The Agglomeration-Differentiation Tradeoff in Spatial Location Choice

Transcription

1 The Agglomeration-Differentiation Tradeoff in Spatial Location Choice Sumon Datta Krannert School of Management Purdue University 403 W. State Street West Lafayette, IN Phone: (765) Fax: (765) K. Sudhir Yale School of Management 135 Prospect St, PO Box New Haven, CT Phone: (203) Fax: (203) February 2011

2 Abstract A central tradeoff in retail store location choice is the balance between spatial agglomeration and differentiation. While agglomeration can potentially increase volume, differentiation can reduce price competition. We develop and estimate a comprehensive structural model of entry and location choice that disentangles the agglomeration-differentiation tradeoff by controlling for rationales consistent with the differentiation motive: (a) zoning regulations that restrict entry in only concentrated areas; (b) high demand at the location; (c) low cost at the location; and (d) the need for spatial differentiation is lower when firms differentiate through store formats. The paper has three key innovations. First, to capture zoning effects, we introduce a new approach to obtain zoning data by using publicly available database (NLCD) and tools (ArcGIS and Google Earth). This approach should be of general interest for a large stream of spatial location applications. Second, to separate demand and cost explanations, we decompose profits into revenues and costs and augment typically used entry and location data with store revenue data. Finally, to separate the agglomeration-differentiation effect, we decompose revenues into consumer choice based volume and competition based price. We find that the agglomeration effect has a significant impact on observed collocation. Though zoning has little direct effect on collocation, it interacts with the agglomeration benefit to explain a surprisingly large fraction of observed collocation. Counterfactuals show that even small changes in zoning regulations can lead to a discontinuous change in the market structure, highlighting the value of the structural modeling framework proposed. Keywords: Entry, Location Choice, Agglomeration, Differentiation, Zoning, Retail Competition, Discrete Games, Multiple Equilibria, Structural Modeling

3 1. Introduction: A growing retailer faces two key questions as it embarks on a store expansion strategy: (1) Should it enter a particular market (entry decision), and if so, (2) Where within the market should it locate the new store (location decision)? A central tradeoff in spatial location choice is the agglomeration-differentiation tradeoff or the volume-price tradeoff. Should a firm collocate with a competitor to increase volume (competitor is a friend who can draw more customers to the location with strategic agglomeration) or locate far away from a competitor to reduce competition and increase price (competitor is an enemy from who one should differentiate spatially)? Empirical research on firms strategic choice of location within a market has only emphasized the benefits of spatial differentiation (Seim 2006; Watson 2005; Orhun 2005; Zhu and Singh 2009). 1 However, there is ample theoretical research to suggest that agglomeration benefits can act as an incentive for firms to forego spatial differentiation (Varian 1980, Stahl 1982, Wolinsky 1983, Dudey 1990, Fischer and Harrington 1996, Bester 1998, Arentze et al., 2005, Konishi 2005). 2 For instance, a quick examination of the distribution of inter-store distance between competing grocery stores in the three states of New York, Pennsylvania and Ohio showed that over 47% of stores are located within 0.5 miles of each other. How can we explain such high observed levels of agglomeration? It is important to recognize that observed collocation may be consistent with pure differentiation rationales such as (a) restrictive zoning regulations which allow entry in only small areas; (b) high demand at the location; (c) low cost at the location; and (d) the need for spatial differentiation is lower when firms differentiate through their store formats. The existing structural models of firms entry and location choice decisions do not incorporate most of these features. Also, in their current reduced form, they cannot disentangle the agglomerationdifferentiation tradeoff. In this paper we develop a comprehensive structural model that 1 The vast majority of papers on spatial choice concentrate on entry decisions (e.g., Bresnahan and Reiss 1991; Berry 1992; Mazzeo 2002; Ciliberto and Tamer 2009, Zhu, Singh and Manuszak 2008; Aguirregabiria and Mira 2007; Bajari et al., 2007). A related literature models consumer choice of locations but treats outlet locations as exogenous (Duan and Mela 2007; Thomadsen 2007). Chan et al., (2006) also model consumer choice of gasoline outlets when a social planner determines the outlet locations. 2 There is some empirical evidence of the benefits of spatial collocation (Fox et al. 2007; Watson 2005). 1

4 disentangles the agglomeration-differentiation tradeoff while simultaneously controlling for the alternative explanations for collocation. We make three crucial contributions to the literature. First, we introduce a novel approach to obtain spatial zoning regulation data for any number of markets. Locations with high population and income are often zoned as residential land and do not have any big-box stores. Previous studies wrongly viewed the absence of stores in such locations as a strategic choice of firms. Similarly, smaller and concentrated retail zones might force firms to cluster together. But previous models would infer such clustering to be the result of low competition between firms. To control for spatial zoning regulations, we use a publicly available, digital dataset called National Land Cover Dataset (NLCD). In conjunction with Geographic Information System (GIS) tools such as ArcGIS and Google Earth, we can recover zoning data in any number of markets across the entire U.S. This is the first application of digital land cover data in Marketing and the approach should be of general interest for a large stream of spatial location applications. Second, we decompose store profits into revenue and cost, and incorporate common unobserved demand and cost shocks Location specific demand (cost) characteristics such as, say, traffic patterns (tax-breaks), which may be common knowledge for firms but which are unobserved by the researcher. For this, we augment firms entry and location choice data with store revenue data. 3 Extant structural models use a reduced form profit function that cannot discern whether a location was chosen because of high revenue or because of low costs. Furthermore, when firms cluster in a location because the increased competition is more than offset by an unobserved high revenue (low cost) shock at the location, existing models would misattribute the collocation to low competition. 4 In our approach, the portion of observed store revenue that is not explained by the observable demand factors is attributed to an unobserved revenue shock at the location which is a draw from a distribution. Using data on firms actions, and allowing for correlations between revenue and cost shocks, we then identify the cost 3 Some recent research that has also used post-action performance data to gain richer insights about the drivers of firms strategic decisions include Ellickson and Misra (2007) and Draganska et al., (2009). 4 Orhun (2005) attempts to control for location-specific common profit shocks. However, with only choice data, one can only model latent profits whose errors have to be normalized for estimation. For instance, Orhun (2005) assumed that the distribution of common profit shocks have a standard normal distribution. 2

5 function. Thus, we are able to infer how the observed market characteristics affect revenue and cost differently which gives us better insights about the drivers of store location choice. Third, we show how to disentangle the agglomeration-differentiation tradeoff by further decomposing store revenue into its components of consumer shopping location choice based volume and spatial competition based price. Specifically, for volume we model consumers shopping location choice, which incorporates the spatial configuration of firms around consumers, and we model price as a function of the spatial configuration of rivals around a store. Hence, the benefits of agglomeration are realized through increased volume potential while the benefits of spatial differentiation emerge from acquiring a greater share of that potential as a result of decreased price competition. As competitors affect both volume and price, a nonparametric identification of the two effects would require additional data on sales or prices. Without this data, one would have to rely on suitable functional form assumptions so that the locations of rivals affect store volume differently from the way they affect store prices. Hence we further augment our data with price data for a set of stores that belong to one store chain. Finally, when different store formats specialize in different product categories or pricing strategies, the need for spatial differentiation may be lower. In the context of grocery stores, format types include Supermarkets, Superstores, Limited Assortment and Warehouse stores, Natural Foods stores, Food and Drug stores and Supercenters and Wholesale Clubs. Hence, we control for format differentiation by accounting for the different store formats. The empirical strategy to investigate firms entry and location decisions involves solving a choice game where firms strategies are interrelated. We estimate a static, structural simultaneous move game for firms entry and location choice decisions with incomplete information between firms. 5 We use maximum likelihood estimation for estimation of the static discrete game. 6 There are a few well-known methodological challenges in estimating discrete games. These include the possibility of multiple equilibria in the model, multiple equilibria in the 5 We do not have store entry dates which are required to solve a dynamic choice game. However, our model can be extended to a dynamic set-up similar to Aguirregabiria and Vicentini (2006) who have proposed a dynamic model of an oligopoly industry characterized by spatial competition. 6 Alternatives to likelihood based approaches include method of moments (Thomadsen 2005; Draganska et al., 2009), minimum distance or asymptotic least square estimators (Pakes et al., 2007; Bajari et al., 2007; Pesendorfer and Schmidt-Dengler 2008) and maximum score estimators (Fox and Bajari 2010; Fox 2007; Ellickson et al., 2010). 3

6 data, and slow convergence or potential non-convergence of the MLE estimation algorithm. 7 The last two issues are usually ignored by the extant literature due to their computational burden. We, build on recent developments in the empirical literature to address each of these challenges and these are explained in detail in the estimation section. Our estimates and counterfactual analysis show that the agglomeration effect is strong and explains a significant fraction of observed collocation of grocery stores across several markets. Surprisingly, zoning has little direct effect on collocation. But tighter zoning restrictions interact with the agglomeration effect to explain a surprisingly large fraction of observed collocation. We find that a small change in zoning can cause a discontinuous impact on the location pattern. This highlights the value of a structural model in understanding how a small perturbation of market characteristics can cause strategic firms to respond in complex and nonlinear ways. The rest of the discussion is organized as follows: Section 2 describes the model and estimation strategy. Section 3 describes the data and the approach for recovering spatial zoning data. Section 4 describes the estimates of the model. Section 5 presents the results of counterfactual simulations. Section 6 concludes with a summary of the findings and the limitations of this research. 2. Model and Estimation Strategy: 2.1. A Comprehensive Model of Strategic Entry and Location Choice The entry and location choice game involves a nested framework with two stages. In the first stage, each firm, i, of type or format, f (f = 1, 2,, F), decides whether or not to enter a market m (m = 1, 2,, M). In the second stage, the entering firms simultaneously choose their respective locations within the market. 7 See Aguirregabiria et. al., (2008) for a discussion on the distinction between multiple equilibria in model and multiple equilibria in data. 4

7 For the purposes of illustration, imagine a square city with a grid of L m discrete blocks or locations (Figure 1(a)). In extant models, firm i's payoff at each location, l (l = 1, 2,, L m ), is modeled as a reduced-form function of the market characteristics at the location, x l, the actions (entry and location choices) of all firms, a = (a i, a -i ), and an idiosyncratic profit shock, ε il, which is the firm s private information and is known to rivals (and the researcher) only in distribution: m m π ( a ) =Π ( x, a) + ε (1) ifl i f l il In this incomplete information setup, a firm cannot exactly predict rivals actions but it has rational beliefs about their strategies. For example, suppose firms are homogeneous, then each firm will make its decision based on its belief about the number of firms that would enter the market, m N, and its belief that an entering rival will choose a particular location as represented by a vector of conditional location choice probabilities, ( P p p p L ) m m P {,,..., 1 2 } m =. For instance, the firm may have a belief that a rival, conditional on entry, will choose location j with probability p j. Hence, for homogeneous firms the expected profit at location l can be written as (after dropping subscript f for format): ( ( )) m m m m E[ π ( a )] =Π x, N, P + ε (2) il i l il We build on this popular modeling approach and introduce several new features. First, in the extant models, firms are allowed to consider all L m locations in the market so that each location has some positive probability of being chosen by a firm. However, since firms are not allowed to set up stores in residential locations, we use our zoning data to exclude such locations and concentrate only on a subset of potential retail locations, l = {1, 2,, l m } (Figure 1(b)). Second, we break down the reduced-form profit into revenue and a cost multiplier. Both revenue and cost will include observed and unobserved components. Third, instead of an idiosyncratic profit shock, we assume an idiosyncratic cost shock. Formally, we revise Equation (1) as follows: ( ) ( ) m r m c π ( a ) = R x, a, υ * C x, υ, ς (3) ifl i fl l l ifl l l il where, revenue has the following multiplicative form: 5

8 r ( υ ) ˆ ( ) r R x, a, = R x, a * υ (4) fl l l fl l l R ˆ fl is the observed component of store revenue that is a function of the store format, f, the market characteristics at the location, x l, and the actions (entry and location choices) of all r firms, a. The unobserved component of revenue, υ l, is a location-specific shock that is common knowledge for all firms at the time of entry. It accounts for location-specific demand characteristics such as traffic density that are unobserved by the researcher. The cost multiplier in Equation (3) has the following multiplicative form: (, υ, ς ) ˆ ( )* υ *exp( ξ )*exp( ε ) C x = C x (5) m c c m ifl l l il fl l l il where, the observed component, C ˆ fl, is a function of the store format, f, and the market characteristics at the location, x l,. The unobserved component of cost consists of three elements: c (a) A location-specific shock, υ l, that is common knowledge for all firms at the time of entry. It accounts for location-specific cost characteristics such as commercial taxes that are unobserved by the researcher. Now, the common unobserved cost shock at a location is likely to be correlated with the common unobserved revenue shock at the location. We empirically check for this correlation through the following assumption about the distribution of these shocks: r ( ) c ( υl ) m (b) An overall market-specific attractiveness, exp( ξ ) but is unobserved by the researcher. ln υ r 2 l ω l 0 σ, r ρσ rσ c = N c 2 (6) ln ω 0 ρσ l rσ c σ c, that is common knowledge for all firms (c) The firm s idiosyncratic cost shock at the location, ς il, that is the firm s private information and known to rivals and the researcher only in distribution. 6

9 Finally, to separate the agglomeration-differentiation effect, we decompose R ˆ fl into a consumer shopping location choice based volume ( v fl ) and a competition effect based price index ( pr fl ). 8 ( ) ( ) Rˆ = v * pr (7) fl fl fl This decomposition of revenue will enable us to distinguish the benefits of agglomeration that increase volume, from the benefits of spatial differentiation that reduce price competition. We now describe the volume and price components of revenue Consumers Shopping Location Choice Based Volume: We have detailed information about consumers up to the Census Block Group (CBG) level. Hence, in what follows, we use demographic data at the CBG level and assume that consumers are located at the population density weighted center of their respective CBG. However, the model can easily be extended to a household level. Consumers choose the store format and the retail location where they want to shop. They may shop at any retail location within a radius, Rad. That is, we assume that Rad is the maximum distance that a consumer will travel for shopping. Note that this automatically implies that the trade radius of a store (region around a store from where the store gets its customers) is Rad. Now, consumers in CBG, g, incur a travel cost (T gl ) to go to a retail location l. This travel cost could be a non-linear function of the distance, d gl, between the consumer s location and the retail location. We also allow the travel cost to differ by the median household income of the CBG (med_hhi), the median age (med_age), and the minimum distance consumers have to travel before they can get to the nearest retail location (min_d). For instance, a consumer, who is located in a residential zone that is far from the nearest retail location, may be more willing to go to a store that is farther away, than say, a consumer who is close to several retail locations. Formally, the travel cost is given by: 8 We use sales-weighted prices across all product categories in a store as the price index of the store. 7

10 ( ) Tvl = α d + α d + α med _ hhi + α med _ age + α min_ d * d (8) 2 gl 1 gl 2 gl 3 g 4 g 5 g gl A consumer who wants to buy, let s say, groceries, may be attracted to a particular grocery store in location l if the location also consists of other commercial activities that cater to the consumer s non-grocery needs (e.g., electronics and apparel stores). That is, there could also be economies of scope from one-stop shopping or multipurpose shopping ( α MS ). Hence, we account for the extent of commercial activity in the location ( comm ). In addition, if consumers expect low prices at the store then they may be even more likely to visit the store. To control for this price effect ( α ), we account for the price index of the store format, pr fl. pr Next, a consumer shopping for groceries likely frequents locations where multiple grocery stores are collocated (store agglomeration effect). Hence, we consider the effect of the total number of competing stores at the location, N l. We also consider any scope economies of shopping within the grocery sector when grocery stores with different formats collocate (format agglomeration effect). For instance, consumers may be more likely to visit a particular Food and l Drug store when it is located close to a Supercenter. Hence, we use an indicator, OF I fl, for the presence of store formats other than the focal format f, and we also allow the format agglomeration effect to be format-specific. Finally, consumers may simply have a strong intrinsic preference ( α f, Pref ) for the store format f and there could also have an unobserved preference for the location, η gl. Formally, for a consumer in CBG g, the utility of shopping in stores with format f in location l is: ˆ U = Uˆ + η gfl gfl gl OF and U Tvl α comm α ln ( pr ) α N α, I α, = (9) gfl gl MS l pr fl SA l f FA fl f Pref We assume i.i.d. Type 1 extreme value distribution for the preference shock so that the probability that a consumer in CBG g will shop in stores with format f in location l is given by the standard logit form: 8

11 p csr gfl = F exp f ' = 1 csr j Lg ( Uˆ gfl ) exp( Uˆ gf ' j ) (10) where, the superscript csr for the probability denotes that this is the choice probability of consumers, and csr L g is the set of retail locations within the radius, Rad, from CBG g. Next, using consumers per capita income as a proxy for their consumption capacity or their purchasing ability, we construct a metric called Customer Value ( CV ) for measuring the net worth of the consumers who are attracted towards stores with format f in location l. For this, note that Equation (9) is also the share of consumers located in CBG g, who will shop in stores with format f in location l. We weigh consumers choice probability by the number of such consumers (CBG population, Pop g ) and their per capita income (PCI g ). 9 Then the customer value metric location: where, CV fl location l: is obtained by aggregating the influx of consumers from different CBGs around the csr ( ) CV = p Pop PCI. (11) fl gfl g g ret g Ll ret L l is the set of CBGs that lie within the trade radius, Rad, of location l. We then transform this customer value metric into volume for stores with format f in fl v CV α fv, fl = fl (12) Hence, in our framework, volume is endogenous to firms actions (through and it also depends on the market characteristics and consumer preferences Competitive Effect Based Price Index: N l and OF I fl ) 9 We use per capita income for convenience. One could, of course, use other better variables such as per capita expenditure on grocery. 9

12 Firms would like to differentiate spatially from rivals to reduce price competition. We model the effect of competition on the price index of stores with format f that are in location l. 10 We use a flexible, semi-parametric approach so that the competition effect is split differentially as a function of the store formats and distances of rivals from the location. Similar to Seim (2006), we divide the area around a location (up to the trade radius, Rad) into concentric circles or distance bands. 11 All rivals of a particular format type that are on a distance band b (b = 1, 2,, B) around location l are assumed to have the same effect on price. Formally, the price index of a store with format f that is in location l is given by: βx pr, *( ) *exp ' ' * pr fl = β f pr xl β f fbn fbl + β f fbn f bl υl b b f ' f and υ = ω N σ (13) pr pr 2 ln( l ) l (0, pr ) where, β f, pr is a format-specific parameter which allows the intrinsic pricing ability of firms to differ in their format (i.e., This could be due to format-level differences in cost, efficiency, product mix, service quality, etc.). The second component on the right-hand side allows the pricing ability of firms to depend on exogenous observable location characteristics, x l. In our application we use the per capita income of consumers within a 2 mile radius of the location to allow for price discrimination or the ability to sell premium brands in affluent neighborhoods. The third component on the right-hand side of Equation 13 includes the intraformat competition effect and the interformat competition effect. For intraformat competition we consider the number of rivals that have the same format, f, as the focal firm and are located in distance band b around location l ( N ). Here, β f fb fbl is the competitive effect of one such rival. For interformat competition, we consider the number of rivals that have a different format, f ( f ' f ), and β f ' fb is the competitive effect of one such f -format rival. Weakening of the competitive effects at greater distances will indicate the benefits of spatial differentiation 10 We use sales-weighted prices across all categories in a store as the price index of the store. 11 Alternatively, one could employ a continuous distance weighting approach as in Orhun (2005). 10

13 whereas differences between intraformat and interformat competitive effects will indicate the benefits of format differentiation. Finally, we introduce a common, unobserved and location-specific price shock ( υ ) that is common knowledge for all firms at the time of entry but is unknown to the researcher. We assume that this price shock has a log-normal distribution. Hence, similar to the volume, the price index also depends on market characteristics and firms actions. As firms actions affect both the volume and the price, a non-parametric identification of the competition effects would require price data for all stores. However, we only have price data for one store chain that has more than one store format in and is spread across most of the markets in our dataset. Hence, for identification, we will partly rely on our functional form assumption of how rivals affect volume in a different way from how they affect prices The Profit Function: Conforming with the multiplicative specifications so far, the observed component of the cost multiplier, C ˆ fl (Equation 5), is specified as: B ˆ Cfl ( xl ) = exp γ fbxxbl (14) b= 1 where, xbl are the observed cost shifters at distance band b around location l and are and band specific cost parameters. 11 pr l γ fbx format Substituting the expressions for revenue and cost into our profit specification, Equation (3), then taking the log transformation, and after making some trivial sign reversals, we have a equation for the transformed profit function that is very similar to equation (1): ( v pr ) ( Cˆ ) ( ) ( ) ( ) ( ) r c m π = ln π = ln + ln + ω ln + ω + ξ + ε (15) ifl ifl fl fl l fl l il 2.4 Equilibrium Choice Probabilities: Recall that the idiosyncratic cost shock, ε il, is known to rivals only in distribution. Due to such incomplete information about rivals profits, a firm cannot exactly predict rivals actions but it can have rational expectations about rivals strategies. Hence, for a given set of vectors of price,

14 pr r c revenue and cost shocks across all locations ( ω, ω, ω ), firm i can form rational expectations about the number of firms that will enter the market, N m, and the location choices of the (N m -1) m m m m entering rivals, P = P1, P2,... P F. That is, corresponding to each format f (f ) firms we will m have a vector of l m conditional location choice probabilities, Pf = { pf 1, pf 2,..., pfl } m ( P ' {,,..., f pf '1 pf '2 pf ' l }) m =. For instance, fj p is a conditional location choice probability p ( f ' j) of a f-format (f -format) firm and it represents the firm s belief that a f-format (f -format) rival will choose location j when a total of m N firms enter the market. Based on these beliefs, we can obtain expressions for the total number of competing stores in a location ( E[ N l ]) ( E OF I ) fl, the chance that there will be rivals with other formats in a location, and the number of f-format (f -format) rivals in distance band b, E N fbl ( E N ) f ' bl (Expressions for these expectations are shown in Appendix A). Consequently, we can get the expected values of volume and price index which would then lead to the following expression for expected profit: ( ( ) ( ) ) ( ˆ ) ( ) pr r c r c m E πifl ω, ω, ω E ln v fl E ln pr = + fl + ωl ln c fl + ωl + ξ + ε (16) il m Since simplifying assumption: v fl is a highly non-linear function of N l and OF I fl, we will make the following OF ( ( )) ( ) [ ] E [ln v ] ln,, ; kl = E vkl X E Nl E I fl α (17) This expected volume can be calculated based on firms prediction of the outcome of consumers shopping behavior as Equation (9) transforms into: ( ) [ ] Uˆ = Tvl + α comm + α E ln pr α E N α E I α OF gfl gl MS l pr fl SA l f, FA fl f,pref We also have: 12. (18) pr ln ( ) fl ln ( β f, pr ) βx ln ( l ) β f fb fbl β = f ' fb f ' bl + ωl (19) E p r x E N E N b b f ' f

15 Thus, the expected profit in equation (16) can be rewritten as a function of the equilibrium number of entrants in the market, in the market for firms of all formats, pr r c ω, ω, ω ), and a set of model parameters, θ = { αβγσρ,,,, } : m N, the equilibrium location choice probabilities m P, the specific draws of price, revenue and cost shocks ( ( ) ( ) pr r c m m pr r c m E π,, ˆ ifl ω ω ω = π fl N, P, ω, ω, ω, θ + ξ + εil (20) Note that m ξ is common for all locations in the market and therefore does not influence the location choice after firm i has decided to enter the market. Thus, if we assume that the idiosyncratic component, ε il, has a Type 1 extreme value distribution that is independent across locations and firms then the conditional probability (conditional on entry) that a f-format firm chooses location l is given by the logit form: fl m m pr r c ( N, P,,,, ) ψ ω ω ω θ = F f ' = 1 j= 1 m m pr r c ( ˆ π fl ( N P ω ω ω θ) ) m m pr r c ˆ π f ' j( N P ω ω ω θ) ex p,,,,, lm ( ) ex p,,,,, (21) Integrating over the distributions of the common unobserved shocks, we have the location choice probability, conditional only on entry: ( N, θ) ( N, ω, ω, ω, θ) g ω( ) f( ω, ω ) dω dω dω (22) Ψ = Ψ m m m m pr r c pr r c pr r c In equilibrium firms beliefs must match with rivals strategies. So: ( ; θ) (, ; θ) m m m m P N = Ψ N P (23) This represents a system of equations that defines firms conditional location choice probabilities as the fixed point of a continuous mapping between firms strategies and their rivals strategies. As the conditional location choice probabilities must add up to 1, by Brouwer s fixed point theorem, this system of equations has at least one solution or fixed point. Next, we normalize the profit from not entering a market to one so that the log of profit is normalized to zero. Then the entry probability for a firm is given by the nested logit form: 13

16 pr r c ( ω, ω, ω, θ) p Entry F lm f = 1 l= 1 ( ˆ fl ( N P )) m m m pr r c exp( ξ )* exp π,, ω, ω, ω, θ f = 1 l= 1 = F lm m m m pr r c 1+ exp( ξ )* exp π,, ω, ω, ω, θ ( ˆ fl ( N P )) (24) Hence, if there are, say, E potential retail entrants then the expected total number of entrants in market m is given by: m N = E * p( Entry) (25) By exogenously fixing E, and by observing the actual number of entrants, the market specific cost parameter is: ( ) m N, the estimate for F l m m pr r c m m m m pr r c ξ ω, ω, ω, θ = ln( N ) ln( E N ) ln ex p ˆ π fl ( N, P, ω, ω, ω, θ) (26) f = 1 l= 1 Again integrating over the distributions of the common unobserved shocks, we have: ( ) m m pr r c pr r c pr r c ξ θ ξ ω, ω, ω, θ g ω( ) f( ω, ω ) dω dω dω = (27) A simultaneous solution for Equations (23) and (27) gives the joint equilibrium predictions for the location choice probabilities and the number of entrants. We assume that Thus the probability that a total of m ξ is i.i.d. across markets, and follows a normal distribution, 14 2 N ( µσ, ). m N firms enter the market is given by the p.d.f. of this normal distribution at the value obtained in Equation (27). Note that the value of m ξ adjusts to the size of E in relation to the outside option of no entry. Hence, although the size of E is not observed by the researcher, varying the size will have only a miniscule effect on our inferences about firms strategies (See discussion in Seim (2006)). Next, note that for a given θ and m N, we can get estimates of price and revenue when firms locations are set to be identical to the observed spatial configuration of stores in the data.

17 We can compare these estimates with our price and revenue data and thus obtain the price and pr r revenue shocks, ( obv, obv ) ω θ ω θ, for the set of chosen locations that correspond to the observed spatial configuration of stores in the data. These price and revenue shocks are included in the likelihood function: L ( ) Θ = M m= 1 l F m I ( fl) m m pr 2 r ( ψ fl ( N, P ; θ) ) * φ( ωobv θ,0, σ pr )* φ( ωobv θ,0, Σ) f = 1 l= 1 Location Choice m 2 * φ( ξ ; µ, σ ) ( θ) ( θ) Entry Choice m m m m s.t. P N ; =Ψ N, P ;, m (28) ( ) 2 where, Θ is the set of all model parameters { θ, µσ, } Θ=, and I( fl ) is an indicator that equals one if location l is chosen by a f-format firm, and is zero otherwise. φ is the pdf of a normal distribution whereas φ has been used to indicate the pdf of the marginal distribution of revenue shocks. 2.2 Estimation Strategy: Simplifying Restrictions In the generalized model specification the number of model parameters increases exponentially with the number of format types (F) due to the interformat and intraformat competition effects (Equation 13). The number of distance bands (B) around each location further explodes the number of parameters. For instance, in our empirical application in this paper, we have six format types (F = 6), we consider five 1-mile width distance bands around each location (B = 5, Rad = 5 miles). For this case, the number of competition effect parameters alone is 180 (F 2 *B = 6*6*5). Also, the number of parameters for the observable component of cost (Equation 14) is proportional to F*B. Furthermore, we are also constrained by data for only 15

18 a limited set of sample markets (small M). Hence, we make two restrictions in the model specification to reduce the model parameters to a manageable number. First, we assume that the competition effect between a pair of rivals is symmetric. That is, for any distance band, b, and for two rivals with formats f and f, we assume β f ' fb = β f f ' b. In our empirical application for the grocery industry, this restriction implies that we treat the competition effect of a Supermarket on a Superstore to be the same as the competition effect of a Superstore on a Supermarket. Note however that we allow intraformat and inter-format effects to be heterogeneous. Therefore, (1) the competition effect between two Supermarkets can be different from that between two Superstores; and (2) the competition effect between, say, a Supermarket and a Supercenter can be different from that between a Superstore and a Supercenter. Second, we assume that the ratio between the competition effect from a rival at a particular distance band, b (b 1) and the competition effect from that rival in the first 0-1 mile distance band is a constant value ( κ b ). That is, we have: β = β κ ; β = β κ ;...; β = β κ f f 2 f f1 2 f f 3 f f1 3 f fb f f1 B β = β κ ; β = β κ ;...; β = β κ (29.1) f ' f 2 f ' f1 2 f ' f 3 f ' f1 3 f ' fb f ' f1 B (# competition effect parameters = ( F*( F + 1) / 2 ) + ( B-1) ) Similarly, the impact of market characteristics on cost ( γ fbx ) are allowed to be formatspecific but we assume a constant ratio between the impact of a variable at a particular distance band to the impact in the first 0-1 mile distance band. The constant is specific to the variable and the particular distance band. For instance, suppose for cost (Equation 14) the coefficients of population and per capita income in different distance bands are denoted by γ 1 fb and γ 2 fb, respectively; then the restriction implies: 16

19 γ1 = γ1 λ ; γ1 = γ1 λ ;... ; γ1 = γ1 λ f 2 f 1 2 f 3 f 1 3 fb f 1 B γ2 = γ2 ζ ; γ2 = γ2 ζ ;... ; γ2 = γ2 ζ (29.2) f 2 f 1 2 f 3 f 1 3 fb f 1 B (# observable cost component parameters ( F + B) ) Note that if we allow the ratios or the multipliers, κb, λb and ζ b to be format-specific then that is equivalent to directly estimating the format-specific coefficients, such as β f fb and, γ 1 fb γ 2 fb. In our estimation, we do not impose any restrictions on the values that the multipliers can take at different distance bands. If these multipliers turn out to be decreasing with distance and less than one then that would imply that the impact of the variable weakens with distance. In particular, weakening of the competitive effects at greater distances would indicate the benefits of spatial differentiation Multiple Equilibria in the Model * * Estimation involves finding the equilibrium solution, ( MLE, MLE ) P Θ, which is the global optimum of Equation (28) where, Θ * MLE are the Maximum Likelihood Estimates (MLE) and * PMLE are the corresponding equilibrium Conditional (location) Choice Probabilities (CCPs). Using a nested fixed-point (NFXP) approach for estimation is computationally demanding as it pr r c involves solving for the fixed-point of Equation (22) for each draw of ω, ω, ω and at each step of the likelihood maximization. More importantly, NFXP suffers from the possibility of multiple equilibria in the model. Specifically, for a value of θ, if Equation (22) has multiple solutions for CCPs then the likelihood is not well defined. 12 Researchers have, therefore, developed two-step estimation approaches that avoid these problems. In a two-step Pseudo Maximum Likelihood (PML) approach, the CCPs are estimated in a parametric or nonparametric first step and the parameter estimates are obtained by maximizing the resulting likelihood in the 12 One way to deal with this problem is to provide sufficient conditions that the parameters, θ, must satisfy to ensure a unique equilibrium (e.g., Seim, 2006; Zhu and Singh, 2009). 17

20 second step (Bajari et. al., 2007). However, in most empirical contexts, consistent and precise first-stage estimates of CCPs are infeasible. A recursive extension of the PML, called the Nested Pseudo Likelihood (NPL) approach addresses this problem at a relatively small additional computational cost (Aguirregabiria and Mira, 2007). 13 The standard NPL approach starts with an initial guess of the CCPs, and converges to an equilibrium solution in the limit. For example, in our case, we would start with initial guess values for firms beliefs about rivals CCPs, (28) we would obtain the likelihood, (, 0 ) P 0. Then, using Equations (21) through L P Θ. Maximizing the likelihood would give the parameter estimates, Θ 1, and new CCPs, P 1. This would constitute one iteration, and the new CCPs would be used for firms beliefs about rivals actions in the next iteration. The n th iteration of the standard NPL approach can be denoted by the following contraction mapping, M: ( Pn, n) ( Pn 1) where, n arg max L( Pn 1, ) ; Pn ( Pn 1, n) Θ =Μ Θ = Θ =Ψ Θ (30) Θ For a graphical illustration of the NPL iterations, suppose that the set ( P, Θ ) could be collapsed onto one axis. In Figure 2(a) the X-axis corresponds to the vector Pn 1, the Y-axis corresponds to the set ( Pn, Θ n), and the solid curve represents the contraction mapping ( P) Μ. The dotted lines represent the track followed by the NPL iterations corresponding to a particular starting value, P 0. Note that a different starting value, ' P 0, would result in a different track for the NPL iterations. With multiple iterations, if there is convergence, the contraction * * mapping would converge to an equilibrium solution or a NPL fixed point, ( P, Θ ). In Figure 2(a), this is the point where Μ ( P) intersects the 45 o line. Furthermore, if the fixed point is * * unique then it is, in fact, the global optimum, ( PMLE, Θ MLE ) Multiple Equilibria in the Data 13 Another application of the NPL approach for a static game can be found in Ellickson and Misra (2008). 18

21 The standard NPL approach, however, does not address the possibility of multiple equilibria in the data which is when the contraction mapping in Equation (31) does not have a unique NPL fixed point. The multiple eqilibria or the multiple NPL fixed points are essentially the different local optima of Equation (29). This is illustrated in Figure 2(b) where Μ ( P) intersects the 45 o line at multiple points. Consequently, the NPL iterations may potentially converge to a local optima and not the global optimum. Further, as the track followed by the NPL iterations depends on the starting value, P 0, different starting values would result in distinct tracks which could potentially converge to different local optima. One option is to spread the search for the global optimum over a wide range of the contraction mapping, Μ ( P), by using parallel-npl where a large number of NPL algorithms, say, T, are run in parallel with different starting values. By thus following T distinct tracks for the NPL iterations, this approach, upon 1* 1* 2* 2* T* T* convergence, would give us a set of T fixed points, ( P, Θ );( P, Θ );...;( P, Θ ) * * However, it does not guarantee that this set will contain the global optimum, ( PMLE, ΘMLE ). 14. For a more efficient search of the global optimum, Aguirregabiria and Mira (2005) propose combining the parallel-npl with a Genetic Algorithm (GA). GA is a search heuristic that mimics natural evolution processes such as selection, crossover or reproduction and mutation, and can be used to obtain the global optimum of complex optimization problems. Combining the parallel-npl with GA has two advantages (1) The crossover and mutation steps spread the search for the global optimum over a much wider range of the contraction mapping than what is feasible with just the parallel-npl, and (2) The selection step steers the tracks of the parallel-npl iterations towards those regions of the contraction mapping that are more likely to contain the global optimum Many of the fixed points may be identical. 15 Su and Judd (2007) suggest using a Mathematical Programming with Equilibrium Constraints approach that finds the parameter estimates and the equilibrium CCPs simultaneously. However, like the parallel- NPL, this approach also relies on multiple runs with different starting values to find different equilibria. Hence, its ability to find the global optimum in problems that have a large action space (as in our entry and location choice problem) is unclear. 19

22 In our estimation, we insert two GA steps after each iteration of the parallel-npl. Note that after the n th iteration of the parallel-npl, we will have T vectors of CCPs, 1 2 T P ; P ;...; P n n n. First, in a selection step, we evaluate each vector of CCPs by using a fitness criterion where the CCPs that are likely to be closer to the global optimum are considered to be more fit. Analogous to the natural selection process in nature, the more fit CCPs are given a greater chance of survival and reproduction so that future search for the global optimum is concentrated in their neighborhood. This is done by drawing, with replacement, T mother CCPs, 1' 2' T ' P ; P ;...; P n n n, and T father CCPs, P ; P ;...; P P ; P ;...; P 1'' 2'' T '' n n n, from the original set, 1 2 T n n n more fit CCPs have a greater chance of getting selected. 1' 1'' 2' 2'' T' T'' Next, each of the T couples, ( Pn, Pn );( Pn, Pn );...;( Pn, Pn ), such that the, go through a crossover step to produce an offspring that inherits the traits of both its parent CCPs. To the extent that both parents are likely to be fit, the resulting offspring also has a high chance of being fit. Hence, we obtain a new generation of T vectors of CCPs that are likely to be quite close to the global optimum. To further reduce the chances of missing the global optimum, some mutations may be implanted into the offsprings so that the search continues to span a wide range of the contraction mapping. With multiple iterations of the parallel-npl and GA steps, if there is convergence, we would obtain a set of T fixed points which almost certainly would contain the global optimum Convergence The algorithm may not converge to the global optimum if the contraction mapping does not have good local convergence properties around the global optimum. Intuitively, as shown in Figure 2(c), convergence to a fixed point depends on the concavity or the convexity of the mapping in the neighborhood of that fixed point. Kasahara and Shimotsu (2008) recommend transforming the mapping by replacing Ψ( P, ) Ψ( P, Θ) and P : Θ with the following log-linear combination of ( ) ( ) 1 δ Λ P, Θ = P, Ψ Θ P ; δ [0,1] δ (31) 20

23 Note that P =Λ( P, Θ ) and P ( P, ) =Ψ Θ have the same fixed-point solution(s). An appropriate value of δ can modify the concavity or convexity of the mapping such that the transformed mapping is Locally Contractive around the fixed point and will converge even if the original mapping does not. 16 Finally, even when the mapping does converge, the rate of convergence could be extremely slow and may require a large number of iterations. To avoid this, Kasahara and Shimotsu (2008) propose the following q-stage operator called q-npl: ( ( ( ( ) ) ) ) Λ q ( P, Θ ) =Λ Λ... Λ P, Θ, Θ,..., Θ, Θ q times q Again, P =Λ ( P, Θ ) and P ( P, ) (32) =Ψ Θ have the same fixed-point solution(s). In q addition, Λ ( P, Θ ) also has the locally contractive property of Λ( P, ) Θ. Hence, in our estimation, we replace the standard NPL operator, Ψ, with the Locally Contractive, q-npl operator, q Λ. The resulting parallel NPL iterations are then combined with GA as described above. This procedure searches efficiently over the space of possible equilibria and converges fast to a set of equilibria which almost certainly contains the global optimum. Details of the sequence of steps involved in estimation are provided in Appendix A Identification: Extant models of location choice that use only spatial location data, exploit two kinds of variations in the data to identify the effects of market characteristics and competition variation in market characteristics conditional on number of rivals around a location, and variation in number of rivals around a firm conditional on market characteristics. For our competitive effect, we allow prices to be affected by the number of rivals and their distances from a location. Here 16 Kasahara and Shimotsu (2008) suggest the following procedure for selecting the value of δ : Simulate a N P = sequence { n} n 0 δ P by iterating the transformed mapping for different values of δ, say for { 0.1,0.2,...,0.9} n+ 1 P n P P N n across n = 1,, N.. Then pick the value of δ that leads to the smallest value of the mean of 21

24 we make use of the variation in number of rivals around a firm. Variations in market characteristics around store locations are allowed to affect prices and the latent cost. A bonus feature of our model is that we also model consumers shopping location choice behavior. The consumer model exploits the variation in the number and geographic locations of firms around consumers. This modeling innovation combined with data on store revenue and (partial) price data aids our identification and separation of the benefits of agglomeration and the benefits of spatial differentiation. As mentioned earlier, we have price information for only a subset of all stores. While using this piece of information aids non-parametric identification, we partly rely on our functional form assumption on how the locations of rivals affect store volume versus how they affect store prices. In Appendix C, we use a stylized example to illustrate how key model parameters are identifed. 3 Data: 3.1 Store Data and Sample Markets: We investigate the spatial configuration of big-box grocery stores. We have store location (latitude and longitude), store format and revenue data at the national level for the period from Nielsen s Trade Dimensions. In a different data set, we have store location and store format data (but no revenue data) for the period and for a sample of local markets in the three states of New York, Pennsylvania and Ohio. This second dataset also has price data for stores belonging to one store chain. In our model, price data from a different time period can be used to estimate the competition parameters and the distribution of price shocks as long as long as we use the market configuration for that period in our price model. Hence, we combine the two data sets so that for a sample of markets we have the market configuration and revenue data for all stores in one period (2008), and the market configuration and price data for one store in each market, but for a different period (2001). The data constraint of having prices for only one store chain may appear as a serious weakness. However, it is interesting from a managerial perspective as it mimics a more realistic situation where firms are likely to have more information about themselves than about others. 22

25 Among the markets for which we have price data, we select a sample of 98 fairly isolated, small and medium sized towns to avoid the problems associated with large markets and suburbs such as unclear market boundaries, cannibalization due to multiple stores of a firm in the same market, and complex zoning regulations. In 2008, our 98 sample markets had altogether 438 big-box grocery stores. 17 These stores have been classified into six format types (i.e., F = 6): Supermarkets (SM), Superstores (SS), Supercenters and Wholesale Clubs (SC), Limited Assortment and Warehouse stores (LA), Natural Foods stores (NF) and Food and Drug stores (FD). Table 1 provides a description of these store formats Consumer and Retail Locations: Data on market characteristics are obtained from the U.S. Census. Although detailed demographic data at a Census Block Group (CBG) level are available only for the year 2000, the U.S. Census provides annual census projections for the county level. Hence, we project the CBG level census data to their 2008 values by the proportion of change in the respective counties between 2000 and As we do not have information about consumers beyond the CBG level, we follow the convention in the literature and place consumers in a CBG at the population weighted center of the CBG. These are our consumer locations. For the location choice game, we divide a market into a uniform grid of discrete 1 sq. mile blocks or market locations. Our 98 sample markets have a total of 4,792 such locations. But zoning regulations dictate which of these locations are available for big-box retailers. Below, we discuss our approach for identifying these retail locations and their commercial centers. Just as consumers are placed at the population weighted center of CBGs, we place retailers within a retail location at the commercial center of the location. Our concept of market locations deviates from the standard approach in earlier research that treats census divisions as market locations and places retail stores at the population weighted center along with consumers. The standard approach simplifies the data setup process but it has severe drawbacks: (1) The population weighted center of a census division is likely to be a residential zone so that placing retail stores there would confound the inclusion of zoning 17 A comparison of the market configurations between 2001 and 2008 showed that the number of stores in these markets increased by only 11% from 399 to

26 regulations; (2) Stores are rarely present in the interior of a census division, rather, they are present on roads that border these census divisions; (3) Census divisions vary extensively in size so that, for large census divisions, stores may be located quite far from the center. In contrast, our approach allows us to incorporate spatial zoning, and it avoids major distortions of the distances between competitors and the distances of stores from population centers. 18 We next describe the National Land Cover Dataset (NLCD) and discuss how it is used in conjunction with Geographical Information System tools such as ArcGIS and Google Earth to recover the potential retail locations and their commercial centers. 3.3 Spatial Zoning Data: Multi-Resolution Land Characteristics Consortium, a conglomerate of several federal agencies, has created two NLCD datasets that provide consistent and accurate digital land-cover information for the coterminous U.S. The first national land-cover mapping project, NLCD 1992, was derived from the early to mid-1990s Landsat Thematic Mapper satellite data. It applied a 21- class, geo-referenced, land-cover classification (see Vogelmann et al., 2001). The second project, NLCD 2001, updated the data for the year 2001 (see Homer et al., 2004). Both datasets have a spatial resolution of 30 meters. That is, every 30 sq. meter area of land is classified as a specific land type (e.g., deciduous forest, grassland, open water, etc.) and is allocated one pixel point with a distinct color code and the associated latitude and longitude. 19 Interestingly, the land type classifications include residential and commercial land. Residential land is further classified into low and high intensity residential land, and commercial land comprises of highly developed areas that do not include residential areas. We use the NLCD data in the following three steps to identify the potential retail locations. Step 1: Constructing Market Boundaries and Market Locations: The residential and commercial land area pixel points in each market are projected on a map by using the ArcGIS software. This gives us the spatial area of interest for each sample market. A simple visual inspection of the pixel density is used to construct the market boundaries 18 In this paper, distance between two points always refers to the great-circle distance. 19 A pixel point is one of the individual dots that make up a graphical image. Each pixel point combines red, green, and blue phosphors to create a specific color. 24

27 where the pixels fade away (See Figure 3(a)). A rectangular shape is preferred so that a market can be easily divided into a uniform grid of discrete blocks or market locations. Thus, we construct imaginary rectangular borders (L miles X H miles where L and H are integers that vary across markets) around the residential and commercial pixel points of each market and then divide the market, specifically, into 1 sq. mile locations (See Figure 3(b)). Step 2: Commercial Activity and Commercial Center in a Location: We isolate the NLCD 2001 pixel points that correspond to commercial land with retail businesses (See Appendix C for more details) and use the number of pixel points in a location as a measure for the extent of commercial activity in that location. The mean of the latitudes and longitudes of the commercial land pixel points in a location gives us the commercial center of the location (See Figure 3(c)). We place all retail stores within a location at the commercial center of that location. Step 3: Discerning Potential Retail Locations from other Commercial Locations: The market locations which contain the commercial land pixel points are the commercial locations and they constitute a very small share of all market locations. The locations without any commercial activity are mostly residential locations and some barren land. Hence, we account for residential zoning by excluding locations that do not have any commercial land pixel points. But even within commercial locations, not all locations may be open to big-box retailers. For instance, some commercial zones like, say, downtown areas, might only allow small businesses such as banks and restaurants. An obvious candidate for a potential retail location for big-box stores is any commercial location that has at least one big-box store which could be a grocery store or a non-grocery store. Hence, we project the locations on to Google Earth and use a tool called Places Categories which shows the locations of various types of businesses in a region (See Figure 3(d)). We carefully comb through the commercial locations, and specifically check for the presence of major retail stores, major grocery stores and shopping centers to identify the commercial locations that have at least one big-box store. Now, the absence of big-box stores in a commercial location does not necessarily imply that such stores are not allowed in that location. In particular, a commercial location that is open to big-box stores may not have any such store if it is in an unfavorable or poor neighborhood and 25

28 cannot support a big store. 20 As we do not have a precise method for identifying such locations, we use a stylized selection procedure. For each market, we find the minimum value of the total income of consumers within a 2-mile radius of the commercial locations that have big-box stores. We use this minimum as a benchmark for a commercial location in the market to be attractive enough to support at least one big-box retail store. That is, if a commercial location does not have any big-box store and the total income of consumers within a 2-mile radius of the location is less than the market benchmark then we presume that the absence of a big-box store is due to the unattractiveness of the location and not necessarily because of zoning restrictions. Hence, a commercial location with no big-box store is still treated as a potential retail location when the following condition is satisfied: Income in 2-mile radius of a commercial location that has no big-box store Income in 2-mile radius of a commercial min location that has a big-box store To summarize, we use the NLCD data to construct market boundaries so that each market can be divided into a grid of 1 sq. mile locations. Then the commercial land pixel points are used to obtain the extent of commercial activity in a location and also to locate the commercial center of the location. Extant models that do not account for zoning, assume that firms are allowed to set up stores in any market location. In contrast, we account for residential zoning by excluding locations that do not have any commercial land pixel points. Finally, we account for zoning regulations particularly against big-box retailers, within commercial locations, by defining potential retail locations as those commercial locations that (1) have at least one big-box store which is either a grocery or a non-grocery store, and (2) do not have a big-box store and are in a poor neighborhood which is below the market benchmark as described above. 4. Results: The estimation results are presented in three parts. Table 2(a) presents the estimates for the consumer choice or the demand side of the model. Consumers experience a negative travel 20 Note that competition between stores in neighboring locations cannot explain the absence of big-box stores in a location as we are considering big-box stores across any segment of the retail industry. 26

29 cost that is convex with respect to distance (The coefficient of 2 dgl is positive and significant). Consumers who are far away from the nearest retail location (That is, when the value of 27 min_dg is large), are more willing to travel long distances to get to a grocery store. Demographic characteristics seem to have very little explanatory power for consumers travel costs. The results show that consumers not only value economies of scope from the presence of other, non-grocery businesses at a location but they also value the agglomeration of multiple grocery stores at the location. The store agglomeration parameter ( α = ) is positive and significant which suggests that consumers likely visit locations with multiple grocery stores. The format agglomeration effect ( α, f FA ) is also positive and even significant for a few store formats (Supercenters, Limited Assortment stores, and Food and Drug stores). Hence, consumers are more likely to visit locations with multiple grocery stores when the cluster of stores consists of different formats. Consequently, strategic store and format agglomeration increase consumers propensity to shop at a location, thus increasing volume at that location. Finally, consumers have a high preference for Supercenters and for Food and Drug stores relative to the Supermarket format. Hence, consumers may be more willing to travel long distances to get to such stores. Consumers have a relatively low preference for Limited Assortment stores. This could be because Limited Assortment stores generally carry more namebrand products and very few national brand products. Table 2(b) presents the results of the price index portion of the model. The formatspecific price constant, β f, pr, is lowest for Limited Assortment stores and Supercenters. This is expected since the stores with these formats are typically EDLP stores or they offer relatively more name-brand products that have low prices. For the effect of competition, recall that we allowed for separate intra-format and inter-format competition, and we considered competition from rivals in five 1-mile width distance bands (B = 5, Rad = 5 miles). Our results show that the competition effect decreases dramatically with distance. Not surprisingly, intraformat competition is generally more severe than interformat competition. The extent of intraformat competition is the highest between Food and Drug combination stores, which is comparable to the competition between Supercenters. Superstores SA

30 are also found to compete quite heavily with each other. Interestingly, for some formats, the interformat competition effect is found to be comparable to the intraformat competition effect. For instance, the competition effect between Supermarkets and Superstores is quite comparable to that between two Supermarkets. The competition effect between Superstores and Food and Drug combination stores also seems to be quite high. The results highlight the importance of accounting for format differentiation, in addition to spatial differentiation. To explore the value of separating the agglomeration-differentiation effects of rivals, we estimated a model that did not incorporate agglomeration benefits in the consumer model (Parameter estimates not shown). The results showed that the competition effects are biased downwards for all format types. The bias was more severe for inter-format competition. Hence, not modeling the agglomeration-differentiation tradeoff can highly underestimates the competition intensity between stores with different formats. In retrospect, this is expected because without an agglomeration effect the model would misattribute observed collocation of stores in the data to low competition. Since the agglomeration benefit is higher when the cluster of stores has different formats, it is understandable that the inter-format competition effect is more biased. Finally, the estimates of cost and unobserved shocks are presented in Table 2(c). The results give some interesting insights. Although the Supercenter format enjoys a high preference from consumers, it also tends to incur high costs in densely populated neighborhoods. We find a strong negative correlation between the location-specific cost shocks and demand shocks ( ). This conforms to the intuition that locations with high revenue potential are likely to be associated with high costs. 5. Counterfactual Simulations: We report two counterfactual simulations which help assess the relative importance of zoning and agglomeration effects. We consider three alternative scenarios: (1) There are no zoning regulations in any market and consumers do not benefit from collocation of stores (i.e., Neither Zoning nor Agglomeration ), (2) Markets have zoning regulations but there are no benefits from collocation (i.e., Only Zoning; No Agglomeration ), and (3) Agglomeration 28

31 benefits exist but there are no zoning regulations (i.e., No Zoning; Only Agglomeration ). For the set of 98 sample markets we estimate the equilibrium location choice probabilities under these alternative market conditions, assuming that the equilibrium number of entrants remains unchanged (An appropriate change in the market-specific terms, 29 m ξ, would ensure this). We use the estimated model parameters and find the fixed point of the system of equations shown in Equation (23). For this, we use the NFXP approach. Figure 4(a) shows the distribution of inter-store distance across the 98 markets, under the first scenario of Neither Zoning nor Agglomeration. We see that only 28% of stores collocate within 1 mile of each other. This level of collocation may be due to concentration of high demand or low cost. When we turn on zoning ( Only Zoning; No Agglomeration ), 32% of stores are located within 1 mile of each other (Figure 4(b)). This suggests that zoning may force firms to come a little closer to each other but it has very limited direct impact on their collocation behavior. With only agglomeration turned on (Figure 4(c) - No Zoning; Only Agglomeration ), 43% of stores located within 1 mile of each other, suggesting that agglomeration effects have a substantial impact on collocation. Interestingly, the interaction between zoning and agglomeration benefit is extremely high because in the observed data, collocation increases to 60% when both effects coexist (Figure 4(d) Both Zoning and Agglomeration ). Thus the impact of zoning on collocation is high only when agglomeration benefits are high. Why do we see such interaction effects between zoning and agglomeration benefits? To understand these effects, we perform our second counterfactual analysis in two hypothetical markets: one with less restrictive zoning and another with more restrictive zoning. For a set of four grocery stores, the optimal locations are shown in Figure 5. In the less restrictive zoning setting, we find that stores are located at the extremes of the zone, suggesting that zoning restrictions constrain the extent of spatial differentiation in this market. When we make zoning more stringent, one would therefore expect that stores would continue to be at the edges of the retail zones. However, the optimal locations reveal a surprising pattern. When zoning is restricted, we find that some stores actually agglomerate and the inter-store distances are lower. In retrospect, we can understand the logic of why this happens. When zoning is relaxed, stores can be more spread out allowing for benefits of differentiation to be large enough. However when zoning is restricted, firms cannot differentiate enough; this leads to a discontinuity where

32 stores now recognize that by collocating they can gain from agglomeration benefits which may outweigh the relatively constrained benefits from differentiation because of the tight zoning regulations. This explains the high interaction effect of zoning and agglomeration that we find in Figures 4(a) 4(d). 6. Conclusion: The literature on retailer entry and location choices has thus far ignored the agglomeration-differentiation tradeoff. We developed a comprehensive static, structural, simultaneous move game model of firm entry and location choice that disentangles this tradeoff while controlling for several alternative explanations for observed collocation. Taking advantage of a publicly available, digital land cover database, NLCD, we are able to control for the effect of zoning on entry and location choices. To control for demand and cost based explanations for collocation, we decompose latent profits into revenue and cost and augment entry and location data with store revenue data. To separate the benefits of agglomeration from the benefits of spatial differentiation, we further decompose revenue into its components of consumer choice based volume and competition based price. We use recent advances in the empirical estimation literature of discrete games to address issues of multiple equilibria in the model and data as well as problems due to slow convergence of the estimation algorithm. The consumer and price model provided interesting insights about the differences in the agglomeration and competition effects across store formats. These results and the subsequent counterfactual analyses lead to the following takeaways: First, zoning, agglomeration effects, spatial differentiation and format differentiation are all key drivers of observed store location patterns. Second, zoning may force firms to locate closer than what they would like but it has little direct effect on collocation of stores. Finally, zoning interacts with agglomeration to drive observed collocation. The interaction between zoning and the agglomeration effect can have a discontinuous impact on the location pattern of stores. This highlights the value of a structural model in understanding how a small perturbation of market characteristics can cause strategic firms to respond in complex and nonlinear ways. 30

33 We conclude with a discussion of some key limitations in this paper that warrant future research. First, our identification of the volume and price effects is partially aided by functional form assumptions for how locations of competitors affect volumes and prices differently. This is because we only have price information for a set of stores belonging to one store chain. Nonetheless, this is managerially interesting as it is closer to a realistic scenario where firms usually have more information about themselves than about others. Second, we treat entry decision in a static equilibrium framework, even though a dynamic model may be more appropriate given that these decisions are made over time. Such a modeling approach requires better data (timing of entry and exits) as well as richer modeling framework to solve the dynamic game. Finally, we have treated store entry decisions across markets as independent, unlike recent work by Jia (2008), who models the chain entry decision, taking into account the interdependence across markets. However, her modeling approach is restricted to a small number of competing chains and is hard to extend to our grocery market setting that involves a large number of players. These important issues await future research. 31

34 L m l m Figure 1(a): An illustrative square market with the geographical space discretized into square blocks or locations. Figure 1(b): Due to zoning regulations, firms can only choose among potential retail location (Area in white). Figure 2(a): Graphical Illustration of the Standard NPL Approach 32

35 Figure 2(b): With Multiple Equilibria, Different Starting Values May Give Different Solutions Figure 2(c): The Contraction Mapping May Not Converge to a Fixed Point 33

36 Figure 3(a): Constructing market boundaries based on visual inspection of residential and commercial pixel density Figure 3(b): Dividing a rectangular market into a grid of 1 sq. mile blocks or discrete locations 34

37 Figure 3(c): Using commercial land pixel data to obtain extent of commercial activity within a location and the commercial center of the location Figure 3(d): Using Places of Interest in Google Earth to check for the presence of big-box stores in commercial locations 35

38 120 28% % Figure 4(a): Neither Zoning nor Agglomeration Figure 4(b): Only Zoning; No Agglomeration % 60% Figure 4(c): No Zoning; Only Agglomeration More Figure 4(d): With Zoning and Agglomeration 36

39 Notes: SM Supermarket format; SS Superstore format; LA Limited Assortment format. Figure 5: Equilibrium Store Locations in a Simulated Market Shrinking Retail Zone (Area in White represents retail locations) 37