Consumer Benefit of Big-Box Supermarkets: The Importance of Controlling for Endogenous Entry Alessandro Iaria∗ First Draft: August—2013 Current Version: April—2014

University of Warwick, CREST-ENSAE, CRETA, and Institute for Fiscal Studies Abstract Many European countries have instituted regulatory barriers that discourage the entry of out-of-town big-box supermarkets. A key policy question is whether such land use regulations are indeed desirable for society. I evaluate the consumer benefit of big-box supermarkets and contribute to inform the policy debate on the efficiency of land use regulations. Differently from existing papers, I directly address the econometric challenge of endogenous store location in demand estimation: big-boxes are more likely to be present where consumers value them more. I propose a novel framework to consistently estimate demand in the context of endogenous product availability. I estimate preferences for big-boxes in the period 2001-2004 with UK home-scanner expenditure data. I use exclusion restrictions such as “distance from historic incumbents” and “distance from London” to separately identify consumer preferences from retailers’ entry decisions. Exploiting observed big-box entry and subsequent market re-adjustments (e.g., exit of incumbents and changes in incumbents’ prices), I evaluate the consumer benefit of big-box entry. Results reveal a consumer benefit of big-box supermarkets lower than estimated in prior research: 41% of the estimated benefit is due to the implicit selection bias that arises when supermarket locations are endogenous to local consumer preferences. These findings help rationalize Town Centres First, a policy frequently criticized as being anti-consumer.

Keywords: Big-box; demand estimation; endogenous product choice; land use regulation; selection bias; Town Centres First; welfare. ∗ Special

thanks for the support and great discussions to Gregory Crawford, Sascha Becker, Andrés Carvajal, Valentina Corradi, and Fabian Waldinger. I thank also to the members of the productivity sector at the Institute for Fiscal Studies for their hospitality and for allowing me to use their data, in particular to Rachel Griffith and Martin O’Connell for their constant help and suggestions. I am indebted for the insightful discussions and useful comments to Dan Ackerberg, Emek Basker, Dan Bernhardt, Clément de Chaisemartin, Tim Conley, Xavier D’Haultfoeuille, Mirko Draka, Ben Faber, Luigi Pascali, Salvador Navarro, David Rivers, Michelle Sovinsky, and the participants of the Pizza Workshop (Warwick), CWIP (Warwick), NIE Colloquium (Nottingham), 5th ICEEE Conference (Genoa), Applied Seminar (Western Ontario), IO Reading Group (IFS), 40th EARIE Conference (Évora), Autónoma (Bercellona, Applied Economics), Lancaster, CUNEF, CREST, and 12th IIOC. I gratefully acknowledge financial support from the European Research Council (ERC) under ERC-2009-AdG grant agreement number 249529. Data supplied by TNS UK Limited. The use of TNS UK Ltd. data in this work does not imply the endorsement of TNS UK Ltd. in relation to the interpretation or analysis of the data. All errors and omissions are my responsibility. [email protected].

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1

Introduction

The UK grocery market is worth £169.7 billion, accounting for 54.9% of total retail spending. Over the last decades, the growing dominance of supermarkets has been a prominent theme in the nation’s life: from eating habits and health, to the architecture of high streets and the look of the countryside. The national and international ascension of the so-called “big four” chain retailers (Asda, Morrisons, Sainsbury’s, and Tesco) leveraged the out-of-town big-box format.1 On the one hand, out-of-town big-box supermarkets generate £74.1 billion, with Tesco representing the largest private employer in the UK. On the other hand, high street independents and in-town specialist grocery stores are slowly disappearing, weakening town centres.2 Similarly to the UK, analogous patterns can be observed in North America and in Continental Europe.3 The fast diffusion of out-of-town big-box supermarkets is a major policy issue. There are competing views about the impact of big-boxes. The rapid expansion of the big-box format suggests consumers like it.4 At the same time, despite the numerous merits (e.g., wide variety of products, lower prices, free parking), out-of-town big-boxes are perceived to generate negative externalities such as damaging the environment and hollowing out town centres.5 Currently, in the UK the “anti bigbox” view is holding sway: in 1996 the Town Centres First policy was introduced. Town Centres First made it harder for retailers to develop new out-of-town big-boxes, inducing retailers to open smaller supermarkets as close as possible to high streets.6 Town Centres First is frequently studied in relation to its detrimental effects on retailers’ loss of productivity and increased unemployment rates.7 However, we still have a limited understanding of the consumer welfare consequences of such land use regulations. To assess the efficiency of land use regulations similar to Town Centres First, one needs to understand consumer preferences for big-boxes and their services.

[ FIGURE 1] . Figure 1 shows that in England and Wales big-box supermarkets are not evenly distributed across locations: there are Local Authorities that do not host any big-box. Heterogeneity in big-box presence across 1 I define as “big-box” any supermarket with a floorsize larger than 30000 f t2 . This is the floorsize threshold commonly used in the industry to define a big-box supermarket [for instance, Tesco defines “Superstores” and “Hypermarkets” as having an area larger than 31000 and 64000 f t2 , respectively—see Sadun (2011)]. 2 See, for example: IGD Retail Analysis (2013), OFT (2012), and The Portas Review (2011). 3 See, for example: Basker et al. (2012), Bertrand & Kramarz (2002), and Schivardi & Viviano (2011). 4 Which is different from saying that big-boxes are “good” for consumers. 5 See, for example, Kahn & Kok (2014). 6 See Office of the Deputy Prime Minister (2005). 7 See, for example: Cheshire et al. (2012), Griffith & Harmgart (2008), Haskel & Sadun (2012), and Sadun (2011).

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locations raises an econometric challenge in demand estimation. If retailers do not open their big-boxes at random on the territory, then there may be sorting among big-box presence and local preferences (i.e., it may be more likely to observe big-boxes where consumers value them more). I refer to this as to endogenous big-box entry.8 Because one cannot estimate demand for big-boxes in those locations where none is available, then the risk is to estimate demand from its “high-end.” My paper makes two contributions. First, it shows that endogenous big-box entry causes economically meaningful biases in demand estimation.9 This leads me to develop an estimation framework that overcomes the empirical challenge that big-boxes are more likely to be observed in places where consumers value them more. Second, it uses this estimation framework to inform the debate on land use regulations by producing “robust” measures of consumer benefits of big-boxes.10 Results reveal a consumer benefit of big-box supermarkets lower than estimated in prior research: in models that do now account for endogenous big-box entry, 41% of the estimated benefit is driven by selection. These findings help rationalize Town Centres First, a policy frequently criticized as being anti-consumer. Smith (2006) concludes that Town Centres First (TCF) imposes suboptimal store characteristics to consumers. My results, somehow, mitigate Smith (2006)’s. In fact, my conclusions are closer in spirit to those by Griffith & Harmgart (2008): in the post-TCF period, the change in retailers’ entry behaviour towards town centres and smaller formats might be, at least partly, driven by demand considerations rather than by tighter regulations (e.g., if Tesco did not open a new big-box in a certain market, it could be that its expected marginal demand was not “high enough”). Terry Leahy, CEO of Tesco between 1997 and 2010, recently confirmed this idea.11 Furthermore, whatever the actual effect of TCF in preventing the efficient expansion of big-boxes, the associated cost in terms of loss in consumer welfare is sensibly lower than previously thought. My paper relates to the recent literature on endogenous product availability.12 In broad terms, these papers address the consequences of endogenous product availability with structural models of demand and supply.13 Despite the great care taken to model firms’ behaviours, none of the papers in the literature controls for endogenous sample-selection due to product availability when estimating demand. Hence, 8I

call big-box entry “endogenous” because it may be related to the object I wish to estimate: demand for big-boxes. an analogous discussion in the context of estimating Wal-Mart’s effects on unemployment, see Basker (2005). 10 On the effects of land use regulations, see for example: Bertrand & Kramarz (2002), Cheshire et al. (2012), Griffith & Harmgart (2008), Sadun (2011), and Schivardi & Viviano (2011). 11 See Leahy (2012). 12 The most relevant examples are: Beresteanu & Ellickson (2006), Crawford et al. (2012), Draganska et al. (2009), Eizenberg (2012), Ho (2009), Ho et al. (2012), Holmes (2011), Nosko (2011), and Sweeting (forthcoming). For a survey, see Crawford (2012). 13 Demand is “standard,” while firms not only choose prices but also the range of products they are going to sell (for brevity: product availability). 9 For

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existing demand estimates are exposed to selection bias.14 Some papers do not discuss the issue altogether. Others, like Draganska et al. (2009) and Eizenberg (2012), recognize the problem might exist, but proceed by assuming it away (rather than testing for it). Sweeting (forthcoming)—in contrast—assumes the problem away, but only after having provided evidence that, in his application, endogenous sampleselection due to product availability may not be strong. To the best of my knowledge, my paper is the first that explicitly controls and tests for endogenous product availability in demand estimation. Moreover, I show—in the UK grocery industry—how policy implications can drastically change if endogenous product availability is mistakenly ignored in the estimation of preferences. I account for endogenous product availability in demand estimation using classic sample-selection models (i.e., Heckman-type models).15 In contrast, existing papers address the consequences of endogenous product availability with structural models of firms’ behaviours. The estimation of any structural supply-side model requires knowledge of the demand parameters as an input. Typically, due to computational complexities, demand and product availability are estimated sequentially, starting from demand.16 This sequential estimation procedure, with demand first and then product availability given demand, “forces” researchers to estimate demand without controlling for endogenous product availability. The part of the model that deals with product availability is the supply-side,17 but this requires demand parameters to be evaluated. Thus, in a sequential estimation that “starts” from demand, one cannot control for endogenous product availability in such a structural fashion. But, estimating demand without accounting for endogenous product availability, if indeed this is a feature of the data, will generally yield biased estimates of preferences. Consequently, estimated structural models of product choice that rely on such preliminary demand estimates may similarly mislead. To control for endogenous product availability, one must either estimate demand and product availability simultaneously, or start the estimation sequence with product availability. As in the other papers in the literature, my estimation procedure is sequential. The key difference is that I invert the sequence of estimation: I first estimate product availability, and then demand.18 Inverting the sequence’s order 14 This is not to say that their demand estimates are necessarily wrong: the strength of such form of endogenous sampleselection may vary from application to application. 15 The availability of products is modeled by “reduced form” selection equations, and then the demand equations are augmented by inverse Mills ratios to account for potential selection on unobservables. 16 None of the aforementioned papers estimates demand and product availability simultaneously. 17 Demand-side sources of endogenous product availability are studied in the “consideration set” literature. Examples are Draganska & Klapper (2010), Jacobi & Sovinsky (2013), Koulayev (2012), Metha et al. (2003), Nierop et al. (2010), and Sovinsky (2008). A common feature of these papers relates to the “nature” of heterogeneity in choice sets. Consumers face different choice sets not (necessarily) because some of the products are not available to them, but rather because they are not aware of the full set of available products. In the current paper I take a different stand: I consider consumers as fully rational and the only source of choice set heterogeneity being observable product availability (i.e., a product does not belong to the choice set of a consumer only if it is not physically available to her). A different source of demand-side endogenous product availability is studied in appendix [8.1]. 18 Similarly, in the context of modeling trade flows between countries Roberts, Fan, Xu, & Zhang (2011) estimate export

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implies the estimation of product availability without having an estimate of demand, hence the need for a reduced form product availability model. Importantly, once correct demand estimates are obtained, nothing prevents one from doing what existing papers do: one can use them to estimate a structural supply. Hence, the proposed reduced form approach should be seen as a pre-requisite for consistent structural estimation rather than an end in itself. My paper also relates to two additional strands of literature: that on entry and store location in retail19 and that on the “causes and effects” of big-boxes (e.g., IT innovation, cost reduction, competition).20 My paper differs from the former literature in objective: my aim is not to shed light on retailers’ entry behaviour, but rather to control for endogenous entry and its detrimental econometric consequences on demand estimation. With respect to the latter literature, the closest papers are Hausman & Leibtag (2007) and Smith (2006). The authors estimate the consumer benefit of big-box supermarkets, but their estimators do not control for endogenous big-box presence. The analysis proceeds in several steps. I propose a general model of demand in a setting with both endogenous prices and endogenous product availability. The classic discrete choice model of demand, which allows for endogenous prices with individual-level data (e.g., Berry, Levinsohn, and Pakes (2004) [BLP]), is augmented by first stage Heckman’s selection equations. The model allows one to test for endogenous product availability in a tractable way. Identification of the model requires, in addition to instruments for price, exclusion restrictions for product availability. I estimate preferences for big-boxes in the period 2001-2004 with UK home-scanner expenditure data. I use exclusion restrictions such as “distance from historic incumbents” and “distance from London” to separately identify local preferences from retailers’ entry decisions. Estimation results show the importance of accounting for big-box presence in the estimation of supermarket demand: big-boxes are more likely to be located in those markets where consumers value them more. Consequently, if one does not control for endogenous big-box entry, estimated preferences for big-boxes will be upward biased. Exploiting observed big-box entry and subsequent market re-adjustments (e.g, exit of incumbents and changes in incumbents’ prices), I evaluate the consumer benefit of big-box entry. My measure of welfare is the compensating variation of big-box availability. Controlling for endogenous big-box entry, 75% of consumers are estimated to value big-box availability as a reduction in distance to their favourite grocery store of, at least, 14.33%.21 Differently, when endogenous big-box entry is ignored, 75% of condecisions (i.e., endogenous product availability) and demand simultaneously; while Helpman, Melitz, & Rubenstein (2008) estimate their model sequentially starting—correctly—from export decisions. 19 See, for example: Holmes (2011), Mazzeo (2002), Seim (2006), Toivanen & Waterson (2005), and Shu & Singh (2009). 20 See, for example: Basker (2007), Basker (2009), Basker et al. (2012), Basker & Noel (2009), Gould et al. (2005), Hausman & Leibtag (2007), Jia (2008), Kahn & Kok (2014), Matza (2011), Schiraldi et al. (2011), and Smith (2004 and 2006). 21 In the period 2001-2002, among the sample of primary shopping trips, the median “distance to chosen store” is 4.57 km,

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sumers are estimated to value big-box availability as a reduction in distance to their favourite grocery store of, at least, 25%. In conclusion, my paper presents the following novel insights. First, it shows that endogenous product availability can give rise to economically meaningful biases in demand estimation. Second, it proposes and implements a new framework to address this econometric issue. Third, the empirical analysis of the UK grocery industry presents evidence of the practical relevance and policy implications of this specific form of selection bias. In particular, if it is true that big-boxes generate a wealth of benefits for consumers, it is also the case that these are of a smaller order of magnitude than previously thought. These findings contribute to a growing academic literature on the welfare effects of retail regulation, and serve to inform the policy debate on the costs and benefits of the expansion of big-box supermarkets. The remainder of the paper proceeds as follows. Section [2] presents a general framework of demand estimation in the context of endogenous product availability. Section [3] presents the data. Section [4] presents the empirical strategy for the estimation of preferences and the evaluation of consumer welfare. Section [5] reports the demand estimation results. Section [6] presents the evaluation of consumer welfare. Section [7] summarizes, discusses the main limitations, and proposes possible extensions. Appendix [8] provides robustness checks and further estimation results.

2

A Demand Model with Endogenous Product Availability

In this section I first outline, in general terms, a discrete choice model along the lines of BLP (2004) [i.e., a demand model for individual-level data that accounts for price endogeneity].22 Second, I describe a source of sample-selection that may bias classic demand estimators: sample-selection due to endogenous product availability. Third, I propose an estimation procedure that controls for this specific form of selection bias.

2.1

Indirect Utility and Choice Probability

As in the standard model of BLP (2004), the indirect utility individual i obtains from choosing alternative j in location l is defined as: while the 75th percentile is 12.91 km. 22 The equivalent class of models for aggregate data is presented in detail by BLP (1995), Nevo (2001), and Petrin (2002). My point about sample-selection due to endogenous product availability directly applies also to models estimated with aggregate data.

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Uijl


≡ δjl? + Vjl p jl , xijl , ηi + ε ijl ; i = 1, . . . , I; j = 1, . . . , J; l = 1, . . . , L.

(2.1)

Notice how (2.1) implies that individuals have complete preferences: each individual i has a well defined Uijl for any ( j, l ) combination. As discussed in detail in section [2.2], completeness of preferences turns out to be essential for my sample-selection story. δjl? represents the location-specific utility shifter for alternative j. This is the portion of indirect utility associated with ( j, l ) that is common across individuals. The remaining part of (2.1) is idiosyncratic to individual i and it consists of an observable part,

Vjl p jl , xijl , ηi , and an unobservable part (to the researcher), ε ijl . The observable Vjl p jl , xijl , ηi is a function of the alternative’s price in location l, p jl , other observable characteristics of individual i (i.e., demographics), alternative j, and location l, xijl ; and individual-specific parameters, ηi . I assume that individuals make choices over the set of ( j, l ) combinations (a set with J · L elements), which I will call products [see chapter 2 of Debreu (1959)]. In other words, individuals consider alternative j in location l1 as a potentially different object from alternative j in location l2 . For example, an apple sold next to my house is a different product from an apple sold twenty five-minute drive from my house. Index j refers to the physical characteristics of the alternative (e.g., color, weight, and grams of sugar describing the apple), while index l refers to the attributes of the place where alternative j is sold (e.g., features of the specific shop and surrounding area). An important special case arises whenever individuals are “stuck” in a specific location: then individuals do not choose over dimension l, and the choice model reduces to the j dimension [see Golsbee & Petrin (2004)]. In appendix [8.1] I show how, if individuals indeed also choose over dimension l, not accounting for it can lead to biased demand estimates. The unobservable ε ijl is assumed to be distributed i.i.d. extreme value. The probability of product

( j, l ) being individual i’s first-best is given by a mixed logit model [see McFadden & Train (2000)]. Since this is standard in the literature, the estimation details are in appendix [8.2]. The location-specific utility shifter for alternative j is characterized as:

δjl? ≡ αp jl + βx jl + ξ jl ; j = 1, . . . , J; l = 1, . . . , L.

(2.2)


The observable part of δjl? depends on the characteristics of alternative j and location l, p jl , x jl , and on the average preferences of individuals for such characteristics, (α, β). The unobservable (to the researcher) part of δjl? , ξ jl , captures the remaining portion of common utility due to further characteristics of product ( j, l ) not controlled for by αp jl + βx jl . 7

At least since Berry (1994), researchers have typically focused on addressing the potential correlation between p jl and ξ jl in the estimation of (2.2) (e.g., products with more desirable unobservable characteristics, such as design, are sold at higher prices).23 I propose to control for an additional problem that may result in biased estimates of (α, β): sample-selection due to endogenous product availability.

2.2

Sample-Selection due to Endogenous Product Availability

Motivating example. Imagine four equally large and independent locations (a, b, c, d) (i.e., individuals are evenly distributed among locations and each individual can only go shopping in her own location).  The local preferences for big-boxes across locations are δa? , δb? , δc? , δd? . Where, for simplicity, δa? = δb? = 2 and δc? = δd? = 1. There is a unique retailer that can develop a big-box in each location for a cost of 2. If the
retailer decides to build a big-box in any of the locations, its expected revenues are R (δa? ) = R δb? = 3
and R (δc? ) = R δd? = 1.5. The retailer develops big-boxes in locations a and b; but not in c and d. Assume the researcher is interested in learning about the average preferences for big-boxes across locations (i.e., the average δ? ). Whatever the technique used to make inference, the researcher can only estimate preferences for existing big-boxes (i.e., there cannot be any revealed preferences for non-existent   big-boxes). If we define δa? , δb? , δc? , δd? as the population of preferences and δa? , δb? , —, — as the sample of preferences, then: (Population average)

More in general.

2·2+2·1 4

= 1.5 < (Sample average)

2·2 2

= 2.

Any purchase dataset from which a researcher hopes to infer something about in-

dividuals’ preferences can be seen as a set of revealed preferences. Unless every alternative j is available in every location l, the most complete purchase dataset the researcher can collect has to be a sample of revealed preferences (as opposed to the population). In addition, the way revealed preferences are “sampled” from the population is likely not to be “random,” but rather endogenous to preferences themselves. If this is the case, then any estimator of (α, β) that does not control for this form of sampleselection may be inconsistent. The researcher observes a sample of market-specific revealed preferences: if an alternative is not sold in a location, the researcher cannot possibly observe any market-specific revealed preferences for it. Thus, the researcher can only observe—in principle—market-specific revealed preferences for those alternatives that are sold in the location. Furthermore, the sample of market-specific revealed preferences observed by the researcher is endogenous: alternative j is sold in location l only if, there, “enough” individuals are expected to like it 23 For

recent surveys regarding the topic, see Nevo (2011) and chapter 13 of Train (2009).

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“sufficiently,” and to buy it in sufficient quantities. This means that the set of alternatives available in each location may be correlated with individuals’ preferences: for example, Italian food is offered only where there are strong enough preferences for it (see Waldfogel (2007) for a book-length treatment of this observation). Hence, there is endogenous sample-selection over the population of market-specific revealed preferences. Because individuals have complete preferences,

n

δjl?

o J·L jl =1

[the set containing a δjl? for every product

( j, l )] is the population of location-specific utility shifters. Unless every alternative j is available in every n o J·L . location l, the researcher will only have access to a sample from δjl? jl =1 n o J·L . However, the researcher does Generally, the researcher does not directly observe any of the δjl? jl =1  J·L observe the market shares of the available alternatives in each location, S jl jl =1 . See appendix [8.2] for a discussion on S jl . For a collection of non-degenerate market shares, the market share of alternative j in location l can be expressed as:24

S jl ≡ Gjl (δ? , x, θ) . Berry et al. (2013) derive sufficient conditions for the invertibility of G:

δjl =

   δ? ≡ G −1 (S, x, θ) jl jl

if 0 < S jl < 1

  —

otherwise

,

(2.3)

because G −1 is not defined on the boundary of the unit simplex [see footnote 1 of Berry et al. (2013)]. n o  J·L Thus, the researcher can only recover the set δjl jl =1 ≡ δjl? 0 < S jl < 1 , which is smaller than the n o J·L population δjl? whenever some alternative j has zero market share in some l. Moreover, if the jl =1

absence of alternative j from location l (i.e., S jl = 0) depends on its unobservable location-specific utility shifter δjl? (to the researcher, indeed δjl = —), then the researcher can only recover a non-random sample n o J·L from δjl? . In turn, this may induce selection bias in the estimation of (α, β). jl =1

Three remarks. First, notice how the threat of selection bias is independent of that of price endogeneity: even with exogenous prices a researcher could still face sample-selection due to endogenous product availability. 24 G

is defined as (ignoring for simplicity the (x, θ) arguments) [see Berry et al. (2013)]:

[ G1 (δ) , . . . , Gk (δ) , . . . , GK (δ)] : ∆K −→ (0, 1)K , where the index k identifies the products whose observed market shares are non-degenerate and δk ∈ ∆. Hence, G is only defined over (and maps to) the group of products whose observed market shares are strictly included in the unit simplex.

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Second, I confine the sample-selection problem to the location-specific utility shifters. More generally, one could have selection on the whole indirect utility Uijl rather than only on a component of it. Loosely speaking, I restrict attention to a “location-level selection,” instead of a more general “individual-level selection.”25 As a consequence, the resulting econometric issues are limited to the estimation of (α, β). Hence, if the question addressed by the researcher does not require correct inference of (α, β), recovering
 J·L δjl jl =1 is enough to conduct valid inference on Vjl p jl , xijl , ηi . This second remark also holds for the popular case of price endogeneity [see BLP (2004)]. Third, my setting is a special case of treatment evaluation.26 In the evaluation of any “treatment” (i.e., welfare effect of some economically relevant event), researchers must choose whether they are interested in the average treatment effect (ATE) (i.e., representative of the population of preferences) or just in the average treatment effect on the treated (ATT) (i.e., representative of the observed sample of preferences). In those situations where preferences are estimated from a random sample of individuals in which “everyone has access to everything” (in the sense detailed above), then ATT and ATE measures of welfare are equivalent,27 and ATT measures can be used to draw general conclusions.28 In many interesting cases, n o J·L though, researchers are forced to estimate preferences from a subset of δjl? .29 In the latter situajl =1

tion, ATE and ATT measures of welfare differ, and researchers must opt for ATE whenever they wish to draw conclusions that are broadly applicable to any randomly selected individual from the population. My paper talks to those interested in ATE measures of welfare. Also, I refer to “biased estimates” with respect to measures that are representative of the population of preferences.

2.3

Proposed Correction

As motivated in section [1], the selection story outlined in section [2.2] is modeled in a reduced-form fashion as a type II tobit model.30 The availability of alternative j in location l can be expressed as:

a jl

=1



π 1jl

− π 0jl





> 0 = 1 µ j w jl + u jl > 0



,

(2.4)

25 As

shown in appendix [8.1], if individuals choose over the set of products ( j, l )’s, but the researcher incorrectly restricts their choice sets to the j dimension, then the resulting bias could be attributed to individual-level selection. This form of sample-selection is distinct from that described in the current section; the two can coexist. 26 For a survey of the treatment evaluation literature, see Heckman & Vytlacil (2005). 27 In the sense that the observed sample used to estimate preferences is representative of the population. n o J·L 28 It is admissible to estimate preferences from the full set δ? and then, in the simulated counterfactual, to remove some jl jl =1

product from individuals’ choice sets; for example, see Petrin (2002). The key point is to estimate preferences from the full set n o J·L δjl? . jl =1 29 For example, 30 For

see the literature on endogenous product choice discussed in section [1]. a definition of type II tobit model, see chapter 10 of Amemiya (1985).

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where π 1jl − π 0jl is a latent index for the profitability of selling alternative j in location l; 1 (·) is an indicator function, µ j are alternative j-specific parameters, w jl are observable characteristics of product ( j, l ), and u jl is an unobservable error term. Regressors w jl are always observed, regardless of whether a jl is 1 or 0.31 Using (2.2) and (2.3) the observed location-specific utility shifter for alternative j in location l, δjl , can be written as:

δjl =

   αp jl + βx jl + ξ jl

if a jl = 1

  —

otherwise

,

(2.5)


where I assume that p jl , x jl is not observed if a jl = 0 (e.g., if an alternative is not sold in a certain location, then, typically, it is not possible to know its counterfactual price without additional assumptions). In the tobit terminology, relationship (2.4) is a selection equation while (2.5) is a truncated outcome equation. In order to make the model operational, I make three standard assumptions [see section 19.6.2 of Wooldridge (2010)]:


  1. u jl , ξ jl is independent of w jl . u jl is i.i.d. N (0, 1). E ξ jl u jl = γ j u jl .
  2. There are valid instruments z jl for p jl , x jl such that E z jl ξ jl = 0; i.e., some instrument for price. 3. At least one element of w jl is not included in z jl ; i.e., some exclusion restriction for selection. Assumption (1) imposes three restrictions. It requires the marginal distribution of the error term in (2.4) to be standard normal and to be independent across locations. This allows one to estimate µ j , and the derived inverse Mills ratio, parametrically via a probit model. This strong distributional assumption greatly simplifies the empirical implementation of the product availability model. On the one hand, maintaining the assumption of independence across locations, one could relax normality [see, for example, Das et al. (2003)], even though the practical payoff from doing so (balancing for simplicity) is not clear. Moreover, from an economic perspective, the message of the paper is not affected by normality. On the other, the assumption of independence across locations is economically restrictive. Indeed, in most cases the decision of selling alternative j across locations is made by the same firm. Hence, u jl should be allowed to be dependent across locations. For the time being I assume 31 This can limit the use of some alternative j’s characteristics as regressors in equation (2.4). Typically, this is the case for those characteristics that are thought to be endogenous (i.e., easily modified by firms in the short run). For example, if alternative j is not sold in location l, then its price p jl might not be easy to infer. In contrast, locations’ characteristics should not be subject to this problem.

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independence, but I am working to allow for spatial dependence of u jl along the lines proposed by Wang et al. (2013).   The assumption on E ξ jl u jl imposes linearity in the regression of the unobserved portion of utility, ξ jl , on the unobserved portion of the latent profitability index, u jl . In line with the suggestion of BLP
(2004), I do not impose any specific distribution for ξ jl p jl , x jl . Moreover, it is necessary not to have any endogeneity issue in the selection equation. Assumption (2) is standard in the BLP framework. With valid instruments, one can account for the potential correlation between p jl and ξ jl using a 2SLS estimator. Notice that, jointly, assumptions (1) and (2) do not particularly restrict the identification requirements on ξ jl with respect to a standard BLP framework. Assumption (3) ensures that selection and preferences are separately identified. Notice that, jointly with assumption (1), it is quite stringent: the exclusion restriction cannot be either an element of z jl or related to ξ jl . In other words, it is required some exogenous (with respect to preferences) “shock” to the availability of alternative j across locations. A natural question at this point is: when can sample-selection be ignored and (α, β) be consistently estimated via a standard BLP procedure (that is, given assumption (2), when can one estimate by 2SLS equation (2.5) on the selected sample of δjl ’s)? The crucial condition for consistent estimation of (α, β) by 2SLS of (2.5) is [see section 19.4 of Wooldridge (2010)]:

  E a jl z jl ξ jl = 0.

(2.6)

  It follows, then, how assumption (2) alone may fail to deliver consistency of the 2SLS estimator: E z jl ξ jl = 0 does not necessarily imply (2.6). There are two special cases in which assumption (2) alone implies con
dition (2.6). First, if selection is at “random:” a jl is independent of z jl , ξ jl . Second, if selection is on   “observables:” E ξ jl z jl , a jl = 0; i.e., a jl can be correlated with z jl but not with ξ jl . If selection is on “unobservables” (i.e., u jl is correlated with ξ jl ), then to satisfy condition (2.6) the researcher needs to make further assumptions along the lines of assumptions (1) and (3). In addition, she needs to augment estimating equation (2.5) with the inverse Mills ratio:

  δjl = αp jl + βx jl + γλ µ j w jl + error jl .

(2.7)

  The researcher does not directly observe the inverse Mills ratio, λ µ j w jl , so she needs to estimate it. Given assumption (1), estimating in a first-step the probit model (2.4) allows one to compute b λ jl = 12

  λ µ b j w jl and to plug it into (2.7).32 Then, in a second-step, equation (2.7) can be estimated by 2SLS on the selected-sample of δjl ’s. Importantly, one can test the hypothesis of “no selection problem,” H0 : γ = 0, using the usual 2SLS b. This is a crucial difference with respect to the existing literature. Even authors who are t-statistic for γ extremely clear about the possibility of sample-selection due to endogenous product availability, usually assume the problem away without gathering much supporting evidence.33 My proposed method, in contrast, allows one to test for selection on unobservables in a tractable way. Equation (2.7) aids in building up intuition with respect to the selection bias. If sample-selection is mistakenly ignored, then the inverse Mills ratio will be an omitted variable. Hence, loosely speaking,  
b can be expected to be worse, when the correlation between p jl , x jl and the selection bias on b α, β   λ µ j w jl is stronger. If instead, the correlation between the included regressors and the inverse Mills ratio is weak, then only the estimated intercept will be affected.

3

Data

I estimate demand model (2.1), (2.4), and (2.7) using three main sources of data.34 Broadly, each source of data contains information about one dimension of the the demand model: 2001 English Census and ODPM (2002) (locations), Institute of Grocery Distribution (supermarkets), and Kantar (formerly TNS) World Panel (individuals). In this section I describe each source of data and how I combine them.

3.1

Location-Definition and Location-Level Data.

I define a location l as an English or a Welsh town centre (or high street). This decision is motivated by existing research on the topic [Griffith & Harmgart (2008), Office of the Deputy Prime Minister (2004) [ODPM], and Schiraldi et al. (2011)] and by the following observations. The definition of location is particularly important for the selection model (2.4). In my demand model, individuals have preferences for supermarkets’ locations. Hence, retailers may choose where to position their supermarkets taking into consideration such preferences. In order to control for sampleselection due to endogenous big-box presence, location-definition has to be as close as possible to what 32 This first-step greatly depends on the application and the assumptions the researcher is ready to make about the joint distribution of the unobservables u jl and ξ jl across j’s [i.e., assumption (1)]. If there are many selection equations, it might be sensible to consider them jointly as a system, and then to have a multivariate probit, for example. In this case, also the relationship between the u jl ’s and the ξ jl ’s might be more complex. Because in my application I only have one selection equation, I limit the discussion to the simplest case of independence of the unobservables across j’s. 33 See, for example, Draganska et al. (2009) and Eizenberg (2012). 34 I kindly thank the Institute for Fiscal Studies for allowing me to use the data described in this paper. Above all, I am particularly grateful to Rachel Griffith.

13

retailers consider as such when developing supermarkets. Since the institution of Town Centres First in 1996, which requires retailers to open their new supermarkets as close as possible to town centres, the major retailers have indeed been opening their new supermarkets mainly nearby town centres.35 Data about English and Welsh town centres and their demographics come from the ODPM and the Office of National Statistics (ONS). They refer to the period 2001-2002. I have complete data for 753 out of 973 town centres in England and Wales [see Griffith & Harmgart (2008) for details on these data]. The “full sample” panel of table 1 reports summary statistics of these data.

[ TABLE 1] . “Density” refers to the number of people per hectare. “Area” is the town centre’s area measured in hectares. “Closest” is the distance, measured in tens of km, of the town centre to its closest neighboring town centre. Each town centre belongs to one of 320 Local Planning Authorities (LPAs); on average a LPA has 2.7 town centres. The LPA which encompasses the highest number of town centres, 16, is Leeds.36

3.2

Alternative-Definition and Supermarket Data

Supermarket data come from the Institute of Grocery Distribution (IGD). The data list supermarket characteristics of all chain stores and all other large stores, as well as around 80% of independent smaller stores. I use IGD data on 8971 supermarkets up to 2004 (the last year these data were collected by IGD). I match the supermarket data with the town centre data via the address information.37 Following Hausman & Leibtag (2007), I define alternative j as simply “small” or “big.” Small refers to supermarkets (belonging to any retailer) with floorsize smaller than 30000 f t2 ; big to larger than 30000 f t2 .38 It follows that my empirical definition of product is ( j, l ) = (format-size, town centre): big is present in a town centre only if there is, somewhere in its territory, at least one big-box supermarket. Similarly for the presence of small. Notice that, given this definition, the “switch” from abig,tc = 0 to abig,tc = 1 in model (2.4) only happens when town centre tc passes from not having any big-box to having at least one. It does not make any difference if town centre tc hosts one or ten big-boxes, in either 35 Since 1996, the entry behaviour of major retailers has dramatically changed: in 1994 only around 25% of Tesco’s new supermarkets were in-town, by 2000 virtually all of them. Similarly, Sainsbury’s passed from 12% to 85% of in-town new openings from 1995 to 1999 [see Cheshire et al. (2012)]. 36 London is divided into many different LPAs. 37 Each supermarket is matched to the closest, in Euclidean terms, town centre. 38 This is the floorsize threshold commonly used in the industry to define a big-box supermarket [for instance, Tesco defines “Superstores” and “Hypermarkets” as having an area larger than 31000 and 64000 f t2 , respectively—see Sadun (2011)].

14

case abig,tc = 1. Using this definition, in 2002, small supermarkets were present in 100% of the 753 town centres, while big-box supermarkets were present in 58.83% of them. Given that j = small is present in 100% of the town centres, I must only estimate a binary probit for j = big. My town centre-specific data (i.e., the regressors wbig,tc in model abig,tc ) is a single cross-section from period 2001-2002, thus I cannot explain entry of big-boxes too far back in time. Moreover, as detailed in section [3.3], my household-purchase data are from period 2001-2004,39 hence I do not actually need to go too far back in time to account for big-box presence. Consequently, I restrict the original sample of 753 town centres to the 352 in which: (a) there was no entry of any big-box in the period prior to the introduction of Town Centres First (TCF) and (b) there was some entry (at least a small corner shop) in the post-TCF period (i.e., 1996-2004).40 In addition to my inability to explain entry prior to 1996, restrictions (a) and (b) make sure I group together “similar objects” in the entry equation.41 Figure 2 shows the geographic distribution of big-boxes both in the full and in the restricted samples.

[ FIGURE 2] . The right panel of table 1 summarizes the demographics of the restricted sample of 352 town centres. Within the restricted sample of town centres, table 2 summarizes the observable supermarket characteristics, separately for big-boxes and for small supermarkets.

[ TABLE 2] . Supermarket characteristics of combination ( j, tc) are computed as averages among all the supermarkets of format j present in town centre tc. The construction of the “price index” is discussed in appendix [8.3]. “Distance” is the average Euclidean distance of town centre tc from the postcodes of the sample households. Because of assumptions (1) and (3) from section [2.3], in case of many different j’s (i.e., different retailer-format combinations), an exclusion restriction that explains entry but not preferences requires 39 2001

was the first year in which these data were collected. decision of using the introduction date of TCF as a cutoff is motivated as follows. Since the institution of TCF in 1996, the entry “rules” for big-box supermarkets changed. Before 1996, retailers could open their big-boxes without requiring any formal municipal approval. After 1996, retailers interested in opening a new big-box have to send an application to the competent Local Planning Authority. Each Local Planning Authority, then, decides whether to grant or to reject the various applications received. In other words, big-box entry before 1996 and after 1996 appear as two very different endeavours. 41 (a) reduces the level of heterogeneity across the town centres with a big,tc = 1 (i.e., in the full sample, some of the 1’s are due to big-boxes developed at the beginning of the 20th century, while others are due to big-boxes developed over a hundred years later). (b) reduces the level of heterogeneity across the town centres with abig,tc = 0: some constantly attract the interest of retailers (i.e., small supermarkets keep entering), while others do not. 40 The

15

data I do not have at the moment. As an exclusion restriction, I would need a variable that varies per retailer within each town centre. For instance, retailer-specific application data (in relation to Town Centres First) or retailer-specific logistic data would be a start. Moreover, model (2.4) is a reduced form for entry decisions. Considering chain retailers separately would imply the necessity of thinking of strategic interactions between the various players across markets (i.e., some complex error structure for u jl across both j and l). Aggregating all the retailers into one category reduces issues about strategic interactions, making assumptions (1)-(3) easier to digest. My search for simplicity in implementing model (2.4) can be motivated in two ways. First, the starting point of this paper is rooted in the complexity of existing entry models that forces researchers to ignore sample-selection in demand estimation. Second, my aim is not to shed light on retailers’ entry behaviour, but rather to control for endogenous entry and its detrimental econometric consequences on demand estimation. Once correct demand estimates are obtained, nothing prevents one from doing what existing papers do: one can use them to estimate a structural supply. Hence, the proposed reduced form approach should be seen as a pre-requisite for consistent structural estimation rather than an end in itself.

3.3

Household-Purchase Data.

Individual-level data about supermarket choice are from the Kantar (formerly TNS) World Panel for years 2001-2004 [see Leicester & Oldfield (2009) for details]. My sample report information about 10083 English and Welsh households. Households record in which supermarkets they shop and what they purchase. Prices are obtained from till receipts. For each household, I aggregate over the sample periods 2001-2002 and 2003-2004 all the observed shopping expenditures at the ( j, tc) level, so to obtain a household-specific expenditure-ranking [see Dubois & Jodar-Rosell (2010)]. This is done for the following reasons. The sample contains millions of shopping trips. A shopping trip is a household going shopping to a supermarket. It is infeasible to use the entire sample without some “reduction.” One strategy is to draw a random sub-sample of shopping trips, and then to estimate the model over it [see Griffith et al. (2010)]. I do not follow this strategy because many households appear to go shopping systematically both to big-boxes and to smaller supermarkets. This behaviour is known as two-stop shopping, and it is the object of current research [see Schiraldi et al. (2011)]: on a weekly basis, households go for their main shopping to a big supermarket, and then top-up from smaller ones. Given such dynamic behaviour, it would then be problematic to estimate households’ preferences only on a subset of their shopping trips. Another strategy is to sample over households, rather than shopping trips (so to get all the shopping 16

trips of a household). This leaves open the questions of how to define “main” and “top-up” shopping trips and how to develop an appropriate dynamic model [see Schiraldi et al. (2011)]. Given the logit assumption for the choice model, it is possible to handle rankings of choices (i.e., first-best, second-best, etc.) [see Beggs et al. (1981), BLP (2004), and Train & Winston (2007)]. I create household-specific rankings of expenditures and let the data disentangle main from top-up. The ( j, tc) combination where the household is observed spending the highest total amount over the sample period is her first-best or main shopping destination. Similarly for the second-best destination and so on. This aggregation alleviates dynamic concerns but also aids the identification of the random coefficients. Indeed, both BLP (2004) and Train & Winston (2007) report that they were unable to identify any random coefficient unless they used data on rankings of choices (i.e., beyond the first-best). In the computation of the contraction (see equation (8.3) in appendix [8.2]), using “sample” market shares instead of “true” market shares introduces an additional layer of variability in the estimation procedure (on top of sampling variance and simulation variance) [see Berry et al. (2004), Berry & Pakes (2007), and Gandhi et al. (2013)]. This problem worsens the smaller is the sample of observations over which market shares are computed and the larger is the total number of products. As in Golsbee & Petrin (2004), I must compute market shares from my sample of households. In my application, the total number of ( j, tc) combinations is of the order of hundreds; but by increasing the interval of time over which I aggregate, the number of observed shopping trips to each ( j, tc) combination gets larger, giving a better approximation of the true market-shares. Therefore, a “long” aggregation over time is required to increase the reliability of my market share measures. Similar observations hold for the construction of price indexes (see appendix [8.3] for details about the construction of price indexes).

[ TABLE 3] . Table 3 reports summary statistics about household supermarket-choice behaviour. Individual households are observed to choose up to seven different ( j, tc) combinations. There is a big gap, in terms of average total expenditure, between the main shopping combination (i.e., the first in table 3) and the top-up ones (i.e., anything below the first-best in table 3). Many households seem to go shopping systematically to different combinations: in the period 2003-2004, 35% of households divided their shopping at least among two ( j, tc) combinations. “Same Town Centre where Living” indicates if the specific ( j, tc) combinations chosen by the household are located in the same town centre where she lives. Around 57% of the households go for their main shopping to town centres different from those where

17

they live. As discussed in section [2.1] and in appendix [8.1], I do not assume households to be “stuck” in the specific town centre where they live (i.e., I do not exclude from the sample those shopping trips towards different town centres). I assume each household to make choices from the full set of ( j, tc) combinations. Households are assumed to be free to go shopping wherever they like: for example, near their workplace, or somewhere in between their workplace and where they live. This assumption implies that “not observing” households going shopping very far from their house is itself a choice outcome, rather than a preference-unrelated constraint. Differently, one could create household-specific choice sets based on some distance from their house town centre (e.g., 20 Km). As shown in appendix [8.1], if this assumption were wrong, then the estimator would be inconsistent. I consider more profitable not to impose such restriction and to learn from the data why certain Pri,j,tc (θ, δ? ) ' 0 (e.g., household i lives very far from town centre tc). As a robustness check, I am planning to repeat the analysis assuming different household-specific choice sets (e.g., 40 km, 30 km, and 20 km from their house town centre).

4

Empirical Strategy

In this section I describe the exclusion restrictions used to separately identify entry from preferences for big-boxes and the counterfactual exploited to measure consumer benefit of big-box supermarkets.

4.1

Exclusion Restrictions for Big-Box Entry

In the context of my application, (2.4) represents a model for entry of supermarket-format j in town centre tc. As explained in section [3.2], supermarket-format “small” is present in each of the 352 town centres (thus, no selection correction is needed for j =small). In the estimation of model (2.4), one requires some variable correlated with entry of big-boxes but not with consumer preferences. I discuss three groups of exclusion restrictions that have appeared in the literature, and argue why I adopt only two of them.

Land use regulation constrains retailers’ entry decisions.

The first exclusion restriction is used, for

example, by Griffith & Harmgart (2008). Since 1996, if a retailer wants to open a big-box supermarket, it has to apply to the relevant Local Planning Authority, and then the request can either be granted or rejected. In case of rejection, contrary to the willingness of the retailer (likely to be correlated with town centre’s preferences for big-boxes), the big-box supermarket does not open. After rejection, if the retailer is still very motivated about entering in the specific town centre, it is forced to open a smaller super18

market. Hence, ideally, a rejection would represent an exogenous shock to entry of big-boxes. Moreover, because the decision process is decentralized to Local Planning Authorities, and Local Planning Authorities are heterogeneous in their rejection rates, one could exploit local variation in the “number of granted applications” to aid the separate identification of entry from preferences. In the estimation of regressions similar to my entry model (2.4), Bertrand & Kramarz (2002), Cheshire et al. (2012), Sadun (2011), and Schivardi & Viviano (2011), question the validity of “number of granted applications” as an exclusion restriction. For example, stronger local preferences for big-boxes may translate into higher investments into lobbying the Local Planning Authority (LPA) to increase its acceptance rate. Similarly, in those places where households like big-boxes more, the LPAs—being an expression of the households who live and shop there—may just be more “lenient” in judging big-box applications. To address such issues, Bertrand & Kramarz (2002), Sadun (2011), and Schivardi & Viviano (2011) instrument “number of granted applications” with the conservatives’ share of votes in the last local elections. They argue that conservatives are reluctant to approve the opening of big-box supermarkets because of their electorate made of owners of small shops and businesses. In my specific case, where preferences are the focus of the analysis (the aforementioned papers focus on unemployment and other sectoral performance indicators), it would be hard to advocate that the share of votes of any political party in local elections is uncorrelated to local preferences for big-boxes; in fact such preferences are “made” of the same households who vote at the elections. I would need to exploit only those LPAs where last election’s outcomes were uncertain, but this would reduce my sample size below any acceptable threshold.42 Consequently, I decide not to exploit Town Centres First as an exclusion restriction.

Retailers soften competition by geographic differentiation. This is the basic Hotelling (1929)’s tradeoff: on the one hand, firms wish to position their products (in characteristic space) in those “locations” where demand is strong; but on the other, the more crowded of competitors a “location” is, the higher the incentive to position their products elsewhere in order to soften competition. Many empirical papers show strong evidence of Hotelling (1929)’s tradeoff in different retail markets.43 Zhu & Singh (2009), for instance, conclude: “The analysis provides insights into a fundamental tension faced by these firms [i.e., Wal-Mart, Kmart, and Target], namely the desire to be in attractive locations while also obtaining insulation from competition through spatial differentiation.” Retailers’ “desire to be in attractive locations” is likely to generate selection bias in demand estimation. I then propose to use “average dis42 I

thank Luigi Pascali for pointing this out. example: Mazzeo (2002) for motels, Seim (2006) for video retailers, and Zhu & Singh (2009) for discount retailers.

43 For

19

tance from historic incumbents” as an exogenous source of variation to “location of subsequent big-box entry.” As argued in section [3.2], I estimate my model only on those 352 town centres in which there were no big-boxes until the end 1996, when Town Centre First was introduced. I define as “historic incumbents” those big-boxes that were developed prior to 1997. Notice that the historic incumbents are not included in my estimation sample (i.e., I do not use them to estimate preferences for big-boxes). In other words, my demand system is not defined over the historic incumbents (i.e., they do not belong to households’ choice sets). My thought experiment is the following: a retailer wishes to open a big-box somewhere in my sample of town centres. First, it looks for those town centres with the strongest expected demand for big-boxes. Assume there are two such town centres with the same expected demand, but that one if further away than the other to well established big-boxes. Then, the retailer has an incentive—independently of local preferences—to develop its big-box in the more isolated of the two town centres.

Distance from logistic network.

This is an exclusion restriction inspired by Graff & Ashton (1994)’s

research: the geographic diffusion of chain retailers is not random, they usually expand “gradually,” radiating from their headquarters to contiguous areas; always maintaining high store density and proximity to their logistic networks. Since then, researchers have been exploiting this idea: beyond local preferences, different town centres may be “targeted” by chain retailers at different times, depending on their distance from the headquarters.44

[ TABLE 4] . Table 4 shows that, in the UK, the average year of entry of big-boxes is lower in the south (e.g., London) than in the north. I propose to use “distance from London” as an exclusion restriction for big-box entry. Notwithstanding their frequent use, geographic exclusion restrictions have fairly been criticized by researchers. For a discussion, see Basker (2006) and Sachs (2003). It is usually simple to convince that “geographic distance” correlates with the outcome of interest. The tricky bit is to persuade that “geographic distance” does not correlate also with every other outcome. To mitigate worries about the robustness of the analysis, my strategy is to re-estimate the model relying on different sets of exclusion restrictions showing that, qualitatively, results do not change. To this end, I am also gathering data on the coordinates of UK highways. I plan to use “distance from closest highway access” as an additional 44 See,

for example: Holmes (2011) and Zhu & Singh (2009).

20

exclusion restriction: avoiding big-boxes from stocking-out may be more costly in some town centres than in others, depending on their proximity to the network of highways.45

4.2

Measuring Consumer Benefit: Observed Counterfactual

The primary objective of this paper is to measure the consumer benefit of big-box supermarkets. Welfare analysis typically requires the formulation of counterfactuals, in my case something like the entry of big-box supermarkets in town centres where none is present. Instead of attempting the formulation of potentially surrealistic counterfactuals, I exploit those readily available in my data: from 2002 to 2004 I observe, in 17 of the 304 town centres previously with no big-boxes, the opening of new big-box supermarkets. I measure consumer welfare of big-box supermarkets by exploiting observed entry (as opposed to simulated entry) of big-boxes in town centres in which that format was previously absent. I do so mainly for two reasons. The first was pointed out by Nevo (2011, section 6.1). The counterfactual I need, in order to measure consumer welfare, is a change to households’ choice sets (which, in my case, is a collection of (supermarket-format, town centre) combinations). My demand model assumes logit errors, and these have been criticized as inappropriate for such a task [see Petrin (2002), Berry et al. (2004), and Berry and Pakes (2007)].46 The second reason relates to the complexity of the adjustments following the entry of new big-boxes. A model of strategic interactions among retailers would unfold over many dimensions (e.g., where to open the new store, how big it should be, what ranges of products it should offer, at which prices) and require strong and potentially unrealistic assumptions to be implemented.

Nevo (2011, section 6.1)’s example.

As Nevo (2011) shows, even with a simple logit model (i.e., no

random coefficients), it is possible to correctly evaluate the welfare effects of a changing choice set. In order to do so, one would need to observe market shares prior and market shares post choice set change. Usually, researchers only have one set of market shares: either pre or post-change; and then “simulate” the remaining set with their estimated model. It is in the market share simulation step that the logit model becomes inappropriate. Then, given wrong simulated market shares, wrong welfare computations follow. Differently, if the logit model is “fed” with the correct market shares pre and after choice set change, then the welfare calculations will be correct. Nevo (2011) makes this point with the following example, the popular red-bus blue-bus example. 45 Stock-outs 46 I

may be extremely detrimental for the profitability of grocery retailers, see Matsa (2011). thank Tim Conley and David Rivers for the insightful discussions on this issue.

21

• Factual data. Imagine to observe data about decisions between “car” and “red bus” in some commuting situation, and that market shares are 50-50. In other words, Pr [car] = Pr [red bus] = 0.5. F = δF Assuming a logit model and normalizing the indirect utility of car to zero, one gets δcar red bus =

0 (where “F” stands for “factual”). The expected consumer surplus of any individual is then WF = ln [exp (0) + exp (0)] = ln [2]. • Simulated counterfactual data. Imagine to simulate data about a situation in which individuals’ choice set includes also an identical bus to the red (in terms of their preferences), the blue bus. F = For this task researchers normally use the logit model estimated with “factual data,” hence δcar F S δred bus = δblue bus = 0 (where “S” stands for “simulated”), which implies simulated market shares

of 33-33-33 and expected consumer surplus of WS = ln [exp (0) + exp (0) + exp (0)] = ln [3]. • Observed counterfactual data. Instead of simulating the introduction of the identical (and redundant) blue bus, imagine to observe such an event. According to intuition, assume individuals to behave so that Pr [car] = 0.5 and Pr [red bus] = Pr [blue bus] = 0.25. Given these new data and C = 0, one gets δC C normalizing again δcar red bus = δblue bus = ln (0.5) (where “C” stands for “counter-

factual”). The expected consumer surplus is then WC = ln [exp (0) + 0.5 + 0.5] = ln [2]. • Welfare effects of redundant blue bus. Comparing the estimated expected consumer surpluses WC and WF , one gets 4WCF = 0. Thus, the simple logit model estimated on the correct factual and counterfactual market shares delivers the right answer. Differently, comparing the estimated expected consumer surpluses WS and WF , one gets a wrong answer, 4WSF = ln [3] − ln [2] > 0. The period covered by my sample, 2001-2004, was a period of great activity from the part of retailers. Many of them were expanding. In my sample, in the period 2003-2004, 17 town centres passed from having only small supermarket formats to hosting big-boxes. By observing market shares pre-entry (i.e., 2001-2002 data) and market-shares post-entry (i.e., 2003-2004 data), I compute two separate sets of δ’s: δ02 and δ04 . Moreover, all the features of the 2003-2004 scenario are observed (e.g., where the new supermarkets are, their size, new equilibrium prices) so that the “regressors” used to describe the counterfactual do not rely on further assumptions (required in the case of simulated counterfactuals).

5

Estimation Results

In this section I present results from the estimation of the household-specific indirect utility model (2.1), the big-box entry model (2.4), and the location-specific utility shifter model (2.7). The majority of the 22

section is devoted to the discussion of the consequences of sample-selection due to endogenous big-box presence on the estimation of model (2.7).

5.1

Computation of Location-Specific Utility Shifters

The first step in the procedure outlined in section [2.3] and appendix [8.2] is to obtain an estimate of the selected sample of δ01−02 and δ03−04 . Here I summarize the results. The utility specification I estimate via maximum likelihood (plus contraction mapping) is:

t t t Ui,j,tc = δj,tc + θdistancei,tc + εti,j,tc ,

t where distancei,tc is the Euclidean distance of household i’s home (in 100 km) from town centre tc in

period t (i.e., 2001-2002 and 2003-2004). It is the basis used for the computation of the average distance of households from a town centre (see table 3). The vectors of location-specific utility shifters, δ01−02 and δ03−04 , have 391 and 408 elements (i.e., the sizes of the choice sets), respectively, in 2001-2002 and 2003-2004. As discussed in section [4.2], my empirical strategy for measuring consumer benefit of big-boxes is to exploit actual entry of big-boxes in 2003-2004 in town centres where there was none up to 2002. Since this involves an intertemporal comparison of welfare, I address the question from the perspective of the most recent measure of preferences: b to compare welfare in 2001-2002 and I estimate θ from the 2003-2004 data and then use this estimate, θ, 2003-2004 [see Fisher & Shell (1972)].47 The estimate of θ is θb =-8.118 and its standard error is 0.0634. Parameter θ is the disutility household i gets by marginally “moving her house away” from town centre tc. Figure 3 summarizes the δ01−02 and δ03−04 estimates obtained with contraction (8.3).

[ FIGURE 3] . Figure 3 is useful to build up intuition about what to expect from the regressions for the estimation of t t , indeed, is the dependent variable. Both δt the preference parameters (α, β): δj,tc big,tc and δsmall,tc sensibly

increased over time, with the location-specific utility of small supermarkets increasing more than that I estimate θb and δ03−04 from 2003-2004 data via ML and the contraction (8.3). Then, given θb and 2001-2002 data, I obtain δ from a further iteration of the contraction (8.3). 47 First,

01−02

23

of big-boxes.48 Such positive and different trends for big-boxes and for small supermarkets warrants t .49 The comparison of various the inclusion of time-specific format constants in the specification for δj,tc

specifications with and without time-specific format constants is examined in appendix [8.4].

5.2

Model of Big-Box Entry

Table 5 reports estimates of the marginal effects from binary probit model (2.4):

ytc = 1 (µwtc + utc > 0) , where ytc equals 1 if at least one big-box is present in town centre tc, 0 otherwise. The model is estimated using the set of regressors summarized in table 1 plus the exclusion restrictions discussed in section [4.1]. Regressors wtc are evaluated at their means. Standard errors are bootstrapped and clustered at the Local Planning Authority level (2000 repetitions).

[ TABLE 5] . Column (i) lists the estimates of the probit model with exclusion restriction “average distance from historic incumbents.” Column (ii) reports results of the probit model with exclusion restriction “distance from London.” The idea is to check results’ robustness using alternative identifying assumptions. The fit of the model is good (Pseudo-R2 = 0.24) and most of the marginal effects have the expected, intuitive sign. The more populated a town centre, the higher the chance of having a big-box supermarket in the neighborhood; but the more densely populated, the lower the chance of big-box entry. Big-box supermarkets are more likely to be present further away from the centers where households live. Locations 48 For

? ’s has to be normalized to zero: the numeraire. This is equivalent to subtracting identification purposes, one of the δj,tc

? δnumeraire

? ’s (i.e. δt ? ? t from all the other δj,tc j,tc = δj,tc,t − δnumeraire,t ). As discussed by Nevo (2003), a positive time trend in δj,tc ? ? could be either due to an increase in δj,tc,t or due to a decrease in δnumeraire,t (or both). This has important consequences for ? ’s stay constant and simply δ? intertemporal comparisons of welfare: if all the δj,tc,t numeraire,t decreases, then households might t . It is not possible to reject with certainty actually be worse-off in 2004 with respect to 2002; despite the positive time trend in δj,tc this hypothesis. However, I make a conservative choice of the numeraire so to suggest the opposite story: the positive time t is due to an increase in δ? ? trend in δj,tc j,tc,t rather than a decrease in δnumeraire,t . I chose the numeraire to be ( small, Tonsbridge ): its market share was the smallest in 2002, and it actually increased by 287.21% while the average market share of “small” decreased by 5.85% (and, by construction, that of “big” increased). h i

t stable preferences over t, a positive trend in Etc δj,tc can be explained in terms of a favourable change in either h i t observable (i.e., xtj,tc ) or unobservable (i.e., ξ tj,tc ) characteristics (or both). In other words, any trend in Etc δj,tc can be due to either observed or unobserved changes in quality (or anything in between) [see Nevo (2003)]. In performing intertemporal comparisons of welfare, it is then important to account for the welfare effects induced by systematic changes in ξ tj,tc (i.e., h i t a unobserved quality). One way to capture time trends due to changes in Etc ξ tj,tc is to include in the specification for δj,tc time dummy interacted with a supermarket-format dummy (i.e., what I call “time-specific format constants”). 49 Given

24

that are more isolated from competition (i.e., with a higher average distance from historic incumbents) are associated with a higher probability of big-box entry. The likelihood of big-box entry is increasing in distance from London.50 In what follows, the estimates reported in table 5 are used to construct inverse Mills ratios to account for possible sample-selection due to endogenous big-box presence as outlined in section [2.3].

5.3

Selection Bias due to Big-Box Presence

t , both without sample-selection correction [model In this section I report estimates of the model for δj,tc

(2.2)]:

t δj,tc = τjt + βxtj,tc + ξ tj,tc ,

and with sample-selection correction for j =big-box [model (2.7)]:


t t t δbig,tc = τbig + βxtbig,tc + γλ µt wttc + errorbig,tc .

t The latter model for δbig,tc is estimated in two steps. In the first step, I estimate the entry model (2.4)

twice: once on the 2002 sample and once on the 2004 sample (i.e., results reported in table 5). Given
these estimates, I compute the inverse Mills ratio λ µ bt wttc , t =2002 and 2004. Standard errors are
bootstrapped to account for the replacement of µ = µ02 , µ04 with its estimate.51 04 02 , and δ04 . It is 02 For each town centre tc there can be up to four observations: δsmall,tc , δsmall,tc , δbig,tc big,tc

likely that these four location-specific utilities are correlated within town centre. I control for this possibility in two ways. First, I exploit such correlation structure to improve the efficiency of the estimator (i.e., FGLS estimator). Second, in the computation of the standard errors: within each bootstrap repetition, a “draw” from the original sample is a town centre. This is equivalent to cluster the standard errors at the town centre level. 50 I

only study big-box entry in the last period of the data (i.e., after 1996). Table 4 suggests that the geographic expansion of big-boxes moved north in time. 51 Bootstrap estimates are performed over 2000 repetitions (i.e., the two-step sequence of the estimation procedure, first µt big and then (α, β, γ), is repeated 2000 times).

25

[ TABLE 6] . t without selection correction. Big*2002 is the interColumn (i) refers to the estimation of the model for δj,tc

action of a dummy for big-box and a dummy for t = 2002. Similarly for Big*2004 and for Small*2004.52 Each of these constants (i.e., small in 2004, big in 2002, and big in 2004) is measured relatively to “small h i t 02 − ξ 02 , where ξ t ≡ E ξ in 2002.” For instance, “big in 2002” can be interpreted as ξ big tc j j,tc . For brevity, small 02 ). Column (i) suggests that the unobserved qualities of I call these interactions τjt s (e.g., Big*2002≡ τbig

big-boxes and of small supermarkets were approximately similar in 2001-2002 (i.e., observed characteristics explain differences in average utility between big-box and small supermarkets pretty well); while in 2003-2004 both big-box and small supermarkets improved their unobserved quality relatively to 20012002. Specifically, in the 2002-2004 period, big-boxes improved their unobserved quality twice as much as small supermarkets. t that controls for endogenous bigColumns (ii) and (iii) refer to the estimation of the model for δj,tc

box presence. These specifications include inverse Mills ratios. The inverse Mills ratio used in column (ii) is based on the exclusion restriction “average distance from historic incumbents,” while that used in column (iii) is based on “distance from London.” In both specifications, the inverse Mills ratios have a significant positive coefficient of comparable magnitude, suggesting a robust and positive correlation between the unobservable of big-box entry, utbig,tc , and the unobservable portion of preferences for t big-boxes, ξ big,tc . Big-boxes tend to be present in those places where people like them more: in those t town centres where there are big-boxes, the ξ big,tc ’s are relatively “higher” (i.e., the selected sample of

? ? δbig,tc,t ’s has a higher average than the population). By estimating δj,tc,t = τjt + βxtj,tc + ξ tj,tc on the sen o813 t lected sample of town centres δj,tc —without controlling for selection—, one is bound to get j,tc,t=1 h   t + βx t t 53 b t τbbig ∑704 tc,t=1 big,tc − τbig + βxbig,tc = Bias > 0. t ’s “absorb” most of the selection bias (i.e., the estimated slope coefficients β b do The constants τbig

not seem to be affected by selection). The inverse Mills ratio is not highly correlated with the observed characteristics of big-boxes. Unfortunately, if the researcher’s aim is the computation of welfare, this is not enough to ignore selection on unobservables in demand estimation (as shown in section [6]). Controlling for big-box presence, the supposed unobserved quality “premium” of big-boxes in 200352 As discussed in appendix [8.4], by including these interactions the price index loses its explanatory power; hence I suppress the term αptj,tc from the exposition. 53 Supermarket-format j is either big-box or small, there are 352 town centres, and two time periods (2001-2002 and 2003? ’s has J · TC · T = 1408 elements: there is a δ? 2004). It follows that the population of δj,tc,t j,tc,t for both big-box and small supermarkets for each town centre in every time period. The population of market-specific utility shifters for big-boxes, the ? δbig,tc,t ’s, has TC · T = 704 elements.

26

04 ≈ 0): only small supermarkets experience an increase in unobserved quality 2004 disappears (i.e., τbbig 04 > 0). This conforms with the expected upward bias in the from 2001-2002 to 2003-2004 (i.e., τbsmall

estimation of big-box preferences discussed above. From an economic perspective, this story is in line with the results of Griffith & Harmgart (2008) and the changes in entry strategy of the major chain retailers discussed in footnote [35]: the fact that retailers are not “pushing” big-boxes as much as in the past, but are rather concentrating towards smaller formats, might not just be the consequence of stringent planning regulations, but also a matter of households’ preferences. Terry Leahy, CEO of Tesco between 1997 and 2010, recently confirmed this idea: “Customers told us that [...] their lives were getting busier and more complicated, giving them less time to plan. [...] If shoppers would not come to Tesco’s big stores, then Tesco would have to come to them. We had to stop thinking that we were in the business of opening big stores and closing small ones. Big was still beautiful, but small could be just as attractive. [...] Express [i.e. the “small” format by Tesco] quickly became our most popular format with customers. [...] Express stores have been introduced into every country where Tesco operates.” Hence, not only in countries with land use regulations. “Highly profitable, the convenience format is the fastest growing after e-commerce. As societies become more urban, and people the world over lead busier lives, the format is bound to expand.” [See pages 216-225 of Leahy (2012).] In conclusion, results from table 6 support the argument that not controlling for endogenous entry leads to an upward bias in the estimation of big-box preferences. How this upward bias maps into consumer welfare is studied in the next section.

6

Welfare Analysis

In this section I evaluate the consumer benefit of big-box availability by exploiting observed big-box entry and subsequent market re-adjustments (i.e., changes in the observable characteristics of small supermarkets, x04 small,tc ). In particular, I compare results obtained by controlling for and by ignoring sampleselection due to endogenous entry.

6.1

Compensating Variation in Distance

Household i’s expected welfare of grocery shopping in period t is the standard logit inclusive value [see Small & Rosen (1981)]:

27

h

t E j,tc Ui,j,tc

i

= E j,tc

 max

( j,tc)∈CSt

n

t Ui,j,tc

=

t δj,tc

t + θdistancei,tc

+ εti,j,tc

o

i h    t ,τ t t b + θdistance b bsmall ≈ ln ∑( j,tc)∈CSt exp δbj,tc xtj,tc , τbbig ,β i,tc   b b t ,τ t bsmall β = Wel X it , τbbig , CSt θ,

E2·352·2 D t where X it = xtj,tc , distancei,tc

( j,tc,t)=1

are the observable characteristics, τbjt is the estimated time-specific

format constant, and CSt is the set of available ( j, tc) combinations in period t. I measure changes in expected welfare of grocery shopping between t = 2002 and t = 2004 as compensating variations in distance [see Smith (2006)]:

CVi = −

h i t 4E j,tc Ui,j,tc MUdist

≈−

 1 Weli04 − Weli02 , θb

(6.1)

where MUdist is the marginal disutility of distance, θ.54 CVi translates “change in the number of utils” into an equivalent “change in the number of km’s traveled for grocery shopping.” The computation of CVi does not involve any simulation of counterfactuals: the estimated preference parameter θb comes 02 ’s and δ04 ’s come from the observed market shares of all the j, tc from the 2003-2004 period; the δj,tc ( ) j,tc

b X 02 , X 04 and CS02 , CS04 are the “actually” observed characteristics and the sets combinations given θ; i i of available ( j, tc) combinations in, respectively, 2001-2002 and 2003-2004. As argued by Nevo (2011), logit demand models require observed market outcomes—as opposed to simulated ones—in order to produce correct welfare measures.55 My strategy for measuring the compensating variation of big-box availability involves an intertemporal comparison of welfare. This helps to address some concerns about the use of logit models for 54 As

t includes some “distance” term. However, this is different one can see from table 6, my empirical specification of δj,tc

t that multiplies θ. As mentioned after table 2, the former “distance” variable, from the household-specific regressor distancei,tc t , is the average Euclidean distance of town centre tc from the sample of households: distancet = 1 I t distancetc tc I ∑i =1 distancei,tc . η t Call the distancetc coefficient η. Then, by saying that MUdist = θ, I am assuming that I = 0. Given the large number of households (i.e., I) in my sample, this is practically true. 55 Because logit models do not usually deliver realistic estimates of substitution patterns (i.e., IIA property), researchers should not rely on them to simulate counterfactuals to be used for welfare computations.

28

welfare computations. But it does so at a cost: an identification issue that is not present with simulated counterfactuals (since time is fixed). In fact, not all the intertemporal difference in welfare, as measured by (6.1), can be attributed to big-box entry. On the one hand, the entry of a big-box in a town centre in which none was present affects many observable and unobservable welfare-relevant dimensions (e.g., entry/exit decisions, prices, product ranges, and service quality of incumbents).56 But, on the other, also the mere passage of time does. I propose to use a differences-in-differences strategy to “filter out” the passage of time from my welfare comparisons.

6.2

Differences-in-Differences Approach

The fact of comparing welfare at two different points in time rises a potential identification issue. On the one hand, big-box entry affects the surrounding environment in many welfare-relevant ways. But, on the other, also the mere passage of time does. In other words, the passage of time has welfare-relevant effects that one may mistakenly attribute to big-box entry. In order to control for this possibility, I use a differences-in-differences approach. I restrict the attention to the households living, for the entire 2001-2004 period, in the 304 town centres in which there were no big-boxes until the end of 2002 [i.e., 2078 households]. The “treated” are those i’s living in Local Planning Authorities in which at least one town centre experienced entry of big-boxes in 2003-2004 [i.e., 332 households].57 In measuring (6.1) following big-box entry, the idea is to “filter out” that part of the increase that would have realized anyway, with or without the opening of big-boxes. The regression used is:

t −Weli,la t = µ + ϑ treatmentla + ω postt + ρ (treatmentla · postt ) + ei,la . b θ

(6.2)

The pre-treatment period is t =2001-2002 (i.e., post=0), while the post-treatment period is t =2003-2004 (i.e., post=1). The key identifying assumption relates to the “counterfactual” time trend of the treated: the t −Weli,la ’s of θb

the treated, had they not experienced any big-box entry, would have had the same time trend

observed in the

t −Weli,la ’s of the controls. b θ

The main point of the proposed sample-selection correction is to

fulfill such an identifying assumption. Any positive estimate of ω—the time trend—can be interpreted as a generalized increase in welfare from grocery shopping (i.e., nothing to do with big-box entry), while a positive estimate of ρ—the treatment effect—can be interpreted as the compensated variation of big-box 56 See,

for example: Basker and Noel (2008) and Matsa (2011). households living in town centres in which big-boxes were already present in 2001-2002 cannot be used: I do not have data about the period prior to big-box entry. 57 The

29

entry.

[ TABLE 7] . Column (i) reports the estimated compensated variation without controlling for selection bias in the computation of the dependent variable. Differently, results in columns (ii) and (iii) are obtained by controlling for selection bias using two different exclusion restrictions: “average distance from historic incumbents” and “distance from London,” respectively. The positive and large estimated coefficients of postt across specifications suggest that, indeed, welfare from grocery shopping generally improved over time. Most of this positive trend comes from increases in the unobserved portion of the indirect utility of small stores, as captured by positive estimates 04 .58 As discussed by Nevo (2003) and in footnotes [48] and [49], due to necessary identifying of τsmall

normalizations, discrete choice models are not ideal to study changes in these unobservables over time. It is possible to control for them, as I tried to do here, but it is hard to pin down the reasons behind these changes. The increase in the unobserved portion of indirect utility of small supermarkets could be explained either by a change in preferences or by improvements in their unobserved characteristics (i.e., unobserved quality) [see Nevo (2003)]. As seen at the end of section [5.3], Leahy (2012) confirms that both explanations played a role: consumers seem to be in the process of changing their preferences (i.e., from “big” but inconvenient to “small” but convenient) and retailers, after having realized this, have been heavily investing in smaller formats to satisfy the need. My main interest is in the estimated ρ coefficient, the compensated variation of big-box entry in “km’s closer.” From column (i), if one ignores endogenous big-box entry the average estimated consumer benefit of big-box availability is equivalent to a 3.22 km reduction in distance to favourite grocery stores. Differently, from columns (ii) and (iii), if one accounts for endogenous big-box entry the estimated benefit is significantly smaller: around 1.85 km’s. In order to put these results into perspective: in the period 2001-2002, among the sample of primary shopping trips, the 75th percentile is 12.91 km. When endogenous big-box entry is mistakenly ignored, 75% of households are estimated to value big-box availability as a reduction in distance to their favourite grocery store of, at least, 25% [from column (i): 3.22 km divided by 12.91 km]. Differently, controlling for endogenous big-box entry, 75% of households are estimated to value big-box availability as a reduction in distance to their favourite grocery store of, at least, 14.33% [column (ii)]. The consumer benefit 58 Table

04 > 0 is all about selection bias rather than about “real” increases in the indirect utility of big-boxes. 5 shows that τbbig

30

of big-box supermarkets is lower than previously thought: 41% of the estimated benefit is due to the implicit selection bias that arises when supermarket entry locations are endogenous to local preferences [comparing the estimates from column (i) and (ii)]. Also, results seem robust to different exclusion restrictions. To confirm that results from table 7 look reasonable, I compare them with those by Smith (2006). By using similar English data, but a different methodology that does not control for endogenous entry, he estimates a compensating variation (in km’s closer) of store availability in the interval between 4.21 km and 2.25 km. My results from column (i) (i.e., that do not control for selection bias either) lie in Smith (2006)’s bounds.

7 7.1

Conclusions Summary

Despite the many benefits, the expansion of big-box supermarkets is perceived as generating negative externalities (e.g., damaging the environment, hollowing out town centres, reducing local variety). Social planners around Europe (e.g., France, Italy, and the UK) attempted to limit such externalities by tightening land use regulations. A key policy question is whether such land use regulations are indeed desirable for society. By evaluating the consumer benefit of big-box supermarkets, I inform the policy debate on the efficiency of land use regulations targeted at big-boxes. The analysis unfolds in various steps. I propose a general model of demand in a setting with both endogenous prices and endogenous product availability. The classic discrete choice model of demand, which allows for endogenous prices with individual-level data [e.g., Berry, Levinsohn, and Pakes (2004)], is augmented by first stage Heckman’s selection equations. The model allows one to test for endogenous product availability in a tractable way. Identification of the model requires, in addition to instruments for price, exclusion restrictions for product availability. I estimate preferences for big-boxes in the period 2001-2004 with UK home-scanner expenditure data. I use exclusion restrictions such as “distance from historic incumbents” and “distance from London” to separately identify consumer preferences from retailers’ entry decisions. Estimation results show the importance of accounting for big-box presence in the estimation of supermarket demand: big-boxes are more likely to be located in those markets where consumers value them more. Consequently, if one does not control for endogenous big-box entry, estimated preferences for big-boxes will be upward biased. Exploiting observed big-box entry and subsequent market re-adjustments (e.g, exit of incumbents

31

and changes in incumbents’ prices), I evaluate the consumer benefit of big-box entry. My measure of welfare is the compensating variation of big-box availability. Controlling for endogenous big-box entry, 75% of consumers are estimated to value big-box availability as a reduction in distance to their favourite grocery store of, at least, 14.33%.59 Differently, when endogenous big-box entry is ignored, 75% of consumers are estimated to value big-box availability as a reduction in distance to their favourite grocery store of, at least, 25%. The empirical analysis of the UK grocery industry presents evidence of the practical relevance and policy implications of this specific form of selection bias. In particular, if it is true that big-boxes generate a wealth of benefits for consumers, it is also the case that these are of a smaller order of magnitude than estimated in previous research. These findings contribute to a growing academic literature on the welfare effects of retail regulation, and serve to inform the policy debate on the costs and benefits of the expansion of big-box supermarkets.

7.2

Limitations and Future Directions

My household model of supermarket demand is an exploded logit along the lines of BLP (2004) and Train & Winston (2007); i.e., with approximately 800 fixed effects, one for each combination supermarket format, town centre, time period. My specification does not include any random coefficient because of lack of identification: (1) I do not observe much choice set variation in the data and (2) not enough households go shopping to more than one combination format-town centre.60 However, (1) is motivated by my assumption of enabling every household to make choices over the full set of (supermarket format, town centre) combinations.61 I am currently re-estimating the model allowing for household-specific restricted choice sets (e.g., all the (supermarket format, town centre) combinations within a 30 km area). This is useful both as a robustness check and as a way to introduce cross-sectional choice set variation in the data, so to aid the identification of random coefficients. The absence of random coefficients is not crucial for my paper. I am not after realistic substitution patterns since I do not simulate counterfactuals for the evaluation of welfare. Indeed, I evaluate welfare the period 2001-2002, among the sample of primary shopping trips, the 75th percentile is 12.91 km. problem I face is known in the literature. BLP (1995, 2004) underline the importance of choice set variation in order to identify preference parameters. When there is not much choice set variation in the data, the exploded logit performs better than the simple logit. Given the same assumptions, the exploded logit exploits ranking data to generate “additional” choice set variation. In fact, both BLP (2004) and Train & Winston (2007) report that they were unable to identify any random coefficient unless they used data on rankings of choices (i.e., beyond the first-best). Unfortunately, in my case the ranking data are not rich enough to generate sufficient “additional” choice set variation so to identify random coefficients. However, also in my application the exploded logit model leads to practical advantages. It allows me to use all the available information about multi-stop shopping (e.g., main shopping to a big-box and top-up shopping to smaller stores) without having to deal with potentially complex dynamic considerations and having to define what “main” and “top-up” shopping trips are. 61 In other words, the only choice set variation I allow for is between 2001-2002 and 2003-2004, namely the entry of 17 new big-boxes for every household. 59 In

60 The

32

exploiting observed big-box entry.62 A realistic way to improve the robustness of the demand estimates would be to implement a nested logit model. This would allow unobserved households’ preferences for supermarket format (i.e., big or small) to be correlated across town centres. (By creating a nest for big-boxes and a nest of small supermarkets.) In addition, I am not currently exploiting any of the rich household-specific demographic data available. I am working to include this information in my model. In the selection model I make strong distributional assumptions (i.e., independent probit). On the one hand, maintaining the assumption of independence across town centres, one could relax normality [see, for example, Das et al. (2003)], even though the practical payoff from doing so (balancing for simplicity) is not clear. Moreover, from an economic perspective, the message of the paper is not affected by normality. On the other, the assumption of independence across town centres is economically restrictive. Indeed, in most cases the decision of developing supermarket-format j across town centres is made by the same restricted group of chain retailer. Hence, u jl should be allowed to be dependent across town centres. For the time being I assume independence, but I am working to allow for spatial dependence of u jl along the lines proposed by Wang et al. (2013). In my application I only have one selection equation, namely for the presence of big-boxes across town centres. A natural question is what to do in the case of multiple selection equations. In terms of identification, there are two options. The first option requires an exclusion restriction (i.e., not correlated with preferences) that varies across locations but that is common across producers. Such location-specific characteristic should affect differentially the various producers.63 The second option requires an exclusion restriction that varies both across locations and across producers. In my context this could be the "proximity" to the logistic network of the retailer (e.g., the closest warehouse). One instrument is enough (i.e., we do not need as many instruments as the number of selection equations), but it is required to be heterogeneous across both markets and producers. In my case, such data are available from IGD and I am planning to use them. 62 The

counterfactual I need, in order to measure consumer welfare, is a change in households’ choice sets. My demand model assumes logit errors, and these have been criticized as inappropriate for such a task [see Petrin (2002), Berry et al. (2004), and Berry and Pakes (2007)]. As Nevo (2011) shows, even with a simple logit model (i.e., no random coefficients), it is possible to correctly evaluate the welfare effects of a changing choice set. This on the premises of having good measures of the market-shares pre and of the market-shares post-change. Usually, researchers only have one set of market-shares: either pre or post-change; and then “simulate” the remaining set with their estimated model. It is in the market-share simulation step that the logit model becomes inappropriate (the blue-bus, red-bus case is an example). Then, given wrong simulated market-shares, wrong welfare computations follow. In contrast, if in the first place the logit model is “fed” with the correct market-shares pre and after choice set change, then the welfare calculations will be correct. 63 As an example, imagine very high rents in central London, common to all retailers; some retailers are not able to handle them, others are. So we see Tesco and Sainsbury’s entering, but not Cost-Cutter.

33

In conclusion, my paper only addresses “half” of the efficiency question in relation to the expansion of big-boxes: the consumer welfare. Further research should consider the inclusion of a structural supply side to quantify the costs associated with big-box entry. This would allow one to better inform the policy debate about the “optimal” expansion of big-boxes and, consequently, about the design of better mechanisms to “internalize” big-boxes’ externalities.

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8

Appendix

8.1

Individual-Level Selection

Assume individuals make choices over the set of products ( j, l )’s. In what follows, I investigate the conditions under which the researcher can ignore the l dimension in the description of the object of individuals’ decisions and restrict individuals’ choice sets to the j dimension. Define CS (l ) ⊆ {1, 2, . . . , J } as the set of alternatives available in location l. Also, define S ( j) ≡

{l | j ∈ CS (l ) } as the collection of locations where alternative j is available. The potential endogeneity of CS = hCS (l )ilL=1 with respect to individuals’ preferences is the main theme of this paper but, for the purpose of this appendix, I assume the d.g.p. is exogenous. Moreover, I assume the indirect utility (2.1) does not include any random coefficient (i.e., ηi = θ, ∀i), so the choice probability in (8.2) is a multinomial logit.64 Suppose in locations l1 and l2 are offered exactly the same sets of alternatives, CS (l1 ) = CS (l2 ), and that each alternative is sold both in l1 and in l2 at the same price; but that individual i is observed choosing an alternative in market l1 . Before attributing this behavior to the unobserved portion of utility, ε ijl1 − ε ijl2 , the estimator controls for other observable attributes (e.g., if the location is a “dodgy” area and distance from i’s house) over which the individual may have preferences that partly determine her choice: location l2 may just be an extra 10-minute walk from i’s house. In other words, going to location l1 , and thus being “matched” to CS (l1 ), may still be the outcome of a choice that does not have anything to do with the attributes of the alternatives in CS (l1 ). Given the current assumptions, choice probability (8.2) can be re-written as:

Prijl ( θ, δ? | CS) = Pri ( alternative j, location l | CS, θ, δ? )

= Pri ( location l | alternative j, CS, θ, δ? ) · Pri ( alternative j| CS, θ, δ? ) .

=

∑

h
i exp δjl? + Vjl p jl , xijl , θ h
i ? +V exp δ p , x , θ gn gn ign ∑ gn

n g∈CS(n)

The first element, Pri ( location l | alternative j, CS, θ, δ? ), is the probability that individual i is matched with location l given that she chose alternative j. The second is the probability that individual i chooses 64 As

it will be clearer later, with random coefficients the problem gets even worse.

40

alternative j. The expressions for the two probabilities are:

Pri ( alternative j| CS, θ, δ? )

=

∑

Pri ( alternative j, location l | CS, θ, δ? )

l ∈S( j)

∑

=

h
i exp δjl? + Vjl p jl , xijl , θ

l ∈S( j)

∑ ∑

h
i ? +V exp δgn gn p gn , xign , θ

n g∈CS(n)

. Pri ( location l | alternative j, CS, θ, δ? ) =

(8.1)

Pri ( alternative j, location l | CS, θ, δ? ) Pri ( alternative j| CS, θ, δ? )

h
i exp δjl? + Vjl p jl , xijl , θ h =
i ∑ exp δjn? + Vjn p jn , xijn , θ n∈S( j)

As it can be seen from (8.1), for j1 , j2 ∈ CS (l ), there is no reason to believe that Pri ( l | j1 , CS, θ, δ? ) = Pri ( l | j2 , CS, θ, δ? ). If this is the case, even in the current specification (i.e., a multinomial logit, no random coefficients), the uniform conditioning property does not hold [see Bierlaire et al. (2008), Fox (2007), and McFadden (1978)], and estimating (θ, δ? ) only via Pri ( alternative j| location l, CS, θ, δ? ) leads to inconsistency (i.e., if we mistakenly assume each individual is “stuck” in a specific location for reasons beyond her preferences).65 We have endogenous individual-level selection whenever Pri ( l | j, CS, θ, δ? ) is a function of j. Again from (8.1), excluding pathological cases (e.g., all the systematic utilities are identical), this happens whenever the universal choice set of alternatives, {1, 2, . . . , J }, is not partitioned across the L locations (i.e., ∃ j ∈ {1, 2, . . . , J } such that #S ( j) > 1). This will always be the case if there are more locations than alternatives, L > J. Instead, if L ≤ J and each location l has an exclusive set of alternatives, Pri ( l | j, CS, θ, δ? ) = 1 for each j ∈ CS (l ) and l (i.e., the uniform conditioning property holds), and the researcher can safely restrict choice sets to the j dimension. 65 To

see this, notice that we can equivalently express Pri ( alternative j| location l, CS, θ, δ? ) as:

Pri ( alt j| loc l, CS, θ, δ? )

=

n   o exp δjl? + Vjl p jl , xijl , θ + ln [Pri ( loc l | alt j, CS, θ, δ? )] n   o . ∑ exp δgl? + Vgl pgl , xigl , θ + ln [Pri ( loc l | alt g, CS, θ, δ? )]

g∈CS(l )

If, mistakenly, the researcher does not include ln [Pri ( loc l | alt g, CS, θ, δ? )] in her specification, there will be an omitted term correlated with the systematic utility.

41

Hence, the key condition for endogenous individual-level selection to be possible is that sets of available alternatives in different locations partially overlap (e.g., there are some “popular” alternatives which are sold in many different locations). This condition is easily observable from the data, so the researcher does not have to guess. Furthermore, the condition is not just statistical, it has intuitive economic meaning. The closer locations are to each other in variety space (in terms of alternatives), the fiercer price competition between locations will be in order to attract individuals (assuming the nonprice characteristics of each alternative are predetermined and only price can be altered from location to location). In my empirical application, I have L = 352 and J = 2; furthermore, I observe individuals choosing the same j from many different l’s (see table 3 and related discussion). Following the above argument, my application might be subject to endogenous individual-level selection, hence I define products as

( j, l ) combinations (i.e., I do not ignore the l dimension). For details about my empirical definition of products, see section [3.2].

8.2

Mixed Logit Model and Its Estimation

In this appendix, I describe the mixed logit model and how it is estimated when the location-specific D E J·L utility shifters, δ? = δjl? , are obtained with Berry (1994)’s contraction mapping. Given the asjl =1

sumptions of section [2.1], the probability of product ( j, l ) being individual i’s first-best is given by the mixed logit model [see McFadden & Train (2000)]: ˆ Prijl (θ, δ? ) =

h
i exp δjl? + Vjl p jl , xijl , ηi h
i f ( ηi | θ) dηi . ? +V gn p gn , xign , ηi ∑ ∑ exp δgn g

(8.2)

n

Market-level demand is the aggregation of individual-level demands. The observed market-level demand for product ( j, l ) is its market share, S jl =

1 I

∑iI=1 yijl . yijl = 1 if individual i’s first best is product

( j, l ), yijl = 0 otherwise. I define market shares so that ∑ jlJ ·=L 1 S jl = 1. In other words, my definition of “market” is the summation of all the locations. The observed market share of alternative j in location l is modeled as [see BLP (2004), Golsbee & Petrin (2004), and Train & Winston (2007)]:

1 I S jl = Sbjl [θ, δ? (θ, S)] = ∑ Prijl [θ, δ? (θ, S)] , I i =1

(8.3)

D E J·L where δ? = δjl? is expressed as a function of θ and S [i.e., the market shares of all products ( j, l )’s] jl =1

42

after Berry (1994): for any value of θ there exists a unique vector δ? such that predicted market shares, b equal observed market shares, S. S, L The fact that ∑ jlJ ·= 1 S jl = 1 is “silent” with respect to the choice set faced by each individual. If one

wishes to exclude, for example, location l from those considered by individual i when making a choice (e.g., because l is “too” far from i’s house), then the corresponding addends from the denominator of (8.2) should be removed, so that Prijl [θ, δ? (θ, S)] = 0, ∀ j ∈ CS (l ). Following Train & Winston (2007), the estimation of (θ, δ? ) can be performed by simulated maximum likelihood (SML) augmented by a “contraction” algorithm. Given the observed market shares, S, at each iteration of the SML search for θ, θr , the contraction algorithm computes the vector δ? (θr , S) which   enforces condition (8.3). When convergence is achieved, b θ and δ? b θ, S are obtained, and the estimation   of (α, β) from (2.2) can be performed as outlined in section [2.3], using δjl? b θ, S as dependent variable.66 As explained in section [3.3], I have data on rankings of ( j, l ) combinations rather than just about the first-best. The use of preference-rankings for the estimation of a logit model [i.e., the exploded logit model, See section 7.3 of Train (2009)] appears to be relevant for the identification of random coefficients [see BLP (2004) and Train & Wiston (2007)]. More in general, it has been shown that using preferencerankings data improves the precision of the estimates when compared to first-best data [see Beggs et al. (1981)]. BLP (1995, 2004) underline the importance of choice set variation in order to identify preference parameters. When there is not much choice set variation in the data (such as in my case, choice set changes from 391 to 408 ( j, tc) combinations because of the entry of big-boxes in 17 town centres where none was present), the exploded logit performs better than the simple logit because, given the same assumptions, it exploits ranking data to generate “additional” choice set variation.67 Furthermore, as discussed in section [3.3], in my application the exploded logit model leads to practical advantages. It allows me to use all the available information about multi-stop shopping (e.g., main shopping to a bigbox and top-up shoppings to smaller stores) without having to deal with potentially complex dynamic considerations and having to define what “main” and “top-up” shopping trips are. Therefore, I estimate an exploded logit model.

8.3

Construction of “Price Index” Variable

I construct price indexes for each ( j, tc) combination. In doing this, I follow Dubois & Jodar-Rosell (2010) and Schiraldi et al. (2011). 66 See

BLP (2004) for GMM estimation of this class of models. on the first-best are used as in the simple logit, but data on less preferred products are included in the model by sequentially “removing” more preferred products from the household’s choice set. 67 Data

43

There are 183 product categories in the Kantar data (e.g., yogurt, cheese, pizza, etc.). Within each product category there are many different products. The prices of these products are recorded from till receipts by households, each time they purchase them. Call o (b) an observation in the purchase data for product b (i.e., within product category K, each household has one of such observations every time she purchases product b ∈ K). expo(b),s is o’s expenditure for product b in supermarket s, and expsK = ∑b∈k ∑o(b) expo(b),s is supermarket s’s total revenue in product category K. Similarly, expKj,tc = ∑s∈( j,tc) expsK is total revenue of format-size j in town centre tc. Then, woK(b),s =

expo(b),s expsK

is the share of

revenues of product category K in supermarket s due to o’s purchase of product b, and wK,s j,tc =

expsK expKj,tc

is

the share of revenues in product category K in format-size j in town centre tc of supermarket s ∈ ( j, tc). Define po(b),s as the unit price recorded by observation o for product b from supermarket s (i.e., expo(b),s divided by volume purchased).68 Then psK = ∑b∈k ∑o(b) woK(b),s po(b),s is the unit price of product category K K in supermarket s, and pKj,tc = ∑s∈( j,tc) wK,s j,tc ps is the unit price of product category K in format-size j in

town centre tc. wKj,tc =

expKj,tc ∑K ∈K expKj,tc

is the revenue-weight of product category K in format-size j in town

centre tc. Finally, p j,tc = ∑K∈K wKj,tc pKj,tc is the price index for combination ( j, tc). By construction, price index p j,tc is endogenous to sampled households’ preferences, because it is computed from the prices of those products that were actually purchased by the sampled households [see Dubois & Jodar-Rosell (2010)]. I might observe certain product categories to be sold in some town centres (where the sampled households like them) but not in others (where the sampled households do not like them) even though the product categories are actually available everywhere. Hence, the set of product categories used in the construction of the price indexes in each town centre might correlate to sampled households’ preferences. We can expect such form of endogeneity to diminish the larger is the sample of prices we observe. As discussed in the main text, I aggregate over time intervals long years. Furthermore, the same sample-selection story discussed in section [2.2] but applied to the population of product categories may hold here (i.e., supermarkets may decide not to offer a product category if households do not like it enough).69 To address this possibility, I include in the set of product categories

K only those K’s that are observed to be sold in at least

2 3

of the town centres, so to consider only those

product categories for which households seem to have similar preferences across the country. Moreover, the estimation procedure outlined in section [2.3] is robust to price endogeneity. 68 All

prices are deflated by the RPI rate of inflation so to be expressed in 2001 terms. gathered evidence (i.e., pictures) related to this hypothesis between London and Birmingham. The interested reader should contact me. 69 I

44

8.4

Price Endogeneity and Time-Specific Format Constants

t In this section I compare different specifications for model δj,tc in (2.3) in order to choose whether to

include in the analysis time-specific format constants (i.e., a time dummy interacted with a supermarketformat dummy). Such a decision is interwoven with the issue of price endogeneity. As detailed in appendix [8.3], the price index is expected to be endogenous with respect to unobserved preferences. Thus, it is required to find instruments to correct for such endogeneity. In the UK, chain retailers adopt a national pricing strategy [see Competition Commission (2000)]. In broad terms, whenever a retailer offers a specific product in any of its stores, it will be sold at the same price everywhere in the UK. Within the same retailer, price indexes still vary across stores because different stores, located in different town centres, offer different ranges of products (and different pack-sizes for given product). A direct implication of national pricing is that cost-shifters, a “classic” choice for instruments, are not expected to explain any price variation. Indeed, even though different stores belonging to the same retailer face different marginal costs, such heterogeneity is simply averaged-out by the retailer across the whole chain. Consequently, most of the variation in price indexes comes from heterogeneity in preferences across town centres rather than from cost-side considerations. Other candidate instruments, first proposed by Hausman (1996), would be the price indexes of the same supermarket-format j but from different town centres. Following the discussion in Nevo (2001), this also does not look promising in my application. Town centres are relatively small areas (compared, for instance, to US cities) and households, as can be seen from table 3, tend to “go around” for shopping. Consequently, it is likely that price p j,tc (i.e., the range of offered products) is set taking into consideration the ξ j,tc ’s of all the neighboring town centres, and not just its own. It is then hard to imagine any source of exogenous (with respect to unobserved preferences) variation in the price indexes beyond the “location” of combination ( j, tc) in characteristic space [i.e., the IV strategy proposed by BLP (1995)]. As said above, heterogeneity in the price index is mainly due to heterogeneity in the ranges of products offered. Unfortunately, I do not have such an information in my data. Floorsize seems to convey some related information, in the sense of being negatively correlated with the price index (see table 2), but unfortunately—after extensive experimentation—it does not appear to work well as a BLP-kind of instrument. The same is true for the remaining observed characteristics. Following Nevo (2001), there is a less structural version of the same BLP-kind of instruments: the time-specific format constants. The idea is to instrument price, in each time period, with the average unobserved characteristics of supermarket-format j across town centres. t regression (without accounting for sampleTable A1 reports four alternative specifications for the δj,tc

45

selection) in model (2.3). The number of observations is 813: all the ( j, tc) combinations in periods 2001-2002 and 2003-2004.

[ TABLE A1] . t on observable characteristics The first column of table A1 lists the results from the OLS regression of δj,tc

of both j and tc. The coefficient on the price index is negative and significant. Also the coefficients on distance and floorsize are significant and have the expected sign. By construction, the price index is endogenous because it is computed only on the disaggregated prices of those products actually purchased by households. In the second and third column, I compare the validity of the different instruments discussed earlier. In column (ii) I use Hausman-kind instruments,70 while in column (iii)—following Nevo (2001)—, I use BLP-kind instruments. As customary in the literature, the magnitude of the estimated price coefficient greatly increases after controlling for potential endogeneity. In line with the discussion above, BLP-kind instruments seem to work better than Hausman-kind instruments. Interestingly, controlling for price endogeneity affects (to a lesser extent, but still significantly) also the floorsize coefficient. This makes economic sense. Table A1 confirms the intuitive idea that a higher unobserved utility is associated with higher prices. Table 2 suggests a negative correlation between prices and floorsize. In other words, households avoid the higher-priced supermarkets less than they would if the higher prices occurred without any compensation in terms of unobserved utility. But, avoiding higher-priced supermarkets less, means going more often to smaller supermarkets than they would if the higher prices occurred without any compensation in terms of unobserved utility. In column (iv) of table A1, I perform again an OLS regression, but here I add three dummies: bigbox in 2002, big-box in 2004, and small in 2004. These are the time-specific constants for big-boxes and for small supermarkets used in column (iii) as instruments for the price index. As soon as we add such variables, the price index loses all its explanatory power. However, the same is not true for the remaining characteristics. As noted by Nevo (2001), the inclusion of such intercepts “absorbs” the effect of any characteristic that does not vary “much” within the j dimension (i.e., big and small) but only across j’s. Hence, the price index does not seem to rationalize enough variation within each j (at least not after having controlled for the other characteristics) and loses its explanatory power once one includes time-specific format constants. A possible explanation for this might be the national pricing strategy discussed earlier. 70 For

price index p j,tc I use instruments p1j,−tc =

1 812

∑m6=tc p j,tc and p2j,−tc =

46

1 812

 2 ∑m6=tc p j,tc − p j,−tc .

The only instruments that seem to be economically and practically convincing are the time-specific constants for big-boxes and for small supermarkets used in column (iii). Unfortunately, using them as instruments prevents their inclusion as regressors. But, in my application, this could be a serious limitation. Indeed, my observed attributes (i.e., price, floorsize, parking lots, and tills) are quite “modest” with respect to the complexity of the “objects” they are supposed to characterize. Using Matsa (2011)’s words: “[i]n the retail sector, a firm’s “product” is the shopping experience it provides its customers. Like the quality of physical products, the quality of the shopping experience has many dimensions, including the store’s location, cleanliness, checkout speed, the courteousness of its staff, the depth of its product assortment, and the availability of ancillary services such as parking and bagging.” Households might be making their shopping choices largely on the basis of unobserved (to the researcher) characteristics, and this strongly warrants the use of alternative-specific constants (such as time-specific constants for big-boxes and for small supermarkets) in order to “pull out” from the ξ j,tc ’s any systematic pattern [see Nevo (2001)]. This is particularly relevant in my application. Indeed, as discussed in footnote [49], in performing intertemporal comparisons of welfare, it is important to account for any observed and unobserved quality change over time [see Nevo (2003)]. In addition, as seen in column (iv), the time-specific constants for big-boxes and for small supermarkets subsume all the information carried by the price index, relieving me from the non simple task of finding convincing instruments for it. For these reasons, I favour the inclusion of the time-specific t . constants for big-boxes and for small supermarkets in the specification for δj,tc

47

FIGURE 1 — Big-Box Presence across Town Centres

Notes: Geographic distribution of big-box supermarkets in England and Wales, 2002. The delimited regions are Local Authorities. Each Local Authority hosts up to 16 town centres (the case of Leeds). The distribution is computed across the 753 town centres for which I have complete data. Source: IGD data.

FIGURE 2 — Big-Box Presence across Town Centres (England & Wales, 2002)

Notes: In th e “ful l sample” there are the 753 town centres for which I h ave complete data. Th e “restricted sampl e,” 352 town centres, excl udes th e town centres i n wh i ch : (a) bi g -boxes entered before 1996 and (b) th ere was not any entry after 1996. Source: IGD data.

FIGURE 3 — Averages of Location-Specific Utility Shifters

Notes: 2001-2002 and 2003-2004 averages, across town centres, of th e esti mated l ocation-speci fic utility shifters for both bi g-boxes and smal l supermarkets.

TABLE 1 — Town Centre Data (2001-2002) Full Sample of Town Centres

Restricted Sample of Town Centres

Variables

Obs.

Mean

SD

Min

Max

Obs.

Mean

SD

Min

Max

People (10,000)

753

5.75

3.96

.615

40

352

3.92

2.02

0.82

14.78

Density

753

48.40

33.12

6.03

243.51

352

43.82

34.57

6.03

230.73

Hamlet (%)

753

.044

.062

0

.382

352

.065

.076

0

.382

Work Class (%)

753

.274

.069

.09

.465

352

.268

.072

.09

.42

Retired (%)

753

.140

.033

.059

.278

352

.147

.038

.067

.278

Area (hectares)

753

29.73

122.25

4

3256.5

352

17.48

29.42

4

319.5

Closest (10 Km)

753

.615

.506

.053

2.81

352

.702

.542

.062

2.69

Local Authority

320

2.69

2.02

1

16

207

2.44

1.74

1

8

Notes: Descri pti ve statisti cs about Town Centre Data, 2001-2002. In th e “ful l sampl e” th ere are th e 753 town centres for whi ch I h ave compl ete data. Th e “restri cted sampl e,” 352 town centres, excl udes th e town centres i n whi ch: (a) bi g -boxes entered before 1996 and (b) th ere was not any entry after 1996. Source: ODPM and ONS.

TABLE 2 — Supermarket Characteristics (2003-2004) Characteristics

Big-Box Stores (65 Obs.)

Mean

SD

Small Stores (352 Obs.)

Mean

SD

Price Index

4.41

.813

5.6

5.09

Distance (100 km)

1.96

.484

1.99

.471

Floorsize (100 m2)

40.08

10.48

8.50

3.52

Parking Lots

500.24

176.43

106.30

123.22

Tills

25.87

5.35

7.70

3.09

Notes: Descri pti ve statistics about supermarket ch aracteristics, separatel y for bi g -boxes and for smal l supermarkets. Source: IGD, ODPM, and ONS data.

TABLE 3 — Households’ Rankings of Supermarket Choices (2003-2004) Ranking Position

Same Town Centre where Living

Different Town Centre where Living

N O Obs. Choices

Dist. (km)

Tot. Exp. (£)

% Big-Box

N O Obs. Choices

Dist. (km)

Tot. Exp. (£)

% Big-Box

1st

3489

1.47

995.8

.167

4684

8.12

415.2

.241

2nd

831

1.52

196.9

.227

2004

9.04

88.9

.191

3rd

119

1.27

73.6

.244

654

9.26

45

.153

4th

28

1

36.4

.107

167

10.32

27.9

.156

5th

8

2.2

20.8

0

39

7.53

13.7

.051

6th

—

—

—

—

13

12.2

12.3

0

7th

1

1.5

12.2

0

3

9.73

4

.67

Notes: Descri pti ve stati sti cs about th e ranki ngs of supermarket ch oi ces made by h ouseh ol ds in Engl and and Wal es, 2003-2004. From observed sh oppi ng beh avi our over th e peri od 2003-2004, I create for each h ouseh ol d a “total expendi ture ranki ng” of (supermarket-format, town centre) combi nati ons. Th e number of ch osen (supermarket-format, town centre) combi nati ons i s 12040. “Same Town Centre wh ere Li ving” li sts descri pti ve stati sti cs about th ose observed (supermarket-format, town centre) choi ces in whi ch ch osen supermarket and h ouseh ol d resi de i n th e same town centre. Si milarl y for “Di fferent Town Centre wh ere Li vi ng.” “Di st.” is th e medi an di stance between h ouseh ol ds and (supermarket-format, town centre) combinati ons among th e “y-best” ch oi ces in h ouseh ol ds’ ranki ngs. “Tot. Exp.” i s th e average total expendi ture among th e “y-best” ch oi ces. “% Bi g-Box” is th e sh are of “y-best” ch oi ces that are bi g-boxes. Source: Kantar (formerly TNS) data, Uni ted Kingdom.

TABLE 4 — Timing of Big-Box Entry (1901-2004) Geographic Area

Big-Box Stores (1179 obs.) Mean (year)

Median (year)

3rd Quartile (year)

North

1994.2

1999

2001

Centre

1991.9

1993

1999

South

1990.9

1992

1997

Notes: Average, medi an, and 3 rd quartil e of “year of bi g-box entry” computed wi thin each of three UK geographi c areas (north, centre, and south ). Th e total number of bi g-boxes devel oped i n th e peri od 19012004 i s 1179. Th e th ree geographi c areas h ave equal l ength in terms of verti cal coordi nates. Source: IGD data.

TABLE 5 — Model of Big-Box Entry (1997-2004) Dep. Var.: Dummy BigBox Presence

(i): ML Est. (SE)

(ii): ML Est. (SE)

—

.702** (.282)

Dist. London Av. Dist. Incumbents Population Density Retired Hamlet Working Class Pseudo-R2 Obs.

1.725** (.761) 1.422*** (.345) -.622* (.344) -3.089*** (.998) -.992** (.395) 1.157 (.710)

1.307*** (.344) -.416 (.321) -2.691*** (.909) -.888** (.395) .809 (.726)

0.240

0.243

352

352

—

Notes: Marginal effects of probi t model for entry of bi g-box supermarkets. Index eval uated at regressors’ means. Number of town centres (observati ons): 352. SEs and Hausman stati sti c’s vari ance are bootstrapped over Local Pl anning Auth ori ti es (206 of th em), 2000 repeti ti ons. Both speci fi cati ons i ncl ude a constant. ***: 1% significance. **: 5% significance. *: 10% si gnificance.

TABLE 6 — Location-Specific Utility Model Dep. Var.: LocationSpecific Utility, Big*2002 Big*2004 Small*2004 Price Index Distance (100 km) Floorsize (100 m 2) Parking Lots Inverse Mills Ratio Controls

Obs.

(i): NO Sel. Corr.

(ii): Av. Dist. Inc.

(iii): Dist. London

Estimate (SE) .404 (.593) 1.494** (.601) .790*** (.086) -.011 (.012) -1.966*** (.267) .054* (.032) .001* (.0005)

Estimate (SE) -.639 (.742) .641 (.714) .783*** (.086) -.012 (.012) -2.012*** (.262) .054* (.032) .0009* (.0005) .748*** (.285)

Estimate (SE) -.642 (.701) .642 (.683) .781*** (.086) -.012 (.012) -1.998*** (.259) .059* (.031) .0009* (.0005) .786*** (.288)

YES

YES

YES

813

813

813

—

Notes: Regression of locati on-speci fi c utility model wi thout [col umn (i )] and wi th [col umns (ii ) and (iii )] sel ecti on correcti on . Col umn (i ) is th e FGLS regressi on of on observabl e ch aracteristi cs of both supermarket-format and town centre. Col umn (ii ) and (iii ) al so incl ude i nverse Mills rati os. Th e inverse Mill s ratio used i n (ii ) is based on th e excl usi on restri cti on “average di stance from hi stori c incumbents,” whil e that used in (iii ) i s based on “distance from London.” Bi g*2002 i s the i nteracti on of a dummy for bi g-box and a dummy for t=2002. Similarl y for Bi g*2004 and for Small *2004. Number of observati ons: 813. SEs bootstrapped o ver town centres, 2000 repeti ti ons. FGLS acco unts for correl ati on across error terms within th e same town centre. Controls: Tills, Fl oorsi ze·Ti lls, Di stance·Tills, Fl oorsi ze2·Distance, Floorsi ze3·Distance, Floorsi ze4·Di stance, Retired, Working Cl ass, and Popul ation 2. ***: 1% si gnificance. **: 5% si gnificance. *: 10% si gnificance.

TABLE 7 — Compensating Variation of Big-Box Entry Dep. Var.: ̂ (km’s closer)

(i): NO Sel. Corr.

(ii): Av. Dist. Inc.

(iii): Dist. London

Estimate (SE)

Estimate (SE) [(i)-(ii)]

Estimate (SE) [(i)-(iii)]

-2.913 (5.159)

-2.929 (5.142) [.015]

-2.949 (5.155) [.036]

10.563*** (.088)

10.166*** (.069) [.397***]

10.113*** (.069) [.450***]

3.222*** (.872)

1.894*** (.537) [1.328***]

1.812*** (.515) [1.410***]

4156

4156

4156

Treatment

Post (2003-2004)

Treatment·Post

Obs.

Notes: Estimati on of compensati ng vari ati on (in km’s cl oser) of bi g-box entry wi th out [col umn (i )] and wi th [col umns (ii ) and (iii )] sel ecti on correcti on. Resul ts in col umn (ii ) are based on th e excl usi on restri cti on “average di stance from hi stori c incumbents,” whil e th ose in col umn (iii ) are based on “distance from London .” Estimates from col umn (i ) are compared with those from col umns (ii ) and (iii ): th e di fferences and th ei r si gni fi cance l evel are reported i n square brackets. Number of h ouseh ol ds: 2078. Number of treated househ ol ds: 332. SEs bootstrapped over Local Pl anning Auth ori ti es (i .e., th e geographi c peri meter of th e treatment), 2000 repeti tions. ***: 1% si gni ficance. **: 5% significance. *: 10% si gnificance.

TABLE A1 — Location-Specific Utility Model (2001-2004) (i) OLS

(ii) 2SLS

(iii) 2SLS

(iv) OLS

Est. (SE)

Est. (SE)

Est. (SE)

Est. (SE)

Big*2002

—

—

—

.654 (.516)

Big*2004

—

—

—

1.703***

Small*2004

—

—

—

.783***

Price Index

-.031***

-.2***

-.348***

-.01(.008)

Distance (100 km)

-2.04***

-2.06***

-2.08***

-1.994***

Floorsize (100 m2)

.096***

.122***

.145***

.063**

YES

YES

YES

YES

Variables

Controls

Notes: Regressi on of l ocati on-speci fi c utility model wi thout sel ecti on-correcti on. Col umn (i ) i s th e OLS regressi on of on observabl e ch aracteri sti cs of both supermarket-format and town centre. Col umns (ii ) and (iii) are th e 2SLS regressi ons of on observabl e ch aracteri sti cs i n whi ch th e instrumented vari abl e i s Pri ce Index. Col umn (i v) is th e OLS regressi on of on observa bl e ch aracteristi cs and time-speci fi c format constants: Big*2002, Big*2004, and Small*2004. Big*2002 i s the i nteracti on of a dummy for bi g-box and a dummy for t=2002. Si milarl y for Bi g*2004 and for Small *2004. Number of observati ons: 813. Instruments in (ii ) [à l a Hausman (1996)]: Average and SD of Pri ce Index of same format (i.e., bi g-box or small ) across town centres. Instruments in (iii ) [à l a BLP (1995)]: Bi g*2002, Bi g*2004, and Small *2004. Controls: Parki ng Lots, Till s, Floorsi ze·Tills, Di stance·Tills, Fl oorsi ze 2·Di stance, Fl oorsi ze3·Distance, Fl oorsi ze4·Distance, Retired, Working Cl ass, and Popul ati on 2. ***: 1% si gni ficance. **: 5% significance. *: 10% si gnificance.