Supermarket Pricing Strategies

Transcription

1 Supermarket Priing Strategies Paul B. Ellikson y Duke University Sanjog Misra z University of Rohester January 8, 2007 The authors would like to thank partiipants at the Supermarket Retailing Conferene at the University of Bu alo, the 2006 BCRST Conferene at the University of Toronto, the 2005 QME onferene at the University of Chiago, the Supermarket Conferene held at IFS London as well as seminar partiipants at Duke, UCLA and Stanford. The authors have bene tted from onversations with Pat Bajari, Han Hong, Chris Timmins, J.P. Dube, Vitor Aguirregabiria, and Paul Nelson. All remaining errors are our own. y Department of Eonomis, Duke University, Durham NC paul.ellikson@duke.edu. z Corresponding author. William E. Simon Shool of Business Administration, University of Rohester, Rohester, NY misra@simon.rohester.edu. 1

2 Supermarket Priing Strategies Abstrat Most supermarket rms hoose to position themselves by o ering either Every Day Low Pries (EDLP) aross several items or o ering 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 the priing strategy the rm has hosen to follow, as reported by the rm itself. Using a system of simultaneous disrete hoie models, we estimate eah store s hoie of priing strategy as a stati disrete game of inomplete information. In ontrast to the preditions of the theoretial literature, we nd strong evidene that rms luster by strategy by hoosing ations that agree with those of its rivals. We also nd a signi ant impat of various demographi and store/hain harateristis, providing some quali ed support for several spei preditions from marketing theory. Keywords: EDLP, promotional priing, positioning strategies, supermarkets, disrete games. JEL Classi ation Codes: M31, L11, L81 2

3 1 Introdution While rms 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 o ering 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 onept of every day low priing (EDLP), the suessful use of EDLP was a primary fator 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 di usion 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 rms following both strategies, and several others who used a mixture of the two. 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 di erent 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 rm 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-store ompetition. 1 The goal of this paper is to ombine newly developed methods for 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 Typial sanner data usually re et deisions made by only a few stores in a limited number of markets. 3

4 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 rms reat to the expeted ations of their rivals? We address eah of these questions in detail. The rst question naturally invites a market pull driven explanation in whih onsumer demographis play a key role in determining whih priing strategy rms 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 rm s strategy and its hain-spei apabilities. In partiular, we examine whether partiular priing strategies (e.g. EDLP) are more pro table when rms make omplementary investments (e.g. larger stores and more sophistiated distribution systems). The empirial evidene on this matter is sare - this is the rst paper to address this issue on a broad sale. Furthermore, beause our dataset inludes every existing supermarket, we are able to exploit variation both within and aross hains to assess the impat of store and hain level di erenes on the hoie of priing strategy. Finally, we address the role of ompetition posed in our third question by analyzing rms reations to the expeted hoies of their rivals. In partiular, we ask whether rms fae inentives to distinguish themselves from their ompetitors (as in most models of produt di erentiation) or instead fae pressures to onform (as in network or swithing ost models)? This question is the primary fous of our paper and the feature that most distinguishes it from earlier work. Our results shed light on all three questions. First, we nd that onsumer demographis play a signi ant role in the hoie of loal priing strategies: rms 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

5 as a oordinating devie for rival rms, helping shape the priing landsape by de ning an equilibrium orrespondene. Seond, we nd that omplementary investments are key: larger stores and vertially integrated hains are signi antly more likely to adopt EDLP. Finally, and most surprisingly, we nd 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 nding is in diret ontrast to existing theoretial models that view priing strategy as a form of di erentiation. While we do not aim to test a partiular theory of strategi priing behavior, we hope a deeper examination 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 o er 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 nd quali ed 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 signi ant ontribution, however, relates to the nding that stores in a partiular market do not use priing strategy as a di erentiation 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 literature on soial interations 2. In partiular, our inorporation of multiple soures of 2 Reent appliations of stati games inlude tehnology adoption by internet servie providers (Augereau et al. 2006), produt variety in retail eyewear (Watson, 2005), loation of ATM branhes (Gowrisankaran and Krainer, 2004), and spatial di erentiation among supermarkets (Orhun, 2005), disount stores (Zhu et al., 2005), and video stores (Seim, 2006). Strutural estimation of soial interations is the fous of papers by Brok and Durlauf (2002), Bayer and Timmins (2006), and Bajari et al. (2005). 5

6 private 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, expliitly de ning eah strategy and illustrating the importane of loal fators in determining store level deisions. Setion 3 introdues our formal model of priing strategy and brie y outlines our estimation approah. 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, our two-step estimation method, and our identi ation 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 2.1 Priing Strategy Choies Competition in the supermarket industry is a omplex phenomenon. Firms ompete aross the entire retail and marketing mix, entiing ustomers with an attrative set of produts, ompetitive pries, onvenient loations, and a host of other servies, features, and promotional ativities. In equilibrium, rms hoose the bundle of servies and features that maximize pro ts, onditional on the types of onsumers they expet to serve and their beliefs regarding the ations of their rivals. A supermarket s priing strategy is a key element in this multidimensional bundle. The vast majority of both marketers and pratitioners frame a store s priing deision as a hoie between o ering every day low pries or deep but temporary disounts, labeling the rst strategy EDLP and the seond PROMO. 3 This is, of ourse, a simpli ation sine a supermarket s priing poliy is losely tied to its overall positioning strategy. Priing strategies are typially hosen to leverage partiular operational advantages and often have impliations for other aspets of the retail mix. For example, suessful implementation of EDLP may involve o ering a deeper and narrower produt line than PROMO, allowing rms to exploit sale eonomies (in partiular ategories), redue their inventory arrying osts, and lower their advertising expenses. On the other hand, PROMO priing gives 3 PROMO is shorthand for promotional priing, whih is also referred to as Hi-Lo priing. 6

7 rms greater exibility in learing overstok, allows them to quikly apitalize on deep manufaturer disounts, and failitates the use of onsumer loyalty programs (e.g. frequent shopper ards). In other words, the hoie of priing strategy is more than just how pries are set: it re ets the overall positioning of the store. 4 Clearly the EDLP-PROMO dihotomy is too narrow to adequately apture the full range of rm behavior. In pratie, rms an hoose a mixture of EDLP and PROMO, varying either the number of ategories they put 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. Both the data and de nitions used in this paper are based on a spei store level survey 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). We believe that priing strategy is best viewed as a ontinuum, with pure EDLP (i.e. onstant margins aross all ategories) on one end and pure PROMO (i.e. frequent sales on all ategories) at the other. This dataset represents a oarse disretization of that ontinuum. 5 4 In this paper we fous only on the priing strategy dimension and take other dimensions of the retail mix as given. While this is limiting, modeling the entire retail mix is beyond the sope of this paper. 5 We will address the issue of data validity - whether these self-reported strategies math up to observed priing behavior - in setion

8 2.2 Supermarket Priing: A Closer Look Without observing data on individual stores, it might be tempting to onlude that all priing strategies are determined at the level of the hain. While there are ertainly inentives to hoose a onsistent poliy, the data reveals a remarkable degree of loal heterogeneity. To examine the issue more losely, we fous in on a single hain in a single market: the Pathmark hain in New Jersey. Figure 1 shows 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 spei to this partiular hain. Table 3 shows the store level strategies hosen by the top 15 U.S. supermarkets (by total volume) along with their total store ounts. As with Pathmark, the major hains are also surprisingly heterogeneous. While some rms do 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 rms. Table 4 shows the priing strategies hosen by large and small hains, using four alternative de nitions of large and small. 6 While large hains seem evenly distributed aross the strategies and small hains seem to favor PROMO, rm 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 di erent 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 on rms that this within-hain spatial heterogeneity is not unique to this partiular example: while some hains learly favor a onsistent strategy, others appear quite responsive to loal fators. 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) 6 The four de nitions of rm size are: hain/independent, vertially integrated and not, large/small store, and many/few hekouts. A hain is de ned as having 11 or more stores, while an independent has 10 of fewer. Vertially integrated means the rm operates its own distribution enters. Large versus small store size and many versus few hekouts are de ned by the upper and lower quartiles of the full store level ensus. 8

9 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 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 an be illustrated using the spatial struture of our dataset. Figure 2 plots the geographi loation of every store in the U.S., along with their priing strategy. As is lear from the panels orresponding to eah priing strategy, there is no obvious pattern: all three strategies exhibit quite uniform overage. 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 the loal market served by stores of eah type. 7 PROMO priing is assoiated with smaller households, higher inome, fewer automobiles per apita, and less raial diversity, providing some initial support for Bell and Lattin s (1998) in uential model of basket size 8. However, the di erenes in demography, while intuitive, are not espeially strong. This does not mean that demographis are irrelevant, but rather that the aggregate level patterns linking priing strategy and demographis are not overwhelming. Isolating the pure impat of demographi fators will require a formal model, whih we provide below. The nal row of Table 5 ontains the share of rival stores in the ompeting market that employ the same strategy as the store being analyzed. Here we nd a striking result: 50% of a store s rivals in a given loation employ the same priing strategy as the foal store. 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 7 Roughly orresponding to areas the size of a ZipCode, these loal markets are de ned expliitly in Setion Bell and Lattin (1998) nd that the most important features of shopping behavior an be aptured by two interrelated hoies: basket size (how muh you buy) and shopping frequeny (how often you go). They suggest that large or xed 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

10 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 to their rivals. This pattern learly warrants a more detailed investigation and is the fous of our strutural model. Three entral features of supermarket priing strategy emerge from this disussion. First, supermarket hains often adopt heterogeneous priing strategies, suggesting that demand related fores an sometimes outweigh the advantages of 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 rm harateristis is not oneptually di ult, quantifying the strutural impat of rival priing strategies on rm 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 rms. We then estimate this model using a two-step approah developed by Bajari et al. (2005). 3 A Strategi Model of Supermarket Priing A supermarket s hoie of priing strategy is naturally framed as a disrete game between a nite set of players. Eah rm s optimal hoie is determined by the underlying market onditions, its own harateristis and individual strengths, and its expetations regarding the ations of its rivals. Notably, the strategi hoie of eah rm is a funtion of the antiipated hoies of its ompetitors, and vie versa. If strategi expetations were ignored, a rm s hoie of priing strategy would be a straightforward disrete hoie problem. However, sine rms 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 of strategi priing in detail. In our framework, rms (i.e. supermarket hains 9 ) make a disrete hoie of priing strategy, 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 rms at simul- 9 Heneforth, we will use hains and rms interhangeably. 10

11 taneously in a stati environment, taking entry deisions as given. 10 A stati treatment of ompetition is not altogether unrealisti sine these priing strategies involve substantial store level investments in ommuniation and positioning related osts that are not easily reversible. 11 In what follows, we assume that ompetition takes plae in loal markets, 12 eah ontained in a global market (here, an MSA). Before proeeding further, we must introdue some additional notation. Stores belonging to a given hain = 1; ::; C; that are loated in a loal market l m = 1; ::; L m ; in an MSA m = 1; ::; M; will be indexed using = 1; ::; N lm The total number of stores in a partiular hain in a given MSA is N m = the total number of stores in that hain aross all MSAs is N = XL m l m=1 : N lm ; while MX N m. In eah loal market, hains selet a priing strategy (ation) a from the three element set K = fe; H; P g ; where E EDLP; H HY BRID; and P P ROMO: If we observe a market l m CX ontaining N lm = players for example, the set of possible ation pro les is then A lm =1 N lm = fe; H; P g N lm with generi element a lm = (a 1 ; a 2 ; :::; a i ; :::; a N ). The vetor of ). = (a 1 ; ::; a i m=1 ations of store s ompetitors is denoted a i 1 ; a In a given market, a partiular hain s state vetor is denoted s m state vetor for the market as a whole is s m = (s m 1 ; :::; sm N ) 2 +1 ; ::a N lm 2 S m ; while the NY m S m : The state vetor s m is known to all rms and observed by the eonometriian. It desribes features of the market and harateristis of the rms that are assumed to be determined exogenously. For eah rm, there are also three unobserved state variables (orresponding to the three 10 Ideally, entry and priing deisions would be modeled jointly, allowing for rms that favor EDLP, for example, to prefer entering 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 rms (the urrent state of the art (Jia, 2006) an handle two rms). Nonetheless, we believe that ignoring entry will not yield signi ant bias in our setting, sine logistial issues (e.g. density eonomies from designing an e ient distribution network) far outweigh priing strategy in determining entry deisions. 11 As disussed above, priing deisions are relatively sunk, due to the positioning osts assoiated with onveying a onsistent store-level message to a group of repeat ustomers. Furthermore, sine this is not an entry game, we are not partiularly onerned about the possibility of ex post regret that an sometimes arise in stati games (Einav, 2003). 12 In our appliation, a loal market is a small geographi trading area, roughly the size of a ZipCode. The proedure we used to onstrut these markets is desribed in Setion 5.2. =1 11

12 priing strategies) that are treated as private information of the rm. These unobserved state variables are denoted i a i ; or more ompatly i ; and represent rm spei shoks to the pro tability of eah strategy. The private information assumption makes this a game of inomplete or asymmetri information (e.g. Harsanyi, 1973) and the appropriate equilibrium onept one of Bayesian Nash Equilibrium (BNE). 13 For any given market, the i s are assumed to be iid aross rms and ations, and drawn from a distribution f i that is known to everyone, inluding the eonometriian. Firms hoose priing strategies in eah store independently, with the objetive of maximizing expeted pro ts in eah store. In market l m, the pro t earned by store i is given by i = i s m ; a i ; a i + i (1) where i is a known and deterministi funtion of states and ations (both own and rival s). This di ers from a standard disrete hoie framework beause the ations of a rm s rivals enter its payo funtion. Sine the s are treated as private information, a rm s deision rule a i = d i s m ; i is a funtion of the ommon state vetor and its own, but not the private information of its rivals. From the perspetive of both its rivals and the eonometriian, the probability that a given rm hooses ation k onditional on the ommon state vetor is then given by P i a i n where 1 d i s; i = k and 0 otherwise. We let P lm = k o Z = n o 1 d i s m ; i = k f i d i (2) is an indiator funtion equal to 1 if store hooses ation k denote the set of these probabilities for a given loal market. Sine the rm does not observe the ations of its ompetitors prior to hoosing an ation, it makes deisions based on these expetations (i.e. beliefs). The expeted pro t for rm from hoosing ation a i is then e i a i ; s m ; i ; P lm = e i a i ; s m + i (3) = X i lm s m ; a i ; a i P i + i (4) a i 13 Treating the types as private information greatly simpli es 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

13 where P i is then = Y n = Pr e i lm j6= a i lm P j (a j js m ) : Given these expeted pro ts, the optimal ation for a store ; s m + i a i > e i lm a 0 ; s m + i a 0 8 a 0 6= a i whih is the system of equations that de ne the (pure strategy) BNE of the game. Beause a rm s optimal ation is unique by onstrution, there is no need to onsider mixed strategies. If the s are drawn from a Type I Extreme Value distribution (i.e. Gumbel errors), this BNE must satisfy a system of logit equations (i.e. best response probability funtions). 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 xed point theorem (MKelvy and Palfrey, 1995). To proeed further, we need to hoose a partiular spei ation for the expeted pro t funtions. We will assume that the pro t that arues to store k in loation l m is given by e i a i lm = k; s m ; i ; P lm = s m0 k + E k1 + P k2 + m o (5) from hoosing strategy (k) + (k) + " i (k) (6) where, as before, s m is the ommon state vetor of both market (loal and MSA) and rm harateristis (hain and store level). The E and P terms represent the expeted proportion of a store s ompetitors in market l m that hoose EDLP and PROMO strategies respetively: (k) = 1 N lm X j6= P j (a j = k) Note that we have assumed that payo s are a linear funtion of the share of stores that hoose EDLP and PROMO, whih simpli es the estimation problem and eliminates the need to onsider the share who hoose HYBRID (H). We further normalize the average pro t from the PROMO strategy to zero, one of three assumptions required for identi ation (we disuss our identi ation strategy in detail in setion 5.7). In addition, we have assumed that the private information available to store additive stohasti omponents: (i.e. i ) an be deomposed into three i (k) = m (k) + (k) + " i (k) (7) 13

14 where " i (k) represents loal market level private information, m (k) is the private information that a hain possesses about a partiular global market (MSA), and (k) is a non-spatial omponent of private information that is hain spei. Following our earlier disussion, we will assume that " i (k) is an i:i:d: Gumbel error. We further assume that the two remaining omponents are jointly distributed with distribution funtion F ( m (k) ; (k) ; ) ; where is a set of parameters assoiated with F. Denoting the parameter vetor = f; ; g and letting i 1 i (k) = 0 (k) be an indiator funtion suh that if a i if a i the optimal hoie probabilities (onditional on m written as = k 6= k (8) (k) ; (k)) for a given store an be a i = kj; P lm ; X; lm (k) = while the likelihood an be onstruted as exp X exp k2fe;h;p g s m0 k + E s m0 k + E k1 + P k2 + m k1 + P k2 + m (k) + (k) (k) + (k) (9) Y Z Y Z 2C (k) m2m m (k) 8 < : Y l m2l m Y 2N lm h a i = kj; P lm ; s; m (k) ; (k) i i (k) 9 = ; df (m (k) ; (k) ; ) s:t: P lm = E f;g [ l m (; P lm ; s; m (k) ; (k))] (10) Note that the onstrution of the likelihood involves a system of disrete hoie equations that must satisfy a xed point onstraint (P lm = l m ). There are two main approahes for dealing with the reursive struture of this system, both of whih are based on methods originally applied to dynami disrete hoie problems. The rst, based on Rust s (1987) Nested Fixed Point (NFXP) algorithm, involves solving for the xed point of the system at every andidate parameter vetor and then using these xed point probabilities to evaluate the likelihood. This is the method used by Seim (2006) in her analysis of the video 14

15 rental market. The NFXP approah, however, is both omputationally demanding and straightforward to apply only when the equilibrium of the system is unique. 14 An alternate approah, based on Hotz and Miller s (1993) Conditional Choie Probability (CCP) estimator, involves using a two-step approah that is both omputationally light and more robust to multipliity. 15 The rst step of this proedure involves obtaining onsistent estimates of eah rm 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 omplexity of our problem, we hose to adopt a two-step approah based on Bajari et al. (2005), who were the rst to apply these methods to stati games. 4 Dataset 4.1 The Priing Survey 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 rms and food manufaturers for marketing purposes. The (establishment level) de nition 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 lassi ed as onveniene stores and are not inluded in 14 It is relatively simple to onstrut the likelihood funtion when there is a unique equilibrium, although solving for the xed 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 rst equilibrium you nd will result in mispei ation. A version of the NFXP that is robust to multipliity has yet to be developed. 15 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 su ient observations (as is the ase in our appliation), this requirement an be weakened even further. 15

16 the dataset. 16 Information on priing strategy, average weekly volume, store size, number of hekouts, and additional store and hain level harateristis was gathered using a survey of eah store manager, onduted by their prinipal food broker. With regard to priing strategy, managers are asked to hoose the strategy that is losest to what their store praties on 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 and Bolton, 2004). The fat that just over a third of the respondents hose the HYBRID option is onsistent with this pereption. 4.2 Survey Validity We should emphasize that all of these variables, inluding the information on priing strategy, are self-reported. This may raise some onerns regarding auray, espeially given the high degree of loal variation we observe in the data. Two questions naturally arise. First, are rms truly willing and able to set pries at suh loal levels? Seond, do these self-reported strategies re et atual di erenes in priing behavior? We will address both issues in turn. First, with regard to loal priing, we should note that supermarket rms learly have the tehnologial resoures to set pries (and therefore priing strategy) at a very loal level. Indeed, Montgomery (1997) provides a novel method for pro tably ustomizing pries at the store level, using widely available sanner data. 17 We ontated priing managers at several major hains and other industry professionals regarding their ability to engage in suh miro-marketing. Even on the ondition of anonymity, they were extremely relutant to disuss the details of their atual priing strategies, but did aknowledge that they ertainly have the data and resoures to do it. Furthermore, a onsultant who was involved in several reent supermarket mergers on rmed that the extent of loal priing was a key 16 Firms in this segment operate very small stores and ompete only with the smallest supermarkets (Ellikson (2006), Smith (2006)). 17 While the emphasis there is on maintaining a onsistent image, Montgomery argues that the potential gains to miro-marketing are quite signi ant. Setting di erent sales frequenies in di erent stores is simply an alternative method of miro-marketing. 16

17 fator in the approval proess. 18 A related issue onerns whether rms may also fae pressure to maintain a onsistent (priing) image aross stores. We suspet not. Unlike many other types of retail food servies (e.g. fast food establishments), supermarket ustomers do the majority of their shopping in a single store. 19 Therefore, while onsumers undoubtedly have strong preferenes over the priing strategy of their hosen store, they have little reason to are diretly about the overall strategy of the hain. Of ourse, hains may have strong operational inentives (e.g. sale eonomies in distribution and advertising) to maintain a onsistent strategy aross several (not neessarily proximate) stores, whih might lead them to adopt a ommon strategy in multiple outlets. Indeed, we are relying on just suh inentives to provide the variation needed to identify the e et of strategi interations (we will return to this identi ation argument in Setion 5.7). The point is that rms may indeed have both strong inentives and the ability to tailor priing to the loal environment. The seond question onerns the validity of the survey instrument itself. We note rst that the survey was of store managers but administered by brokers (who explained the questions), providing an additional level of ross-validation. It is 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 and onsistently mis-report their praties (for no obvious personal gain). However, to further allay suh fears, we ross-veri ed the data ourselves using publily available data from the Dominik s Finer Foods (DFF) supermarket hain in Chiago. In partiular, we extrated store level pries from four major produt ategories for every store in the DFF dataset and mathed them up to the priing lassi ations reported by Trade Dimensions. The vast majority of the Dominik s stores are identi ed as PROMO (93%), while the remainder are HYBRID, whih is itself enouraging sine Dominik s is known to be a PROMO hain. We then heked whether the inidene of promotions (i.e. whether a UPC was on sale ) varied aross PROMO and HYBRID stores. In all four ategories that we 18 While detailed information on the degree of miro-marketing in the supermarket industry is not publily available, expliit evidene of loal priing was a major issue in the proposed merger between Staples and O e Depot (Ashenfelter et al, 2006). 19 Aording to the Food Marketing Institute, onsumers alloate 78% of their overall budget to their primary store. Moreover, their seondary store is almost always part of a di erent hain. 17

18 examined (Soft Drinks, Oatmeal, Paper Towels, and Frozen Juie), we found a signi antly lower inidene of promotions at the HYBRID stores. The di erenes ranged from 8.1% in Soft Drinks (a very heavily promoted ategory) to 23.4% in Oatmeal. All di erenes were signi ant at the 1% level. In addition, we also ompared the HYBRID and PROMO stores for equality in the variane of the pries using standard folded F tests. One would expet PROMO stores to have higher varianes. For three of the four ategories (Oatmeal, Paper Towels and Frozen Juie) the variane in pries was indeed higher in the PROMO stores, validating the survey data. The di erene was not signi ant for Soft Drinks ategory. We also repeated eah analysis for only the highest selling UPC in eah ategory and found qualitatively similar results. While these tests use only a few produt ategories from a single hain in a single market, the sharpness of the results should provide additional on dene in the integrity of our data. 5 Empirial Implementation The empirial implementation of our framework requires three primary inputs. First, we need to hoose an appropriate set of state variables. These will be the market, store and hain harateristis that are most relevant to priing strategy. To determine whih spei variables to inlude, we draw heavily on the existing marketing literature. Seond, we will need to de ne 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, onluding with a disussion of unobserved heterogeneity and our strategy for identi ation. 5.1 Determinants of Priing Strategy The fous of this paper is the impat of rival priing poliies on a rm s own priing strategy. However, there are learly many other fators that in uene priing behavior. Researhers in both marketing and eonomis have identi ed several, inluding onsumer demographis, rival priing behavior, and market, hain, and store harateristis (Shankar and Bolton, 2004). Sine we have already disussed the role of rival rms, we now fous on the additional 18

19 determinants of priing strategy. Several marketing papers highlight the impat of demographis on priing strategy (Ortmeyer et al., 1991; Hoh et al.,1994; Lal and Rao, 1997; Bell and Lattin, 1998). Of partiular 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 entire basket in a single trip or at a single store. Clearly, the ability to substitute over time 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 di ering levels of xed investment (Lattin and Ortmeyer, 1991), it is important to ontrol for both store and hain level harateristis. For example, large and small hains may di er in their ability to e iently 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 (to satisfy large basket shoppers), while PROMO stores might need to advertise more heavily. Therefore, we inlude a measure of store size and an indiator variable for whether it is part of a vertially integrated hain. Finally, sine the e etiveness 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 De nition The supermarket industry is omposed of a large number of rms operating anywhere from 1 to 1200 outlets. We fous on the hoie of priing strategy at an individual store, 19

20 abstrating away from the more omplex issue of how deisions are made at the level of the hain. Sine we intend to fous on store level ompetition, we need a suitable de nition of the loal market. This requires identifying the primary trading area from whih eah store draws potential ustomers. Without disaggregate, onsumer-level information, the task of de ning loal markets requires some simplifying assumptions. In partiular, we assume markets an be de ned by spatial proximity alone, whih an be a strong assumption in some irumstanes (Bell, Ho, and Tang (1998)). However, absent detailed onsumer level purhase information, we annot relax this assumption further. Therefore, we will try to be as exible as possible in de ning spatial markets. Although there are many ways to group rms using existing geographi boundaries (e.g. ZipCodes or Counties), these pre-spei ed regions all share the same drawbak: they inrease dramatially in size from east to west, re eting established patterns of population density. 20 Rather than imposing this struture exogenously, we allow the data to sort itself 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. 21 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 signi antly smaller than the average ounty. We varied the number of lusters and found about eight thousand to best desribe the spatial patterns in the 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 di erent ways, we believe that these geographi lusters onstitute a reasonable 20 One exeption is Census blok groups, whih are about half the size of a typial ZipCode. However, we feel that these areas are too small to onstitute reasonably distint supermarket trading areas. 21 ZipCodes are required to ensure ontiguity: without ZipCode information, stores in Manhattan would be inluded in the same market as stores in New Jersey. 20

21 hoie of market de nition for this industry. As robustness heks, we experimented with the number of lusters, broader and narrower de nitions of the market (e.g. ZipCodes and MSAs), as well as nearest neighbor methods and found qualitatively similar results (see Appendix A.1). 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 xed point. The rst step is to obtain a onsistent estimate of P lm ; the probabilities that appear (impliitly) on the right hand side of equation (9) 22. These estimates ( b P lm ) are used to onstrut the i 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. We note in passing that onsisteny of the estimator is maintained even with the inlusion of the two random e et terms ( and ), sine these variables are treated as private information of eah store. A nal note relates to the onstrution of standard errors. Sine the two-step approah preludes using the inverse information matrix, we employ a bootstrap approah instead The Likelihood In our eonometri implementation, we will assume that and are independent, mean zero normal errors, so that F ( m (k) ; (k) ; ) = F ( m (k) ; (k)) F ( (k) ; (k)) ; (11) where both F and F are mean zero normal distribution funtions with nite ovariane matries. For simpliity, we also assume that the ovariane matries are diagonal with elements 2 (k) and 2 (k). For identi ation, onsistent with our earlier independene and 22 The i s are funtions of P lm. 23 In partiular, we bootstrapped aross markets (not individual stores) and held the pseudorandom draws in the simulated likelihood xed aross bootstrap iterations. To save time we used the full data estimates as starting values in eah bootstrap iteration. 21

22 normalization assumptions, we assume that m (P ) = (P ) = C; m 2 M: These assumptions allows us to use a simulated maximum likelihood proedure that replaes (10) with its sample analog ~L () = Y 2C R 1 R X Y r =1 m2m 2 4R 1 R X r =1 8 < : Y l m2l m Y 2N lm h a i = kj; b P lm ; s; m (k) ; (k) In the simulation proedure, [ m (k)] r and [ (k)] r are drawn from mean zero normal densities with varianes 2 (k) and 2 (k) respetively. We use R = R = 500 and maximize (12) to obtain estimates of the strutural parameters. Note that the xed point restrition, P lm = l m ; no longer appears sine we have replaed P lm with b P lm in the formulae for E and P ; whih are used in onstruting (see 9) : We turn now to a disussion 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 exible non-parametri methods (e.g. kernel regressions or sieve estimators). Unfortunately, given the large number of ovariates we have inluded in our state vetor, this is not feasible. Instead, we employ a parametri approah for estimating ^ i ; using a mixed multinomial logit (MNL) spei ation to reover these rst stage hoie probabilities (Appendix A.4 ontains a semi-parametri robustness analysis). Note that this is essentially the same spei ation employed in the seond stage proedure (outlined above), only the store s beliefs regarding rivals ations are exluded from this redued form. Note that we do not require an expliit exlusion restrition, sine our spei ation 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 oe ients on the i s (i.e. s) set to zero. Let the parameters in the rst stage be denoted by 1 = f 1 ; 1 g 24 and the rst stage likelihood for a given store be denoted by L i (; m (k) ; (k)) : Using a simulated maximum likelihood (SML) approah, we obtain ^ 1 ; the SML estimate of 1 : 24 The subsript 1 indiates that these are rst stage estimates. (12) i i (k) 93 = 5 : ; 22