expeted ations of a given store from ) the perspetive of the other stores in the market. We let P lm denote the set of these probabilities for a given loal market. Sine the firm does not observe the ations of its ompetitors prior to hoosing an ation, it makes deisions based on these expetations. Theexpetedprofitforfirmi lm fromhoosingationa i isthen π i (a i,s m,ɛ i,p lm ) = π i (a i lm = Π i a i,s m) +ɛ i (3) ( lm s m,a i,a i )P i +ɛ i (4) 9 Treating the types as private information greatly simplifies the omputational burden of estimation. By avoiding the ompliated regions of integration that arise in the omplete information ase, we an aommodate a muh larger number of players and potential ations. 12

12 wherep i = isgivenby j i l m P j (a j s m ).Giventheseexpetedprofits,theoptimalationforastore { Ψ i =Pr ɛ i π i (a i,s m) +ɛ i (a i )> π i lm (a i lm,s m) +ɛ i (a i lm ) a i lm } a i. (5) Iftheɛ i saredrawnfromatypeiextremevaluedistribution(i.e. Gumbelerrors),the Bayesian Nash Equilibrium to this stati game must satisfy a system of logit equations(i.e. best response funtions). Beause a firm s optimal ation is unique by onstrution, there is no need to onsider mixed strategies. The general framework desribed above has been applied in several eonomi settings and its properties are well understood. In partiular, existene of equilibrium follows easily from Brouwer s fixed point theorem(mkelvy and Palfrey, 1995). To proeed further, we need to hoose a partiular speifiation for the expeted profit funtions. Wewillassumethattheprofitthataruestostorei lm from hoosing strategy kinloationl m isgivenby π i (a i lm =k,s m,ɛ i,p lm )=s m β k +ρ E i lm α k1 +ρ P α i lm k2 +ξ m (k)+ζ (k)+ε i (k). (6) where,asbefore,s m istheommonstatevetorofbothmarket(loalandmsa)andfirm harateristis(hainandstorelevel). Theρ E andρ P terms represent the expeted i lm i lm proportion of a store s ompetitors in market l m that will hoose EDLP and PROMO strategies respetively: ρ (k) = 1 P i lm j (a j =k) N lm j i l m Notethatwehaveassumedthatpayoffsarealinearfuntionoftheshareofstoresthat hoose EDLP and PROMO, whih simplifies the estimation problem and eliminates the need toonsiderthesharewhohoosehybrid(h). Wefurthernormalizetheaverageprofit from the PROMO strategy to zero, one of three assumptions required for identifiation. We disuss our identifiation strategy in detail in setion 5.6. In addition, we have assumed thattheprivateinformationavailabletostorei lm (i.e. ɛ i )anbedeomposedintothree additive stohasti omponents: ɛ i (k)=ξ m (k)+ζ (k)+ε i (k). (7) 13

13 whereε i (k)representsloalmarketlevelprivateinformation,ξ m (k)istheprivateinformationthatahainpossessesaboutapartiularglobalmarket(msa),andζ (k)isanonspatial omponent of private information that is hain speifi. Following our earlier disussion,wewillassumethatε i (k)isani.i.d.gumbelerror. Wefurtherassumethattheother omponentsarejointlydistributedwithdistributionfuntionf(ξ m (k),ζ (k);ω),whereω isasetofparametersassoiatedwithf. DenotingtheparametervetorΘ={β,α,Ω}and lettingδ i (k)beanindiatorfuntionsuhthat δ i (k)={ 1 0 ifa i =k ifa i k the optimal hoie probabilities for a given store an be written as (8) ) Ψ i (a i =k Θ,P lm,x,ξ lm (k) = while the likelihood an be onstruted as ( exp exp k {E,H,P} s m β k +ρ E i lm ( s m β k +ρ E i lm ) α k1 +ρ P α i lm k2 +ξ m (k)+ζ (k) α k1 +ρ P α i lm k2 +ξ m (k)+ζ (k) (9) ) m M ζ (k) C ξ m (k) l m L m i lm N lm [ )] Ψ i (a i =k Θ,P lm,s,ξ m δi lm (k),ζ (k) (k) df(ξm (k),ζ (k);ω) s.t.p lm =Ψ lm (Θ,P lm,s,ξ m (k),ζ (k)) (10) Note that the onstrution of the likelihood involves a system of disrete hoie equations thatmustsatisfyafixedpointonstraint(p lm =Ψ lm ). Therearetwomainapproahesfor dealing with the reursive struture of this system; both are based on methods originally applied to dynami disrete hoie problems. The first, based on Rust s (1987) Nested Fixed Point(NFXP) algorithm, involves solving for the fixed point of the system at every andidate parameter vetor and then using these fixed point probabilities to evaluate the likelihood. ThisisthemethodusedbySeim(2006)inheranalysisofthevideorentalmarket. The NFXP approah, however, is both omputationally demanding and straightforward to 14

14 applyonlywhentheequilibriumofthesystemisunique. 10 Analternateapproah,basedon Hotz and Miller s (1993) Conditional Choie Probability(CCP) estimator, involves using atwo-stepapproahthatisbothomputationallylightandmorerobusttomultipliity. 11 The first step of this proedure involves obtaining onsistent estimates of eah firm s beliefs regarding the strategi ations of its rivals. These expetations are then used in a seond stage optimization proedure to obtain the strutural parameters of interest. Given the omplexityofourproblem, wehosetoadoptatwo-stepapproahbasedonbajarietal. (2005),whowerethefirsttoapplythesemethodstostatigames. 4 Dataset The data for the supermarket industry are drawn from Trade Dimension s 1998 Supermarkets Plus Database, while orresponding onsumer demographis are taken from the deennial Census of the United States. Desriptive statistis are presented in Table 1. Trade Dimensions ollets store level data from every supermarket operating in the U.S. for use in their Marketing Guidebook and Market Sope publiations, as well as seleted issues of Progressive Groer magazine. The data are also sold to marketing firms and food manufaturers for marketing purposes. The (establishment level) definition of a supermarket used by Trade Dimensions is the government and industry standard: a store selling a full line of food produts and generating at least $2 million in yearly revenues. Foodstores with less than $2 million in revenues are lassified as onveniene stores and are not inluded in thedataset. 12 Information on priing strategy, average weekly volume, store size, number of hekouts, 10 Itisrelativelysimpletoonstrutthelikelihoodfuntionwhenthereisauniqueequilibrium,although solving for the fixed point at eah iteration an be omputationally taxing. However, onstruting a proper likelihood(for the NFXP) is generally intratable in the event of multipliity, sine it involves both solving for all the equilibria and speifying an appropriate seletion mehanism. Simply using the first equilibrium you find will result in mispeifiation. A version of the NFXP that is robust to multipliity has yet to be developed. 11 Orignally developed for dynami disrete hoie problems, two-step estimators have been applied to dynami disrete games by Aguirregabiria and Mira (2006), Bajari et al. (2006), Pakes, Ostrovsky and Berry(2002), and Pesendorfer and Shmidt-Dengler(2002). Instead of requiring a unique equilibrium to the whole game, two-step estimators simply require a unique equilibrium be played in the data. Futhermore, if the data an be partioned into distint markets with suffiient observations(as is the ase in our appliation), this requirement an be weakened even further. 12 Firms in this segment operate very small stores and ompete only with the smallest supermarkets (Ellikson(2006), Smith(2005)). 15

15 and additional store and hain level harateristis was gathered using a survey of eah storemanager,ondutedbytheirprinipalfoodbroker. 13 Withregardtopriingstrategy, managersareaskedtohoosethestrategythatislosesttowhattheirstorepratieson a general basis: either EDLP, PROMO or HYBRID. The HYBRID strategy is inluded to aount for the fat that many pratitioners and marketing theorists view the spetrum of priing strategies as more a ontinuum than a simple EDLP-PROMO dihotomy(shankar andbolton,2004). ThefatthatjustoverathirdoftherespondentshosetheHYBRID option is onsistent with this pereption. 5 Empirial Implementation The empirial implementation of our framework requires three primary inputs. First, we needtohooseanappropriatesetofstatevariables. Thesewillbethemarket, storeand hain harateristis that are most relevant to priing strategy. To determine whih speifi variables to inlude, we draw heavily on the existing marketing literature. Seond, we will need to define what we mean by a market. Finally, we need to estimate beliefs and onstrut the empirial likelihood. We outline eah of these steps in the following subsetions. 5.1 Determinants of Priing Strategy Thefousofthispaperistheimpatofrivalpriingpoliiesonafirm sownpriingstrategy. However, there are learly many other fators that influene priing behavior. Researhers in both marketing and eonomis have identified several, inluding onsumer demographis, rival priing behavior, and market, hain, and store harateristis (Shankar and Bolton, 2004). Sinewehavealreadydisussedtheroleofrivalfirms,wenowfousontheadditional determinants of priing strategy. Several marketing papers highlight the impat of demographis on priing strategy(ortmeyeretal.,1991;hohetal.,1994;lalandrao,1997;bellandlattin,1998). Ofpartiular 13 It should be noted that all of these variables, inluding the information on priing strategy, are selfreported. However, it is extremely unlikely that the results reported below ould be the produt of systemati reporting error, as this would require oordination between tens of thousands of managers and thousands of brokers to willfully mis-report their praties(for no obvious personal gain). 16

16 importane are onsumer fators suh as inome, family size, age, and aess to automobiles. In most strategi priing models, the PROMO strategy is motivated by some form of spatial or temporal prie disrimination. In the spatial models(e.g. Lal and Rao, 1997; Varian, 1980), PROMO priing is geared toward onsumers who are either willing or able to visit more than one store (i.e. those with low travel osts) or, more generally, those who are more informed about prie levels. The EDLP strategy instead targets those with higher travel osts or those who are less informed(perhaps due to heterogeneity in the ost of aquiring prie information). In the ase of temporal disrimination (Bell and Lattin, 1998; Bliss, 1988), PROMO priing targets the ustomers who are willing to either delay purhase or stokpile produts, while EDLP targets ustomers that prefer to purhase their entirebasketinasingletriporatasinglestore. Clearly,theabilitytosubstituteovertime or aross stores will depend on onsumer harateristis. To aount for these fators, we inlude measures of family size, household inome, median vehile ownership, and raial omposition in our empirial analysis. Sine alternative priing strategies will require differing levels of fixed investment(lattin and Ortmeyer, 1991), it is important to ontrol for both store and hain level harateristis. For example, large and small hains may differ in their ability to implement priing strategies(dhar and Hoh, 1997). Store level fators are also likely to play a role(messinger and Narasimhan, 1997). For example, EDLP stores may need to arry a larger inventory and PROMO stores might need to advertise more heavily. Therefore, we inlude a measureofstoresizeandanindiatorvariableforwhetheritispartofavertiallyintegrated hain. Finally, sine the effetiveness of priing strategies might vary by market size(e.g. urban versus rural), we inlude measures of geographi size, population density, and average expenditures on food. 5.2 Market Definition The supermarket industry is omposed of a large number of firms operating anywhere from1to1200outlets. Wefousonthehoieofpriingstrategyatanindividualstore, abstratingawayfromthemoreomplexissueofhowdeisionsaremadeatthelevelofthe hain. Sine we intend to fous on store level ompetition, we need a suitable definition of the loal market. This requires identifying the primary trade area from whih eah store 17

17 draws potential ustomers. Without disaggregate, onsumer-level information, the task of defining loal markets requires some simplifying assumptions. In partiular, we assume markets an be defined by spatial proximity alone, whih an be a strong assumption in some irumstanes(bell, Ho, and Tang(1998)). However, without onsumer level purhase information we an t relax this assumption. Therefore, we will try to be as flexible as possible in defining spatial markets. Although there are many ways to group firms using existing geographi boundaries (e.g. ZipCodes or Counties), these pre-speified regions all share the same drawbak: they inrease dramatially in size from east to west, refleting established patterns of population density. 14 Ratherthanimposingthisstrutureexogenously,weallowthedatatosortitself by using luster analysis. In partiular, we assume that a market is a ontiguous geographi area, measurable by geodesi distane and ontaining a set of ompeting stores. Intuitively, markets are groups of stores that are loated lose to one another. To onstrut these markets, we used a statistial lustering method(k-means) based on latitude, longitude and ZipCode information. 15 Our lustering approah produed a large set of distint lusters that we believe to be a good approximation of the atual markets in whih supermarkets ompete. These store lusters are somewhat larger than a typial ZipCode, but signifiantly smaller than the average ounty. We varied the number of lusters and found that about eight thousand best aptures the retail supermarket landsape. A typial ounty and the lusters within it are depited in Figure 3. As is evident from the map, our lustering method appears to apture geographi proximity in a sensible manner. While there are undoubtedly other fators(suh as highways or rivers) that might ause onsumers to pereive markets in slightly different ways, we believe that these geographi lusters onstitute a reasonable hoie of market definition for this industry. As robustness heks, we experimented with both broader and narrower definitions of the market(e.g. ZipCodes and MSAs) and found qualitatively similar results (see Appendix A.1). 14 OneexeptionisCensusblokgroups,whihareabouthalfthesizeofatypialZipCode. However,we feel that these areas are too small to onstitute reasonably distint supermarket trading areas. 15 ZipCodes are required to ensure ontiguity: without ZipCode information, stores in Manhattan would beinludedinthesamemarketasstoresinnewjersey. 18

18 5.3 Estimation Strategy As noted above, the system of disrete hoie equations presents a hallenge for estimation. We adopt a two stage approah based on Bajari et al. (2005) that avoids solving for a fixedpoint. ThefirststepinvolvesobtainingaonsistentestimateofP lm,theprobabilities that appear (impliitly) on the right hand side of equation (9) 16. These estimates ( P lm ) are then used to onstrut the ρ s, whih are then plugged into the likelihood funtion. Maximization of this (pseudo) likelihood onstitutes the seond stage of the proedure. Consisteny and asymptoti normality has been established for a broad lass of two-step estimators by Newey and MFadden(1994), while Bajari et al. (2005) provide formal results for the model estimated here. 5.4 The Likelihood In our eonometri implementation, we will assume that ζ and ξ are independent, mean zero normal errors, so that F(ξ m (k),ζ (k);ω)=f ξ (ξ m (k);ω ξ (k)) F ζ (ζ (k);ω ζ (k)), (11) whereboth F ξ andf ζ are mean zero normaldistribution funtions with finite ovariane matries. For simpliity, we also assume that the ovariane matries are diagonal with elementsτ 2 ζ (k)andτ2 ξ (k). Foridentifiation,onsistentwithourearlierindependeneand normalizationassumptions,wewillassumethatξ m (P)=ζ (P)=0 C,m M.These assumptions allows us to use a simulated maximum likelihood proedure that replaes(10) with its sample analog L(Θ)= m M R 1 ζ R ζ r ζ =1 C R 1 ξ R ξ r ξ =1 l m L m i lm N lm [ )] Ψ i (a i =k Θ, P lm,s,ξ m δi lm (k),ζ (k) Inthesimulationproedure,[ξ m (k)] rξ and[ζ (k)] rζ aredrawnfrommeanzeronormal densitieswithvarianesτ 2 ξ (k)andτ2 ζ (k)respetively. WeuseR ξ=r ζ =500andmaximize (12) to obtain estimates of the strutural parameters. Note that the fixed point restrition, 16 Theρ sarefuntionsofp lm. (12) (k). 19

19 P lm = Ψ lm, no longer appears sine we have replaed P lm with P lm in the formulas for ρ EDLP i lm andρ PROMO,whihareusedinonstrutingΨ i lm i (see9).wenowmovetoadisussion of how we estimate beliefs. 5.5 Estimating Beliefs In an ideal setting, we ould reover estimates of eah store s beliefs regarding the onditional hoie probabilities of its ompetitors using fully flexible non-parametri methods (e.g. kernel regressions or sieve estimators). Unfortunately, given the large number of ovariates we have inluded in our state vetor, these methods are infeasible here. Instead, we employ a parametri approah for estimating ˆρ i, using a mixed multinomial logit (MNL) speifiation to reover these first stage hoie probabilities(appendix A.3 ontains a semi-parametri robustness analysis). Note that this is essentially the same speifiation employed in the seond stage proedure(outlined above), only the store s beliefs regarding rival s ations are exluded from this initial redued form. Note that we do not require an expliit exlusion restrition, sine our speifiation already ontains natural exlusion restritions due to the presene of state variables that vary aross stores and hains. We implement an estimator similar to (12), but with the oeffiients on the ρ s (i.e. α s)settozero. LettheparametersinthefirststagebedenotedbyΛ 1 ={β 1,Ω 1 } 17 and the first stage likelihood for a given store be denoted by L i (Λ,ξ m (k),ζ (k)). Using a simulatedmaximumlikelihoodapproah,weobtainˆλ 1,themaximum(simulated)likelihood estimateofλ 1.Giventheseestimates,andapplyingBayes rule,theposteriorexpetation ofp(a i =k s,ξ m (k),ζ (k))anbeobtainedviathefollowingomputation ζ ξ ) ) ( ) Ψ i (a i =k ˆΛ,ξ m (k),ζ (k) L i (ˆΛ,ξ m (k),ζ (k) df ξ m (k),ζ (k);ˆω 1 (k) ζ ξ ) ( ) m L i (ˆΛ,ξ (k),ζ (k) df ξ m (k),ζ (k);ˆω 1 (k) While this expression is diffiult to evaluate analytially, the vetor of beliefs defined )] byˆρ (k) =E i lm {ζ,ξ} [Ψ i (a i =k ˆΛ,ξ m (k),ζ (k) an be approximated by its simulation 17 Thesubsript1denotesthatthesearefirststageestimates.. (13) 20

20 analog ˆρ (k) i lm R Ψ r=1 i lm ( ) a i =k ˆΛ,[ξ m m (k),ζ (k)] r )L i (ˆΛ,[ξ (k),ζ (k)] r ). (14) (ˆΛ,[ξ m (k),ζ (k)] r R L r=1 i lm in whih [ξ m (k),ζ (k)] r are draws fromadistribution F ( ) ξ m (k),ζ (k);ˆω with similar properties to those desribed in Setion 5.4. Again, we use R = 500 simulation draws. Reallingthatk K={E,H,P},weannowdefineaonsistentestimatorofρ (k) as i l m ˆρ (k) = i lm v N lm v 1 h i lm ˆρ (k) h. (15) We note in passing that the onsistenyof our estimator is maintained even with the inlusion of two types of random effets, sine these variables are treated as private information of eah store. As noted earlier, allowing for random effets that are ommon knowledge to the players, but unobserved to the eonometriian(e.g. market level heterogeneity) would violatethei.i.d.assumptionrequiredforonsistenyofthetwo-stepestimationproedure. 18 However,wewillrelaxthisassumptionbelowinoneofourrobustnessheks. Afinalnote relates to the onstrution of standard errors. Sine the two-step approah preludes using theinverseinformationmatrix,weemployabootstrapapproahinstead Identifiation Bajari et al. (2005) establish identifiation of the strutural parameters of a disrete game provided three assumptions are satisfied. The first two have already been(impliitly) stated, butwillberepeatedheremoreformally. Thefirstassumptionisthattheerrortermsɛ i are distributed i.i.d.aross players and ations in anygivenmarket 20, and aredrawn froma 18 Bajari et al. (2005) suggest using fixed effets whih are restrited to be smooth funtions of the observed state variables. We do not have enough data to estimate their non-parametri first stage and prefer an approah based on Aguirregabiria and Mira s (2006) Nested Pseudo Likelihood approah to ontrol for loation speifi unobservables. 19 Inpartiular,webootstrappedarossmarkets(notindividualstores)andheldthepseudorandomdraws in the simulated likelihood fixed aross bootstrap iterations. To save time we used the full data estimates as starting values in eah bootstrap iteration. 20 Notethattheiidrequirementonly needs tohold atthe marketlevel. Forexample, it s fine to inlude random effets in the error term, provided these effets are treated as private information of the partiular storeinquestion. Thisisinfattheapproahweadoptbelow. 21

21 distribution of known parametri form. This is learly satisfied by the assumptions imposed above. The seond assumption requires that the expeted profit assoiated with one strategy be normalized to zero. This is a standard normalization required to identify any multinomial hoie model. We normalize the mean profit of the PROMO strategy to zero. The final assumption is an exlusion restrition. The reason for imposing an exlusion restrition an be illustrated using equation(9). Our two-step estimation proedure involves estimating the shares(ρ s) on the right hand sideof(9)inafirststage. Theseshares,whiharesimplefuntionsofeahfirm sbeliefs regarding the onditional hoie probabilities of its rival s (via the ρ s in (9)), depend on the same state vetor (s) as the first term of the profit funtion (s β k ), reating a potential identifiation problem. Note that identifiation an be trivially preserved by the non-linearity of the disrete hoie problem, although this follows diretly from funtional form. A non-parametri alternative, suggested by Bajari et al. (2005), is to identify one or moreontinuousovariatesthatenterfirmi spayoffs,butdonotenterthepayoffsofany ompeting firm. This exlusion restrition ensures that both the payoffs and the estimates of firms beliefs regarding the ations of their rivals are identified. Bajari et al. (2005) suggest using the idiosynrati shoks of rival firms as the exlusion. Sine our state vetor varies aross stores and hains, we have a natural exlusion restrition whih is similar in spirittothisidea. Inotherwords,whilethestatevariablesarethesametheydonotontain the same values aross stores and hains. This results in different patterns of variation in the ρ s and the profit omponent related to state variables (s β k ) helping identify the parameters leanly. 21 Identifiation of all other parameters is straightforward and we do not disuss them here. Having desribed both our theoretial model and empirial strategy, we now present our main results. 6 Results and Disussion As noted earlier, hoosing an optimal priing strategy is a omplex task, foring firms to balane the preferenes of their ustomers against the strategi ations of their rivals. A major advantage of our two-step estimation approah is that, by estimating best response 21 We are indebted to Vitor Aguirregabiria and Han Hong for helpful disussions on this topi and to Vitor in partiular for pointing out the presene of natural exlusion restritions in our model. 22

22 funtions rather than equilibrium orrespondenes, we an separately identify strategi interations, reations to loal and market level demographis, and operational advantages assoiated with larger stores and proprietary distribution systems. Our empirial results highlight eah of these fores. First, we find that firms hoose strategies that are tailored to the demographis of the market they serve. Moreover, the impat of demographis orresponds losely to existing empirial studies of onsumer preferenes and onventional wisdom regarding searh behavior. Seond, we find that the EDLP strategy is favored by firms that operate larger stores and are vertially integrated into distribution. Again, this aords with onventional wisdom regarding the main operational advantages of EDLP. Finally, with regard to strategi interation, we find that firms oordinate their ations, hoosing priing strategies that math their rivals. This identifies an aspet of firm behavior that has not been addressed in the existing literature: exatly how firms reat to rival strategies. Our main empirial results are presented in Table 6. The oeffiients, whih represent the parameters of the profit funtion represented in equation(6), have the same interpretation as those of a standard MNL model: positive values indiate a positive impat on profitability, inreasing the probability that the strategy is seleted relative to the outside option(in this ase, PROMO). 6.1 The Role of Demographis The oeffiients on onsumer demographis are presented in the seond and third setions of Table 6. With the exeption of two MSA-level ovariates, every demographi fator plays a signifiant role in thehoieof EDLPas apriing strategy. This is importantfroman eonometri standpoint, sine we use these very same fators to onstrut expetations in thefirststage. Inpartiular,thesignifianeoftheestimatesmeansthatwedonothaveto worry about ollinearity. The statistial signifiane of the parameters is also substantively important. It suggests that the even after aounting for ompetitive and supply side (store/hain) harateristis, onsumer demand plays a strong role in the determination of priing strategy. Fousing more losely on the demand related parameters, we find that (relative to PROMO), EDLP is the preferred strategy for geographi markets that have larger house- 23