SPATIAL DIFFERENTIATION IN THE SUPERMARKET INDUSTRY

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1 SPATIAL DIFFERENTIATION IN THE SUPERMARKET INDUSTRY A.YEŞIM ORHUN May 2, 2005 Haas School of Business, University of California at Berkeley Abstract. This paper investigates the positioning choice of strategic firms and infers the tradeoff between demand and competition factors in their optimal decisions. It shows that controlling for spatially correlated unobservable common factors as well as pre-existing systematic differences across retailers is essential for explaining the spatial positioning decisions in the supermarket industry.. Introduction Observed decisions of firms and consumers reveal valuable information about the underlying factors in their decision making. To this end, purchase decisions of consumers and pricing decisions of firms are extensively studied in the marketing literature. Positioning decisions such as where to open a retailer, how to design a new product, which combination of alternatives to offer, are all decided before the pricing game takes place, and demand is realized, and thus reflect the firms knowledge and expectations of these factors. When positioning a product, each firm in the market has to consider the proximity to the consumer base of interest and the perceived distance from competing alternatives. These factors will determine the extent of price competition and demand conditions. Although the positioning decision is a key marketing strategy which incorporates information Preliminary, comments appreciated. Address for correspondence: Haas School of Business, University of California at Berkeley, 545 Student Services Building #900, Berkeley, CA orhun@haas.berkeley.edu.

2 2 A.YEŞIM ORHUN on the sensitivity of demand and competition to the change in product attributes, this source of information has not been empirically explored. In this paper I present a model that recovers the relative importance of competition and demand factors and their sensitivity to geographic distance in the supermarket industry. Spatial positioning is a major differentiating factor in this industry, as in many retail industries. Consumers shopping trips usually originate from their residences, and distance to the store is one of the major determinants of their choice of where to shop. In this industry, the favorable demand conditions translate to being close to the customer base of interest, due to travel costs of consumers. Therefore distance to different segments of consumers, as well as other competitors, is well defined. Thus studying location choice of supermarkets as a form of positioning is advantageous in terms of the alignment of what the econometrician can observe and what the firms observe. In the model each firm simultaneously makes a spatial positioning decision with expectations of the decisions of the competitors. The decision that maximizes expected payoffs trades off being close to consumers of interest and avoiding possible competition. Firms are assumed to have some private information about their payoffs across locations. The model also investigates details specific to the supermarket industry which prove to be important in understanding the spatial differentiation outcomes. In the this industry, pre-existing systematic differences at the brand level are another source of differentiation. These preexisting differences are found to be significant in their effect on firms spatial positioning choices, providing evidence of consumer segmentation as well as asymmetric competition intensities. Since these preexisting differentiating factors are independently decided at the national level, the econometrician can condition on this information in order to isolate the spatial positioning decisions. The empirical results illustrate the importance of allowing for differences across firms. The competition intensity is greater between the firms of the same type than between those firms of different types. Competition among different types of firms is softened by the fact that they target different demographic segments.

3 Moreover, the assumption that the information sets of the econometrician and of the firms are aligned is relaxed by introducing location specific unobservables to the model. Some examples of unobservable factors are major road intersections, zoning laws and traffic flow. These factors will be observed by the firms at the time of the location decision, however will not be observed by the econometrician. In the case of a positive location shock, such as easy parking amenities and major road intersections, a model that does not allow for such unobservables will wrongly attribute the high number of supermarkets to low competition intensity between these supermarkets. The results show that introducing some common information to the game, in the form of location specific shocks, is important for the supermarket industry. The competition effect is stronger when unobservables are included in the model. The location specific unobservables are found to be spatially positively correlated. Next I summarize related literature, and present the data. I proceed with the discrete location choice model and the payoff formulations, followed by estimation and discussion of results Literature Review In order to study the implied demand and competition conditions from the location choice of retailers, one needs to define an equilibrium that leads to the observed outcomes. In this section, I outline the discrete location choice models in the literature. The discrete product type choice literature stems from a literature that estimate entry equilibrium models, which are models of binary decisions in nature. Bresnahan and Reiss (990) examine the decisions of potential entrants in monopoly automobile dealer markets, and find that differentiation increases profit margins of the duopoly more than competition decreases them. Berry(992) estimates a game where firms are making simultaneous decisions of entry with complete information about their competitors. The estimation of this model hinges on the fact that the number of the entrants is unique, even if identity of entrant may not be. This study brings problems of estimating complete information discrete choice games to our attention, such as dimensionality problems due to complicated

4 4 A.YEŞIM ORHUN regions of integration, as well as potential multiplicity of equilibria. Bresnahan and Reiss (99) detail the empirical estimation of discrete games and further discuss the multiplicity of equilibria and dimensionality problems in different models simultaneous choice of entry with complete information. The transition from the binary strategic choice to multiple strategic choice proves to be challenging due to the complete information setup. The first step in this direction comes with Mazzeo (2002), who extends entry models to allow for firm differentiation by incorporating entry and quality choice in the motel industry. This study also compares estimates from simultaneous and sequential complete information models and finds the results to be very similar. However, due to the complete information assumption, introducing more than three levels of product choice proves infeasible. This dimensionality problem is addressed by Seim (2004), who estimates the location choice of video rental stores. In her model, symmetric firms make a nested decision about entry and location simultaneously, where each firm has private information about its profitability in a particular location. Asymmetric information assumption turns the discrete actions of competitors into smooth location choice probabilities, thus both simplifies computation and reduces the regions of possible multiplicity of equilibria. This framework allows her to estimate a game where firms have many discrete choices. The use of the asymmetric information assumption makes advances in product type choice research feasible. Watson (2002), models eyeglass retailers variety choice after an entry decision, and Einav (2003) estimates the discrete timing choice of movies. Einav s sequential-move game setting guarantees a unique equilibrium in pure-strategies. The solution method to this model can also allow for heterogeneity in firms, thus asymmetric probabilities of timing choice. In studying a social planner s decision of locations of gasoline retailers, Chan, Padmanabhan, Seetharaman (2003) estimate a very flexible model which incorporates the pricing game as well as the location choice. Their model does not involve a multiple agent discrete choice game, since the location choices are made by a It should be pointed out that asymmetric information does not theoretically rule out multiple equilibria. This particular study finds empirical evidence that equilibrium choice probabilities are unique.

5 social planner instead of competing firms. Gowrisankaran and Krainer (2004) are able to estimate a flexible model of strategic location choice, similar in setup to Seim (2004), by substituting equilibrium probabilities from data, instead of solving for them. This paper concentrates on estimating the strategic tradeoff between demand and competition factors in the location choice of firms. Product type choice is conditional on entry, as in Einav (2003). The model is one in which firms choose locations simultaneously and have private information. Furthermore, the model allows for location specific common knowledge that is unobservable to the econometrician, as well as pre-existing asymmetries between firms The Data Due to the advances in Geographic Information Systems and the initiatives of the U.S. Census Bureau to make cartographic resources available, data on firms and consumers can be matched to geography. This allows researchers to construct a realistic picture of the distribution of consumers with different characteristics. Moreover, the distance between any pair of consumer and firm, as well as between any pair of competitors can be calculated. The data on the grocery stores in 25 metropolitan areas in the U.S. are provided by TDLinx. The data include the street addresses, size in square feet, brand name, number of employees, number of checkouts, and average weekly revenues of all grocery stores in these markets. 2 The data on consumers are obtained from the 2000 U.S. Census, such as population, average per capita income, number of households, household income distribution, family type and average upper quartile rent at the census block group level. Once the addresses of supermarkets and population weighted centroids of census block groups are geocoded onto latitude and longitude axes using a cartography software, any pair of distances 3 can be calculated taking the Earth s ellipsoid surface into 2 I concentrate on the location choice of supermarkets, which are defined as grocery stores with more than 00, 000 dollars of weekly revenue, and are also categorized in the data as supermarkets. 3 Distance between two locations (lon a, lat a ), (lon b, lat b ) can be found as d a,b = arcsin(min(, sin(dlat/2) 2 + cos(lat a ) cos(lat b ) sin(dlon/2) 2 )) where dlon = lon a π/80 lon b π/80 and dlat = lat a π/80 lat b π/80

6 6 A.YEŞIM ORHUN account. Using the FFIEC Geocoding System, supermarkets are assigned to the census block group they fall into. In Figure, the population weighted centroids and boundaries of locations of a sample market are mapped. Note that the population weighted centroids might be far from the geographic centroids, especially for peripheral locations. Figure : Centroids in Hayward Distribution of consumer demographics over the map is obtained by matching the U.S. Census data to the centroid coordinates of census block groups. These data are used to describe a block group s own characteristics, as well as the weighted characteristics of neighboring block groups. Figure 2 displays an example of demographic data assignment to the block groups. Figure 2: Demographic Assignment at the Census Block Group Level

7 Furthermore, data on the total area of each block group and retailer density is collected in order to proxy for unobserved zoning rules. The table below summarizes the variables in the data set. 7 Summary Statistics at the Block Group Level Mean Std. Dev. Min Max Population, , ,562 Income per Capita 24, ,07.2 4,748 24,4 Area of Block Group (mi 2 ) Density 6,623.34, ,638.8 Upper quartile rent Number of Retail Establishments Number of Supermarkets observed I identify 53 isolated markets, with considerable variation in size, as seen in the table below. An isolated market is a city or bundle of cities that are at least 8mi to another area of settlement with a supermarket. Market Level Variation in Size and Competitors Mean Std. Dev. Min Max Number of Block Groups Total Number of Supermarkets Discrete Location Choice Model The strategic location choice is assumed to be simultaneous among competitors 4. The unit of location choice is a census block group, and the locations are indexed by l = {, 2,.., L m } in each market m. It is assumed that firms have private information about their own location specific profitability shocks, following Seim (2004). 4 Asymmetric information assumption does not guarantee uniqueness of equilibrium in simultaneous discrete choice games. In my estimation, I don t run into uniqueness problems for the region of parameters I am searching over. The data has considerable variation, and so the equilibrium conjectures are always the same, for different starting values. Seim (2004) also finds evidence for empirical uniqueness in her estimation.

8 8 A.YEŞIM ORHUN Let the set of players in market m be j =, 2,.., J m and the discrete action space for player j be A m j. Market superscripts are suppressed since markets represent independent games. Let η j be the vector of private information of firm j over the discrete action space. Given the actions of all players, a = {a,.., a j,..a J m} the payoff for player j is given as π j (a) = βx aj + αc aj (a j ) + η j a j () where X aj is a vector of location specific demand and cost shifters, which includes own and some weighting of other locations demographic factors, incorporating the effects of distance on demand due to consumer travel costs. C aj (a j ) is the measure of competitive intensity, defined by the number of competitors in the particular location as well as some weighting of competitors in other locations. Demand and competition factors are assumed to be separately additive. Construction of X aj and C aj (a j ) will be detailed in the next section. The private information of firm j, denoted η j a j is i.i.d across locations and firms, and is assumed to follow a type I extreme value distribution. Each player, in equilibrium, will choose a location that optimizes its expected payoff, given its self-confirming beliefs about other players actions based on the distribution of private information, which is known to all players. Thus a( ) is a pure strategy Bayesian Nash equilibrium, if for each player j, a j (η j ) arg max{e[π j (a j )] = π j (a j (η j ), a j (η j ), ηa j a j )P r(η j )dη j } j η j In other words, a firm will choose action a j only if its expected payoff as a function of the specific draw of ηa j j is thus maximized. Since the private information of other firms only affect a firm s payoff through others optimal strategies, the expected profits can be expressed as E[π j (a j, a j, η j a j )] = a j P r(a j X, J, β, α) π j (a j, a j, η j a j ) or passing the expectation of others actions through the payoff function, as E[π j (a j, a j, η j a j )] = βx aj + αe[c aj (a j )] + η j a j. (2)

9 Due to the distributional assumption on the private information, the probability that the expected profits at a given location is weakly greater than expected profits at other locations simplifies to P r(a j ) = exp(βx aj + αe[c aj (a j )]) a j A exp(x j a + αe[c jβ a (a j )]) j The expectation of the number of competitors across locations is based on the beliefs of others optimal strategies, which means E[C a (a j )]) is a function of j P r(a j ). Therefore the optimal response of a firm depends on its beliefs of the other firms location choice probabilities. Players form these beliefs the same way that the econometrician does, as in the logit formulation above. This is due to the asymmetric information assumption that aligns the information set of the econometrician with the other firms. Moreover, since all firms are assumed to be symmetric up to their private information, the probability of any firm choosing a particular location is the same for all firms. 5 9 (3) Therefore the probability of each location choice is described by the logit formulation in Equation 3. This constitutes a mapping where one equations is of the form P r(a j ) = f(p r(a j )) and the fixed point solution to this system of L m nonlinear equations for each market, gives us the L m vector of reduced form equilibrium location probabilities P r(a j ) = g(x, J m, β, α) of any firm. Then the probability of observing an outcome a = {a,.., a j,..a J m} can be written as a j. P r(a) = J P r(a j X, J m, β, α) (4) j= where P r(a j X, J m, β, α) is the equilibrium probability of a firm choosing action 5. Payoff Specifications and Estimation In the game formulated above, the firms maximize their expected payoffs as a function of their beliefs of competitors strategies. In this section, I detail this 5 The symmetry assumption is relaxed below by allowing for discrete types of supermarkets. However the equilibrium solution concept remains the same.

10 0 A.YEŞIM ORHUN payoff function under different assumptions, and show how the payoff function and the game structure are taken to the data. The payoff function needs to capture the sensitivity of the demand and competition factors to distance. Moreover, the payoff function should be flexible in order to handle different number of location alternatives in different markets. To this end, one could use bands of distance and assume that the effect of characteristics of locations within a band of distance is homogenous, as in Seim(2004). This approach identifies differing effects of demographics and competitors for discrete bands of distance. Alternatively, one could use continuous distance measures to weight the effect of characteristics of a neighboring location on the location at hand. A flexible weighting function can be estimated to describe the distance sensitivity at a finer level. 5.. Discrete Bands Approach. Distance sensitivity of competition and demand effects are captured by allowing these measures to have different coefficients for different bands of distance. It is assumed that the rivals within the same band of distance to the firm exert the same competitive pressure on the firm. However rivals in different bands of distance to the firm potentially have different effects. Similarly, the effects of demographics are modelled homogenously within a band, and allowed to differ across bands. Bands are constructed by choosing cutoff distances. Thus bands b = {, 2,..., B} can be described by cutoff distance set d b = {0, d, d 2,..., d B } where band b around a location includes all the locations within d b and d b miles of the location at hand. Following the structure of Equation 2, such a payoff function for firm j can be written as B π j (a) = β b Za b j + b= B b= Ma b j lh l + ηa j j (5) α b Lm l= where Za b j denotes the demographic data of the locations within band b of the location choice of firm j. L m is the total number of locations in the market, h l is the number of rivals in location l, and M aj l equals if the location l is within band b of location of choice a j, in other words M aj l = {d b d aj l < d b }. Therefore, L m l= M b a j l h l denotes the total number of competitors in the locations within band

11 b of the location choice of firm j. This payoff is realized after the simultaneous location choice of firms. However, firms maximize expected profits based on their beliefs about where competitors will locate, since they do not know h l before it is realized. The expected profits of firm j if it chooses a j can be expressed as E[π j (a j )] = B β b Za b j + (J m ) b= B b= Ma b j lp l + ηa j j (6) α b Lm where p l is the probability that a firm will choose location l, and (J m ) is the total number of competitors in market m. Thus, actualized number of competitors, h l, is replaced by the expected number of competitors, (J m )p l. The symmetric probability of any firm choosing location l is the probability that expected profits are greatest in that location. information, this probability is p l = l= Due to distributional assumption on the private L m exp( B b= β bzl b + (J m ) b α b k= M lk b p l) L m i= exp( B b= β bzi b + (J m ) b α L m b k Mki b p k) Given parameters {β, α}, we can numerically find the fixed point solution to the mapping p = f(p) in order to obtain the vector of reduced form equilibrium conjectures p l (X, α, β, J m ) that depend only on the data and parameters. Once we solve this system of L m equations in each market, the estimation consists of maximizing the following log-likelihood LL = M L m m= l= y l ln p l (8) where y l is the observed number of entrants in a location within a market, and p l is the equilibrium conjecture we solved for. This procedure necessitates identifying the block groups centroids that fall in the distance rings, or bands, highlighted with different colors in Figure 3. Note that the membership depends on the distances between centroids of locations. The store counts, and demographics for each band are constructed using these neighborhood definitions. (7)

12 2 A.YEŞIM ORHUN Figure 3: Band Construction The first band includes location of interest, at the bull s eye, as well as location that are within d of it. The third band includes all the locations that are farther away than distance d 2 to the location of interest. One could potentially get finer definitions of distance by using more bands, however the parameters to be estimated increase by the number of distance sensitive variables for each additional band. In some cases, there might not be any locations in the second band of a particular location, although there are locations in the first and third bands. Moreover, locations with higher percentages of area outside the band may be included in the band, and others that need to be included may be avoided. These discretization errors may not be random, since the magnitude of errors are positively correlated with the size of the location, and its neighboring location sizes, where the size of a location is correlated with population density, since it is endogenously defined by the U.S Census Bureau. For small enough location sizes, the discretization approach generates band definitions that are close to boundary inclusion, just as uniform-sized locations would. Whereas when the location sizes are bigger, more errors are possible due to discretization. Although we cannot observe the population distribution over the location s area, using population weighted centroids rather than geographics centroids of locations increases the precision with which we can identify consumers distances to a location. Errors due to discretization are minimized when location definitions are as

13 small as possible, therefore I use the census block groups as decision units rather than census tracts Continuous Distance Weighting Approach. The problems related to discretization can be circumvented by directly using distance measures to weigh the effect of a variable on profits. Otherwise similar in its assumptions, the model below allows the weights of characteristics of locations to be flexible functions of the locations distances to the location of interest. The expected payoff for firm j can be written as E[π j (a j )] = L m β(d aj l)x l + (J m ) L m l= l= 3 α(d aj l)p l + η j a j (9) where L m is the total number of locations in the market, X l are the demographic variables for location l and d aj l is the distance between location choice a j and any other location indexed by l, and p l is the probability that a firm will choose location l. In this approach, the effect of each location s attributes on the attractiveness of the location of interest is weighted by its distance to that location. A flexible polynomial for the β(d) function can be estimated within the system. The probability of any firm choosing location l is p l = exp( L m k= β(d lk)x k + (J m ) L m k= α(d lk)p k ) L m i= exp( L m k= β(d ik)x k + (J m ) L m k= α(d ik)p k ) (0) Discrete bands approach provides an advantage in computation with respect to using continuous distance weighting, if the number of bands are relatively few. On the other hand, continuous weighting by distance is better in circumstances where discretization of bands induce biases to the estimation. Moreover, having the distance weighting function over the whole range of distances provides us with interesting insights from local changes in the function that might be lost due to averaging and the particular choice of cutoff in the discrete bands approach. 6 Results at the census tract level are available on request.

14 4 A.YEŞIM ORHUN The following extensions address two facts that characterize the supermarket industry. The first fact is that the firms may have some common information about the attractiveness of a location that the econometrician may not. The second fact is that the supermarkets are differentiated in other dimensions than spatial, which then can affect their spatial positioning decisions Location Specific Unobservables. The models above assume that all the demand and cost conditions that make a specific location preferable to supermarkets are observed by the researcher. However in case of the failure of this assumption, the competition effects will be biased. Including location specific errors in the model introduces some extra correlation of strategies across players, and it might be interpreted as adding common information to the game or accounting for location specific omitted variables. It might also be of interest to allow for spatial correlation in the unobservables. In this light, the expected payoff function in the discrete bands model can written as E[π j (a j )] = B β b Za b j + (J m ) B Ma b j lp l + α b Lm b= b= l= b= l= B Ma b j lε l + ηa j j σ b Lm () where p l is the probability of any firm choosing location l and ε is drawn from N(0, I). Similarly for the distance weighting model, the expected payoff function is E[π j (a j )] = L m β(d aj l)x l + (J m ) L m α(d aj l)p l + L m l= l= l= σ(d aj l)ε l + η j a j (2) By including σ(d aj l)ε l instead of just σε aj I investigate spatial correlation among the location specific unobservables. Introducing common location unobservables requires solving for the equilibrium conjectures for a set of simulated ε in order to integrate out the distribution of ε in the Maximum Likelihood estimation. This approach assumes that ε is uncorrelated with the explanatory variables. For each simulation r =, 2,...R of the

15 unobservable vector over all locations, the probability of location choice of firm j is, p r l = b= α L m b exp( B b= β bzl b + (J m ) B L m i= exp( B b= β bzi b + (J m ) B b= α b for the discrete bands approach, and b= σ L m b k= M lk b p k + B L m k= M ik b p k + B b= σ b 5 k= M lk b εr k ) L m k= M ik b εr k ) (3) p r l = exp( L m k= β(d lk)x k + L m k= α(d lk)p k + L m k= σ(d lk)ε r k ) L m i= exp( L m k= β(d ik)x k + L m k= α(d ik)p k + L m k= σ(d ik)ε r k ) (4) for the distance weighting approach. This system of equations for all firms is solved numerically for each simulation r. Then these R sets of conjectures are averaged, thus integrating out the distribution of ε for a given set of parameters (β, α, σ). The log-likelihood taken to estimation is LL = M L m m= l= y l ln( p l (ε)f(ε)dε) (5) Finding the fixed-point solution to the set of equations for the equilibrium conjectures can be time consuming. Estimations which have a large number of independent calculations within a minimization routine are very suitable for parallelization. In order to gain magnitudes of speed, I parallelize the algorithm in C and ran it on the Datastar in the San Diego Supercomputer Center. The algorithm is generally parallelized over the simulations of ε and in cases where I am interested in models without the unobservable, it is parallelized over the markets. Costs of communications outweighs the benefits of double parallelization (for both R and M). The minimization routine is a downhill simplex method Asymmetric Types. In the supermarket industry, geographic positioning segments consumers according to their proximity and travel costs. Preexisting

16 6 A.YEŞIM ORHUN brand level differences at the time of location choice further segments them according to their tradeoff between distance and quality and price concerns. This may result in relative geographic targeting of consumer segments by different types of firms. Moreover, if preexisting differences play a role in differentiation, competition across firms that are more differentiated will be softer. In order to investigate these effects, we can allow for discrete types of firms which results in asymmetries in location probabilities across different types. When predetermined systematic differences across players are denoted as types t =, 2,...T, the discrete bands expected payoff function of firm j of type t can be written as E[π t j(a j )] = B βbz t a b j + b= T (Js m I t=s ) s= B b= α ts b L m l= M b a j lp s l + η j a j (6) where I t=h equals one if t = h, and Js m is the number of firms of type s in the market. The probability of a firm of type s choosing location l is denoted by p s l. The coefficient αb ts captures the effect of competitors of type s within band b, on the profits a type t firm. Similarly, for the distance weighting model, the expected payoff function is or E[π t j(a j )] = L m l= β t (d aj l)x l + T (Js m I t=s ) s= L m l= α ts (d aj l)p s l + η j a j (7) The probability of a firm of type t choosing location l can be expressed as p t l = p t l = L m b= αts b exp( B b= βt b Zb l + T s= (J s m I t=s ) B L m i= exp( B b= βt b Zb i + T s= (J s m I t=s ) B b= αts b k= M lk b ps k ) L m k= M ik b ps k ) (8) exp( L m k= βt (d lk )X k + T s= (J s m I t=s ) L m k= αts (d lk )p s k ) L m i= exp( L m k= βt (d ik )X k + T s= (J s m I t=s ) L m k= αts (d ik )p s k ) (9) The equilibrium conjectures p t The log-likelihood taken to the estimation is LL = M L m T m= l= t= are found by solving L m T equations. y t l ln p t l (20)

17 where y t t is the observed number of entrants of type t, in location l within a market Results In the estimation, the demand shifters such as population density and average income are assumed to be distance sensitive. 7 On the other hand, upper quartile rent and retailer density of a particular location only affect the profits for that location. 8 I operationalize the discrete bands approach with 3 bands which are defined by 0.5 mi, 2mi cutoffs. 9 Table shows the estimates from the discrete bands model. The parameters of Equation 7 are reported in the first column, and the second column reports the results of Equation 3, which introduces common location unobservables. Let s concentrate on the first column. The effect of population density on profits is positive and decreases with distance to the store location. In fact, there is no significant effect of population density from the 3rd band, which includes locations farther than 2 miles. The fact that the effect decreases with distance reflects consumer travel costs. The effect of income per capita in the immediate band is negative, however in the second and third bands it is positive and decreasing with distance. The effect of upper quartile rent in the location of choice is negative, but insignificant. A location with very few or no retail establishments is much less likely to be chosen, possibly reflecting unobserved zoning rules. 0 As expected, the effects of competitors are negative and decreasing in magnitude with distance. In the second specification which introduces location specific unobservables to the estimation, the effects of competitors get more pronounced in every band. This is due to the fact that the model can attribute clusters or non-existence of supermarkets to unobservables. For example, take a case where 7 I do not find significant effects of education, family size, or travel time to work. 8 I have also used restaurant density and business density instead of retailer density and got very similar coefficients. 9 Results for distance cutoffs (, 2.5), (0.5, 2) and (0.5,.5, 2.5) are available upon request. Results are not very sensitive to cutoff choice. 0 Results using density of large retailers (comparable to supermarkets) are very similar.

18 8 A.YEŞIM ORHUN there is a positive unobservable for a given location, say an intersection of major avenues, and parking lot facility nearby. When the model is forced to attribute a higher number of supermarkets in this location to observed demographics only, this will dilute the effect of demographics and the competitive effect will be underestimated. The difference in results provides evidence that allowing for some common information of players is important. The unobservables show a significant variance and positive spatial correlation. I do not include retail density as an explanatory variable, since the location specific unobservables capture zoning rules and more. The effect of rent on profits becomes significant and more negative in this specification. Table 2 displays the estimates of the continuous distance weighting approach. The first column report the results of the model in Equation 0 and the second column report the results of the model with location specific unobservables, as in Equation 4. For each distance sensitive parameter, I use θ(d) = θ d + θ 2 or d 2 θ(d) = θ d + θ 2 + θ d 2 3 to approximate the effect of distance on the weighting of d 3 the variable. This functional form is intuitive and flexible. This approach avoids discrepancies due to ad hoc discretization of neighborhoods and provides a more detailed picture of distance varying effects. The results are in the same direction as the discrete bands model results. In Display, estimated weighting functions in two specifications are graphed as a function of distance for demand and competition factors. As before, the effect of a competitor is negative and decreasing with distance. Allowing for location specific unobservables increases this effect in magnitude. The effect of population density is positive and decreasing with distance. The effects of income per capita are negative for locations that are very close, and positive and decreasing with distance for the rest. The effect of rent is negative as expected. The results of the model with asymmetric types of players are presented in Table 3. The first column of Table 3 shows the results of the model presented in Equation To the degree that explanatory variables are correlated with the unobservable factors, the parameters on the explanatory variables will reflect the effect of this correlation with the unobservable factors, not just the effect of population for example. Then the estimates need to be viewed in this light.

19 7. Supermarkets are divided into two types, Type A supermarkets are brand names such as Whole Foods, Andronico s, Nob Hill, Trader Joe s and specialty supermarkets and Type B supermarkets are Safeway/Vons, Albertsons, Smart and Final, Grocery Outlet, Food4Less and other nonbranded stores. For estimation purposes, it is assumed that the competitive pressure of a type t supermarket on a type s super market is the same as that of a type s on type t, in other words α ts = α st. It is also assumed that supermarkets of the same type exert the same competitive pressure on each other, regardless of their type, so α tt = α ss. This method differentiates between within-type and across-type competition effects. Moreover, supermarkets are allowed to differ in their sensitivities to income per capita of their consumers. The specification presented in the second column introduces the variance of income in a location as an explanatory variable that each type is allowed to respond differently to. This aims to capture the effect of distribution of income, rather than just the mean of income. Consider two locations with the same mean income per capita. Let one have a unimodal distribution of income per capita, with a small variance around the mean. Let the other have a bimodal distribution, reflecting a mix of poor and rich consumers. The second location might attract two entrants of different types, where as the first location may attract none, or one. In this scenario, if the distribution of income is omitted, then the competitive effect between supermarkets of different types might be underestimated. The results for the two specifications are graphed in Display 2. The effect of population density is positive and decreasing with distance as before. The income per capita sensitivities for each type is quite different. Type B firms prefer low income locations, and the effect of income decreases sharply with distance. For Type A firms the effect of income is positive and generally decreases with distance. The results of the first specification show a considerable difference in within-type competition intensities and across-type intensities. Competition between firms of the same type is much fiercer for all distances, although the effect decreases sharply within the first mile of proximity. The competition between firms of different types is softer and decreases slowly with distance. This competition effect must 9

20 20 A.YEŞIM ORHUN be interpreted as the result of consumer choice among supermarkets, as a function of the substitutability or complementarity of competitors. The estimates from the second specification are similar, with the competition across types being fiercer. The comparison can be seen more clearly in the last graph of Display 2. This is in line with the earlier intuition that distribution of income might be a determinant of location choice of different types. 7. Discussion This paper investigates the geographic differentiation of supermarkets, taking into account other differentiating factors that are pre-existing at the time of the location choice. The contribution of the results is to provide evidence that such preexisting differences matter in spatial differentiation decisions. The supermarkets are categorized into types outside the model. There may be alternative ways of categorizing supermarkets, such as with respect to size and variety or type of pricing scheme that this paper does not yet explore. To this end, the results that point to the importance of such pre-existing differences might be understated. The competition effect is modeled as the effect of an additional competitor on the firm s profits. By construction, this effect will include any possible spill-over effects. Supermarket industry, unlike other retailer industries such as restaurants, is not expected to exhibit large magnitudes of positive clustering externalities. Moreover, allowing for location specific unobservables in the model prevents misattribution of unobservables to competition intensity. However, results should be interpreted keeping the model in mind. For example, when we allow for asymmetric competition intensities within and across different types of supermarkets, we find that the within type competition is tougher than across type competition. One can interpret these results as pre-existing differences creating asymmetric substitutability between different types of supermarkets for the consumer. These results, to some extent, may also be due to the complementarity of supermarkets of different types, which may induce positive externalities of locating together.

21 The payoff function is designed to capture the tradeoff between being close to favorable demand conditions and being far from competitors. The separably additive formulation of these effects is prominent in the literature. The competitive effect is a linear, additive function of the expected number of competitors. This formulation assumes that the effect of an additional firm is constant, regardless of the number of existing firms. The fixed point solution to the system of conjectures is greatly aided by this assumption. If one were to allow for a more flexible payoff function, the estimation would not be feasible under these assumptions. Two studies deal with this problem. Einav(2003) models a flexible payoff function, under a sequential discrete choice assumption. The game structure does not require solving for the fixed point, it is a backwards induction solution method. He estimates one parameter of this flexible payoff function, where other parameters are substituted in. I do not have the order of entry information in my data set. Then, in order to estimate a sequential choice model, I would have to randomize over the order of choice with respect to some parametric distribution. However, with a more complicated payoff function, where I am interested in estimating all the parameters from the location choice data, I do not find it feasible to randomize over order of choice and to estimate the parameters of the model. The second study that is able to estimate a more flexible payoff function is Gowrisankaran and Krainer (2005). This paper uses the same simultaneous discrete choice game setup, however instead of solving for the equilibrium beliefs, substitutes actual actions of competitors in the market in the place of beliefs of competitors location choices Conclusion I estimate a simultaneous game of asymmetric information of location choice in order to gain insight on the tradeoff between demand and competition factors in the supermarket industry, and to recover sensitivities of these factors to distance due to consumer travel costs. In the model, firms face uncertainty regarding the number of competitors they will face, since each firm possesses private information on their profitability across locations. Each firm maximizes its expected profits, however might face ex-post regret due to the risk in payoffs caused by uncertainty in

22 22 A.YEŞIM ORHUN the optimal strategies of competitors, which is a well suited description of decision making in the real world. The model is applied to the supermarket industry where location choice is a major differentiating factor, and other pre-existing differentiating factors can be controlled for. The findings indicate that competition intensity decreases significantly with distance, which gives firms the incentive to avoid locating in proximity. On the other hand, the demand effects also weaken with distance, giving firms a counter incentive to locate close to favorable demand conditions. Empirical results also show that these two counteracting incentives are traded off differently by different types of supermarkets. For a fixed distance, the competition intensity is greater between firms of the same type than between firms of different types. Also, results indicate that firms of different types are targeting different segments of consumers. This result highlights the importance of considering all pre-existing differentiating dimensions when modelling geographic position choices of firms. Furthermore, this paper illustrates how controlling for unobservable location specific factors can explain clustering or thinning of supermarkets which otherwise would be misattributed to competition intensity by the model. This research is a step towards incorporating positioning decisions of firms in marketing strategy models. This study shows that positioning decisions of firms can convey valuable information on the demand and competition conditions in the market. Combining demand and supply models with product location choice models is a natural direction for future research.

23 23 References [] Steve Berry. Estimation of a model of entry in the airline indstry. Econometrica, 60:889 97, February 992. [2] Timothy Bresnahan and Peter Reiss. Entry in monopoly markets. The Review of Economic Studies, 57(4):53 553, October 990. [3] Timothy Bresnahan and Peter Reiss. Empirical models of discrete games. Journal of Econometrics, 48:57 8, 99. [4] Liran Einav. Not all rivals look alike: Estimating an equilibrium model of the release date timing game. Working Paper, Stanford University, June [5] Gautam Gowrisankaran and John Krainer. The welfare consequences of atm surcharges: Evidence from a structural entry model. Working Paper, Olin School of Business, Washington University, November [6] Micheal Mazzeo. Product choice and oligopoly market structure. RAND Journal of Economics, 3(2): 22, Summer [7] Katja Seim. An empirical model of entry with endogenous product-type choices. Working Paper, Graduate School of Business, Stanford University, February [8] Randal Watson. Product variety and competition in the retail market for eyeglasses. Working Paper, University of Texas, Austin, March 2004.

24 24 A.YEŞIM ORHUN Table : Results of Discrete Bands Approach () (2) Population density, band (0.594)* (0.257)* Population density, band (0.0952)* (0.288)* Population density, band (0.094) (0.208) Income per Capita, band (0.0439)* (0.034)* Income per Capita, band (0.0992)* (0.04)* Income per Capita, band (0.0208)* (0.0047) Upper quartile rent (0.0523) (0.0363)* Retail density (0.66)* Competition, band (0.262)* (0.2238)* Competition, band (0.058)* (0.38)* Competition, band (0.096)* (0.054)* σ.762 (0.755)* σ 2.83 (0.4358)* σ 3.07 (0.34)* LLF

25 25 Table 2: Results of Distance Weighting Approach () (2) Population density d (0.0793)* (0.058)* Population density d (0.005)* (0.003)* Income per Capita d (0.0670)* (0.0440)* Income per Capita d 2 (0.0080)* (0.0052)* Upper quartile rent (0.0276)* (0.0494)* Retail density (0.074)* Competition d (0.480)* (0.508)* Competition d (0.096)* (0.0099)* Competition d (0.005)* (0.0005)* σ d (0.8)* σ 2 d (0.0059)* LLF

26 26 A.YEŞIM ORHUN Display Graph of Competition Coefficient Graph of Population Density Coefficient

27 Graph of Income per Capita Coefficient 27

28 28 A.YEŞIM ORHUN Table 3: Results of Distance Weighting Approach with Asymmetric Types () (2) Population density d (0.047)* (0.0705)* Population density d 2 (0.0044)* (0.0038)* Upper quartile rent (0.0854) (0.0468)* Retail Density (0.73)* (0.323)* Income per Capita - type A d (0.0978) (0.085)* d 2 (0.006)* (0.0)* Income per Capita - type B d (0.0263) (0.058) d 2 (0.0055) (0.002) Within-type Competition d (0.2550)* (0.293)* Within-type Competition d 2 (0.0042)* (0.006)* Across-type Competition d (0.0774)* (0.255)* Across-type Competition d 2 (0.0067)* (0.0074)* Variance of Income - type A (0.2886) Variance of Income - type B (0.2745)* LLF

29 29 Display 2 Population Density Coefficient Income Coefficients

30 30 A.YEŞIM ORHUN Competition Coefficients from () Competition Coefficients from (2)

31 Across type competition comparison 3