Spatial Competition in the French Supermarket Industry

 
Spatial Competition in the French
               Supermarket Industry∗
                               Stéphane Turolla†
                          INRA UMR SMART – Rennes
          First version: February 2008. This version: May 2010

                                          Abstract
           This papers develops a structural model of spatial competition to analyze
       the competition intensity among large grocery stores at geographical market
       level. The model is estimated for a metropolitan area of South of France
       and uses a cross-sectional household survey containing detailed information
       on stores visited for the main food product categories. Using estimates of
       demand parameters and assuming a particular pricing rule, we recover both
       stores’ marginal cost and margin. The results point out that on the whole
       retailers exert a significant local monopoly power due to important differ-
       entiation forces, especially for the hypermarket format. We then perform
       counterfactual policy simulations based on propositions formulated by the
       Competition Authority that aim to restore effective competition in this in-
       dustry. We show that imposing a hypermarket divestiture to a dominant
       retailer is always beneficial to consumers whatever the purchaser identity.

       Keywords: Spatial competition, Structural model, Discrete choice model,
       Differentiated products, Supermarket industry
       JEL Classification: C35, L13, L81

   ∗
     We are grateful to Aurélie Bonein, Stéphane Caprice, François Gardes, Marc Ivaldi, Jean-
Louis Monino, Vincent Réquillart and several participants at the JMA 2007 conference, Journées
doctorales de l’ADRES 2008, the AFIO-INRA seminar in Toulouse and the ESEM 2008 conference
in Milano. We are most grateful to the CCI of Montpellier for financial assistance and data
accessibility. All errors are my own.
   †
     Address: INRA UMR SMART, 4 Allée Adolphe Bobierre, CS 61103, F- 35011 Rennes Cedex
(France). Email: stephane.turolla@rennes.inra.fr
1       Introduction
Over the last fifteen years, prices for a wide range of food products raised signifi-
cantly in France; while they are remained stable in the Eurozone, even decreased
for some countries (e.g. Germany, Netherlands).1 This inflationary trend has led
the French government to commission a series of investigations in order to question
pricing practices and market power enjoyed by French retailers.2 The conclusions of
these inquiries have stressed unanimously that the decrease of the price competition
level results from the passing of the Galland Law and the Raffarin Law (both en-
acted in 1996). These laws were promoted in order to counterbalance the increasing
power of retail chains over both manufacturers and small independent stores. The
Galland Law was dedicated to prevent retailers from engaging in below-cost pricing
by defining clearly the below-cost selling threshold. Unfortunately, instead of restor-
ing a faithful negotiation framework, the Galland Law has shifted the bargaining
process from “upfront margins” to “hidden margins” to the expense of final prices.
The mechanism by which this regulation has relaxed intra-brand competition has
been widely documented in the theoretical literature (see for instance Allain and
Chambolle, 2009). Further, Biscourp, Boutin, and Vergé (2008) confirmed empiri-
cally the price-raising effect of the Galland Law. At the same time, concerned by
preserving small independent stores from the entry of German mass discounters (i.e.
Aldi, Lidl), the legislator toughened the entry regulation through the passing of the
Raffarin Law. The administrative authorization, prerequisite for the granting of the
building permit, has been enlarged to stores with sales areas over 300 m2 (1,500 m2
under the previous regulation). As a result, important barriers to entry were estab-
lished that secured the rent of the incumbents by preventing them from potential
entrants and, consequently, soften both upstream and downstream competition.
    Nowadays, it is well admitted that the entry into force of these regulations has
reinforced retailers’ market power. According to the producer association ILEC,
retailers’ average gross margin has raised by 49.1% from 1998 to 2004. As a con-
sequence, since the middle of the 2000’s, the French government seeks to restore
an effective competition in the grocery retailing. This led first to define a new net
invoice price that aims to transfer part of “hidden margins” to consumers. If the
intention was laudable, it resulted in practice a slight decrease of retail prices. This
rigidity is mainly explained by the concentrated market structure of the downstream
sector that prevents a fierce price competition. In 2009, the largest five retailers had
a share of 75.6%, placing France second in Europe. Recognizing that lower re-
tail prices can not occur without enhancing price competition into the downstream
market, France has applied itself to amend its retail planning regulation in order to
stimulate the entry of new competitors in trading areas. Hence, in October 2007,
the French Minister of Economy asked the Competition Authority (CA) to issue an
opinion on the entry regulation (Competition Authority, 2007). The CA has stressed
    1
     The average price of food products corrected for inflation increased by 5.9% in France over the
1996-2009 period (source: Eurostat, IPCH).
   2
     For a recent overview of experts reports on these issues, see Commission Attali (2008), Com-
mission Hagelsteen (2008) and Rapport Charié (2009).

                                                 1
that beyond the degree of concentration at the national level, one may pay attention
to retailers’ local monopoly power. The presumption is strong that retailers exert
locally a significant market power that distorts price competition. In addition, the
CA has suggested several lines of inquiry likely to evolve the market structures in
favor of an increased competition.
    The primary goal of this paper is to assess empirically the extent of retailers’
market power for a typical local area and uncover its drivers. To that end, we
develop and estimate a structural model of demand among spatially differentiated
grocery stores that accounts for consumers’ preferences over stores characteristics
and geographic proximity. We resort to a mixed logit model, rather than a logit or
nested logit model, so as to capture consumers unobserved heterogeneity and give
an accurate appraisal of substitution patterns. The estimated demand parameters
are then used to compute retailers’ margins under alternative pricing rules. With
these results in hand, we are able to perform some counterfactual experiments and
quantify the effects on retail prices and consumer welfare regarding the hypothetical
measures considered by the CA. Doing so, we provide valuable insights into the
competitive landscape of this industry.
    Researches on supermarket competition are numerous. However, they usually
rely on observation of purchasing decisions for a limited number of product cat-
egories or players in the market (see, for instance, Richards and Hamilton, 2006,
and Richards, 2007, respectively), which limits the scope of their conclusions. One
exception is the empirical study of Smith (2004) on the UK supermarket industry.
Using a household panel survey, Smith investigates the extent of retailers’ market
power derived from multi-stores ownership under the particular assumption that
retail chains adopt a zoning pricing strategy at the regional level. The shopping
patterns are estimated using a discrete-continuous choice model where consumers
choose where to shop and how much to spend. Once the parameters estimated, he
runs several experiments to evaluate the price response of stores for different own-
ership structures (demerger/mergers). Following the methodology of Smith (2004),
Dubois and Jódar-Rosell (2008) extend his analysis for the case of France. In ad-
dition to the pricing strategy, these authors consider that retailers can adjust their
ratio of private labels offered with respect to national brands in order to maximize
their profits.
    In this paper, we exploit a unique database that is not subjected to the prelim-
inary remarks formulated. Besides, we differ from the studies of Smith (2004) and
Dubois and Jódar-Rosell (2008) owing to the nature of our data that allows us to
examine more precisely (from a geographical point of view) the features of spatial
competition among grocery stores within a trading area. Concretely, consumers are
asked in our survey for the stores visited according to eight food product categories
covering a large part of food sales. The richness of the data allows us to observe
a significant heterogeneity among consumers for product categories purchased in
large grocery stores. We depart from this observation to modelize consumer’s store
choice decision as a two-stage process: (1) whether or not buying a particular food
product category in a large grocery store and, conditional on the shopping basket
constituted, (2) which store to visit. We argue that the consideration of an individ-

                                          2
ual shopping basket is more adapted to capture the competition effects of pricing
strategies differentiated by product categories adopted by retailers.
    The model is estimated for a metropolitan area of South of France that is rep-
resentative of the high level of concentration encountered on the French territory.
Using a unique cross-section survey of 1,654 households and a database of stores
characteristics, we find that on the whole large grocery stores exert a substantial
local monopoly power. Among store formats, hypermarkets appear as the most
profitable (on median) due to important differentiation forces. However, the within-
format heterogeneity observed in our results points out that local competitive envi-
ronment (i.e. spatial competition) accounts greatly in the extent of market power.
Our simulation results support the proposition of the CA that implies stores di-
vestitures to limit the anti-competitive effects ensuing from an abuse of dominant
position. We show that imposing a hypermarket divestiture to a dominant retailer
is always beneficial to consumers whatever the purchaser identity.
    This paper is related to the growing literature in empirical industrial organiza-
tion devoted to the estimation of structural model of competition for differentiated
products (see Ackerberg, Benkard, Berry, and Pakes, 2007, for a review). Sev-
eral recent papers extend the methodology proposed by Berry (1994) and Berry,
Levinsohn, and Pakes (1995) to analyze retail markets where firms compete in a
‘Hotelling-type’ model. For example, Manuszak (2001) and Thomadsen (2005) eval-
uate empirically the competitive effects of mergers in the Hawaiian gasoline market
and US fast food industry, respectively. Davis (2006) carefully investigates product
positioning and the effect of distance on rivals in the US movie theater industry;
likewise Thomadsen (2007) for the US fast food industry. McManus (2007) also ex-
amines the product design efficiency under nonlinear pricing for the specialty coffees
market. In the spirit of these papers, Chiou (2009) evaluates consumers’ preferences
for buying DVD at Wal-Mart, compared to others mass merchants and alternative
retail channels.
    In a broader sense this paper is also related to empirical studies focusing on
contract distortions and price-raising effects observed after the introduction of the
Galland Law. Hence, by explicitly specifying a model of vertical relationship with
nonlinear pricing between retailers and manufacturers, Bonnet and Dubois (2010)
have shown that manufacturers in the bottled water industry used resale price main-
tenance to the detriment of retail price. Using CPI data, Biscourp, Boutin, and
Vergé (2008) have also stressed that the passing of the Galland Law has favored the
decrease of the intra-brand competition for the whole range of food products.

    The remainder of the paper is organized as follows. First, we briefly depict the
market structure of the French supermarket industry and compute some concentra-
tion indicators to highlight the high level of concentration at geographical market
level (Section 2). Section 3 provides an overview of the data used for the estimation.
The empirical model used to determine households’ store choice is then specified in
Section 4 as well as the pricing equations that allow us to back out stores’ margin.
We then present the estimation method in Section 5 and discuss the assumptions
required to identify the estimates of demand parameters. Section 6 presents both
the estimates of demand parameters and stores’ margin, and also reports the results

                                          3
of robustness tests performed. We discuss the impact of some counterfactual policy
simulations on retail prices and consumer welfare in Section 7. Finally, we conclude
in Section 8 and outline some refinements for future researches.

2       The French supermarket industry
In 2008 the French food retail industry had sale revenues of e196,8 billions and
represented 594,000 jobs. Since its expansion from the end of the 1950s to these
days, the supermarket industry appears as one of the most dynamic sector of the
French economy. Over the years, this sector became the favorite distribution channel
of the French and accounts for, to date, 70% of sales in the food retail market and
20% for non food items.
    One of the most striking features of this success is the low number of players who
share it. The French grocery retailing industry is then dominated by six firms that
together had 84% of the market shares in 2009: Carrefour (24%), Leclerc (17%),
Intermarché (13%), Auchan (11%), Casino (10%) and Système U (9%). This con-
centrated market structure is not specific to the French market, since we observe the
same tendency to concentration in a large majority of European countries. Several
reasons are in force to explain this. First, Maican and Orth (2009) have shown that
the productivity gains that have accompanied the entry of large grocery stores have
fostered exit of the less productive firms (including a substantial number of small
independent stores). Alongside, incumbents have influenced the contestability of
the market because of the nature of competition they engage in it. According to
Ellickson (2006), the explosion of product variety and stores size have led to increase
significantly endogenous sunk costs, reducing the threat of entry of new competi-
tors.3 It is also largely documented that large entrants used their buyer power to
increase their market dominance (Inderst and Mazzarotto, 2009). In addition to
these market mechanisms, European countries have adopted entry regulations that
have established important barriers to entry that favored incumbents, even if their
nature differs substantially across countries. This last effect being more pronounced
for France (see Boylaud and Nicoletti, 2001).
    In its first opinion on the French grocery retailing industry, the CA did not
consider that the market structure of the downstream sector may be harmful to
competition; contrary to tariff practices encountered into the upstream sector (see
Competition Authority, 1997). Indeed, none of the retailers have a dominant posi-
tion nationally. However market configurations differ noticeably from one geograph-
ical market to another which presumes that retailers may have strong positions
in a number of trading areas. Therefore, it seems more relevant to conduct such
analysis for geographical markets. As an illustrative example, we compute some
simple statistics summarizing the concentration at the market level. Similar to the
approach used by Barros, Brito, and de Lucena (2006) and Biscourp, Boutin, and
Vergé (2008), we assume that a given store competes with rivals located within a
    3
     Assuming that consumers value store size as a ‘vertical’ characteristic, Ellickson (2006) demon-
strates with help of a structural approach that “escalating investments in variety enhancing dis-
tribution systems yield a natural oligopoly of high quality firms”.

                                                 4
Table 1: Market structure for the 500 largest French cities

                                       Fascia                                                   Firm
                       Nb         Mkt Sh. 1 (%)              HHI                Nb         Mkt Sh. 1 (%)              HHI
 Q1                   15.42           27.88                1664.31              8.84           33.47                2189.05
 Median               18.08           24.63                1436.48              9.67           31.16                2024.85
 Q3                   22.60           23.68                1372.29             10.30           30.84                1999.82
 Total                25.11           23.80                1389.49             10.32           32.12                2093.41
 Montpellier          18.00          19.88                 1087.82             10.00          34.60                 2340.05
 Notes: Descriptive statistics are reported for the first quarter of 2000 and data from the 1999 census population. The database
surveyed all the hypermarkets (selling area over 2500 m2 ), supermarkets (selling area between 400 and 2500 m2 ) and hard discount
stores. In total, we count 46 fascias and 14 firms. The average of the statistics are reported. Source: author’s calculations.

radius of 10 km. Since we do not have other information than the ZIP-code of stores,
we assume that stores are positioning at the center of their respective city. We limit
our analysis to the 500 largest cities, so a relevant market consists in one of these
cities surrounded by neighboring cities located by less than 10 km.4 Table 1 reports
the number of fascias and retailers per market, the market share of the leader and
a measure of concentration through the computation of the Herfindahl-Hirschman
Index (HHI) based on selling areas (again considering fascia and retailer). We detail
the results by quartile of the population distribution of the cities. It appears that
the extent of market concentration is more pronounced at the market level. For a
significant number of markets, we observe that market leader has a market share
higher than 32%. Also, the HHI suggests that a majority of trading areas are con-
centrated (highly concentrated) at the fascia level (firm level), following a standard
interpretation.5
    According to several recent empirical studies in the European food retailing
sector, this local concentration is not costless for consumers since a clear positive
relationship has been emphasized between market concentration and food prices (see
Barros, Brito, and de Lucena, 2006; Biscourp, Boutin, and Vergé, 2008). Besides,
even if it has been demonstrated that the Galland Law has implicitly introduced
an industry-wide price floor, in practice stores operating under a same fascia charge
different prices. A recent survey conducted by the consumers association UFC-Que
Choisir reveals that prices may vary up to 20% between two hypermarkets of a same
retailer, depending on competition encountered.6
    Beyond market structure, price competition is also strongly distorted by vari-
ous differentiation strategies carried out by retailers. Hence, when choosing which
stores to visit, a consumer accounts for a variety of factors other than price. For in-
stance, private labels, product range, quality of products (e.g. freshness), consumer
services are important components of the consumer decision making process that
relax price competition. One factor seems, however, raised more attention because
of its leading part in a grocery store success: location. Highlighted by the aphorism
   4
    This distance corresponds to a 12-minute drive time for an average driving speed of 50 km/h.
   5
    Formally, the HHI is defined as the sum of squares of all the market shares in the market.
According to the 2004 EU Merger Guidelines, a HHI over 2000 indicates a highly concentrated
market.
  6
    UFC-Que Choisir (26/12/2007).

                                                                5
“location, location, location”, spatial positioning appears as a major differentiation
force in grocery retailing, similarly to other retail industries. According to a survey
of the French national institute for statistics and economic studies (INSEE), 67%
of households consider that accessibility is their primary criteria for choosing their
shopping destination. Due to the importance attached by consumers to distance
traveled, stores location plays a prominent role in competition among retailers.7
    Taken together, market structures and spatial differentiation appear as key ele-
ments to investigate whether retailers exert local monopoly power to dampen price
competition.

3       Data
3.1     Presentation and descriptive statistics
We use a original database that surveys households’ store choice, dwelling in a
metropolitan area of South of France, for several food and non-food categories. The
area of study is the French administrative aire urbaine of Montpellier, covering a
total number of 459,916 people.8 According to Table 1, it is representative of the
concentrated market structure observed in other geographical markets. The survey
was conducted jointly by the chamber of commerce of Montpellier and the depart-
ment of economics of University Montpellier I during the year 2000.9 It follows the
quota sampling methodology to create a sample to be representative of the geograph-
ical, age and socio-economic group composition of the population of concerns. The
data was collected at the household level. A total of 1,654 households were asked
for stores visited according to 49 product categories. In the following, we restrict
our analysis to the most purchased height food categories (for twelve recorded) due
to the computation burden of the model. One appeal of the database stems from
the richness of information collected at the category level. For instance, we know
for each category, all stores patronized by the household regardless the distribution
channel (e.g. specialized store, retail store, market place) and the corresponding fre-
quency of purchase (by class amplitude of 25%, plus an epsilon option). Besides, the
survey gives numerous information on households’ characteristics like head house-
hold’s age and socio-economic group, household’s income, number of persons per
household as well as their location residence among others.

    We supplement this database with information on stores characteristics obtained
from the Atlas de la distribution, a national survey of French outlets, and in situ
survey. We obtain stores characteristics information such as fascia, location, store
size, the number of employees, the existence of a gas station among others. In
order to determine distances traveled by consumers to visit stores, we geocoded
    7
     The importance of stores location has led the UK Competition Commission and the CA to
put under scrutiny the presumed anti-competitive practices of land banking by retailers (see Com-
petition Commission, 2008 and the inquiry started by its own initiative by the CA in February
2010).
   8
     Source: population census INSEE 1999.
   9
     See LSA n◦ 1563 for further details.

                                               6
Table 2: Summary statistics

       Store data
       Variable                             N           Units             Mean           SD           Min           Max
       Hypermarket                          62         Binary             0.19          0.40           0              1
       Supermarket                          62         Binary              0.42          0.50           0            1
       Hard discount                        62         Binary             0.31          0.46           0              1
       Convenience store                    62         Binary             0.08          0.27           0              1
       Surface                              62           m2              2167.14       2503.56       450.00       11799.94
       Parking slots/m2                     62        Nb./m2               0.14          0.09           0           0.55
       Cash registers/m2                    62       Nb.*100/m2            0.66          0.20         0.33          1.25
       # Stores                             62
           # Hypermarkets                   12
           # Supermarkets                   26
           # Hard discounts                 19
           # Convenience stores              5

       Household data
       Variable                             N                                 % of households
       Age group 1                                                                 11.76
       Age group 2                                                                 11.27
       Age group 3                                                                 19.23
       Age group 4                                                                 22.96
       Age group 5                                                                 15.21
       Age group 6                                                                 19.57
       Credit card holder                                                          81.74
       Living in a house                                                           56.64
       Montpellier                                                                 52.42
       Rural town                                                                  28.77
       # Households                        1446
   Notes: There are 6 age groups (20 to 24, 25 to 29, 30 to 39, 40 to 49, 50 to 59, ≥ 60). Source: author’s calculations.

in a geographical information system stores address, as well as census tracts and
Montpellier’s block-group. Thus we are able to compute euclidian distances between
each household and stores belonging to their respective choice set by assuming that
households live at their block-group or census tract’s centroid, respectively.10
    Since we are focusing on the supermarket industry, we aggregate outlets other
than hypermarkets, supermarkets, hard discounts and large convenience stores in
a single outside option. This leads to a total number of 80 + 1 alternatives. Also,
we limit our analysis to household primary shopping destination (see the discussion
below). Since some outlets are only visited for top-up shopping, this reduces the
potential household’s choice set to a lower, but still important, number of 62 + 1
alternatives. Nonetheless, the area of study sprawls approximately over an area of
1,500 km2 which could lead to believe that only a subset of the alternatives is effec-
tively considered by each household. In order to account for a more realistic choice
  10
    By specifying a single-address model, we argue that household’s residence corresponds mainly
to the point of departure of the shopping trip. Multi -address models are more a matter of concern
for markets where purchase is motivated by impulsive behavior or immediate need (see for instance
the study of Houde (2010) for the gasoline market).

                                                                7
set for each household, we follow the methodology applies by the European Com-
mission or the CA in previous investigations and include in household’s choice set
outlets that are located within a radius of 20 km around its residence.11 Departing
from this choice set, we decide to restrict the number of potential stores visited by
allowing only one store by fascia (the nearest to the household’s residence), except
the case where two stores of a same fascia are distant up to one kilometer. This last
condition being imposed to account for the lack of precision of lower computed dis-
tances owing to the positioning of households at their block-group or census tract’s
centroid.
    Note that one limitation of our definition of households’ choice sets is that we
exclude de facto purchases realized in outlets far from households’ residence which
typically may arise for consumers living in a small peripheral rural town but working
at the metropolitan city. We count 208 households in this case. Hopefully, this
concerns a small part of our sample (i.e. ≈12.5%) that we remove in the rest of the
study. To resume, after eliminating these households, the database used to conduct
our analysis corresponds to a cross-section survey of 1446 households.
    We present some summary statistics of stores and households characteristics in
Table 2.

3.2    The price index
The database in our possession contains a rich set of information about households
and stores characteristics. Nevertheless, we do not observe prices paid by households
for items which make up their shopping basket and let alone the entire set of prices
across all stores that composed their respective choice set. This is problematic to
infer correctly the drivers of consumers store choice.
    To solve this problem, we first run a survey on a sample of items’ price for a
subset of stores of the area of study. Thereafter, we follow recent studies facing
the same issue (see, for instance, Chiou, 2009) and estimate a price index for each
category for stores non-surveyed. More precisely, we collect the price of 91 national
brand products and first price products in 27 stores of the area of study.12 The choice
of including national brand products in our prices report lies on their availability
in almost all stores (excepted hard discount stores) and accounts for the need to
work with homogeneous varieties (e.g. a 400g jar of hazelnut spread of brand name
Nutella). However in order to construct price indices which encompass all store
formats - specifically hard discounters - the selection of first price products appears
unavoidable. Then for a store j and a category c composed of k = 1, .., K items,
the price index is computed according to the following expression:
                                          �K
                                                pk,j,c
                                   p�j,c = k=1                                      (1)
                                              K
 11
    See, for example, decisions in cases No. IV\M.1085 Promodes/Catteau, No. COMP/M.1221
Rewe/Meinl or No. COMP/M.1684 Carrefour/Promodès. A 20 km radius corresponds approxi-
mately to 20 to 30 minutes, depending the average driving speed assuming.
 12
    A list of the selected products is available upon request.

                                           8
Table 3: Hedonic regression of Log-price

                                                                                                                SUR Model
                                Fruits & vegetables               Meat          Cooked meat              Cheese    Other dairy product                   Grocery item          Alcoholic drink          Soft drink
     Constant                        4.6550***                 4.6673***         4.4256***             4.4959***       4.5845***                          4.5683***              4.5427***              4.5580***
                                      (0.1713)                  (0.0776)          (0.0758)              (0.0514)        (0.0520)                           (0.0522)               (0.0259)               (0.1025)
     Hypermarket                         -0.0601                 -0.0278             0.0078             -0.0307*                  -0.0206                    -0.0206               -0.0174**            -0.0667**
                                        (0.0531)                (0.0241)            (0.0235)            (0.0159)                 (0.0161)                   (0.0162)                (0.0080)             (0.0318)
     Variety index                       0.0240                -0.1606**          0.2084***            0.1893***                  0.0080                   0.1427***               0.1078***              -0.0508

9
                                        (0.1619)                (0.0734)           (0.0716)             (0.0486)                 (0.0491)                   (0.0494)                (0.0245)             (0.0969)
     # rivals
The store with the biggest turnover of the metropolitan area is chosen as base
100 of the price indices (Carrefour #2 ). Besides, the sample of stores surveyed was
constructed so that to be representative of store formats, fascias as well as locations.
Prices report has been realized in three days in order to avoid seasonal variations,
especially for the fruits and vegetables category. Thereafter price indices for stores
non-surveyed are estimated by requiring a hedonic price regression. But instead of
running separate regressions for each category, we argue that unobserved hetero-
geneity in the pricing decision across categories may be correlated. For example,
items of different categories share identical transportation and logistic costs. Conse-
quently, we assume that this unobserved heterogeneity is distributed according to a
multivariate normal distribution and specify a seemingly unrelated regression (SUR)
equations model. The log of the price of the selected basket of items is regressed on
a set of retailer fixed-effects and variables describing both the competitive environ-
ment and the demand. Table 3 reports the estimates.13 The correlation matrix of
residuals are reported in appendix.
    It may be pointed out that calculation of price indices for hard discount stores
follows a separate procedure. Since hard discounters set uniform prices across their
stores, the use of a hedonic regression is no more necessary. Instead, we depart from
our price report and simply refer to Eq.(1) to compute the average price of their
shopping basket for each category. Finally, to insure a correct computation of the
indices, we remove from the price index of the base outlet, (i.e. Carrefour #2 ), the
national brand products in order to deal with similar products.

4      The empirical framework
In this section, we first specify the formulation of our demand model, then we derive
the pricing equations from the pricing game supposed played by French retailers.
Then we back out stores marginal cost and thereafter their price-cost margin.

    Departing from our data, several modelisation approaches could be carry on to
estimate households’ preferences on store choice. The more intuitive consists in
using the information at the category level and specify a model that explains house-
hold’s store choice, conditional on a category. The central point of this approach
relies on the model faculty to handle the multiple choices of a given household. In
this view, we could refer to the multiple discrete choices model proposed by Dubé
(2005) in the context of multiple purchases of carbonated soft drinks. Another way
would consist in estimating a ‘logit-type’ model where household’s choices should be
both correlated over category purchase occasions and stores, which implies a large
set of parameters in our context. We observe however no variation among categories
(except the price), which prevents us to fully adopt one of these models and esti-
mate households’ preferences on the basis of their category purchases. Instead, we
propose a more parsimonious model where households are supposed to purchase a
bundle of goods, which belong to those categories. Consequently, households choose
  13
    It is worth noting that
                        � the Breusch-Pagan LM test� for error independence supports the resort
to a SUR specification χ2 (28) = 202.62; p = 0.0000 .

                                              10
Table 4: Supermarket channel choice by category (in %)

        Category                        Mean (S.D.)               Category                         Mean (S.D.)
        Fruits & vegetables             0.4682 (0.4992)           Other dairy product              0.8755 (0.3302)
        Meat                            0.6065 (0.4887)           Grocery item                     0.8416 (0.3652)
        Cooked meat                     0.5712 (0.4951)           Alcoholic drink                  0.7040 (0.4566)
        Cheese                          0.7906 (0.4041)           Soft drink                       0.8831 (0.3214)
       Notes: S.D. corresponds to standard deviation. The number of observations is 1446. Source: author’s calculations.

their primary shopping destination among retail stores, conditional on a bundle of
goods (i.e. a shopping basket). This implies to aggregate households store choices
over the whole set of product categories in order to determine their primary shop-
ping destination for the entire food products.14 Doing so, we limit our analysis
to competition among stores and leave aside the issues of multi-stop shopping and
between-categories complementarities.
    Nonetheless, it seems realistic to assume that beyond retail store choices, between-
households heterogeneity is also observable in the type of retail channel visited ac-
cording to product category. A simple look at descriptive statistics on frequency of
purchase for the supermarket channel confirms this fact (see Table 4). The pattern
being more pronounced for the fresh products. Therefore we argue that competition
does not necessarily take place fully for the entire product range sold in a store ac-
cording to the household who visits it. Depending on households’ habits, households
may pay attention or not to some product categories which could either strengthen
or lower competition consequently. For instance, some consumers may prefer to buy
perishable products in specialized stores due to a higher marginal utility for quality
which reduces their shopping list for retail stores compared to large-basket shoppers.
Hence, the within-household variation observed among categories individualizes the
price of the consumer’s shopping basket. A well-documented consequence of this
behavior is that retailers price discriminate regardless product type and market de-
mand configuration (Giulietti and Waterson, 1997; Walsh and Whelan, 1999), but
also adopt different kinds of pricing strategies (e.g. EDLP or HiLo) in order to
attract a larger share of consumers.
    In order to account for heterogeneity among consumers in terms of product cat-
egories purchased in the supermarket distribution channel, we propose a two-stage
model where in the first stage we estimate the probability that a household buy
a certain category in a large grocery store. Thereafter, we use these probabilities
to weight the price of the corresponding category such that households pay higher
attention to categories’ price they usually buy in large grocery stores. Our formula-
tion of a weighted average price of the shopping basket is closer to the one adopted
by Briesch, Chintagunta, and Fox (2009). Nonetheless, we differ to these authors
by at least two points. First, in our model, the household’s choice relies on the
  14
     In the following, we determine household’s primary shopping destination by computing a
weighted average of visits for each store of its respective choice set. To account for the relative
importance of each category in the aggregate decision, we compute from the TNS Worldpanel
survey the share of expenditures for each category and weight the binary decisions (see the appendix
for further details).

                                                               11
decision to realize its purchases in the supermarket distribution channel whereas
the occurrence in Briesch, Chintagunta, and Fox (2009) encompasses all types of
retail channels. Second, we adopt a modelisation which accounts for the potential
correlation between households’ choices which Briesch, Chintagunta, and Fox (2009)
do not.

4.1     Demand model: retail channel choice
For each household h, (h = 1, . . . , H), we observe its decision to buy a category
c, (ch = 1, . . . , Ch ), in a retail store across a set of C categories. Following the
discrete choice literature, its purchase incidence can be represented by a vector
ih = �ih1 , ih2 , · · · , ihC � of binary dependent variables. We estimate the probability
Pr (ihc ) of a single decision through a system of simultaneous probit equations. We
denote i∗hc the underlying latent variable associated with the c-th category. The link
between the purchase incidence and the latent variable is expressed as follows:
                                             �
                                               1 if i∗hc > 0
                                       ihc =
                                               0 otherwise
    These latent variables are defined by a linear combination of a set of explanatory
variables and a error term. Using the matrix notation, the system can be written
as follows:
                                    I ∗ = Xβ + ε                                   (2)
where X = �x1 , . . . , xp � is a C × p vector of p explanatory variables, β �β1 , . . . , βp �
is a corresponding vector of parameters of same dimension and ε is a C × 1 vector
of error terms that accounts for unobservable heterogeneity. We assume that the
choice of a large grocery store for a category purchase is explained both by house-
hold’s characteristics (age groups, house, card, work) and by its surrounding retail
environment (montpellier, # hypermarket 10km).
    However, we believe that the household’s decision of whether or not to buy
the c-th category in the supermarket retail channel may not be independent of
its decisions with respect to other categories. In other words, household’s choices
may be related due to cross-effects that reflect complementarities among categories,
but also unobservable factors like shopping cost considerations (e.g. search costs,
travel costs) or quality seeking behavior that appear at the retail channel level.
This assumption is corroborated by the calculation of the tetrachoric correlation
coefficients between all the categories (see Table 5). As we observe, the entire set
of estimated correlations are significant and positive. Besides, the magnitude of the
estimates for certain pair of categories, for instance {meat, cooked meat} or {cheese,
other dairy products}, suggests a strong complementarity effect to purchase jointly
certain kinds of items in a same retail channel. Similarly to Chib, Seetharaman,
and Strijnev (2004), we argue the necessity to model jointly households’ purchase
decisions at the category level when it is possible.15 Therefore to control for possible
correlations arising from unobservable factors we assume that the error terms of the
  15
    Nonetheless, we differ from the marketing literature that addresses the subject of multicategory
purchasing behavior by the level at which the co-incidence occurred, i.e. the retail channel.

                                                12
Table 5: Tetrachoric correlation matrix of food categories
                             Fruits & veg- Meat             Cooked meat    Cheese    Other dairy   Grocery item   Alcoholic   Soft drink
                             etables                                                 product                      drink
     Fruits & vegetables     1.0000
     Meat                    0.7586*         1.0000
     Cooked meat             0.6507*         0.9289*        1.0000

13
     Cheese                  0.6515*         0.7529*        0.7408*        1.0000
     Other dairy product 0.6943*             0.7792*        0.7789*        0.9335*   1.0000
     Grocery item            0.5760*         0.6618*        0.6783*        0.7613*   0.9012*       1.0000
     Alcoholic drink         0.3322*         0.4128*        0.4626*        0.4931*   0.6223*       0.6121*        1.0000
     Soft drink              0.5052*         0.6005*        0.5762*        0.7834*   0.8892*       0.8263*        0.7238*     1.0000
     Note: * significance at the 1% level. Source: Author’s calculations
latent equations are distributed according to a multivariate normal distribution,
ε ∼ N (0, Σ), where Σ = {ρjk } is the correlation matrix obtained considering the
Cholesky decomposition of the covariance matrix of the errors: Σ = Lee� L� , where
e are independent standard normal random variables and L the lower triangular
matrix with diagonal elements equal to unity:
                                                    
                                   1 ρ12 · · · ρ1C
                                 ρ21 1 · · · ρ2C 
                                                    
                           Σ =  ..     .. . .    .. 
                                 .      .     . . 
                                  ρC1 ρC2 · · · 1
   It results that the outcome for the C different choices, for the household h, is
now specified through a Multivariate Probit model (Chib and Greenberg, 1998; MVP
hereafter). The probability of the corresponding combination of choices, conditioned
on parameters β and Σ is given by:

                             Pr(I h = ih |β, Σ) = ΦC (xβ1 , . . . , xβC )

where ΦC (·) denotes the C-variate standard normal distribution. The results are
reported in the appendix.

4.2       Demand model: household’s store choice
The second part of the demand model is more familiar with respect to the liter-
ature on structural model of demand (Berry, 1994; Berry, Levinsohn, and Pakes,
1995; Nevo, 2001). Given the discrete nature of household’s decision, we follow the
standard random utility approach and specify a discrete choice model to assess the
drivers of households’ store choice. Households preferences are assumed to differ
due to their location residence as well as observed and unobserved heterogeneity
in their taste for stores characteristics. To account for this flexibility, we define a
random coefficients logit model (or mixed logit) which allows to estimate more re-
alistic substitution patterns than simple ‘logit-type’ model. Concretely, the mixed
logit model yields flexible estimates of own- and cross-price elasticities by avoiding
the problematic independence of irrelevant alternatives (IIA) assumption involved
in discrete choice models where heterogeneity is solely captured through the idiosyn-
cratic term.16
    We assume that a household h chooses its primary shopping destination ac-
cording to the highest utility rule derived from patronizing one of the stores j,
(j = 1, . . . , J), including in its choice set Jh , or choosing an outside option j = 0.
Recall that household’s choice set is defined as the closest store by fascia located
within a radius of 20 km around its residence. Thus, following the typical notation
for discrete choice models of demand, the indirect utility that a household h, who
 16
      See Train (2003) for further insights.

                                                 14
resides in location Lh , gets from visiting store j ∈ Jh located in Lj is:
                      6
                      �
    Uhj = α0 p�hj +         αg p�hj dage
                                     hg + δ (D (Lh , Lj ) ; λh )
                      g=2
            �                            �                 ��
        +       γm D (Lh , Lj ) zhm +          φn xjn +                ϕsq vq dfs ormat + ξf + εhj   (3)
            m                              n                 s    q

where p� is the household specific price of the shopping basket, dage
                                                                   hg is a dummy vari-
able equals to one if household h is in age group g, δ (·) is a parametric function of
the distance between Lh and Lj (i.e. D (Lh , Lj )) know up to the parameter λh which
is assumed varying by household, zhm are M observed household characteristics and
xjn are N observed store characteristics. Similarly to the distance parameter, we as-
sume that the parameter of store size varies by household. We also include a dummy
variable dfs ormat for one of the S store formats (s=hypermarket, supermarket, hard
discount store, convenience store) that are interacted with Q variables representing
a mix of household and store characteristics denoted by v. Finally, ξf is an index
of unobserved – to the econometrician – fascia attributes and εhj the idiosyncratic
term supposed i.i.d. according to a type I extreme value distribution.
    Price sensitivity is supposed to vary by six head household’s age groups (with
the youngest taken as the reference). Thus, the coefficient α0 corresponds to the
marginal utility of price of a ‘representative’ household and deviation from this mean
depends on the coefficients of the interaction of price with households characteristics.
Recall that following the first stage of our model, the price variable is defined as the
sum over the eight categories of the category purchase probability Pr (Ihc ) multiplied
by its corresponding price index p�j,c :
                                               C
                                               �
                                      p�hj =         Pr (Ihc ) p�j,c                                 (4)
                                               c=1

    Similarly, we allow the coefficient of distance λh to vary by household. But in-
stead of introducing heterogeneity through households categories, we specify a ran-
dom coefficient on distance which is more appropriated to account for the diversity
of households location. We denote by ω these unobserved household characteris-
tics. Precisely, we assume that the coefficient of distance is normally distributed
and independent to the idiosyncratic term ε. Again, we interact the distance with
observed households characteristics (e.g. the number of cars, the type of residence
and whether household’s residence is in a rural town).
    The set of store characteristics xjn includes the number of parking slots and
cash registers both per square meters as well as store size to which one associates a
random coefficient supposed distributed according to a normal distribution. Besides,
we supplement these variables by interacting store’s format with rivals counts (by
store type) in a radius of 0.5 km and 2 km to account for the competitive environment
of their vicinity. Unobserved stores characteristics (like shelfs display or assortment,
for instance), are supposed captured by the fixed-effects ξf . We argue that these
unobserved characteristics reflect essentially national strategies enacted by retailers

                                                     15
for their fascia. These common shocks are thus captured by fixed-effects set at the
fascia level. As usual, we assume that households value identically these unobserved
characteristics.
    Similarly to the “outside good” in classical demand models, households may
decide to visit other channels of retailing than large grocery stores (e.g. small
convenience store, specialized store, market place) or not purchasing those food
categories at all; which is resumed through the outside option j = 0. Without
additional information on characteristics of this alternative, we decide to normalize
to zero the characteristics of the outside option, i.e. p�h0 = D (Lh , L0 ) = x0n = ξ0 =
0.
    According to the highest utility rule, it results that household h visits store j
with probability:                    �
                               Phj =      dF (εh )dF (ωh )
                                        Ahj

with Ahj = {(εh , ωh ) |Uhj > Uhl ; l �= j} and F (·) denotes the distribution function.

4.3    Supply side: The pricing equation
We now describe the pricing rule that retailers follow. We take as given that stores
compete in prices and set their price simultaneously, conditional on their charac-
teristics supposed chosen prior to this decision (e.g. location, store size, quality,
etc.). The prices that result from this behavior are thus an equilibrium of a Nash-
Bertrand game. By deriving the pricing equations from the first-order conditions
of the profit maximization problem, we will be able to recover stores marginal cost
and consequently compute their price-cost margin.
     We assume that stores manager seek to maintain the price competitiveness of
their store across the entire product categories. This suggests that stores manager
think in terms of price positioning of the shopping basket and do not adopt a cate-
gory management. Besides, an important feature of the French market is that two
types of pricing behavior coexist depending on store format: (i) hypermarket and
supermarket prices are fixed by store manager based on local competition whereas
(ii) hard discount chains use national pricing.

    Consider the problem of a retailer R that sets uniform prices in a set of JR of
its stores. The profits of the retailer R are:
                                  �
                           ΠR =        (pj − cj ) M sj (p) − Cj                 (5)
                                 j∈JR

where cj denotes the constant marginal cost of selling a unit of a shopping basket
for store j, M is the size of the market, sj (p) is the market share of j and Cj a
fixed-cost.
Assuming the existence of a pure-strategy Nash equilibrium in prices, the first-order
condition for a typical store j is:
                                �                        ∂sl (p)
                      sj (p) +      TR (l, j) (pl − cl )         =0               (6)
                                 l
                                                          ∂p  j

                                              16
where TR corresponds to the retailer’s ownership matrix with general element TR (j, l)
equals to one when both stores l and j belong to the same retailer and zero otherwise.
This gives us a system of JR equations. Note that the second term of the left hand
side of the equation simplifies to a single element if prices are set by stores man-
ager. Define ∆R as the retailer’s response matrix with element (j, l) = ∂sj (p)/∂pl ,
retailer’s price-cost margins can now be expressed in matrix notation by stacking
up the first-order conditions and rearranging terms:

                              (p − c) = − [T ⊗ ∆ (p)]−1 s (p)                                  (7)

where ⊗ corresponds to the kronecker product. It follows that estimated stores
marginal cost depends exclusively on the parameters of the demand system and the
market conduct assumption:

                                 ĉ = p + [T ⊗ ∆ (p)]−1 s (p)                                  (8)

It is worth noting that manufacturers are absent from this scenario. As a result,
the stores marginal cost estimated from Eq.(8) include both manufacturers prices
and manufacturers margins. Depending on the vertical pricing model (linear, two-
part tariff, etc.), the distortion between the estimated and the true store’s marginal
cost could be sizeable. However, if manufacturers offer a two-part tariff contract by
setting their prices equal to their marginal costs, the double marginalization problem
vanishes and the estimated store’s marginal cost coincides with its true value. Since
our model is defined at the shopping basket level and does not refer explicitly to a
set of manufacturers, we do not specify a vertical relationship. Thus, we have to
keep in mind when discussing the results that a gap might exist between estimated
and true stores’ margins depending on vertical contracts adopted by parties.17

5      Identification and estimation strategy
The demand parameters expressed in Eq.(2) and Eq.(3) are estimated with simulated
maximum likelihood (SML). We denote θM V P = {β, ρ} and θM XL = {α, λ, γ, φ, ϕ}
the set of demand parameters corresponding to the multivariate probit model and the
mixed logit model, respectively. Conditional on θM V P , the log-likelihood function
of the combination of the category purchase incidences may be written as:
                       �        � � �             �         ��
                     L I; θM V P =     1 log ΦCh X; θM V P                       (9)
                                            h

The multivariate probability ΦCh (·) does not have a closed-form formula due to the
problem of high order multivariate normal integrals. A standard approach consists in
  17
    Although resale price maintenance (RPM) is illegal per se in France, it is well-documented that
the adoption of the Galland Law has indirectly promoted this practice. Bonnet and Dubois (2010)
have thus shown that manufacturers, in the retail market bottled water, use nonlinear pricing
contracts with RPM. Furthermore, their estimates of other nonlinear pricing contracts suggest
that manufacturers margin accounts for a limited part of retailers marginal cost.

                                                17
approximate its value by simulation. To that end, we employ the so-called Geweke-
Hajivassilou-Keane (GHK) simulator and draw from an upper-truncated standard
normal distribution R values.
   Identically, the log-likelihood of store choice conditional on θM XL is given by:
                                            Jh
                                           ��
                      �     M XL
                                         �      � � �              ���
                   L Y ;θ             ,I =     1 log shj θM XL , I                       (10)
                                                     h   j=1

where Y is the vector of store choices and shj is the probability that household h
chooses store j as primary shopping destination. Since we specify a mixed logit
model, the latter is defined as:

                                                          eVhj (θh ,I )
                                                                 M XL
                                �                �
                          shj       θhM XL , I       =�    �                   �         (11)
                                                       Jh      Vhj (θh
                                                                     M XL ,I
                                                                             )
                                                       j=1 e

Unfortunately, this closed-form expression is conditional on θhM XL . Since we do
not know the true value of θhM XL , we need to integrate Eq.(11) over all possible
values of θhM XL . The unconditional store choice probability is then approximated by
numerical simulation:
                                    1�
                                       R     �             �
                             s�hj =       shj θhM XL,r , I                       (12)
                                    R r=1
    As we explain, we refer to simulation to evaluate accurately the probability terms
in both parts of the model. By proprieties, these simulated probabilities are unbiased
and their variance diminishes as the number of draws rises. Instead of using random
draws, we follow recent advances in simulation methods and generate 100 Halton
draws. Note that, we keep the same set of draws for each iteration.18
    At this point, two estimation strategies are conceivable: a full information maxi-
mum likelihood (FIML) or a two-step method. The adoption of one of them reflect-
ing the trade-off between an efficiency gain and the burden of computation required
to achieve it. Indeed, the joint estimation of the log-likelihood functions (see Eq.(9)
and Eq.(10)) gives the true standard errors of the estimates, whereas a sequential
estimation introduced a measurement error for the estimates of the second model.
Hence, adopting the two-step approach would bias the variance-covariance matrix
of the mixed logit since the shopping basket’s price is computed from the estimated
probabilities of the category purchase incidences. Nonetheless, the matter of con-
cern of the empirical model is to provide accurate estimation of the substitution
effects, which results from the demand parameters. Efficient estimates then appear
as second-order concern. In addition, the computation time needed to estimate the
multivariate probit for eight categories is sizeable itself. As a result, we decide to
adopt a two-stage approach and adjust the standard errors of the mixed nested logit
by using the correction methods proposed by Murphy and Topel (1985).
  18
    A consensus exists in the literature regarding the superiority of Halton draws over random
draws (see Bhat, 2001; Train, 2003; Chiou and Walker, 2007, among others). For a given number
of draws, Halton draws achieve greater efficiency and coverage since successive Halton draws are
negatively correlated.

                                                         18
The demand parameters are identified through several sources of variation. First,
each choice occasion differs from one other due to heterogeneity observed in house-
holds characteristics. This allows the identification of parameters {α, γ}. Further,
for a given choice occasion, household faces a set of stores whose characteristics
differ. Hence, the average valuation of stores characteristics identifies φ and, for the
same reason, the unobserved characteristics of each fascia ξf . Note that by spec-
ifying the fixed-effects at the fascia level rather than at the store level, we avoid
the identification problem that may arise for the stores characteristics parameters
since stores dummy variables should be strongly correlated with observed stores
characteristics.
    Beyond, the main source of variation among choice occasions provides from the
heterogeneity in the spatial distribution of households’ residence and stores; that
induces different choice sets among households. It results that we observe different
distributions of distance among households dwelling in separate block-groups. This
permits the identification of the parameter λh . Finally, since the price of the shop-
ping basket is specific to a household and varies across alternatives for a given choice
set, there exists sufficient variation to identify parameters associated with p�hj .
    The literature on discrete choice models of demand has stressed many times
that an endogeneity bias may arise between prices and unobserved characteristics
(Berry, 1994; Berry, Levinsohn, and Pakes, 1995). If stores managers set their price
by taking into account what the econometrician can not observed, then the price
parameter appears correlated with these unobserved characteristics and would be
upward-bias. In our model, fixed-effects ξf are introduced in order to control for
unobserved fascias characteristics. Since we have cross-section data, we are not con-
cern by time-varying unobserved quality for fascia. In our study, the occurrence of
an endogeneity problem then relies on the existence of unobserved stores character-
istics that participate to the price-setting decision of stores manager. More precisely,
the likelihood of the endogeneity bias depends in what extent stores unobserved at-
tributes might deviate from the mean of the fascia. In order to control for this bias,
we could introduce store-specific dummy variables in the indirect utility function
and regress, in a second step, theses parameters on stores characteristics similar to
the approach followed by Goolsbee and Petrin (2004). However, we exclude this
possibility due to the number of dummy variables needed regarding the number of
observations in our database. The second method, developed by Petrin and Train
(2010) for controlling the endogeneity bias and known as the “control function”, is
also inapplicable. Its principle consists in regressing the price variable on all exoge-
nous factors and includes thereafter the residuals obtained in the utility specification
along with the price variable. Yet, since our price variable is estimated from our
SUR model, we can not use this two-stage error correction method. Thus, to insure
that our price estimate is not biased we check the absence of several outcomes de-
scribed in the literature when the endogeneity bias occurs (see section Robustness
below).

                                          19
6     Results
6.1    Mixed logit demand model
Estimation results are reported in Table 6. Recall that the parameter estimates must
be interpreted relative to the outside option. Almost all the coefficients are both
statistically and economically significant. Overall, we note that shopping patterns
differ significantly by households, store formats and the area of living. As expected,
households express a disutility of price and distance. Precisely, households between
30 to 49 years (age groups 3 and 4) appear less sensitive to price contrary to youngest
people. The utility specification in Eq.(3) allows the marginal valuation of distance
to vary by observable and unobservable households characteristics. We thus observe
that the high disutility of traveling, revealed by the estimated mean of the distance
coefficient distribution (mean=-2.1065), is reinforced for people living in a house or
in a rural town. Conversely, the higher the number of cars owned by a household
is, the lower is its sensitivity to distance. Nonetheless, the statistical significance of
the estimated standard deviation of the random coefficient on distance reveals that
beyond these interaction terms unobserved heterogeneity exists among households
regarding the willingness to travel. Similarly to the distance coefficient, we allow the
store size parameter to vary by household. On average, households value positively
the log of the selling area of a store (mean=1.5820), albeit important heterogeneity
around this mean is observed (S.D.=2.6664). Moreover, we remark that households
seems to pay greater attention to the waiting time at cash registers, as suggested by
the estimated parameter of this variable.
     We introduce several interactions terms with store formats in order to capture
variety in shopping patterns according to store formats. As we note, the willingness
expressed by single household to visit a large grocery store diminishes whatever
the format is. Besides, living in a rural town rises the marginal valuation of the
supermarket format. In addition, we count for a given store the number of rivals
within a radius of 0.5 km and 2 km by format, and interact these variables with
its format. The interest of introducing these variables is twofold. First we inves-
tigate the nature of the competition among store formats, but we also control for
the endogeneity bias discussed above by accounting for elements that may influence
the price setting of stores’ manager. Interestingly, it appears that the willingness to
choose a hard discount store increases with the number of hypermarkets and super-
markets located within a radius of 0.5 km, whereas the effect is opposite if we extend
the radius to 2 km. This may suggest that hard discount stores take advantage of
store traffic generated by large grocery stores in its surrounding environment. On
the opposite, hypermarkets suffer from this close competition as suggested by the
estimated parameter (-2.8008). However, when we extend the radius to 2 km, the
effects are reversed revealing that the complementarity effect at play between hyper-
markets and hard discounts stores may turn into a substituability effect depending
the distance between them.
     One advantage that a mixed logit model has over a simple logit model is that
it provides accurate estimates of substitution patterns since cross-price elasticities
vary by competing alternatives. We determine the elasticities of the market share

                                           20
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