Multi-Product Competition, Shopping Costs, and
Market Power: A Model of Supermarket Pricing
Howard Smithy
Øyvind Thomassenz
February 2015
Abstract
A supermarket brings together product cateogories (e.g. bread, meat) that traditionally are sold separately in specialist stores on a street (e.g. baker, butcher). This paper
measures the pricing incentives of large supermarkets by considering the role of multistore shopping, shopping costs, and pricing cross-e¤ects between product categories. We
estimate a discrete/continuous model in which consumers have demands for multiple categories and can buy from more than one store (incurring shopping costs). This type of
model has been used widely in the theoretical literature but rarely in empirical analysis. We compute cross-elasticities between the categories within a store and compare the
pricing incentives of a category manager (who maximizes category pro…t) with those of
the supermarket owner (who maximizes store pro…t). We …nd that the latter implies a
very substantial increase in the intensity of price competition compared to the former.
To investigate the sources of this e¤ect we compare pricing incentives for di¤erent types
of consumers: two-stop shoppers and one-stop shoppers. We …nd that supermarkets have
much stronger incentives to cut prices for one-store shoppers, which suggests that consumers with relatively high shopping costs constrain the market power of supermarkets
more than those with low shopping costs.
1
Introduction
The supermarket industry’s sales represent about 5.5% of disposable income in the US ($562bn
in 2010, Food Marketing Institute), 8% of GDP in the UK (£ 150bn in 2010, Competition Commission (2007)), and similar shares in other EU countries. In recent years competition authorities in the US and EU have considered a range of issues in supermarket competition, focusing
on the prices set for grocery products in the presence of high market concentration. Some
Comments welcome. We thank Mark Armstrong, Martin Browning, Peter Davis, Thierry Magnac, Ariel
Pakes, John Thanassoulis and seminar participants at Royal Economic Soeicty Annual Conference, for comments. We are grateful to DairyCo UK and DEFRA for …nancial assistance.
y
Oxford University and CEPR z Seoul National University
1
campaigners have opposed further supermarket development, in order to protect traditional
high street stores.
A de…nitive feature of supermarket organization is that a supermarket brings together
products that fall into distinct demand categories— dairy products, drinks, meat, bread, fruit
& vegetables, household products etc. The traditional alternative to supermarket organization
is separate specialized stores for each category: a butcher for meat, baker for meat, pharmacy
for household goods, and so on.1 Supermarket organization allows shoppers to avoid shopping
costs. A consequence is that reducing the price set by a supermarket for one product category
increases demand for products in other categories in the same store, by drawing visitors to the
store, generating “cross-category”complementarity e¤ects.
If consumer shopping costs are high enough to rule out two-store shopping, consumers buy
everything from a single store and …rms compete by o¤ering the best utility for the consumer’s
bundle, which generates cross-category e¤ects between the price of any product and all other
products in the consumer’s bundle.2 Separate sellers then set prices that are ine¢ ciently high
relative to a single …rm that internalizes these e¤ects, a problem …rst noted by Cournot in
his complementary monopoly problem. If consumers have the option of shopping in multiple
stores, on the other hand, then the shopper’s bundle is split across stores and the cross-category
e¤ect of a price cut is more limited.
Cross category e¤ects that arise through of shopping costs have featured widely in IO theory.
The theory literature has widely adopted a multi-store multi-product framework to study issues
in retail pricing in a “mixed bundling”setting, for example Armstrong and Vickers (2010), Lal
and Matutes (1994), Chen and Rey (2012), and Klemperer (1992). This theoretical framework
is also used more widely in the compatibility literature, see the “mix and match” models of
Matutes and Regibeau (1988), Economides (1989), and Nalebu¤ (2000). Despite its prominence
in the theory literature, the multi-store multi-product framework has not been studied widely
in the empirical literature.
This paper adapts this multi-store multi-category framework for empirical analysis to measure the cross-e¤ects between broadly de…ned product categories in supermarkets, and to study
the impact that internalizing the externalities generated by these e¤ects has on the market
power of supermarkets. We compare supermarket pricing— where the cross e¤ects are internalized to maximize …rm-wide pro…ts— with the alternative where the task of setting each
category’s price is decentralized to a “category manager” who maximizes just the category’s
pro…ts. We measure the extent to which the internalization of this pricing complementarity
intensi…es price competition. Similar to the literature on pricing pressure in merger analysis
(see Farrell and Shapiro (2010)) we compute the implicit marginal cost reduction that would
be needed to replicate the observed prices (generated under supermarket pricing) if stores
1
The term “category”refers to a group of similar product lines. We are interested in pricing incentives that
the supermarket format generates between largely unrelated, broadly-de…ned, products, rather than between
close substitutes. Existing single-category empirical studies, such as Villas Boas (2007) for the yoghurt category,
have considered within-category pricing incentives, but not cross-category pricing incentives.
2
For models where one stop shopping is imposed see Bliss (1982), Stahl (1982) Smith and Hay (2005) and
Armstrong and Vickers (2005)
2
decentralized pricing to individual category managers.3
It is important to allow for multi-stop shopping to allow a ‡exible model that does not
impose high shopping costs exogenously, which would lead to an overestimate of the importance
of cross-category pricing e¤ects. We also do not impose that the consumer buys all categories a
given shopping period, i.e. we allow for zero demands in the speci…cation which are a commonly
observed feature in retail demand. We consider the consumer’s problem in a weekly shopping
period in which the consumer makes three shopping decisions: (i) which stores to visit, (ii) a
category-store allocation decision of which categories to allocate to each visited store, and (iii)
a continuous choice decision of how much of each category to buy. Utility is speci…ed to allow
that demand for each category depends on the attributes of the store it is allocated to (price,
store size, and …rm). The …rm operating the store is relevant because it a¤ects the quality
and range of the stores in its chain, not least because of the importance of private label goods
whose quality is determined by the retail …rm. We allow consumers to view …rms di¤erently for
each category— i.e. one …rm may be preferred to another for a given category— so that in the
absence of shopping costs the consumer would bene…t from buying di¤erent categories from
di¤erent stores. The consumer has shopping costs of visiting a store that are independent of
which categories are bought and which depend on the locations of stores.
We estimate the model using a consumer survey and a dataset giving store characteristics.
The data is from Great Britain for the years 2002-2005. The store choice dataset gives a record
of the category purchases of the households and the stores used for a large number of products.
We aggregate the data to a weekly shopping period and to eight product categories. The data
also includes household characteristics such as size, income, and location. The store dataset
and gives the location, store size, and …rm of each grocery store, allowing us to construct the
store choice set for each consumer in the data. There is considerable variation across consumers
in the composition of these choices sets, which is exploited in the estimation of the model’s
parameters.
A number of econometric challenges are faced in the estimation of the model. First is the
presence of many zero demand observations in the quantity decisions at category level, as some
people do not buy all of the categories each week. Second is a selection issue when estimating
demand conditional on store choice: it is possible that unobservable store-speci…c tastes will
determine both the choice of store and the continuous demand for a category. If this is the case
then estimating a category demand equation conditional on store choice will result in bias, as
the error terms in such conditional demands are not orthogonal to the store attributes. We
overcome both these problems by estimating the model using a simulated GMM approach (see
McFadden (1989)) in which the store choice, the category-store allocation decision, and the
continuous category demands are all estimated simultaneously in a single step.
We …nd that cross e¤ects are large and generate substantial downward pressure on prices,
3
The importance of cross category e¤ects in the context of shopping malls has been established indirectly by
looking at the retail rents set by shopping malls to alternative stores. Gould et al (2005) show that the owners
of shopping malls internalize cross-category e¤ects by setting lower rental rates for stores that sell categories
that are likely to draw consumers to the mall and hence generate pro…t on other product categories.
3
with important implications for the market power of stores of di¤erent formats. The parameters of the model suggest that shopping costs are signi…cant, which means that there is a
substantial cost from buying products from more than one store, and that categories are pricing complements at …rm level, i.e. a price increase for one product category drives consumers
away from the store for other categories. We quantify the downward pressure of supermarket
organization on pricing by computing the implicit subsidy (per unit of demand) required to
maintain prices at the observed level in the counterfactual setting where pricing is decentralized
to category managers who only consider category-speci…c pro…ts at the …rm. Under Pigou tax
principles the subsidy equals the “positive externality” that an extra unit of the category has
on the pro…ts of other categories at the store. These subsidies are found to be high as a fraction
of the category price, which is consistent with the theory derived in multi-category multi-…rm
settings with shopping costs. We …nd that the subsidy is larger for some supermarket formats
than others: supermarkets that operate large stores and that specialize in attracting one-store
shoppers have larger externalities than …rms that operate small-store formats. This lessens the
market power of the large-store …rms, and greatly o¤sets the market power that these …rms
might have enjoyed from their large share of the market.
We decompose this e¤ect and …nd that the externalities between categories are greater for
shoppers that have high shopping costs. To analyze the e¤ects of consumer shopping costs on
market power we consider a counterfactual in which …rms can price discriminate between onestore and two-store shoppers. The question of which of these two groups of shoppers has the
greater downward pressure on supermarket prices has been discussed in competition reports
including CC(2000), and theoretical work including Klemperer (1992), where it is suggested
that a large number of two-store shoppers might intensify price competition because two-store
shoppers can switch between stores in response to any price change without incurring extra
shopping costs. We …nd that …rms would like to raise prices to two-store shoppers and cut them
for one-store shoppers, which indicates that it is actually the presence of one-store shoppers
that intensi…es competition. The consumers with low shopping costs thus bene…t from the
presence of high shopping-cost consumers. Our results indicate the importance of accounting
for cross-category e¤ects when estimating the market power of …rms selling product categories
in supermarkets, as a given set of consumer tastes can imply very di¤erent market power
depending on whether cross-e¤ects are internalized. More generally the results are of relevance
to public policy relating to the organization of the food retailing industry, for example when
judging between “decentralized” and “supermarket” forms or pricing, and when comparing
policies that induce changes to the extent of one-store shopping.
The paper is related to the IO literature on market power and supermarket pricing. There
is currently a contrast between the theory literature on supermarket pricing— where the multicategory nature of shopping has had a major role— and the empirical IO literature on supermarket pricing where most empirical studies have not considered cross-category e¤ects or shopping
costs. One strand of the empirical literature on supermarket competition has aggregated all
in a supermarket products to a single commodity (Smith (2004), Dubois and Jodar-Rossell
4
Table 1: Demand Categories: Illustrative Product Lines
Category
Bakery
Dairy
Drink
Dry
Fruit & Veg
Household
Meat
Milk
Illustrative product line examples
Total Bread, Ambient Cakes+Pastries, Chilled Desserts
Total Cheese, Yoghurt, Total Ice Cream, Butter
Wine, Spirits, Beer+Lager, Cola
Breakfast Cereals, Confectionery, Instant Co¤ee
Vegetables, Fruit, Frozen Potato Products
Cat Food, Machine Wash Products, Toilet Tissues,
Chilled Ready Meals, Cooked Meats, Fresh Beef
Milk
(2010)) to focus on store choice. Another strand of the empirical literature has focused on a
single-category to study within-category pricing incentives but not cross category e¤ects (e.g.
Villas Boas (2007) and Nevo (2000)). In a related paper Schiraldi Seiler and Smith (2015)
estimate a model of grocery demand which studies the trade-o¤s between competition and
environmental objectives in policy towards market structure. The marketing literature has
focused either on store choice without looking at quantity decisions, or on the interaction between categories without looking at the role of shopping costs. Song and Chintagunta (2007)
estimate a discrete-continuous model of brand and quantity choices but do not model store
choice. Bell et al. (1998) model store choice but do not allow for two-stop shopping, and
quantity decisions are exogenous. Vroegrijk et al. (2013) estimate a nested logit model where
consumers choose between one-stop and two-stop shopping but do not estimate the consumer
decisions jointly or allow quantities by category to be endogenous. The paper is also related to
the econometric demand literature on discrete-continuous systems and zero expenditures (see
Dubin McFadden (1984) and Wales and Woodland (1982)). Mostly these papers have taken
a maximum likelihood approach and used closed form estimation methods. We recast these
methods into a GMM approach, which facilitates estimation of demand systems with more
choice dimensions.
The paper is organized as follows. In Section 2 we discuss industry background and present
some patterns in the data. Section 3 presents the theoretical model, Section 4 details the speci…cation of the model, Section 5 discusses the estimation method and identi…cation assumptions,
and Section 6 presents estimates and their implications for pricing incentives. Section 7 concludes.
2
2.1
Industry Background
Categories
We group products into eight categories. The concept behind the grouping is to relate approximately to products sold in separate specialist sellers (most of whom are found on a conventional
high street)— the type of items under “meat” can be found in a butcher’s shop, those under
5
Table 2: Demand Categories: Weekly Per Household Statistics
Bakery
Dairy
Drink
Dry
Fruit & Veg
Household
Meat
Milk
Mean Spending
£ 3.94
£ 3.61
£ 5.50
£ 6.33
£ 7.91
£ 6.10
£ 11.41
£ 1.37
Zero spends
8.8%
17.8%
31.2%
10.3%
6.4%
22.1%
7.9%
28.0%
Share
8.54%
7.81%
11.92%
13.70%
17.13%
13.21%
24.71%
2.98%
Table 3: One Stop and Multi Stop Shopping
A: One Stop Shopping (Discrete)
Proportion of consumers going to 2 stores: 61%
B: Average Sales Share: (all shoppers)
Consumer’s Top Store (C1)
80%
Consumer’s Second Store
14%
Consumer’s Third Store
4%
“household” in a high street chemist, “fruit and vegetables” can be obtained from a greengrocer, and so on. This allows us to imagine supermarkets as an organizational form that
internalizes cross-category e¤ects relative to the more traditional alternative of specialized
sellers arranged along a street or mall.
Discussion of and evidence of supermarkets thinking at category level.
Table 1 lists the eight categories and gives some illustrative leading product lines within
the category. The narrowest category is milk— which contains only one main product line.
To give an idea of their relative importance, Table 2 shows the average per-household weekly
spending on each category, and the proportion of household-weeks in which a zero expenditure
is recorded. The number of zeros is quite large for some categories, suggesting the need for
zeros to be modelled explicitly in the framework. The …nal column gives the share of total
consumer expenditure accounted for by each category.
2.2
Stores
The importance of cross category e¤ects depends on how many products the consumer buys in
a single store. In this subsection we present some evidence from the data. Table 3 gives some
evidence on the number of stores visited per week. Panel A shows that about 60% of shoppers
go to more than one store. In Panel B we see that expenditure is allocated unevenly, and that
the third store in any week receives only 4% of shopping.
We now look to see how many categories are bought (out of the 8 that are de…ned above).
Panel A of Table 4 shows the weekly number of categories bought by all shoppers, regardless of
how many stores they visit. The median number of categories is seven. Panel B considers only
multi-stop shoppers. We see that the median number of categories bought in the second store
6
Table 4: Categories and Stores
Percentile
25% 50% 75%
A: All shoppers (one- and multi-store shoppers)
# categories per week (across stores)
B: Multi-store shoppers only:
# categories per week (main store)
# categories per week (second store)
Share of spending in main store (store level):
Share of spending in main store for category:
5
7
8
4
1
0.57
0.67
6
2
0.71
0.94
7
3
0.84
1.00
Table 5: Category Market Shares for Two Store Shoppers: Two Examples
Store Pair
Tesco and...
Discounter
M&S
Bakery
0.27
0.38
Share of
Dairy Drink
0.36
0.51
0.10
0.10
shoppers for row store
Dry FruitVeg House
0.38
0.35
0.35
0.13
0.19
0.04
Meat
0.34
0.41
Milk
0.24
0.11
is much smaller than in the main store. We also see that about 70% of spending is allocated
to the main store. The …nal row shows however that there is a much higher concentration of
spending by store when we compute the share of spending by category: for each category we
identify the main store (by expenditure share) among multi-store shoppers and we …nd that
the median consumer allocates nearly all of their spending (94%) to a single store. Thus among
multi-store shoppers there is a pattern of one-store shopping per category for the weekly time
period considered here.
Table 5 gives some illustrative evidence on market shares by category among two-store
shoppers. We consider two groups of two-store shoppers: those that visit both Tesco and a
“Discounter” store and those that visit both Tesco and Marks & Spencer. These shoppers
account for 4% of all shoppers.4 The table shows that there are some product categories that
seem to have particular strengths for some of the …rms. For example the Drink category is an
important reason for people to visit a Discounter: more than 50% of those visiting both Tesco
and Discounter use the Discounter as their main store for the Drink category. In contrast the
Meat category is the strongest for M&S, where 41% of shoppers (who visit both M&S and
Tesco) use M&S for meat. Not surprisingly, Household is the weakest category for M&S, as it
o¤ers only a limited range of household goods.
2.3
Retail Margins
Given the importance that retail margins play in the analysis it is important to have a feel
for their magnitude. One of the advantages of retail milk in this context is that gross milk
margins are relatively transparent. Table 6 presents a number of alternative computations
4
Tesco is a major …rm operating many full-line stores. Discounters are small limited-range outlets, operated
by three …rms Aldi, Lidl, and Netto, selling products at low prices. Marks & Spencer focuses on high-quality
ready-to-eat food.
7
Table 6: Gross Pro…t Margins for Milk with Alternative Cost Assumptions
Alternative x
(a): x = marginal cost of industry (exc sup lab costs)
(b): x = wholesale price paid by supermarket
(c): x = (a) + supermarket labour costs
(d): x = (b) + supermarket labour costs
Pro…t Margin (p-x)/p
30%
23%
25%
18%
of gross margins using data from industry sources (see Smith and Thanassoulis (2008) for a
discussion and a description of the data sources). We see that the gross margins vary from 18%
to 30% depending on (i) whether the relevant marginal cost that …rms optimize against is the
“true” marginal cost or the wholesale price paid by the retailer and (ii) whether supermarket
labour costs should be included as part of this marginal cost) We will return to these margins
when evaluating the markup predictions of the estimated demand model under alternative
assumptions about pricing behavior.
3
3.1
Theory: Utility and Demand
General Description of the Model
In a given shopping period consumer i makes a shopping choice c consisting of one or two
stores from the set Ji . We write a shopping choice c as a set with two elements: c = fj; j 0 g.
If the consumer visits only one store j 0 this is indicated by setting j = 0: Let n(c) denote the
number of stores in c; and let Ci be the set of possible shopping choices, i.e. all combinations
from fJi ; 0g such that n(c) 2 f1; 2g.
Each consumer has K categories of demand k 2 f1; :::; Kg and all categories are on o¤er
from each store. Given shopping choice c a consumer selects a store j 2 c for each category
k: This decision is summarized by category-store allocation D: The consumer chooses a nonnegative quantity qk for each category, summarized in the vector q (q1 ; :::; qK ) 2 RK0 :
pjk is the price at store j for category k and p = (pjk )j2Ji ;k2f1;:::;Kg is all prices. Each
category-store allocation D implies a 1 K vector pc (D) of relevant prices— e.g. if D indicates
“store j for category k”then the k’th element of pc (D) is pjk :
There is product di¤erentiation at two levels. The …rst arises from the quality of the
products. We specify this at category-store level to allow that “store j for k”and “store j 0 for
k” are viewed di¤erently by di¤erent consumers, depending on preferences i : Preferences are
comprised of a scalar e¤ect for each category and store, i.e. i = ( ijk )j2Ji ;k2f1;:::;Kg :
The second level of di¤erentiation is at the level of the shopping choice c and comes about
because each consumer has a di¤erent shopping cost ic for each c: Shopping costs are summarized in the vector i = f ic gc2Ci . Shopping costs are incurred by visiting the stores in c
do not depend on the quantities or categories purchased. One factor causing shopping costs to
vary across choices c is the transportation costs.
The variable utility of consumer i for shopping choice c, category-store allocation D, and
8
quantity q; is
uc (D; q; i )
ai pc (D)q
where ai is consumer i’s marginal utility of money. The utility after shopping costs, or net
utility, is given by
Uic (D; q; i ; ai ;
Tastes ( i ; ai ;
3.2
3.2.1
i)
i)
= uc (D; q; i )
ai pc (D)q
(1)
ic :
vary in the population with cumulative distribution F ( ; a; ).
Two Stores and Unit Demands
Demand
To understand pricing incentives in the full model we consider a simple version with two stores
J = fA; Bg and three categories (K = 3).5 We assume all consumers buy all categories, unit
demand q = 1; and unit price sensitivity for all consumers, i.e. ai = 1 for all i.
With these simpli…cations the store-category allocation D can be represented as a vector
indicating the store chosen for each category. For example D = (A; B; A) represents “store
A for category 1; store B for 2, and store A for 3” and in this case the price vector p(D) =
(pA1 ; pB2 ; pA3 ). There are eight possible allocation alternatives D to chose from: D f(A; A; A);
(A; A; B); :::; (B; B; B)g: Given the assumptions of this subsection: (i) we can suppress the
notation q and (ii) store combination c is implied by D (e.g. if D = (A; A; A) then c = f0; Ag).
Consumer i’s choice problem is
max u( i ; D)
D2D
p(D)1
(2)
ic(D)
where 1 is a 3-vector of ones and ic(D) is consumer i’s shopping cost for category allocation
D.
The shoppers at store A can be decomposed into di¤erent types depending on which categories they allocate to the store. There are seven allocation choices that imply demand for
store A.
The number of shoppers QAAA that allocate all three categories to A; conditional on prices p;
is given by integrating the distribution F ( ; ) over the taste region AAAA for which consumers
make this choice, i.e.
Z
QAAA (p) =
dF ( ; )
( ; )2AAAA
where
AAAA =
(
( ; ) : u( ; (A; A; A)) (pA1 + pA2 + pA3 )
c(AAA)
0
0
0
u( ; D ) p(D )1
c(D0 ) for D 2 D
)
:
There are corresponding expressions for the other allocations QAAB (p); ::: QBBB (p).
5
We use K = 3 because one fo the the substitution responses below, namely (2b), is not present with K = 2.
9
3.2.2
Pro…ts and Pricing
The pro…t of store A can be decomposed into the pro…ts from each of the allocation choices
that imply demand for A, i.e.
A
= QAAA (p) [pA1 + pA2 + pA3 ] + QAAB (p) [pA1 + pA2 ] + QABA (p) [pA1 + pA3 ]
(3)
+QBAA (p) [pA2 + pA3 ] + QABB (p)pA1 + QBAB (p)pA2 + QBBA (p)pA3 :
where we have assumed marginal costs are zero.
To consider pricing incentives suppose store A increases the price of category k:Some of
A’s consumers are inframarginal and will not respond. Others are marginal and respond in
alternative ways, with di¤erent implications for how much they damage the store’s pro…t.
Throughout the paper we use the following classi…cation of marginal consumers depending
on whether they are is initially one- or two-store shoppers and whether the price increase
induces them to leave store A or continue at store A (“store-keeper”):
1. Initial one-store shopper c = f0; Ag:
(a) Store leaver. The consumer leaves A altogether transferring all categories (in our
example D changes from from AAA to BBB). There is a new shopping choice c
and shopping cost ci :
(b) Store keeper. The consumer keeps store A for at least one category but stops using
it for at least category k (e.g. D changes from e.g. AAA to ABB for k = 3).6
2. Initial two-store shoppers c = fA; Bg:
(a) Store leaver. The consumer leaves A altogether transferring all categories away (e.g.
D changes from e.g. ABA to BBB for k = 3). This implies a change to store choice
c and shopping costs ci .
(b) Store keeper. The consumer continues to shop at A for other shopping and only
transfers category k to the other store (e.g. D changes from e.g. ABA to ABB).
Here there are no consequences for c or ci as the consumer uses the same stores
before and after the response.
The impact of each response class on store pro…t varies because they each imply di¤erent
numbers of categories are reallocated when the price of category k increases. Response (1a)
implies the reallocation of all categories, so has a high impact. In our three-category example
the pro…t loss is [pA1 + pA2 + pA3 ] : This is triply-unpro…table as two categories are lost along
with category k.7 At the other extreme, response (2b) implies no category loss other than
category k.
6
This implies a new c and ci . in our simple example. But in the more general case, studied outside this
subsection, this response class includes the case where the consumer stops buying category k altogether, which
results in no change to c.
7
The terminology “doubly-pro…table”is introduced by Armstrong and Vickers (2010) for the case of K = 2.
10
Related Theoretical Literature The 2-seller K-category framework is used widely in the
theory literature. Many of these papers use the case of J = K = 2; where a consumer has
four possible category-store allocations, and three of our four response classes are possible
(namely (1a-2a)).8 The fourth response class (2b) is not present unless K > 2 because with
two categories it is not possible for a two-store shopper to reallocate a category while continuing
to buy from both stores.
The application of the framework extends beyond supermarket pricing to topics such as
compatibility between the products of rival …rms. When shopping costs are high enough to
rule out two-store shopping then the model is similar to those that study incompatible systems,
in which components or products must be bought from one supplier or another. Here much
of the interest is in whether shopping costs or incompatibility intensi…es price competition.
(On one-stop shopping see Bliss (1988) and Armstrong and Vickers (2005). For models of
compatibility see Matutes and Regibeau (1988), Economides (1989), and Nalebu¤ (2000)).
When shopping costs reduce but do not prohibit two-store shopping shoppers fall into two
classes, those that buy from one store and those that buy from two. Much of the interest is on
how the mixture between these two classes in a …rms customers impacts on the market power
of the …rms. Theoretical works on this case include Klemperer (1992), Lal and Matutes (1994),
Armstrong and Vickers (2010), and Chen and Rey (2013).
E¤ect of Supermarket Organization and Shopper Mix on Market Power We use the
model to analyze the impact of supermarket organization on market power. We compare the
incentives under two alternative organizational forms: supermarket pricing, where prices are
set to maximize pro…t at the whole supermarket, and decentralized pricing, where the pricing
decision is delegated to a category manager who sets prices to maximize category pro…t. As
supermarket pricing internalizes negative impact of a price increase on the demand for other
categories, we expect it to reduce market power and increase the intensity of competition
relative to category pricing. We measure the importance of this e¤ect, which is not picked up
in single-category studies of supermarket pricing.
We also analyze the e¤ect on a store’s market power of the distribution between one-store
and two-store shoppers. These can be seen as separate groups to whom the …rm might like to
set di¤erent prices. We calculate the direction in which …rms would like to price-discriminate.
If the …rm would prefer to set lower prices to one-store shoppers, that indicates these shoppers
are the greater constraint on a store’s market power. The theory is ambiguous on this question.
From a position of uniform pricing a store may prefer to cut prices to one-store shoppers because
each customer gained brings with it many categories. Alternatively the store may prefer to
favour two stop shoppers because (unlike one-store shoppers) they can reallocate category
demands between their two stores without incurring new shopping costs, so relatively more of
them are likely to switch, compared to one-store shoppers. The framework we take to the data
is ‡exible enough that either alternative is possible depending on the parameters of the model.
8
These papers often use unit-square preferences which allows the three respone classes to be illustrated in a
diagram. See in particular Figure 2 in Armstrong and Vickers (2010).
11
(See Appendix 9 for a numerical example).
3.3
3.3.1
Full Model: Many Stores and Continuous Demands
Choice of Store, Category-Store Allocation, and Quantities
In this section we relax the restrictions imposed in subsection 3.2. The set-up is as in section
3.1. In particular the number of stores in Ji is no longer limited to two and category demands
are variable (and may be zero).
The consumer can select any shopping choice c = fj; j 0 g from the set Ci . Given this choice
the category-store allocation D indicates which store (if any) is used for each category. We
write this as a K 2 matrix of indicator functions. The …rst and second element in row k
are indicators for whether the consumer buys k from the …rst or second store in c respectively;
both are zero if the consumer does not buy from either store.
Given any shopping choice c = fj; j 0 g 2 C, the maximum utility the consumer can achieve
by selecting an allocation D of categories to stores, and a K-vector of quantities q; is given by
the indirect utility function
wc ( i ; ai ; pc ) =
max
D2Dc ;q2RK0
[uc ( i ; q; D)
ai pc (D)q] :
(4)
and imply the following category-store allocation D and category demands q
D = Dc ( i ; ai ; p)
(5)
q = qc ( i ; ai ; p):
Consumer i chooses the shopping choice that gives the best utility net of shopping costs,
i.e. the solution to
max [wc ( i ; ai ; p)
ic ] :
c
Let Ac (p) be the set of values for ( i ; ai ;
Ac (p) = f i ; ai ;
i
i
) that induces the choice c at prices p, i.e.:
: wc ( i ; ai ; p)
ic
wc0 ( i ; ai ; p)
ic0 ;
for c0 6= cg :
We now derive three implications of the model that we can to their empirical counterparts.
The probability at prices p that consumers choose shopping choice c is given by
sc (p) =
Z
dF ( ; a; ):
(6)
( ;a; )2Ac (p)
The unconditional probability that consumers allocate category k to the lth store in shopping
choice c is given by row k and column l of
Pc (p) =
Z
Dc ( i ; ai ; p)dF ( ; a; ):
(7)
( ;a; )2Ac (p)
The unconditional expectation of the demanded quantity of category k in the lth store in
12
shopping choice c is given by row k and column l of
Qc (p) =
Z
diag (qc ( i ; ai ; p)) Dc ( i ; ai ; p)dF ( ; a; )
(8)
( ;a; )2Ac (p)
where Pc (p) and Qc (p) are K 2 matrices and diag(q) creates a diagonal matrix with the
vector q along the main diagonal.
3.3.2
Pro…ts and Pricing
To analyze …rm f ’s pricing incentives we aggregate to obtain demand at store level. The Kvector of total demands qf (p) for …rm f is given by aggregating the demand at each shopping
choice c that includes one of …rm f ’s stores
qf (p) =
X
j2Jf
X
c2C
Qc (p)Ijc
(9)
where Jf is the set of stores belonging to …rm f and Ijc is a 2 1 vector of indicator functions
with lth element indicating if the lth store in c is store j: The total pro…t of …rm f is given by
adding pro…ts from each category
f
=
X
k=1;:::;K
qf k (p) [pf k
mcf k ]
(10)
where mcf k is the marginal cost to …rm f of category k. In our analysis we will assume that
…rms set uniform prices across their stores, so that pf (j) = pj , which is consistent with observed
…rm behaviour in Great Britain.
The e¤ect of an increase in pf k on marginal consumers can be classi…ed into the same four
response classes as in Subsection 3.2.2 depending on (i) whether the consumer is initially a
one- or two-…rm shopper and (ii) whether he is a …rm-j leaver or a …rm-j keeper as a result of
the price change. There are two minor di¤erences from 3.2.2: …rstly the losses from a …rm-j
leaver may be felt on many more categories (given the relaxation to K > 3) and secondly since
demands q are sensitive to price the consumer can respond by reducing demand for k (possibly
to zero) without reallocating category k to another …rm.
If a …rm adopts decentralized pricing (by a category manager) then it maximizes category
k pro…t at f , i.e.
max qf k (p) [pf k mcf k ] for k = 1; ::; K
pf k
and if it adopts supermarket pricing then it maximizes …rm-wide pro…t, i.e.
max
pf 1;::; pf k
X
k=1;:::;K
qf k (p) [pf k
mcf k ] :
Let f 2 f0; 1g equal 1 if …rm f uses supermarket pricing. The …rst order condition for optimal
choice of pf k is
13
qf k (p) +
@qf k (p)
[pf k
@pf k
mcf k ] +
f
X
k0 6=k
@qf k0 (p)
[pf k0
@pf k
mcf k0 ] = 0:
(11)
The …rst two terms are the pro…t maximization condition when …rms adopt category pricing.
The …nal term is the e¤ect of price on the pro…t of the other categories and is considered when
the …rm adopts supermarket pricing; if this term is negative then this implies that supermarket
pricing reduces equilibrium prices.
We can divide this expression by @qf k (p)=@pf k to obtain obtain the …rst order condition in
terms of marginal quantity as follows
qf k (p)
|
.
@qf k (p)
@pf k
{z
+ pf k
}
+
f
marginal category revenue (“mrf k ”)
where
X
|
k0 6=k
@qf k0 (p)
@pf k
.
@qf k (p)
@pf k
{z
[pf k0
external pro…t e¤ect (“mef k ”)
X
@qf k0 (p)
0
k 6=k @pf k
.
mcf k0 ] = mcf k :
}
@qf k (p)
@pf k
(12)
(13)
is total demand lost to …rm f on other categories for every unit of k that is lost from a pf k
increase. This is a special kind of “diversion ratio”which captures the cross-category cost of a
price increase.
The terms in (12) can be interpreted as marginal e¤ects when price pf k falls by enough to
increase the quantity qf k by one unit. The term labelled mrf k is the marginal change in the
category revenue. A category manager will set this to marginal cost mcf k .
The term labelled mef k is the marginal e¤ect on the pro…t from other categories. It is
category k’s marginal external pro…t: the e¤ect on the pro…t of other categories at f . The
di¤erence between category pricing and supermarket pricing is given by this term. Equivalently,
it is the subsidy per unit of sales that must be o¤ered to a category manager to ensure that
she sets price of k to maximize supermarket f (rather than category k) pro…ts. This is an
intuitive measure of the downward pricing pressure that comes from supermarket organization.
Its magnitude increasing in that of the diversion ratio (13).
4
4.1
Utility Speci…cation: Functional Forms
Quadratic Direct Utility
We now give the speci…cation of the model. We assume that the direct utility (1) of consumer
i with shopping choice c; category-store allocation D; and quantity vector q is given by the
quadratic form
Uc (q; D; i ; ai ;
ic )
=[
ic (D)
1
ai pc (D)]0 q + q 0 q
2
ic :
(14)
The expression ic (D) is a K 1 vector that picks the relevant category-store taste e¤ects from
the full vector of preferences i given the consumer’s choice of store for each category: thus if
14
the chosen allocation D selects category k from store j then the k’th element of ic (D) is ikj ;
i.e. consumer i’s scalar taste term for k at j This mirrors the de…nition of pc (D) introduced in
3.1.
We assume that the second order term in the quadratic, , is una¤ected by the categorystore allocation decision D. A change in the allocation of categories to stores D only in‡uences
utility through the …rst order term [ ic (D) ai pc (D)]. This simpli…es the model as it means
that for each k and any shopping choice c = fj; j 0 g it is optimal to use the store in c with the
higher …rst order term in (14). Thus we can replace the kth element of the …rst order term
with maxj2c ( ijk ai pjk ) for k = (1; ::; K) so that (14) becomes
0
c ( i ; ai ; pc ) qj
1
+ q0 q
2
(15)
ic
where
c ( i ; ai ; pc )
= [max(
j2c
ij1
ai pj1 ); :::; max(
j2c
ijK
ai pjK )]:
The quadratic form in (15) generates a system of K demands conditional on the choice
(c; D). If nonnegativity constraints do not bind these conditional demands are linear in prices
and taste e¤ects: The second order terms determine how sensitive category demands are to
own- and cross-category price changes (conditional on (c; D)): the diagonal terms determine
the own-price e¤ects and o¤ diagonal terms determine the cross-price e¤ects. The variation in
ai allows these price e¤ects to vary depending on the price sensitivity of the consumer.9
Consumer i’s category demands qc ( i ; ai ; p ) conditional on shopping choice c = fj; j 0 g are
given by the maximization of (15) with respect to q subject to nonnegativity constraints q 0:
They therefore satisfy the Kuhn-Tucker conditions:
q 0;
c ( i ; ai ; p)
q 0;
[ c ( i ; ai ; p)
q]0 q = 0
The indirect utility (4) is
9
>
=
>
;
=) qc ( i ; ai ; p):
1
wc ( i ; ai ; p) = qc ( i ; ai ; p)0 c ( i ; ai ; p) + qc ( i ; ai ; p)0 qc ( i ; ai ; p)
2
(16)
(17)
Consumer i’s store-category allocation choice Dc ( i ; ai ; p); conditional on shopping choice
c = fj; j 0 g; is obtained by the maximization of (14) with respect to D: Dc ( i ; ai ; p) is a K 2
matrix of optimal store-category allocation choices given by:
Dc ( i ; ai ; p) =
9
h
djc dj 0 c
i
The quadratic utility demand system is studied in Shubik and Levitan (1980) and Shaked and Sutton
(1990).
15
where
2
j = arg maxj2c ( ij1
6
djc = 1 4
:::
j = arg maxj2c ( ijK
ai pj1 )
ai pjK )
30
7
5 1 [qc ( i ; ai ; p) > 0]
and dj 0 c is de…ned analogously (using j 0 = arg maxj2c ( ij1 ai pj1 ) in the de…nition). The
allocation decision is zero for both stores if the consumer does not buy a positive quantity of
a given category.
4.2
First Order Terms
The …rst order terms in (14) are composed of store-category tastes and a price-sensitivity
parameter.
The consumer’s category-store taste e¤ects i play a central role in the model, determining
the shopping choice, the category-store allocation, and the quantities demanded. Consumer i’s
category-store taste e¤ect for category k at store j is
ijk
=
0k
(
=
k xij
1
+
+
2 ti
f (j)k
+
+
3 hzi
ijk
+
4 szj )
+
f (j)k
+
ijk
(18)
(19)
where 0k ( 0 + 1 ti + 2 hzi + 3 szj ) depends on the following observable variables. ti is a time
dummy, which allows demand to depend on year and quarter.10 The variable hzi is i’s household
size to allow a larger household to have a greater demand. Finally szj is the ‡oorspace of store
j and is included because we expect that the variety on o¤er for any category is increasing in
the size of the store. To avoid a very large number of parameters in the model, 1 - 4 are not
category-speci…c. They are each scaled by the category-speci…c parameter 0k to allow their
combined e¤ects to vary across categories.
The …rm that operates a store an important determinant of the quality of its products in
any category. Firms tend to have centralized procurement policies with respect to the product
that are stocked. In particular the private label goods that appear in any store are determined
by the …rms and the average perception of the quality of these private label goods di¤ers across
…rms. Moreover some …rms are likely to be perceived as being stronger in some categories than
others, a feature of the grocery market that we noted in Section 2. To accommodate these
e¤ects the component f (j)k in (18) is the mean unobserved quality of category k at stores of
…rm f .
Individual consumers may deviate from the mean …rm-category quality perception f (j)k .
The component ijk in (18) is the consumer-speci…c deviation for store j and category k and
10
We estimate the model using only one observation for each household and di¤erent consumers are observed
at di¤erent time periods.
16
is speci…ed as follows
ijk
1
i;
2
ik ; ;
1
1 i
=
3
ijk
2
2 ik
+
+
3
3 ijk
(20)
iid N (0; 1):
(21)
The taste draw 1i enters consumer i’s taste for all categories, allowing a consumer’s tastes
to be correlated across categories. This allows that there are unobserved e¤ects that cause
households to vary in their overall taste for groceries. 2ik is household i’s unobserved taste for
category k. 3ijk is household i’s store-category e¤ect, which allows di¤erent consumers to view
store j and store j 0 di¤erently for category k.11
The other part of the …rst order term is the price sensitivity parameter. This is speci…ed
as follows to allow heterogeneity in price sensitivity
ai ( ;
4
i)
=(
1
+
4
i ( 3)
2 / yi )
(22)
where y i is household i’s income per capita and 4i ( 3 ) is a Rayleigh( 3 )-distributed random
draw, which is distributed on the positive real line. A household with a relatively low income
per capita yi , or a high draw for 4i , is relatively sensitive to prices and is more likely to opt
for low-price stores when deciding on shopping choices or category-store allocations.
The full set of draws for consumer i is denoted vi :
4.3
Fixed Utility
The shopping cost, ic , depends on two observable attributes of c: the number of stores visited
n(c) and the locations of the stores. The number of stores is included to allow people to have
…xed costs for every store that is visited. The locations of the stores allow shopping costs to
depend on distance to store j from the consumer’s home, distij : We specify shopping costs as
follows
X
distij "ic
(23)
ic = ( 11 + 12 ! i1 ) n(c) + ( 21 + 22 ! i2 )
j2c
where taste shocks
! i = (! i1 ; ! i2 )
iid N
"
0
0
# "
;
1 0
0 1
#!
:
(24)
allow for variation of shopping costs across consumers, a natural assumption made in many
theoretical models. Finally the term "ic is consumer i’s unobserved deviation. We assume that
"ic is a Type-1 Extreme Value.12
11
A consumer has the same realization of the store-category speci…c shock in all the shopping choices c
containing the store.
12
As enters utility with a negative sign, "ic enters utility with a positive sign, as is standard in models with
Type-1 Extreme Value disturbances.
17
4.4
Store Choice Probabilities and Expected Category Demands
To reduce notation we let the parameters and observables in gross utility be denoted =
( ; ; ; ; ) and xi = (ti ; hzi ; szj ; f (j))j2J . This allows us to write the conditional indirect
utility function wc ( i ; ai ; p) with the parameters separated from the taste draws i :
wc ( ; i ; p)
and similarly for the conditional store category allocation and demand decisions
Dc ( ; i ; p)
(25)
qc ( ; i ; p):
Consumer i selects the shopping choice c with the highest utility, i.e.
h
max wc ( ; i ; p)
c2C
(
11
+
12 ! i1 ) n(c)
(
21
+
22 ! i2 )
X
j2c
i
distij + "ic :
Since "ic is a Type-1 Extreme Value we have the following form for the probability the consumer
selects c given taste draw ( i ; ! i ):
c(
; ; i ; ! i ; p) = Pr(i chooses cj ; ; i ; ! i ; p)
exp wc ( ; i ; p)
= P
c0 2C
(
exp wc0 ( ; i ; p)
11
+
(
11
12 ! 1i ) n(c)
+
12 ! 1i ) n(c
(
0)
+
22 ! 2i )
P
distij
P
( 21 + 22 ! 1i ) j2c0 distij
21
j2c
We now derive expressions for the three predictions of the model, (6), (7), and (8), that we
match to their empirical counterparts to estimate parameters ( ; ).
To obtain the probability of choice c we integrate over the joint distribution G( ; !):
sc ( ; ; p) =
Z
c(
; ; p; i ; ! i )dG( ; !):
(26)
The unconditional probability that consumers allocate category k to the lth store in shopping
choice c is given by row k and column l of
Pc ( ; ; p) =
Z
Dc ( ; p; i ) c ( ; ; p; i ; ! i )dG( ; !)
(27)
and the unconditional expectation of the demanded quantity of category k in the lth store in
shopping choice c is given by row k and column l of
Qc ( ; ; p) =
Z
diag[qc ( ; p; i )]D( ; p; i ) c ( ; ; p; i ; ! i )dG( ; !):
(28)
The category-speci…c demand predictions Pc and Qc are “unconditional”in the sense that they
do not condition either on the choice of c or on the taste draws ( i ; ! i ).
18
5
5.1
Estimation
Discussion of Econometric Issues
There are two major econometric challenges in estimating multi-category models of supermarket demand.
The …rst is the presence of a non-negligible number of zero demands in the continuous
demand system. The quadratic demand system that we have speci…ed is linear in prices
and other variables before considering nonnegativity constraints. However the non-negativity
constraints truncate demand at zero and yield expected demands that are not linear in prices
or other characteristics, so that a linear regression of demand on these variables will lead to
inconsistent estimates, a problem discussed in Tobin (1958) and Amemya (1973).
The second problem is that consumers are not randomly assigned to stores, resulting in
a selection problem which creates endogeneity of the regressors in the continuous demand
expressions. As the consumer’s continuous and discrete choices are made jointly, and both
depend on the consumer’s unobservable taste draw vi ; the expectation of vi is not independent
of the observed characteristics of the chosen store. Therefore a regression of demand on store
characteristics and …rm dummies would be inconsistent.
To overcome these challenges we estimate the store choice and category demand components
of the model jointly in a single step. We use simulated method of moments (see McFadden
(1989)) matching the unconditional predictions of the model, in terms of shopping choice
(26), category-store allocation (27), and continuous category choice (28) to their empirical
counterparts. A likelihood approach has a number of computational drawbacks, as is detailed
further in Appendix 10.
A third challenge is that prices are set by retailers and therefore may be correlated with
taste shocks. This is a standard problem in demand estimation. Simulated method of moments
hat the further advantage relative to likelihood that it is easier to instrument for prices to allow
for endogeneity.
5.2
Moment Conditions
Let sic 2 f0; 1g indicate whether consumer i selects shopping choice c; and let Pic and Qic be
the observed K 2 matrices of category-store allocation, and quantity, decisions observed for
shopping choice c: These are the empirical counterparts to the predictions (26-28). To estimate
the parameters of the model we use the following moment conditions
E [sic
E Picjk
E Qicjk
sc ( ; ; p) j Zica ] = 0
b
Pcjk ( ; ; p) j Zicjk
b
Qcjk ( ; ; p) j Zicjk
(29)
= 0 for k = 1; ::; K
(30)
= 0 for k = 1; ::; K:
(31)
In none of these moments do we condition on the chosen store, so that the selection e¤ect is
not a problem.
19
Zica is a 1 12 vector that is contains instruments for the discrete shopping choice part
of the model. We use the observed non-price variables that enter the consumer’s shopping
choice plus an instrument for prices. The non-price instruments are (i) total size szj + szj 0 , (ii)
total distance distij + distij 0 , (iii) dummies for supermarket …rm 1 [f = f (j))] + 1 [f = f (j 0 ))]
for 8 di¤erent …rms f , and (iv) a dummy for two stop shopping 1 [n(c) = 2]. Notice that the
instruments are the sum of the characteristics of the two stores in shopping choice c because
this is the level at which the store choice is speci…ed to make predictions. This implies 11
instruments. The twelfth is an instrument for price. We discuss the construction of the price
instrument below.
b
Zicjk
is a 1 20 matrix that contains instruments for the category allocation and quantity
choice predictions of the model for each category k. It contains 19 non-price instruments and
one price instrument. Here unlike Zica the instruments are at the level of the individual store
within c. That is because the model now predicts decisions at the level of the individual store.
The 19 non-price instruments are (i) size szj , (ii) distance distj , (iii) dummies for supermarket
…rm 1 [f = f (j))] for 8 di¤erent …rms f , (iv) a dummy for two stop shopping 1 [n(c) = 2], (v)
time dummies for year (two dummies) and quarter (three dummies), (vi) household size, (vii)
household income, and (viii) a constant. This implies a total of 19 instruments, plus a price
instrument. Of these the price instrument is the only one that varies by category k.
The construction of the objective function and the covariance matrix of the estimator are
standard but we present them for clarity. The objective function is
g( ; ; p)0 W
where the vector g( ; ; p) is N
1
PN
i=1
1
g( ; ; p)
gi ( ; ; p) with
3
2 P
a
Z
[s
s
(
;
;
p)]
ic
ic
ic
c2Ci
P
7
6 P
b
7
6 c2Ci j2c Zicj1
[Picj1 Picj1 ( ; ; p)]
7
6
7
6 :::
7
6 P
P
7
6
b
gi ( ; ; p) = 6 c2Ci j2c ZicjK
[PicjK PicjK ( ; ; p)] 7
7
6 P
P
b
7
6
Z
[Q
Q
(
;
;
p)]
icj1
icj1
icj1
c2C
j2c
7
6
i
7
6
5
4 :::
P
P
b
QicjK ( ; ; p)]
c2Ci
j2c ZicjK [QicjK
P
0
W is the covariance matrix of gi ( ; ; p): W = N 1 N
i=1 gi ( ; ; p)gi ( ; ; p) : In the objective
function W is evaluated at a …rst-stage estimate of ( ; ).13
5.3
Informal discussion of Identi…cation
Let us begin with the parameters in the …xed shopping costs ic . These parameters are critical
to determining the importance of one-store shopping and hence the size of the cross-category
13
The …rst stage uses a block-diagonal weighting matrix with blocks fN 1
P
b0 b
for moment conditions (29) and (30), and fN 1 i;c Zic
Zic g 1 for (31).
20
P
i;c;j
a 0 a
Zicjk
Zicjk g
1
; k = 1; : : : ; K,
e¤ects in the model. The parameters on distance and store numbers are identi…ed primarily by
the discrete moment condition (29) which requires the prediction error in the discrete choice
of shopping choice c to be orthogonal to distance and number of stores n(c) in the shopping
choice. The identi…cation is greatly facilitated by the fact that each consumer has a di¤erent
choice set, with di¤erent distances to each shopping choice. The parameters in the model
are determined by observed data on how much consumers are willing trade o¤ higher shopping
costs (of visiting two stores or visiting more distant stores) in return for variable utility bene…ts
such as larger stores or, when n(c) = 2, a wider choice of products. The identi…cation of the
random coe¢ cient on distance in particular is facilitated by the combination of micro data
and the variation in choice sets. Consider two consumer groups from the sample that are
similar in other respects but where choice sets di¤er in the distance to a store: the random
coe¢ cient has implications for how the consumers that stop buying at the more distant store
redistribute to other stores. Those that are already at nearby stores will redistribute to other
nearby stores, while those at more distant stores (and care less) will redistribute di¤erently.
This type of variation in observed visits across di¤erent choice sets allow us to identify the
extent of unobserved heterogeneity in the cost of distance. Similar reasoning applies to the
random coe¢ cient on the number of stores in the store pair.
We now turn to the parameters in the quadratic direct utility function, beginning with the
…rst order e¤ects in 18. These play a role in all three levels of consumer decision and so are
identi…ed partly by the discrete shopping choice moment condition (29) and by the categoryspeci…c moment conditions (30,31) that relate to the quantity and category-store allocation
decisions. Thus the …rm-category taste e¤ects f (j)k are identi…ed by ensuring orthogonality
between …rm dummies and the prediction errors for quantity purchased and the categorystore allocation choice. A similar identi…cation argument applies to the parameters on the
other variables in quadratic utility, namely time dummies, household size, and store size. The
parameters on these attributes are multiplied by a category-speci…c scaling term which is
identi…ed because there are separate moment conditions for each category.
The spread parameters ( 1 ; 2 ; 3 ) on the random draws in the …rst-order coe¢ cient of
the quadratic utility function are identi…ed by the dispersion in purchases of households with
similar characteristics and similar choice sets. If all coe¢ cients 1 ; 2 ; 3 were zero, di¤erences
in household purchases would be driven exclusively by observed di¤erences. Given the other
parameters, 1 allows the model to match heterogeneity in purchases for a given store and a
given category which cannot be explained by di¤erences in store or household characteristics. 2
allows for heterogeneity in quantities purchased within a category— but common to all stores—
which cannot be explained by observable characteristics. Finally 3 captures heterogeneity at
store level. For instance, if it is observed that households with similar choice sets and observed
characteristics tend to spend similar amounts overall, but that the share of spending allocated
to di¤erent categories varies widely, this would tend to give small values for 1 and 3 and a
large value for 2 .
A standard concern is that price is endogenous because of unobserved quality which is
21
correlated with price because …rms take it into account when setting prices. We reduce the
importance of unobserved quality through the use of category-…rm level …xed e¤ects f (j)k ;
time varying household characteristics, quarter dummies and year dummies. To deal with any
remaining endogeneity problem we use exogenous …rm- and category-speci…c cost shifters as
instrumental variables for price: we construct price instruments by regressing observed price
on exogenous data and using the …tted value as an instrument. Regressions are performed
separately for each category and the exogenous data are (i) agricultural input prices relevant
for the production of the category, (ii) …rm dummies (iii) quarter dummies and year dummies,
(iv) exchange rates between UK and EU, and (v) prices of related products in other EU
countries. The price instruments are further discussed in Appendix 12
We now discuss how the parameters ( 1 ; 2 ; 3 ) that enter the price sensitivity term (22) are
identi…ed. The …rst price parameter ( 1 ) determines the mean level of price sensitivity. This
parameter a¤ects both the slope of the inverse demands for each category and the sensitivity to
price di¤erences when making the shopping choice decision c and the store allocation decision
D. It is identi…ed by ensuring that prediction errors in quantities, category-store allocation,
and discrete store choice, are independent of the price instrument. Thus the extent to which
these decisions change when price varies identi…es this parameter. Since …xed e¤ects f (j)k
absorb time-constant …rm-category speci…c unobservables, variation in demanded quantities
across these dimensions will not contribute to identifying 1 . Instead, we rely on variation
within categories and …rms across time. The parameter ( 2 ) that governs how price sensitivity
is a¤ected by per-capita household income is identi…ed by a comparison of the quantities
purchased at low- and high-price stores for low- and high-income households. The parameter
( 3 ) representing unobserved heterogeneity in price sensitivity is identi…ed using choice set
variation and micro data: e.g. a high level of 3 implies a greater degree of substitution
between any two low price stores (or between any two high price stores) than otherwise. Such
substitution is observed implicitly, for example, by observing two identical choice sets one with
with and the other without a nearby low price store.
Finally we discuss the identi…cation of the matrix of second-order terms. These parameters determine the pattern of own- and cross- price e¤ects on category level demands. The
diagonal terms kk determine the rate at which marginal utility of category k declines in its
own quantity while o¤-diagonal terms kk0 determine the rate at which the marginal utility
of k declines in category k 0 ’s quantity. Since the parameters determine the marginal rates
of substitution between categories, they act as category-speci…c price coe¢ cients. They are
identi…ed by observing the extent to which changes in the price of one category a¤ects the
continuous demand for a second category, after controlling for store choice and store-category
allocation decisions. Separate identi…cation of correlation and complementarity: if kk0 are
estimated we include 1 so as to estimate them separately. They are identi…ed because there
are
22
Variable
Household size
Household Income (£ )
Household Income per Head
Spending per Week (£ )
Number of Stores Visited per Week
Number Categories with Zero Expenditure
Number of Observations
Mean
2.67
532.15
227.30
41.11
1.34
1.33
2000
St. Dev.
1.34
236.62
116.19
29.67
0.47
1.47
Table 7: Summary Statistics: Consumer Data
5.4
Standard Errors and Computation
We complete this section by detailing how we compute the parameters and standard errors.
Ignoring simulation noise the standard asymptotic covariance matrix of the (second-stage)
estimates ( ^ ; ^ ) is given by14
N
1
rg( ^ ; ^ ) W ( ^ ; ^ )
1
rg( ^ ; ^ )0
1
:
In the estimates that we present we correct for simulation noise by instead using
N
1
rg( ^ ; ^ ) [W ( ^ ; ^ ) + S( ^ ; ^ )]
1
rg( ^ ; ^ )0
1
;
where S( ^ ; ^ ); the variance of the simulation noise, is given by15
S( ^ ; ^ ) = N
1
XN
i=1
gi ( ^ ; ^ )
Er [gi ( ^ ; ^ )]
gi ( ^ ; ^ )
0
Er [gi ( ^ ; ^ )] :
Here gi are the moments as given above, computed with a limited number of simulation draws,
while Er (gi ) is the same quantity as the number of simulation draws gets large.16 Both quantities are evaluated at the estimates ( ^ ; ^ ). The estimates are obtained with one simulation
draw per observation while the limit is found using 1000 draws per observation. The objective
function is minimized with a genetic algorithm.17
6
6.1
Data and Estimates
Data
We estimate the model using a survey of consumer shopping choices and a dataset of stores.
The data covers the period Oct 2002-Sept 2005 and the geographic area of Great Britain.
The consumer survey, provided by TNS (now Kantar), gives comprehensive information on
14
See Wooldridge, J. M.: The Econometric Analysis of Cross-Section and Panel Data, 2nd ed. p. 535.
See Train K. E.: Discrete Choice Methods with Simulation, 2nd ed. p. 256.
16
We use 3000 draws for each of the 2000 households to compute Er [gi ], and one draw per household for
estimation. Correction for simulation noise on average increased standard errors by 30.6%.
17
Matlab’s ga.
15
23
A: Variation between Choice Sets: Store Availability for Selected Firms
Firm
Distance to nearest …rm f store Firm f stores in choice set
Lower
Median
Upper
#stores=0
#stores
Quartile
Quartile
%
Mean
ASDA
2.54
5.07
13.88
16.1
1.40
Tesco
1.09
2.05
4.09
0.4
3.95
Waitrose
5.47
56.5
0.80
Co-op
0.70
1.43
2.75
0.3
4.76
Discounter
1.89
3.92
10.34
11.4
2.48
B: Variation within consumer choice sets:
Average of Choice Set Statistics
Min
Median
Max
Mean
St. Dev.
Distance km
1.14
8.28
13.42
8.08
3.86
Floorspace 1000sqft
1.57
8.45
63.97
15.49
16.10
Table 8: Variation across and within Consumer Choice Sets
Data for the choice sets of the 2000 consumers used in estimation.
shopping behaviour. For each household it gives a record of daily shopping choices, categorystore allocation decisions, and consumer demands covering grocery items including fresh produce, food, alcoholic drinks, and cleaning products. We use a cross section of consumers rather
than a panel to maximize the choice set variation in the data for any given number of observations. We draw 2000 consumers from the survey and pick a week at random for each
consumer.18 We aggregate spending to store-week-category level, and consider visits to the top
two stores per week. Table 7 presents summary statistics for these consumers. We see that
average expenditure per week is £ 41.11, average number of stores visited per week is 1.34 and
average number of categories with zero expenditure is 1.33, a signi…cant proportion of zero
demand observations.
The store data, obtained from the Institute for Grocery Distribution (IGD), contains information on all grocery outlets in Great Britain including sales ‡oorspace (in square feet),
…rm, and exact location. Using consumer location information from the shopping survey we
compute distances between each consumer and each store and construct a choice set for each
consumer, Ji .19 We assume that consumer choice sets consist of the nearest 30 stores.20 Where
a …rm operates more than one very small convenience store, less than 3000 sq ft, we use the
nearest of these, which avoids choice sets from being …lled up with very small stores.21
18
There are more than 26 thousand consumers in the survey. To avoid households who uncommitted to the
data-sampling process, we restrict the sample to households that participated for at least 10 out of 12 months
per year. To ensure that location of consumers is accurately recorded we drop those households whose mean
(known) distance travelled changes by more than 10 km between the …rst and last year quarter of the survey.
This removes people who move house, whose new location is not updated frequently.
19
The location is up to postal sector, small geographic areas covering a few thousand consumers. We assume
households are located at the average postal address easting and northing, as given in the Central Postcode
Directory; we are grateful to X for permission to use this data. The TNS data is home-scanned by consumers.
For more on the data see Gri¢ ths et al.
20
A choice set of 30 stores results in 99% of consumers having a store of their chosen …rm in the choice set.
Where the individual chosen store is known, a choice set of 30 (20) contains more than 91% (86%) of chosen
stores.
21
For about 70% of observations the consumer survey identi…es the exact store visited. For remaining
24
Firm
Mean
Std. Dev.
Category
ASDA
Morrison
Sainsbury
Tesco
Waitrose
Aldi
Iceland
M&S
Other
All …rms
Overall
Between …rm
Within …rm
Bakery
1.03
1.06
1.16
1.11
1.42
0.76
1.14
1.80
1.09
1.15
0.21
0.21
0.04
Dairy
1.02
1.08
1.17
1.14
1.46
0.84
1.19
1.62
1.17
1.18
0.17
0.17
0.04
Drink
0.98
1.07
1.02
1.08
1.45
0.78
1.02
2.15
1.11
1.14
0.29
0.29
0.07
Dry
1.00
1.06
1.12
1.08
1.40
0.87
1.11
2.12
1.07
1.16
0.26
0.27
0.03
Fr,Veg
1.04
1.04
1.41
1.26
1.67
0.84
1.48
2.10
1.22
1.31
0.29
0.29
0.05
Hhold
0.96
0.99
1.03
1.00
1.23
0.73
1.07
1.80
1.02
1.07
0.21
0.22
0.05
Meat
1.00
0.98
1.21
1.05
1.55
0.83
1.03
1.86
1.04
1.14
0.24
0.24
0.04
Milk
1.06
1.07
1.11
1.11
1.19
0.95
1.09
1.25
1.16
1.11
0.08
0.07
0.05
Table 9: Descrpitive Statistics: Price Data
We use the variation in choice sets between consumers to estimate the model. The extent
of variation is illustrated in Panel A of Table 8. The main variation across consumers is in the
distance to each …rm’s stores. For example the distance from consumers to the nearest ASDA
has a lower quartile of 2.54km and an upper quartile of 13.88km, and 16% of consumer choice
sets do not have an ASDA store at all. Panel B of Table 8 shows there is variation in store
attributes within choice sets: a typical consumer chooses between stores with a wide range of
distances and sizes.
For each category-…rm-week we compute a price index using the information on prices
recorded in the consumer survey. We compute price indices at …rm level because the main …rms
in the market adopt the policy of setting prices nationally. For …rms with a wide variation in
store sizes we compute up to three price indices with one for each store size class to allow for
the di¤erent product ranges in stores of di¤erent size. The price indices are constructed using
individual product prices and revenue weights observed in the consumer data. These price
indices are computed separately for each of eight demographic groups to re‡ect the di¤erent
tastes of these groups for products within each category. The prices are normalized relative
to the price of ASDA in the …rst week of the data. Quantities for each category are obtained
by dividing the consumer’s expenditure on the category by the category price. Table 9 gives
summary statistics for some of the …rms. M&S and Waitrose generally set the highest prices,
and Aldi (along with other discounters not on the Table) tend to set the lowest prices. The
between-…rm standard deviation is highest for drink, and fruit and vegetables, which are likely
to vary across …rms, and lowest for milk, which is least likely vary in quality across …rms.
Further details of the construction of price indices are given in the Appendix. The price
instruments are discussed in Subsection 5.3 and Appendix 12.
observations we know the …rm but not the store. In cases where the …rm has only one store in the choice
set we allocate the consumer to that store. In the remaining cases where a …rm has more than one store in
the choice set set we allocate the consumer to one of the …rm’s stores using reduced form probability model
25
26
Full Line
Full Line
Full Line
Full Line
Full Line
Discount
Discount
Discount
Freezer
Premium
Local
Local
ASDA
Morrison
Sainsbury
Tesco
Waitrose
Aldi
Lidl
Netto
Iceland
M&S
Co-op
Somer…eld
Others
All
Store Floorspace
(1000 sq ft)
Mean St. Dev.
45.3
14.23
30.3
8.54
28.7
17.11
17.01
21.07
19.13
9.18
7.85
1.40
9.55
2.82
6.53
1.59
4.86
1.14
8.40
1.96
4.33
5.35
8.62
5.13
7.71
5.65
12.75
15.02
Average Price
(1=ASDA week 1)
Mean
S Dev
1.01
0.01
1.04
0.02
1.16
0.02
1.10
0.01
1.43
0.03
0.82
0.01
0.82
0.01
1.14
0.01
1.85
0.03
1.25
0.02
1.19
0.02
1.09
0.02
Househ. Income/Head
(£ per week)
Mean
St. Dev.
209.59
98.15
212.24
103.66
266.99
128.34
232.79
117.26
296.55
125.12
210.38
92.89
190.16
90.38
196.37
109.37
184.84
91.00
255.93
115.37
217.68
116.37
196.51
114.08
204.27
95.28
Market Share by #Shoppers
Among Shoppers Visiting:
One store
Two Stores
20.6%
14.4%
12.2%
9.5%
15.4%
12.5%
31.0%
23.2%
1.9%
1.9%
1.1%
3.5%
0.4%
2.2%
1.1%
1.8%
1.1%
4.7%
1.0%
4.8%
4.5%
5.4%
3.9%
6.4%
1.5%
2.4%
100%
100%
Table 10: Descriptive Statistics by Supermarket Chain for the Consumer Sample
273
351
522
1,380
166
263
115
133
689
316
2,430
792
289
7719
#Stores
Notes: The table reports data for the 7719 stores in the choice sets of the 2000 consumers drawn for estimation. Share of shoppers is the proportion of
these households visiting each …rm for two groups: shoppers visiting one store and those who visit two stores. The reported price is the average across
categories for each …rm.
–
Format
Firm
Table 10 reports information on the full set of …rms in the data. It shows how the supermarket …rms di¤er in terms of what they o¤er and the consumers they attract. The Table
presents store information for the 7791 stores that are in the choice sets of the 2000 consumers
we have selected for estimation. We can classify …rms into a number of formats, shown in the
…rst column. The …rst …ve …rms are “Full Line” format, as their stores (when they are large
enough) are suitable for shoppers who only want to visit a single store for weekly shopping.
Store size for these …rms are on average larger than for other …rms, though they can vary
widely in size. There are some price di¤erences among these …rms: prices are lowest at ASDA
and highest at Waitrose. This is re‡ected in the fact that customers (in the survey) who shop
at ASDA have lower incomes per head than those who shop at Waitrose. We compute two
measures of market share. The …rst, in the column marked “One Store” gives the share that
each …rm gets of one-store shoppers (shoppers visiting just one store in the week); the “Two
Store”column gives share each …rm gets of two-store shoppers, divided by 2, so that shares add
up to 100%. The market shares show that the …rst four Full Line format …rms (known as the
Big Four) take a very high proportion of the shoppers, especially the one-store shoppers. The
remaining …rms o¤er a number of alternative formats. They all, however, have a much higher
share of two store than one store shoppers. Three …rms in the format “Discount”specialize in
selling a few key products at low prices from small stores, and attract low-income households.
M&S is a “Premium”format as it has the highest prices and its customers have high incomes.
Iceland specializes in frozen food. The remaining …rms (“Local” format) specialize in convenient locations. All …rms stock all the eight categories of demand, though they have di¤erent
strengths, as we noted in Section 2.
6.2
Estimated Parameters
The estimated parameters and their standard errors are in Tables 11 and 12.
We present two speci…cations. Model 1 restricts the cross-category second order terms kk0
in the quadratic utility to be zero. Model 2 relaxes this assumption for some category pairs.
This allows that, conditional on shopping choice c and store allocation D, buying more of one
category may reduce the quantity demanded of another. This is identi…ed by observing the
patterns of substitution between categories using variation across households. As explained in
Section 5.3 it is important, to identify the o¤-diagonal terms in kk0 , to allow for the possibility
that consumers have tastes that are correlated across categories, which is done in Model 2 by
estimating 1 .
We now discuss the individual parameter estimates. The …rst order term (18) contains
three components: an “observed” part with parameters, a …rm-category …xed e¤ect f k ,
and a random term v with spread parameters : The …rst parameters in Table 11 are for the
“observed” part. Parameters 1
8 determine the e¤ect of store size, household size, and
year and quarter e¤ects, on the …rst order term for each category, and hence on the quantities
demanded. To allow di¤erences between categories they are multiplied by the category-speci…c
estimated using the data on store choices, store size and distance, using the data where store choices are known.
27
Model1
Estimate Std. Error
Parameter
First Order Quadratic Parameters
bakery
2.78
0.41
01
dairy
1.52
0.28
02
drink
1.49
0.30
03
dry
2.99
0.56
04
fruit, vegetable
3.73
0.57
05
household (hh)
1.34
0.12
06
meat
2.39
0.25
07
Constant
-2.73
0.58
1
ln ‡oorspace
5.74
0.37
2
household size
5.76
0.54
3
quarter 2
6.44
0.43
4
quarter 3
0.94
0.29
5
quarter 4
4.65
0.46
6
year 2
3.45
0.47
7
year 3
4.48
0.44
8
Firm-Category E¤ects
Yes
fk
Parameters on Random Taste Draws ( )
overall
–
–
1
category
17.76
0.82
2
store category
11.67
0.48
3
Model2
Estimate Std. Error
2.69
1.50
1.53
2.69
3.57
1.36
2.35
-2.60
5.79
5.91
6.54
1.10
4.67
3.56
4.59
0.29
0.26
0.02
0.41
0.55
0.14
0.06
0.45
0.07
0.56
0.10
0.61
0.51
0.57
0.47
Yes
3.38
18.81
11.38
4.72
0.28
0.17
Table 11: Estimated Parameters (Part 1)
scaling term ( 0k ) which is normalized to 08 = 1 for category eight (milk). The signs of
the parameters make sense. The positive sign on household size re‡ects the greater demands
of larger families. The positive sign on store size re‡ects the greater variety available in a
larger store of a given …rm. The parameters ( 1 ; 2 ; 3 ) determine the variance of the random
shocks to taste de…ned in (20). The positive value for 1 in Model 2 implies that category
tastes are positively correlated across households. The category level variance parameter 2
indicates substantial variation in category tastes across households. The category-store level
taste variance 3 suggests that consumers have di¤erent views as to which store is best for each
category.
Table 12 reports parameters kk in the second order quadratic term. The diagonal terms,
11 ; ::: 88 ; determine for each category the extent to which marginal utility declines as quantity
increases. As expected the sign is negative, indicating a downward slope for the conditional
demand functions. The o¤ diagonal parameters (in Model 2) are negative (as expected for
substitutes) but are small and not signi…cantly di¤erent from zero, which suggests that the
categories are largely independent in terms of intrinsic utility. We only estimate a few of these
parameters, for the categories most likely to be substitutes, to keep a limit on the number of
parameters to estimate.
The parameters ( 1 , 2 ; 3 ) in the price sensitivity term (22) are of the expected sign. 1
is positive which implies that consumers prefer lower prices. 2 is positive which implies that
28
Model1
Parameter Estimate Std. Error
Second Order Quadratic Parameters
bakery
-5.87
0.62
11
dairy
-4.00
0.57
22
drink
-2.54
0.44
33
dry
5.02
0.62
44
fruit,vegetable
-5.06
0.47
55
hh
2.54
0.17
66
meat
-3.27
0.20
77
milk
-4.62
0.20
88
meat - fruit and veg
–
–
57
dairy - milk
–
–
28
bakery - dry
–
–
14
Price Parameters and Shopping Costs
Constant
3.57
0.51
1
Income Per Capita
0.23
0.03
2
Rayleigh
7.01
0.69
3
Shopping Cost
-1.47
0.47
11
Standard Deviation
2.59
0.97
12
Distance Cost
-14.77
2.27
21
Standard Deviation
13.07
2.72
22
Objective Function
0.2911
Model2
Estimate Std. Error
-5.79
-4.00
-2.63
-4.69
-4.97
-2.60
-3.27
-4.67
-0.01
-0.00
-0.01
0.35
0.64
0.12
0.48
0.56
0.18
0.15
0.99
0.09
0.14
0.10
3.84
0.24
6.63
-1.74
3.14
-14.56
13.32
0.286
0.05
0.00
0.02
0.75
1.48
1.50
1.91
Table 12: Estimated Parameters (Part 2)
price sensitivity decreases as income per capita increases. 3 allows unobserved variation in
price sensitivity across consumers.
The last set of parameters ( 11 ; :::; 22 ) determine the consumer’s shopping costs ic . The
parameter on distance is negative, as expected, and varies across consumers. The parameter
on the number of stores is also negative and again varies across consumers.
6.3
Observed and Predicted Choices
In this subsection we compare observations and predictions from Model 2. Model 1 gives very
similar predictions.
Our model includes …rm-category …xed e¤ects f k to ensure a good …t at category-…rm level.
To assess the model’s …rm-category …t we compare the predictions of the model to the data. We
present the demands from the 2000 consumers in the data aggregated to category-…rm level.
In Tables 13 and 14 show observed data (in the column marked “Obs”) alongside the models
prediction (“Pred”) and a 95% con…dence interval. We show the total quantities purchased
(“Quantities”, a continuous prediction) and the number of consumers choosing to allocate the
category to the …rm (“#Allocations”, a discrete prediction). The data show a high degree
of correlation between the predictions and the observed demand: the correlation coe¢ cient
between the observed and predicted “Quantities” in the table is 99% and for “#Allocations”
the same correlation coe¢ cient is found. Model 1 generates the same high correlations between
29
Category
Firm
Bakery
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
Dairy
Drink
Dry
Quantities
Obs Pred
140.6 133.0
16.5
19.6
10.1
5.6
91.3
82.0
12.5
16.9
57.4
84.2
98.6
92.6
195.0 172.7
11.2
8.2
131.1 133.0
23.5
20.0
8.9
5.5
64.8
53.0
2.5
5.0
48.4
62.8
85.6
86.1
182.2 164.3
8.2
7.5
187.0 192.8
42.6
37.7
7.0
12.7
122.2 109.3
1.0
6.7
104.0 90.1
175.6 157.6
280.4 286.0
12.5
9.5
243.7 225.8
38.5
27.4
8.2
12.9
132.9 127.3
4.6
8.4
101.0 131.6
149.8 147.2
313.7 284.5
18.0
15.4
95 pct conf
interval
111.4 152.8
13.7
27.5
2.4
14.5
66.6
99.7
12.9
30.2
71.7
99.4
77.2 112.5
150.7 194.3
4.6
16.1
107.6 151.2
13.0
31.4
2.7
11.8
40.5
68.1
1.5
13.5
51.1
76.4
69.1 105.3
136.5 184.3
4.3
13.5
157.9 236.2
23.1
64.5
7.4
21.9
80.7 147.8
1.9
22.6
67.7 121.4
123.6 207.6
241.2 336.9
4.0
23.6
187.4 253.9
17.3
42.0
8.8
20.1
102.5 151.6
3.1
19.1
110.1 154.8
122.7 173.4
243.3 314.5
8.8
28.8
Visitors
Obs Pred
360.0 360.9
58.0
72.0
29.0
24.7
224.0 234.0
49.0
36.0
262.0 301.5
267.0 260.7
556.0 497.2
35.0
28.1
342.0 350.1
71.0
67.1
37.0
18.6
194.0 183.0
12.0
10.9
203.0 220.1
247.0 236.3
495.0 465.7
27.0
20.6
267.0 291.5
64.0
59.7
16.0
21.5
159.0 164.3
9.0
8.0
178.0 161.4
205.0 215.0
404.0 410.6
25.0
16.2
364.0 373.1
77.0
62.3
26.0
30.1
218.0 231.1
18.0
14.4
255.0 287.2
269.0 256.6
524.0 520.7
33.0
29.6
95 pct conf
interval
312.8 395.1
53.9
93.1
12.8
49.4
200.4 269.7
28.3
60.9
261.2 334.9
224.2 298.7
444.2 536.4
17.4
47.1
259.4 390.4
44.9
92.8
9.9
35.9
130.7 214.3
4.0
28.2
157.2 267.9
170.7 271.8
352.8 512.2
11.8
34.8
246.7 323.9
37.7
88.7
13.6
33.8
128.8 200.6
2.2
24.8
121.7 198.6
173.2 258.4
351.2 458.5
8.3
32.8
323.7 408.8
44.3
88.1
21.6
42.7
199.3 266.1
6.4
31.0
248.3 325.2
220.7 295.3
459.0 564.4
19.2
47.2
Table 13: Quantities and Allocations: observations and predictions (part 1)
30
Category
Firm
Fr,veg
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
Hhold
Meat
Milk
Quantities
Obs Pred
285.2 241.6
42.3
47.6
9.8
13.1
167.9 147.1
7.5
9.3
84.4 137.2
186.5 154.9
376.2 324.4
18.6
18.1
272.9 249.2
34.6
47.3
1.1
3.6
145.1 130.6
1.2
7.7
95.9
95.5
168.4 152.5
387.8 350.7
22.0
24.4
438.9 345.4
41.9
34.8
50.3
39.8
241.3 236.5
28.6
32.6
142.0 217.3
286.6 245.7
550.3 535.3
28.6
23.8
43.7
39.0
6.3
3.4
2.0
1.6
26.6
23.4
1.2
2.2
30.6
32.7
31.0
30.4
74.0
71.1
2.2
2.9
95 pct Conf.
Interval
199.0 274.3
34.4
65.8
8.3
21.8
117.9 177.0
4.5
17.6
115.7 158.6
126.1 187.2
280.9 361.0
10.7
30.0
209.8 283.0
36.2
64.8
2.0
6.2
102.7 163.0
3.3
17.2
76.0 117.2
121.7 188.8
300.4 394.4
17.3
38.5
295.2 404.8
21.5
53.2
24.1
65.8
194.9 288.2
22.0
60.8
187.5 259.3
204.4 300.0
476.8 593.1
12.7
46.6
33.0
71.3
1.4
11.9
0.7
4.6
18.4
47.8
0.9
7.9
28.0
55.2
25.7
57.3
63.3 118.8
1.6
7.2
#Allocations
Obs
Pred
378.0 370.3
75.0
78.1
33.0
25.6
233.0 241.6
24.0
15.6
230.0 275.5
284.0 242.5
565.0 527.3
37.0
28.9
329.0 332.1
59.0
76.7
6.0
8.9
185.0 186.4
5.0
9.3
206.0 181.1
224.0 211.4
488.0 481.5
29.0
28.3
370.0 345.5
63.0
46.0
45.0
42.1
214.0 235.8
46.0
26.9
250.0 272.9
264.0 245.7
530.0 525.5
37.0
25.5
277.0 250.5
38.0
32.7
19.0
14.4
167.0 162.1
16.0
14.3
225.0 227.9
198.0 197.7
454.0 429.5
16.0
21.3
95 pct Conf.
Interval
316.3 403.1
59.9 104.3
16.6
38.6
197.8 277.1
8.6
26.9
232.1 306.2
203.9 280.1
460.1 564.6
18.8
45.3
288.0 362.6
63.2
98.9
4.8
14.9
152.1 223.1
3.7
21.3
146.3 212.2
172.5 251.7
416.8 524.2
20.6
44.5
303.6 382.2
30.8
64.1
26.3
63.4
200.7 272.7
18.6
47.9
233.5 306.4
208.2 284.2
471.7 561.0
15.7
44.3
181.0 273.5
15.1
58.7
5.7
25.3
109.8 192.6
5.7
27.5
150.6 282.9
139.5 233.0
302.4 476.2
11.6
31.3
Table 14: Quantities and Allocations: Observations and Predictions (part 2)
31
predicted and observed choices.
Tables 13 and 14 present within-sample predictions. As a further check Table 15 presents
out-of-sample predictions using 3000 randomly drawn consumers from the same survey, all
di¤erent from the 2000 used to estimate the model. To save on space we do this for only 4
of the 8 categories. Given the focus in our model on the choice between one-store and twostore shopping, we present observed and predicted choices separately for one- and two-store
shoppers. Thus for example we can compare the total predicted demand for the “Drink”
category at ASDA for 1-store shoppers with its observed counterpart. It is encouraging to see
that the model predicts the choice between one- and two-store shopping accurately on out-ofsample data. The observed and predicted “Quantities” across all categories (including those
not in the table) have a correlation coe¢ cient of 98%.
Table 16 compares predictions and observations at …rm level for the major …rms and selected
other …rms. The …rst two columns present the market shares, predicted using the alternatives
of share of revenue (“Revenue”) and share of households that visit the store (“Shoppers”).
Here we see the “big four”…rms: Asda, Morrisons, Sainsbury, and Tesco with a predicted joint
share of about 85% of revenue, which matches closely to the observed counterpart. The next
two columns record the proportion of shoppers that visit no other store. The …gure of 0.74
for ASDA indicates that about 3 out of 4 of their shoppers go to no other store in the week
besides the ASDA store they visited. For the big four …rms, ASDA, Morrisons, Sainsbury, and
Tesco, this …gure is consistently more than 70% but the …gure is much lower for other …rms
e.g. 50% for the discounter store Aldi, and 40% for Iceland and M&S. Looking at the mean
demographics of shoppers by …rm we see that the income levels of those who shop in the …rms
vary from Waitrose (at the high end) to Iceland, ASDA, and Aldi (at the low end). The table
shows a good match between predictions and observations.
An innovative feature in our model is that the consumer makes a shopping choice c that can
reuslt in a combination of …rm pairs. Table 17 presents the observed and predicted frequency
of each …rm combination for the 2000 consumers in the data. The upper triangle summarizes
the predicted number of shoppers, and the lower triangle gives the corresponding observations,
so the more symmetric are these triangles the better the …t of the model..The numbers along
the “diagonal”of each triangle is the number of one-…rm shoppers: thus for example the model
predicts that 281.2 shoppers shop at ASDA only, while the observed …gure is 287, and the
number predicted to combine ASDA and Tesco is 39.9, while the observed …gure is 42. There
is a good match between the predictions and the data in which …rms are combined.
Finally we evaluate the models predictions for distances travelled. Figure ?? presents
histograms of the observed distances and the predicted distances travelled per store for the
2000 shoppers in the data. We see a high degree of match between the two. Most shoppers
shop at stores within 5km and relatively few shop more than 10km away from home. This is
consistent also with the distances found in surveys for competition reports such as CC (2000)
and CC (2007).
32
Category
Drink
Fr,veg
Meat
Milk
Firm
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
ASDA
Discount
Iceland
Morrisons
MS
Other
Sainsbury
Tesco
Waitrose
1-Store Shoppers
Quantities
#Allocations
Obs Pred
Obs Pred
207.9 202.1 300.0 300.0
16.2
21.1
29.0
40.2
3.9
7.4
12.0
12.7
99.8 102.0 195.0 164.0
0.6
3.0
4.0
4.4
94.7
88.1 146.0 171.2
214.4 145.9 205.0 214.6
327.1 253.0 474.0 374.2
9.4
9.3
15.0
18.5
307.6 260.2 393.0 404.9
17.8
42.6
36.0
71.3
8.8
11.6
27.0
21.6
206.7 158.5 255.0 251.3
5.4
5.6
18.0
12.3
88.5 144.2 232.0 287.6
190.9 165.1 287.0 263.0
444.4 311.9 635.0 495.3
14.4
13.7
33.0
23.0
487.7 382.1 379.0 395.6
27.9
34.3
38.0
51.0
41.7
21.5
33.0
26.3
293.9 235.6 259.0 244.8
14.5
16.2
20.0
13.8
146.4 213.3 223.0 272.6
336.3 260.8 289.0 261.7
742.8 472.2 619.0 477.7
15.3
21.6
29.0
23.1
54.9
38.2 307.0 278.4
4.7
3.7
22.0
30.1
2.2
0.9
18.0
6.9
34.5
22.6 197.0 173.9
0.9
1.4
9.0
9.7
24.7
27.7 182.0 192.8
31.9
26.5 211.0 191.1
85.4
62.5 485.0 380.9
3.0
2.6
19.0
17.6
2-Store Shoppers
Quantities
#Allocations
Obs Pred
Obs Pred
95.2
96.6 121.0 132.2
40.1
36.0
62.0
57.7
10.5
11.2
17.0
20.2
44.6
47.8
52.0
70.9
4.0
0.9
8.0
2.0
76.8
58.9 130.0
93.8
61.5
82.6
83.0 116.7
104.0 137.0 140.0 194.5
1.4
4.2
5.0
8.6
100.8 123.2 155.0 173.9
40.3
43.1
69.0
69.9
7.9
8.3
25.0
17.4
59.8
69.8
95.0 103.5
7.1
4.1
21.0
7.1
47.4
82.1 135.0 145.1
48.8
85.6
93.0 124.7
119.5 144.7 204.0 229.1
7.6
11.8
18.0
16.5
156.1 180.1 151.0 167.9
40.3
22.2
51.0
28.3
63.4
30.3
49.0
31.6
104.1 106.6 106.0 104.3
25.3
31.0
38.0
23.4
70.7 125.4 124.0 140.0
89.4 116.3
94.0 113.0
180.8 248.6 182.0 239.4
11.5
19.4
16.0
19.7
19.9
19.7 116.0 119.2
9.4
4.0
42.0
29.1
1.7
0.7
14.0
7.0
8.2
12.8
55.0
76.4
0.4
1.6
7.0
8.2
21.9
24.3 154.0 150.2
9.9
14.4
71.0
88.5
25.6
36.5 165.0 201.3
2.5
1.1
13.0
5.6
Table 15: Out-of-sample predictions
33
Firm
ASDA
Aldi
Iceland
Morrisons
M&S
Other
Sainsbury
Tesco
Waitrose
pred
obs
pred
obs
pred
obs
pred
obs
pred
obs
pred
obs
pred
obs
pred
obs
pred
obs
Share of All Shoppers
Revenues Shoppers
0.234
0.204
0.215
0.203
0.033
0.038
0.032
0.036
0.013
0.016
0.014
0.014
0.133
0.121
0.128
0.127
0.008
0.014
0.013
0.011
0.089
0.137
0.123
0.151
0.158
0.148
0.152
0.146
0.316
0.304
0.310
0.299
0.016
0.018
0.014
0.014
% 1-Store Shoppers of Firm
Revenue
Shoppers
0.742
0.719
0.685
0.706
0.525
0.469
0.494
0.526
0.441
0.483
0.465
0.515
0.744
0.715
0.704
0.734
0.311
0.397
0.417
0.403
0.632
0.620
0.627
0.664
0.730
0.712
0.675
0.702
0.755
0.725
0.674
0.684
0.638
0.657
0.672
0.672
Mean Demographics
Income HH
Dist
53.269 2.861 0.051
52.664 2.872 0.056
52.430 2.845 0.072
46.679 2.595 0.053
48.411 3.138 0.051
51.490 2.504 0.045
50.188 2.759 0.054
54.328 2.852 0.061
49.090 2.245 0.066
57.971 2.666 0.086
46.879 2.645 0.059
51.532 2.663 0.052
61.156 2.596 0.042
57.226 2.557 0.048
55.466 2.705 0.053
56.213 2.760 0.064
65.429 2.486 0.037
59.909 2.378 0.036
Table 16: Firm Level Predictions: Market Share, One Stop Shoppers, Average Demographics
6.4
Estimated Shopping Costs and Elasticities
In this section we compute the implications of the estimated model for shopping costs and for
cross-elasticities at store-category level. Other than the idiosyncratic shock "ic , there are two
components to the shopping cost ic in equation (23): the per store portion ( 11 + 12 ! i1 )n(c)
P
and the transport cost portion ( 21 + 22 ! i2 ) j2c distij : The per-store portion can be thought
of a …xed cost to using an additional store per week. The additional cost of visiting a second
store determines whether a consumer will engage in two-store shopping; in addition to the
…xed cost of a second store, this involves travelling a larger total distance, and therefore higher
transport costs. To express the cost for the second store and per kilometer travelled in money
terms, we divide by the price coe¢ cient:
…xed cost of extra store :
1
(
11
+
12 ! i1 )
(32)
(
21
+
22 ! i2 ):
(33)
i
cost per kilometer :
1
i
To get an intuitive estimate of the additional distance consumers need to travel in order to
visit a second store compare the mean distance travelled for two-store shoppers, 8:74 km, and
the mean distance travelled for one-stop shoppers, 3:76 km. The di¤erence between these is
4:98 km. Assuming that this represents a typical extra transport cost for two store shopping
(relative to one store shopping) then the cost of going to a second store is the term (33) times
4:98 plus the term (32). Since there is a distribution of shopping costs in the population (due
to the distribution of i , ! i1 and ! i2 ) Table 18 gives the mean, 20 percentile, median and 80th
34
35
Aldi
ASDA
Other
Icel
Lidl
Morr
M&S
Netto
Coop
Sains
Somer
Tesco
Wait
16
13
0
1
1
7
0
0
0
4
2
8
0
Aldi
287
5
11
4
33
6
3
5
19
12
42
2
ASDA
Aldi
28.6
0
0
0
0
0
0
0
2
0
1
1
Other
ASDA
5.5
281.9
3
4
0
1
1
4
8
9
0
Lidl
Icel
2.3
7.8
0.5
24.4
166
5
1
0
14
5
35
0
Morr
Lidl
0.9
3.8
0
0.5
0.8
20
1
1
11
3
21
4
M&S
Morr
3.2
20
0.8
4.6
5.4
186.4
15
0
2
2
8
0
Netto
M&S
1.1
4.8
0.4
1.2
0.8
5.2
9.4
0
5
2
9
1
Coop
Netto
0.4
3.3
0
0.3
0.6
2.7
0.2
6.6
216
10
51
6
Sains
Coop
0.2
4
0
1.2
0.2
1.4
0.3
0.3
0.8
57
20
1
Somer
Sains
5.7
21.9
1.6
5.5
3.1
9.5
6.8
1.8
1.7
197.5
Table 17: Observed and predicted visits by …rm pair
21
2
6
0
1
1
4
5
16
1
Icel
Other
2.8
17.2
0.4
436
8
Tesco
Somer
1
11
0.3
3.4
1.3
9.4
0.9
0.3
1
7.7
55.7
25
Waitr
Tesco
8.8
39.9
3.2
17.9
9.3
22.5
11.6
4.6
5.9
41.2
18.3
416.2
Wait
0.9
2.9
0.5
1.1
0
1.7
0.4
0.1
0.1
4.1
2.1
7.4
21.4
Aldi
ASDA
Other
Icel
Lild
Morr
M&S
Netto
Coop
Sain
Somer
Tesco
Wait
Distance travell ed (predicted)
200
150
100
50
0
0
5
10
15
20
25
20
25
km
Distance travell ed (observed)
200
150
100
50
0
0
5
10
15
km
Figure 1: Histograms of Observed and Predicted Distances
percentile of this number in the population of consumers. It also gives the numbers for (32)
and (33), as well as predicted and observed total weekly spending on grocery shopping, for
comparison.
There are two panels in the table, one for consumers who are one-store shoppers and one for
two-store shoppers in the model’s predictions.22 In addition to the average cost of going to a
second store if that entails an additional 4:98km of travel, the table shows the same calculation
for the case where the second store visited is (a) the 5th nearest store (to the consumer’s home)
and (b) the 10th nearest. For instance, if visiting a second store means an additional trip of
4:98km the total additional shopping cost is $2:84 for the average one-store shopper. This is
7:2% of the mean (predicted) weekly spending for this group of consumers.
We now consider the e¤ect of changes to shopping choices on store shopping choices. The
22
In the model’s prediction, all
Pconsumers have a positive probability Pci for each of the #C store pairs in
their choice set. Then Ei (#c) = c2C Pci #c , where 1 E(#c) 2. For most consumers this number is quite
close to either 1 or 2. The classi…cation into one-store and two-store consumers is done by rounding Ei (#c) to
the nearest integer. Because of the random terms in the shopping cost and price parameter, the classi…cation of
one-store and two-store shoppers is not the same in the data as in the model’s prediction. Still the proportions
of each are almost the same: the mix between one-store and two-store shoppers is 1396/604 in the model’s
prediction and 1397/603 in the data.
36
One-store shoppers:
(33) 4:98+(32)
(33) dist5th +(32)
(33) dist10th +(32)
(33) median(dist)+(32)
Cost per km: (33)
Fixed cost of 2nd store: (32)
Weekly spending (predicted)
Weekly spending (observed)
Two-store shoppers:
(33) 4:98+(32)
(33) dist5th +(32)
(33) dist10th +(32)
(33) median(dist)+(32)
Cost per km: (33)
Fixed cost of 2nd store: (32)
Weekly spending (predicted)
Weekly spending (observed)
Mean
20th %ile
Median
80th %ile
2.84
2.38
3.72
5.16
0.55
0.12
40.95
37.00
0.57
0.28
0.45
0.64
0.10
0.03
15.82
21.15
1.94
0.95
1.70
2.51
0.37
0.08
34.11
36.32
4.28
2.76
4.77
6.87
0.83
0.17
63.61
52.61
1.96
1.04
1.78
2.58
0.40
-0.06
39.51
42.76
0.08
-0.01
0.01
0.07
0.02
-0.09
16.06
24.19
1.53
0.54
1.06
1.54
0.32
-0.03
33.54
42.16
3.55
1.75
3.21
4.52
0.72
-0.00
58.42
59.93
Table 18: Weekly shopping costs implied by the model
Change in
#Stores visited n(c) Distance travelled (km)
Type of shopping cost increasing by 10%:
Per-store shopping costs
Transport cost
-0.018
-0.004
Table 19: E¤ects of Changes to Shopping Costs
37
-0.053
-0.328
38
Aldi
bkey -1.09
drnk -0.21
fv -0.23
hh -0.23
meat -0.28
milk -0.22
Tesco
bkey 0.01
drnk 0.00
fv 0.00
hh 0.00
meat 0.00
milk 0.00
Waitrose
bkey 0.00
drnk 0.00
fv 0.00
hh 0.00
meat 0.00
milk 0.00
bkry
0.01
0.00
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.00
0.00
0.01
0.00
0.00
0.01
0.01
0.01
0.13
0.01
0.01
0.00
0.00
0.00
0.00
0.01
0.00
0.01
0.00
0.01
0.01
0.01
0.00
-0.48
-0.35
-0.36
-0.37
-2.16
-0.40
meat
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.05
-0.05
-0.04
-0.05
-0.05
-1.99
milk
0.12
0.05
0.06
0.06
0.06
0.06
-1.02
-0.14
-0.16
-0.15
-0.16
-0.14
0.19
0.08
0.08
0.08
0.10
0.09
bkry
0.09
0.18
0.08
0.09
0.08
0.09
-0.22
-1.31
-0.19
-0.21
-0.19
-0.21
0.10
0.30
0.09
0.11
0.11
0.13
drnk
0.13
0.09
0.22
0.11
0.11
0.11
-0.34
-0.26
-1.01
-0.28
-0.29
-0.27
0.13
0.11
0.12
0.23
0.12
0.13
-0.28
-0.25
-0.25
-1.24
-0.25
-0.26
0.15
0.16
0.12
0.32
0.15
0.19
Tesco
hh
0.21
0.16
0.32
0.18
0.20
0.19
fv
0.16
0.13
0.14
0.14
0.27
0.15
-0.45
-0.35
-0.39
-0.37
-1.16
-0.36
0.20
0.16
0.16
0.17
0.51
0.19
meat
0.03
0.02
0.02
0.03
0.02
0.05
-0.06
-0.05
-0.05
-0.06
-0.05
-1.16
0.02
0.02
0.02
0.02
0.02
0.07
milk
-0.95
-0.18
-0.22
-0.20
-0.21
-0.21
0.01
0.00
0.00
0.00
0.00
0.00
0.01
0.00
0.00
0.00
0.00
0.00
bkry
-0.23
-1.53
-0.20
-0.23
-0.21
-0.24
0.00
0.01
0.00
0.01
0.00
0.01
0.00
0.01
0.00
0.00
0.00
0.00
drnk
-0.51
-0.36
-1.38
-0.41
-0.41
-0.42
0.01
0.01
0.02
0.01
0.01
0.01
-0.46
-0.39
-0.40
-1.56
-0.40
-0.45
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.01
0.01
0.02
0.01
0.01
Waitrose
fv
hh
0.01
0.01
0.01
0.01
0.01
0.01
Table 20: Cross Elasticities at Category-Firm Level
Each element is the elasticity of “column”demand with respect to “row”price.
0.01
0.01
0.02
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.00
0.00
hh
-0.53
-0.48
-0.42
-3.89
-0.50
-0.55
Aldi
-0.66
-0.49
-1.42
-0.53
-0.62
-0.54
fv
-0.36
-2.16
-0.28
-0.35
-0.34
-0.39
drk
-0.66
-0.50
-0.55
-0.56
-1.82
-0.60
0.01
0.01
0.01
0.01
0.02
0.01
0.01
0.00
0.01
0.01
0.02
0.01
meat
-0.06
-0.05
-0.05
-0.06
-0.05
-1.09
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
milk
numbers in Table 19 are based on the derivatives of demand with respect to the parameters 11
and 22 , calculated to show the e¤ect of a 10% change in costs. For instance, a 10% increase
in transport cost reduces mean distance travelled by 0:33km. This is a 6:2% reduction in the
mean distance travelled.23 A 10% increase in the …xed cost of visiting a second store reduces
the number of stores visited by 0:02 on average (or 2% of consumers go from visiting two stores
to visiting only one). These numbers assume that prices are held constant.
Finally we look at price elasticities. A matrix of cross- and own-price elasticities for the
model are presented in Table 20. Each element is the elasticity of “column” demand with
respect to “row”price. It is impossible to present all the cross-elasticities, so we present them
for six categories at three …rms: Aldi, Tesco, and Waitrose. The cross-elasticity matrix consists
of blocks of 6 6 sub-matrices.
The block-diagonal sub-matrices (three blocks of 6 along the diagonal of the matrix) give
the cross-elasticities between categories within a …rm. What is interesting to note here is that
the …gures in these blocks are all negative: this shows the pricing complementarity that is
central to the supermarket pricing incentives, which is an implication of the shopping costs in
the model. (A consumer with no shopping costs would make category-store allocation decisions
independently across categories.) These cross-elasticities show that there are complementary
cross-e¤ects between categories at the same …rm, brought about by store visiting decisions. For
example meat at Tesco has an own-price elasticity of 1:16 and a cross price elasticity with
respect to the price of household goods of 0:37. The cross elasticities between di¤erent …rms
shown in the o¤-diagonal blocks are positive, as expected.
7
Analysis of Supermarket Pricing
In this section we analyze market power when …rms compete for consumers with shopping
costs. We …rst measure the extent to which competition is intensi…ed by supermarket pricing
compared to decentralized category pricing. Second we analyze the extent to which the market
power of a …rm is a¤ected by the mix of shopper types between one-…rm and two-…rm shoppers.
To study these questions we back out marginal costs using the …rst order condition for
prices, assuming …rms engage in supermarket pricing, as opposed to decentralized category
pricing. Thus we assume that …rm f sets prices on category k to maximize …rm-wide pro…ts,
internalizing e¤ects on the pro…ts of other categories. We assume that …rms internalize crossstore e¤ects for stores owned by the same …rm, which can generate considerable market power.
The …rst order condition (12) for k = 1; ::; K, combined with the estimated demand model, can
be solved to give the marginal cost mcf k cost each …rm f optimizes against when setting retail
prices for each k. Note that under e¢ cient bargaining this need not be the wholesale price but
may be the marginal cost to the retailer-supplier bilateral pair, if e¢ cient contracting is used.
The marginal costs are used to compute the margins (pf k mcf k )=pf k for each f and k
reported in Table 21. The rows of the table present average estimates for all …rms, average
23
Using the observed mean distance travelled of 5:26km. (The predicted mean is 5:60km.)
39
Firm (f)
All …rms
Big4 Firms
Non-Big4
ASDA
Tesco
Aldi
M&S
All
0.31
0.32
0.27
0.35
0.37
0.23
0.27
All …rms
Big4 Firms
Non-Big4
ASDA
Tesco
Aldi
M&S
0.18
0.14
0.39
0.03
0.05
0.42
0.36
All …rms
Big4 Firms
Non-Big4
ASDA
Tesco
Aldi
M&S
0.50
0.54
0.35
0.54
0.59
0.35
0.36
A: Pro…t Margins (p-mc)/p
Bakery Dairy Drink Dry Fr, Veg Hhold Meat
0.34
0.22
0.26
0.36
0.44
0.26
0.34
0.35
0.21
0.28
0.37
0.46
0.27
0.36
0.30
0.23
0.22
0.29
0.35
0.21
0.24
0.38
0.28
0.29
0.38
0.54
0.27
0.39
0.38
0.20
0.33
0.43
0.51
0.31
0.42
0.23
0.20
0.20
0.21
0.40
0.22
0.14
0.32
0.26
0.32
0.26
0.23
0.21
0.28
B: Marginal revenue (divided by price) mr/p
-0.15
0.30
0.36
0.03
0.06
0.33
0.30
-0.23
0.28
0.33 -0.03
0.01
0.29
0.24
0.19
0.38
0.53
0.31
0.34
0.52
0.53
-0.39
0.04
0.25 -0.11
-0.18
0.26
0.16
-0.32
0.34
0.24 -0.17
-0.09
0.23
0.13
0.19
0.40
0.54
0.39
0.33
0.52
0.56
0.41
0.07
0.33
0.26
0.35
0.44
0.55
C: Marginal externality (divided by price) me/p
0.81
0.49
0.37
0.61
0.50
0.41
0.36
0.88
0.51
0.40
0.66
0.54
0.43
0.40
0.51
0.39
0.25
0.40
0.31
0.27
0.22
1.01
0.68
0.46
0.72
0.64
0.46
0.45
0.95
0.45
0.44
0.74
0.58
0.46
0.45
0.58
0.40
0.25
0.40
0.27
0.26
0.30
0.27
0.26
0.32
0.26
0.23
0.21
0.28
Milk
0.22
0.22
0.24
0.21
0.31
0.17
0.22
0.35
0.35
0.38
0.34
0.14
0.50
0.02
0.42
0.43
0.39
0.44
0.56
0.33
0.22
Table 21: Pro…t Margins, External E¤ects, and Downward Pricing Pressure
The column “All”is a revenue-weighted average of all categories; the row “All”is a
revenue-weighted average of all …rms.
40
estimates for the Big Four …rms (that together take up about 80% of the market), average
estimates for the non-Big Four …rms, and estimates for four selected individual …rms. The
averages are weighted by the sales at each …rm.
Panel A gives implied margins as a percentage of price. As we expect the markups vary
somewhat by …rm and category, depending on the own-price elasticity of each category. Overall
the margins are about 0.31 which seems a reasonable estimate. The markups are slightly greater
for the Big Four …rms than for the other …rms such as the Discounters. Earlier, in Section
2, we presented data on markups for milk under alternative assumptions about marginal cost
and found …gures in the range 18%-30%, which serves as a check on our results. Table 21
shows average markups for milk that fall within this range, suggesting our demand estimates
combined with the assumption of Nash multi-product pricing, generate realistic markups.
We now compute our main measure of the degree to which competition is intensi…ed by
supermarket pricing relative to category pricing. The measure we use is the positive e¤ect (or
“externality”) on the pro…ts of other categories when the price of category k is cut by enough
to increase sales by one unit. We call this the marginal externality mekf : This externality is one
of the three components de…ned in the …rst order condition (12). The other two components
are the marginal cost mckf to the …rm f of an extra unit of category k, and the marginal
revenue mrkf to …rm f on revenues earned directly on category k. Condition (12) states that
mef k + mrf k = mcf k for all f and k.
We have seen from Table 20 that categories sold at the same …rm are complements once
the e¤ects of price on consumer shopping choices are endogenized, so that a cut in the price
of k increases demand for k 0 after allowing consumers to switch store. It follows that the
marginal externality mekf (which is generated by a price cut on k) is positive hence …rms
have an incentive to set prices such that category-speci…c marginal revenue mrkf is lower
than category-speci…c marginal cost mcf k : The marginal externality has the following intuitive
interpretation. It is the subsidy per unit of category k that the owner of a …rm would have to
o¤er to a hypothetical decentralized category manager, who maximizes category pro…t, to align
his incentives with that of the supermarket as a whole. Equivalently, it is the amount by which
marginal costs mcf k would have to fall for a switch from supermarket pricing to decentralized
category pricing to not to have any “upward pricing pressure”as de…ned in Farrell and Shapiro
(2010).
The …gures for marginal revenue and marginal externality are reported in Panels B and C
of Table 21 for each k. To aid interpretation the marginal e¤ects are expressed as a proportion
of the price pf k . Take for example the case of meat at Tesco. Its pro…t margin is 0:42 which
implies that marginal cost is 0:58 of price. The externality for meat at Tesco is 0:45 of price,
which is equal to the di¤erence between the marginal cost 0:58 and the marginal revenue 0:13
of the category, each expressed as a fraction of price. This equation follows because the …rm
equates the marginal cost to the sum of the marginal revenue and the positive externality.
The rows marked “All Firms” in Table 21 show the (revenue weighted) average marginal
e¤ects across all …rms. The average marginal externality is 0:50 of the price of a product.
41
This is substantial, as expected. It implies that …rms set prices much closer to the competitive
level than would be the case under category pricing. The …gure implies that for a change from
supermarket pricing to decentralized category pricing not to cause an increase in retail prices,
marginal costs would have to fall by by 50% of the price on average. Thus the cross category
pricing externality intensi…es competition between the large supermarket …rms that dominate
the market.
The other rows in the table show the marginal externality mef k for individual …rms and
for di¤erent …rm formats. Overall the externality e¤ects are substantial for all …rms, but vary
depending on the …rm. The table reveals an interesting pattern when comparing di¤erent
…rms: the largest externalities tend to be associated with the Big Four …rms, and the lowest
externalities are associated with the other non-Big Four …rms such as M&S or the discounters.
Speci…cally, when comparing the Big Four with the non-Big Four we see that the externality
e¤ect of the Big Four is greater by an extent that is equivalent to 10% of price, which has an
e¤ect on their market power equivalent to marginal cost falling by an amount equal to 10%
of price. This is a signi…cant constraint on the market power of the Big Four relative to the
non-Big Four …rms.
The fact that the externality varies across …rms suggests that the market power depends
on the nature of the …rm’s demands. One likely factor is the proportion of one-store shoppers
among the …rms customers; one-store shoppers tend to have high shopping costs and are likely
to take all their category demand with them when they change stores, which leads to large
external e¤ects between categories. The Big Four …rms tend to have a much greater proportion
of one-store shoppers, as we saw in Table 16 and this may explain their greater external e¤ects
and lower values of mrf k (in relation pf k ) than other …rms such as M&S or Netto.
We now decompose the price e¤ects to understand the market power of supermarkets. We
…nd it useful to analyze the category allocations of consumers at …rm level. To do this we
de…ne the K 1 vector of category allocations for …rm f as follows
df (p) = (df 1 ; :::; df K ) =
X
j2Jf
X
c2C
Pc (p)Ijc :
The term df k indicates the total number of consumers who allocate category k to …rm f
for positive purchase. The same-…rm diversion ratio in terms of consumer allocations is the
reduction in the total number of allocations to …rm f of categories other than k for every loss
of a category k purchase caused by the increase in pf k . Suppose that a 10% increase in price
pf k leads to a change df k in allocations to f of category k and a change df k0 in allocations
for other categories k 0 6= k. Then the same …rm diversion ratio is
same-…rm diversion ratio =
X
k0 6=k
df k 0 / df k :
When a supermarket raises its price for category k, its consumers may limit their response
to continuous-choice changes only— changing q only— or may change their discrete choices c
and category allocations d. Those consumers who make a discrete response can either change
42
43
18.8%
26.5%
21.0%
33.7%
2.5
3.5
1.9
-1.1%
10.1%
28.7%
35.3%
12.0%
24.0%
3.1
3.7
2.1
-0.2%
18.2%
19.7%
-18.7%
-3.7%
-1.6%
0.23
0.26
0.88
-2.5%
-0.9%
0.42
0.36
1.15
13.0%
-10.0%
Disc
-3.2%
46.0%
Big4
-2.5%
70.6%
-0.4%
9.0%
4.4
5.4
2.6
52.7%
11.7%
18.0%
17.6%
9.1%
-7.1%
-3.8%
-3.2%
0.57
0.29
1.98
Big4
-4.0%
74.6%
-0.6%
7.2%
3.9
4.7
2.7
49.1%
8.4%
32.0%
10.6%
13.2%
-12.0%
-6.5%
-5.7%
0.31
0.19
1.61
Disc
-5.5%
59.4%
Fruit, Veg
-0.3%
19.5%
2.0
3.9
3.2
29.6%
31.4%
11.4%
27.5%
13.0%
-10.0%
-2.9%
-2.9%
0.44
0.39
1.13
Big4
-2.8%
72.3%
-0.7%
77.5%
3.3
4.6
2.1
34.1%
16.3%
22.0%
27.7%
20.3%
-14.6%
-4.8%
-4.8%
0.30
0.28
1.07
Disc
-4.0%
61.8%
Household
-0.5%
11.1%
4.6
5.8
2.6
56.1%
8.5%
18.1%
17.3%
11.9%
-9.22%
-5.2%
-4.5%
0.41
0.35
1.20
-0.8%
22.2%
3.8
4.8
2.3
49.8%
11.7%
16.9%
21.7%
21.9%
-16.1%
-4.2%
-3.8%
0.30
0.25
1.19
Disc
-3.4%
75.7%
Meat
Big4
-5.4%
75.7%
Table 22: E¤ect of Ten Per Cent Price Increase of category k at …rm f.
#Allocations df k
of which (sum to 100%):
(1a) Initial one-…rm shopper, …rm-leaver
(1b) Initial one-…rm shopper, …rm-keeper
(2a) Initial two-…rm shopper, …rm-leaver
(2b) Initial two-…rm shopper, …rm-keeper
D: Same-f diversion ratio ( k0 6=k df k0 )= df k0 :
One- & two- …rm shoppers
One-…rm shoppers
Two-…rm shoppers
E: E¤ect on Pro…t:
All pro…t f
Category k pro…t f k
quantity
C2: E¤ect on category k & decomposition
Average Margin other cats
diversion ratio
A: E¤ect on # consumers choosing f:
proportion of which one-…rm shoppers
B: E¤ect on categories other than k:
#Allocations
k0 6=k df k0
Revenue
k0 6=k (pf k0 qf k0 )
C1:
External e¤ect as % of price
Drink
-0.1%
17.3%
1.5
1.7
1.2
6.3%
51.1%
2.2%
40.3%
12.9%
-10.4%
-0.5%
-0.5%
0.48
0.34
1.41
Big4
-0.5%
73.9%
-0.1%
36.3%
1.3
3.0
1.1
4.2%
11.8%
4.2%
79.2%
28.8%
-21.4%
-0.5%
-0.4%
0.24
0.20
1.19
Disc
-0.4%
51.4%
Milk
allocations d only, or change the shopping choice c . The market power of a …rm depends on
how its consumers respond in terms of these alternatives.
Table 22 presents the e¤ects of a series of unilateral 10% price increases for individual …rms
f and categories k. We compute the average e¤ects for two groups of …rms: the Big Four and
the Discount …rms (“Disc”). The …gures in the columns marked Big Four are the average of
the individual unilateral e¤ects for each of the four Big Four …rms, weighted over …rms using
…rm revenues. The …gures in the columns marked “Disc” are the equivalent …gure for each of
the three discounters. Thus the table allows us to compare the average e¤ects of a 10% price
increase for these two types of …rm.
Panel A considers the impact of the price change for category k on the number of consumers
choosing …rm f . The e¤ect is generally lower in percentage terms at a Big Four …rm than at a
Discounter. The second row in Panel A shows that the consumers who switch from a Big Four
store are much more likely to be one-store shoppers than those who switch from a Discounter.
Given that the cross-category externality e¤ects are greater for one-store shoppers, this may
be the reason why we found that Big Four …rms have larger external e¤ects than Discounters.
Panel B considers the impact of the price increase on categories other than category k. The
…rst row is the change in allocations df k0 and the second row the change in revenue. The panel
shows very similar percentage e¤ects to the number of customers leaving the store, shown in
Panel A. This shows that there are signi…cant negative e¤ects on the other categories from the
increase in the price of category k.24
Panel C shows the e¤ect of the price increase on the number of consumers allocating category
k to …rm f and decomposes these consumers into the four discrete response types classi…ed
in Section 3.2.2. We …nd that the percentage drop in the number of allocations is lower for
Big Four …rms than for the Discounters, which is consistent with the idea that shoppers at
Discounters have higher price elasticity. Of those who reallocate their demands there are
substantial numbers in each response class and there are di¤erences across categories and …rm
type. The di¤erences between Big Four and Discounter …rms can be summarized as follows.
The Big Four …rms are more likely to have consumers in the response class (1a), initial one-…rm
shoppers who leave the …rm altogether, and (1b) initial one-…rm shoppers who retain …rm f ,
who nevertheless switch away from f for category k; Big Four …rms were much less likely to
have consumers in category (2a) initial two-…rm shoppers who leave Tesco altogether, or (2b),
initial two-…rm shoppers who did not change the stores (“c”) they shop at but switched the
category from one store to another. The high number of shoppers falling into the group (1a)
for the Big Four …rms helps to explain their relatively large negative externalities (as shown in
Table 21 above), as this group takes all its category demands away when they stop shopping
for category k.
Panel D counts the number of other categories that are reallocated from …rm f on average
along with category k. The number of categories reallocated is greater for one-store shoppers
than for two-store shoppers. Thus it is worse (in terms of allocations lost) to lose a one-store
24
The percentage change to revenue is the same as that to gross pro…ts, as pro…ts are a …xed share of revenue
for k 0 6= k:
44
Category and Shopper Group Targeted by 10% p
Drink
FV
Meat
Milk
1-…rm 2-…rm 1-…rm 2-…rm 1-…rm 2-…rm 1-…rm
2-…rm
A: E¤ect of p on categories other than k
Positive demand
-2.0% -0.5% -3.2% -0.6% -4.4% -0.7% -0.4%
-0.1%
k0 6=k df k0
0
0
0
Revenue
-1.8% -0.4% -2.7% -0.5% -3.8% -0.6% -0.4%
-0.1%
k 6=k (pf k qf k )
B: E¤ect of p on category k allocations df k : [make clear what’s on bottom line is all and targeted]
(B1) All consumers -6.3% -3.6% -4.5% -2.5% -5.9% -3.2% -5.9%
-4.5%
(B2) Targeted consumers -9.2% -14.1% -6.7% -11.0% -8.8% -14.7% -7.9% -18.3%
Decomposition of B2 (sum to 100%):
Leave f 40.8% 34.7% 72.5% 46.8% 76.1% 48.6% 10.2%
6.1%
Keep f, increase n fr 1 to 2 6.5%
10.7%
11.7%
1.7%
Keep f, reduce n fr 2 to 1
7.7%
15.1%
15.9%
1.4%
Keep c, stop buying k from f 52.7% 57.6% 16.8% 38.1% 12.2% 35.5% 88.2% 92.5%
C: E¤ect on Firm and Category Pro…t
All Pro…t f -0.3%
0.0%
-0.4%
0.1%
-0.7%
0.1%
-0.4%
0.0%
Category k Pro…t f k 13.6%
4.5%
7.0%
1.9%
9.9%
2.6%
17.3%
3.5%
Diversion Ratio
Elast (%change in all demand)
1.15
10.5%
0.19
10.4%
1.39
10.5%
0.29
11.5%
1.77
8.5%
0.26
9.6%
1.08
11.1%
0.27
10.9%
Table 23: Pricing Incentives by Type of Shopper for Big Four Supermarkets
The …gures in the table are the average of the unilateral e¤ects for each of the Big Four …rms.
shopper than a two-store shopper. The Panel also shows that typically the Big Four …rms
lose more allocations on average than the Discounter …rms, which contributes to their greater
externality e¤ect. The last two rows, Panel E, highlight the intensi…cation of competitive
downward pricing pressure that arises from supermarket shopping. The e¤ect of the 10% price
increase decreases …rm-wide pro…t slightly, but increases category pro…t by 9%.
Overall Table 22 shows are large cross-e¤ects between categories, particularly for one-…rm
shoppers, and suggests that one-…rm shoppers have a powerful constraining e¤ect on the ability
of supermarkets to raise prices.
Table 23 establishes whether one-…rm shoppers intensify or soften competition by considering a discriminatory 10% category k price increase that a¤ects either 1-…rm shoppers or 2-…rm
shoppers (but not both). We consider category speci…c price discrimination to see if the results
are consistent across categories. The category that is subject to the price increase is noted in
the …rst row and the targeted group of shoppers (by number of …rms n) is displayed in the
second: the column marked “1-…rm” shows the e¤ect of a 10% increase to the price paid by
one-…rm shoppers, while the column marked “2-…rm” shows the e¤ect of a 10% increase to
two-…rm shoppers. We consider results for the Big Four …rms: each …gure is an average of the
unilateral e¤ects found for the four …rms.
Panel A reports the e¤ect of the price change on categories other than k. The e¤ect on
positive purchases of other categories is much greater when the targeted group is the the 1-…rm
45
shoppers than when it is the 2-…rm shoppers. A similar result is found for revenues (or equivalently gross pro…ts). We can conclude that the external e¤ects have a much greater magnitude
for a price increase to one-…rm shoppers. As the e¤ect on positive purchases (denoted df k ) is
similar to the e¤ect on revenues we proceed to look at the e¤ect on df k in the rest of the table.
Panel B reports the e¤ect on allocations of category k from the discriminatory price increases. Row B1 is the e¤ect on all allocations of category k to …rm f (from both 1-…rm and
2-…rm shoppers) and row B2 is the e¤ect on the allocations of the shoppers targeted in the
price increase. The shoppers can change from being two-store shoppers to one-store shoppers.
There is a much larger percentage reduction in allocations when 2-…rm shoppers are targeted
than when 1-…rm shoppers are targeted. The reason for this is explored in the next four rows
in B, which decompose the e¤ects of the price increase on the targeted group. These rows show
that one-store shoppers, who stop allocating the category to …rm f; are much more likely to
leave …rm f altogether. In contrast, two-store shoppers are more likely either (i) to convert
status to become a one-store shopper or (ii) to switch demand for category k without changing
shopping choice c.
Panel C reveals the e¤ect on …rm pro…ts of each type of price discrimination. It shows
that the price increase to two-…rm shoppers is pro…table but not the price increase to one…rm shoppers. This suggests that 2-…rm shoppers are not the ones that are constraining the
market power of the …rms, and that if 2-…rm shoppers were reduced as a proportion of …rm f’s
customers the market power of the …rm would decrease.
Table 24 considers price discrimination when a …rm unilaterally imposes price discrimination
on all categories. We compare the price discrimination incentives of Big 4 …rms and Discounters.
The …rst two columns consider the average e¤ect for Big Four …rms and the next two columns
show the average e¤ect for Discounters.
The …rst row in Panel A shows the number of consumers who change shopping choice c
as a result of the price change. Not all of these people leave …rm f altogether: a signi…cant
proportion are recaptured: one store shoppers convert to two store shoppers to take advantage
of the price discrimination, and vice versa. The net change in consumers at …rm f is shown in
the last row of Panel A.
Panel B shows the number of category allocations lost by …rm f as a result of the price
increase. We can see that in the case of the price increase to one-store shoppers there is a
much larger adverse change in the number of allocations, before and after these are recaptured
when people change shopping mode. Notice that the number of allocations recaptured from
two-store shoppers is high, which suggests that one of the advantages of discrimination against
two-store shoppers is the opportunity to convert them to one store shoppers, who then allocate
all their categories (with positive demand) to the …rm.
Panel C shows that a number of consumers are willing to change from one-store to two-store
shopping (and vice versa) when there is price discrimination between the two groups.
Panel D of Table 24 shows that it is not pro…table to raise prices to one-store shoppers but it
is pro…table to raise them to two-store shoppers. The decomposition of this e¤ect demonstrates
46
% Price change for
Consumer group a¤ected:
Big 4 Firms
Discounters
1-store 2-store 1-store 2-store
Panel A:
% change c
recaptured to …rm as 2-store shopper
recaptured to …rm as 1-store shopper
net change #consumers at f (after recapturing)
Panel B:
gross allocations lost
of which recaptured
net allocation change
Panel C:
proportion 1-stop before change
proportion 1-stop after change
increase in 1-stop percentage
Panel D:
gross change Pro…t from n-stop shoppers
recaptured as pro…t on 1 store shoppers
recaptured as pro…t on 2-store shoppers
net pro…t change
-3.8%
0.5%
-1.8%
-3.3%
0.3%
-2.6%
-3.3%
0.4%
-1.4%
-3.0%
0.2%
-2.5%
-4.6%
9.0%
-4.2%
-1.7%
26.0%
-1.3%
-5.5%
3.7%
-5.2%
-3.3%
7.8%
-3.0%
63.0%
61.3%
-1.7%
63.0%
64.3%
1.3%
38.8%
36.6%
-2.2%
38.8%
39.9%
1.1%
-0.90%
-0.30%
0.47%
-1.79%
0.33%
0.57%
0.17%
-0.39%
0.45%
-0.45%
1.40%
0.90%
Table 24: Further Price Discrimination Analysis
that the conversion of two-store shoppers to one-store shoppers is one of the reasons why it is
pro…table to discriminate against them.
We summarize the …ndings in this section. We have measured the size of the externality
between product lines at supermarkets: considering a price cut on a category that is enough to
generate one extra unit of sales, the positive externality on other categories is on average about
50% of the price of the product being discounted. This suggests that supermarket competition
imposes considerable downward pressure on prices compared to decentralized pricing (where
a category manager maximizes category prices), which constrains the market power of the
large retailers considerably. We found that the largest retailers (the Big Four) who attract a
relatively high share of one-store shoppers, had the greatest externality between product lines.
We further decomposed the e¤ects of price changes, which revealed the importance of one-stop
shoppers in generating this downward pricing pressure.
8
Conclusions
A supermarket brings together a range of broad product categories that more traditionally are
sold separately in specialist stores. The theory literature on retail pricing suggests that crosse¤ects between categories— that are in e¤ect “bundled”together to a considerable extent— are
large and should have a major impact on retail margins. In contrast to the theory literature on
supermarket pricing, in the empirical IO literature inter-category e¤ects have not been incorporated into the analysis of market power for individual product categories sold in supermarkets.
To measure the importance of these e¤ects we have speci…ed a model of supermarket choice
47
in which consumers buy a number of product categories. We allow for multi-store shopping,
and we allow consumers to switch stores category-by-category in the event of a price rise for
an individual category. The model is estimated on consumer survey data and predicts store
choice and category demands as a function of retail prices. We compute the externalities between product categories and …nd that these subsidies are a substantial fraction of retail price.
The results indicate the importance of accounting for cross-category e¤ects when estimating
the market power of individual product categories sold in supermarkets, and more generally
the results are of relevance to public policy relating to the organization of the food retailing
industry (for example when judging between “street”and “supermarket”forms).
9
Two stores and unit demands. Results from a simple
model
The setup here is the same as in subsection 3.2: there are two …rms, j = A; B, each of which
sells 3 product categories. For each category, consumers have unit demands which cannot be
split between stores. Consumers therefore choose a category-store mix, D, from among 23 = 8
alternatives
D = f(A; A; A); (A; A; B); : : : ; (B; B; B):g
Consumer i’s utility from mix D is
VDi = uDi
p(D)
c(D)i :
For simplicity uDi = 0 for all i and D. p(D) is the total price paid with mix D.
Half of the consumers, those i in the set IA , live near …rm A, and the other half, IB live
near …rm B. The shopping-cost term is given by:
c(D)i
8
>
<
>
:
+ "Di
; D2
= f(A; A; A); (B; B; B)g
+ "Di
; D = (j; j; j) & i 2 Ij ; j = A; B
+ + "Di ; D = (j; j; j) & i 2
= Ij ; j = A; B
where is a transport-cost (or …rm-loyalty) parameter, and "Di is a type 1 extreme value
idiosyncratic shock for category-store mix D, independent across D and i.
Firms may charge an additional fee to consumers who visit only that …rm. This fee can
be either positive or negative, but at the moment we assume that
= 0:
Letting VDIj be the utility of mix D for consumers in Ij , j = A; B, the share of consumers
choosing mix D is
eVDIB
eVDIA
+
0:5
:
QD = 0:5 P
P
VD 0 I
VD 0 I
A
B
e
e
0
0
D 2D
D 2D
48
Brand Loyalty Parameter ( )
0
Number of Product Categories (K)
3
E¤ect of one-store shopping fee (@ =@ ) -.25
Pr (only one store visited)
.25
Pr (both visited)
.75
price
2.00
0
5
-.125
.06
.94
2.00
6
3
.024
.99
.01
26.03
6
5
.027
.93
.07
4.82
Table 25: Table Caption
Based on these demand functions, …rms choose prices for each of their products to maximize
pro…ts
K
X
X
=
Q
pkj 1[D(k) = j]; = A; B;
j
D
D2D
k=1
where D(k) is element k of D.
Equilibrium prices are found by solving the system of K J equations with K J unknowns
given by the …rst-order conditions for pro…t maximization.
The table below shows results for K = 3 and also K = 5, and for transport-cost (or
brand-loyalty) parameter 0 or 6.
The table shows that with positive transport costs, = 6, the pro…t of a …rm goes up if
@
it charges higher prices from one-stop shoppers ( @ jj > 0). On the other hand, when = 0,
pro…ts are higher if …rms charge lower prices from one-stop shoppers.
10
Appendix: the Likelihood Function
P
The likelihood for the sample is N
i=1 fg(qj c; D) Pr(c; D)g where the conditional density g(qj
c; D) for the vector of category demands, q; is derived from the unconditional density f (v) as
follows. Let ck = ck (qk ; dk ) be the unique value of ck that that rationalizes the interior …rst
order condition (the …rst Kuhn Tucker) for observed quantity qk . We re-index the errors in
vc so that vc = vc1 ; ::; vcK , where 1; ::; l are goods that are observed with positive demand and
l + 1; ::; K have zero demand. Then as we condition on D the dimension of v is l and the
dimension of 0 is 2(K l). (One for each j in c): The density of the observed quantities is
g(qj c; D) =
Z
vcl 2A
f (vc ; vcl j
cl
2 A(c; D); c; D) jJl (q)j dvl
2 A vl is the errors for categories not observed and A(c; D) the set that yields a zero demand.
Jl () is the Jacobian of the transformation from (vc1 ; ::; vcl ) to (qc1 ; ::qcl ) when (qc1 ; ::qcl ) = 0.
The construction of f (vc ; vcl j cl 2 A(c; D); c; D) must be done for each consumer.
l
11
Appendix: Category De…nitions
Each of the transactions in the data has a variable that classi…es it as one of 170 categories
de…ned by TNS (e.g. “Breakfast Cereals”). We de…ne our eight categories by allocating these
49
170 categories as follows— where abbreviated forms, such as “amb”for ambient, etc., are those
of TNS.
Bakery: Amb Pizza Bases, Ambient Cakes and Pastries, Ambient Christmas Pudding, Ambient Sponge Puddings, Canned Rice Puddings, Childrens Biscuits, Chilled Breads, Chilled
Cakes, Chilled Desserts, Chilled Pizza and Bases, Crackers & Crispbreads, Everyday Biscuits, Fresh/Chilled Pastry, Frozen Bread, Frozen Savoury Bakery, Healthier Biscuits, Morning
Goods, Savoury Biscuits, Seasonal Biscuits, Tinned Sponge Puddings, Toaster Pastries, Total
Bread.
Dairy: Butter, De…ned Milk and Cream Prd, Fresh Cream, Fromage Frais, Instant Milk,
Margarine, Total Cheese, Total Ice Cream, Yoghurt, Yoghurt Drinks And Juices.
Drink: Ambient One Shot Drinks, Ambnt Fruit oor Yoghurt Juice and Drnk, Beer and
Lager, Bottled Colas, Bottled Lemonade, Bottled Other Flavours, Bottled Shandies, Canned
Colas, Canned Lemonade, Canned Other Flavours, Canned Shandies, Chilled One Shot Drinks,
Cider, Fabs, Food Drinks, Forti…ed Wines, Ginger Ale, Lemon and Lime Juices, Mineral Water,
Soda Water, Sparkling Wine, Spirits, Tonic Water, Wine.
Dry: Ambient Condiments, Ambient Slimming Products, Ambient Vgtrn Products, Arti…cial Sweetners, Breakfast Cereals, Chocolate Biscuit Bars, Chocolate Confectionery, Chocolate
Spread, Confect. & Other Exclusions, Cooking Oils, Crisps, Dry Meat Substitutes, Dry Pasta,
Dry Pulses and Cereal, Ethnic Ingredients, Everyday Treats, Flour, Frozen Confectionery,
Gum Confectionery, Herbal Tea, Herbs and Spices, Home Baking, Honey, Instant Co¤ee,
Lards and Compounds, Liquid and Grnd Co¤ee and Beans, Mincemeat (Sweet), Mustard,
Packet Stu¢ ng, Peanut Butter, Pickles Chutneys&Relish, Powd Desserts&Custard, Preserves,
R.T.S. Custard, Ready To Use Icing, RTS Desserts Long Life, Salt, Savoury Snacks, Sour and
Speciality Pickles, Special Treats, Suet, Sugar, Sugar Confectionery, Sweet and Savoury Mixes,
Syrup & Treacle, Table Sauces, Table and Quick Set Jellies, Tea, Vinegar.
Fruit and Vegetables: Ambient Olives, Ambient Rice and Svry Noodles, Ambnt Salad
Accompaniment, Baked Bean, Bitter Lemon, Canned Fish, Canned Hot Meats, Canned Salads,
Canned Vegetables, Chilled Fruit Juice and Drink, Chilled Olives, Chilled Prepared Frt and
Veg, Chilled Prepared Salad, Chilled Rice, Chilled Salad Accomps, Chilled Vegetarian, Cous
Cous, Frozen Potato Products, Frozen Vegetables, Frozen Vegetarian Prods, Fruit, Instant
Mashed Potato, Nuts, Prepared Peas&Beans, Tinned Fruit, Tomato Products, Total Fruit
Squash, Vegetable.
Household: Air Fresheners, Anti-Diarrhoeals, Antiseptics&Liq Dsnfctnt, Bath Additives,
Batteries, Bin Liners, Bleaches&Lavatory Clnrs, Body Sprays, Carpet Clnrs/Stain Rmvers,
Cat Litter, Cat and Dog Treats, Cleaning Accessories, Cold Sore Treatment, Cold Treatments,
Conditioners and Creme Rinses, Contact Lens Cleaners, Cotton Wool, Cough Liquids, Cough
Lozenges, Decongestants, Dental Floss or Sticks, Dentifrice, Denture Cleaners/Fixature, Deodorants, Depilatories, Dog Food, Electric Light Bulbs, Eye Care, Fabric Conditioners, Facial
Tissues, First Aid Dressings, Foot Preparations, Furniture Polish, Hair Colourants, Hairsprays,
Hand Wash Products, Hayfever Remedies, Home Perms, Household Cleaners, Household Food
50
Wraps, Household Insecticides, Incontinence Products, Indigestion Remedies, Kitchen Towels,
Laxatives, Liquid Soap, Machine Wash Products, Mens Hairsprays, Mens Mass Fragrances,
Mens Skincare, Moist Wipes, Mouthwashes, Oral Analgesics, Oral Lesion/teething Mrkt, Pot
Prri and Scntd Cndls and Oils, Razor Blades, Sanpro, Shampoo, Shaving Soaps, Shoe Care
Products, Skincare, Sleeping Aids, Sun Preparations, Talcum Powder, Toilet Soap inc.Mens,
Toilet Tissues, Topical Analgesics, Topical Antiseptics, Total Cat Food inc.Bulk, Total Dry
Dog Food, Total Male and Female Styling, Total Toothbrushes, Upset Stomach Remedies,
Vitamin and Mineral supplements, Wash Additives, Washing Up Products
Meat: Ambient Cooking Sauces, Ambient Dips, Ambient Pastes and Spreads, Ambient
Sandwich Fillers, Ambient Soup, Canned Pasta Products, Chilled Black and White Pudng,
Chilled Burgers and Grills, Chilled Cooking Sauces, Chilled Dips, Chilled Gravy and Stock,
Chilled Pate and Paste and Spread, Chilled Prepared Fish, Chilled Processed Poultry, Chilled
Ready Meals, Chilled Sausage Meat, Chld Frnkfurter/Cont Ssgs, Chld Sandwich Fillers, Cold
Canned Meats, Complete Dry/Ambient Mls, Cooked Meats, Cooked Poultry, Fresh Bacon
Joint, Fresh Bacon Rashers, Fresh Bacon Steaks, Fresh Beef, Fresh Flavoured Meats, Fresh
Lamb, Fresh Other Meat & O¤al, Fresh Pasta, Fresh Pork, Fresh Poultry, Fresh Sausages,
Fresh Soup, Frozen Bacon, Frozen Beef, Frozen Cooked Poultry, Frozen Fish, Frozen Flavoured
Meats, Frozen Lamb, Frozen Meat Products, Frozen Other Meat & O¤al, Frozen Pizzas, Frozen
Pork, Frozen Poultry, Frozen Processed Poultry, Frozen Ready Meals, Frozen Sausage Meat,
Frozen Sausages, Hens Eggs, Instant Hot Snacks, Lse Fresh Meat & Pastry, Meat Extract,
Other Chilled Convenience, Other Frozen Foods, P/P Fresh Meat and Veg and Pastry,
Packet Soup, Shell…sh, Wet or Smoked Fish.
Milk: Total Milk.
12
Appendix: Price Instruments by Category
The instrumental variables for prices are from four main sources. (i) The Agricultural Price
Index (API) published by the O¢ ce for National Statistics (ONS) measures the monthly price
changes for UK agricultural outputs (denoted below as (i,a)) and inputs (denoted below as
(i,b)). The output series re‡ects price farmers receive for their products, also referred to as farmgate prices, including major crops (e.g. wheat, potatoes) and livestock and livestock products
(e.g. sheep, milk, eggs). The input series re‡ects the price farmers pay for goods consumed,
e.g. feed, fertiliser or seed. (ii) The Producer Price Index (PPI) published monthly by ONS
measures the price changes of goods bought and sold by UK manufacturers; the coverage of the
index includes food and non-food products sold in supermarkets— e.g. “prepared meals and
dishes” and “soaps and detergents”. (iii) The Consumer Price Index in Ireland, prepared by
the Central Statistical O¢ ce, Dublin, (CSO), is a monthly series of prices of consumer goods
and services collected directly from retail outlets. The fourth source (iv) is used only for the
dairy and milk categories: monthly prices of milk-related commodities— such as Skimmed Milk
Power, Butter, and Whey Powder— on international spot-markets, available from DairyCo (a
51
body that represents UK dairy farmers). (Also included in (iv) are three price indices (IMPE,
AMPE, and MCVE respectively) constructed by DairyCo that measure the price farmers can
achieve by selling milk to the following alternative destinations: the EU under its price-‡oor
for intervention; world butter and skimmed milk powder commodity markets; and world cheese
commodity markets.
For each category we pick variables from each source (i)-(iv) that relate broadly to the
inputs of each category— e.g. in the bakery category we include crop products from (i,a) and
the price of bread from (iii), and in the dairy category we include the cost of oat cattle feed
from (i, b). Full details are given in the next paragraph. For all categories we include the
GB-Euro exchange rate, as this a¤ects the cost of imported products, as well as …rm dummies,
year dummies, and quarterly dummies.
We now give the full category-speci…c details, listing variables names from sources (i)–
(iv) for each category. Bakery: (i, a) Cereals, Crop products, Total of all products; (i, b)
Feed Barley, Feed Oats, Feed Wheat; (ii) Food Products, Food Products— EU Imports, Food
Products— Non EU Imports; (iii) Bread. Dairy (i, a) Eggs, Milk, Total of all products; (i,b)
Feed Barley, Feed Oats, Feed Wheat; (ii) manufacturer milk price; (iv) AMPE, IMPE, MCVE,
Bulk Cream, Butter (Unsalted), EU farmgate milk price, Mature Cheddar Cheese, Mild Cheddar Cheese, Skimmed Milk Powder, Whey Powder. Drink (i, a) Crop products; (ii) Alcoholic
beverages including duty, Beer, Beer including duty, Beverages— EU imports, Beverages— non
EU imports, Dairy products, Distilled Alcholoic Beverages, Fruit & vegetable juices, Processed
& preserved fruit & vegetables, Soft drinks mineral waters & other bottled waters, Cocoa
chocolate & sugar confectionery, Wine from grape & cider; (iii) Alcoholic beverages, Fruit,
Non-alcoholic beverages, Sugar. Dry (ii) Cocoa chocolate & sugar confectionery, Condiments
& seasonings, Food products, Food Products - EU Imports, Food Products - Non EU Imports, Fruit & vegetable juices, Ice cream, Meat & poultry meat products, Mineral waters &
other bottled waters, Other food products, Prepared meals & dishes, Preserved meat & meat
products, Processed & preserved …sh crustaceans & molluscs, Processed & preserved fruit &
vegetables, Processed & preserved potatoes, Processed tea & co¤ee, Soft drinks mineral waters
& other bottled waters, Wine from grape & cider; (iii) Bread, Meat, Dairy, Oils, Fruit, Vegetables, Sugar, Condiments, Soup, Other. Fruit & Vegetables: (i a) Cabbage, Cereals, Crop
products, Dessert apples, Fresh fruit, Fresh vegetables, Lettuce, Oilseed rape, Onions, Other
fresh vegetables, Other fresh fruit, Potatoes for consumption, Seeds, Sugar beet, Total of all
products, Other crop products; (i b) Feed barley, Feed oats, Feed wheat; (iii) Fruit, Vegetables.
Household goods: (ii) Basic pharmaceutical products & pharmaceutical preparations - non EU
imports, Cleaning & polishing preparations, Household & sanitary goods & toilet requisites,
Paper stationery— EU imports, Paper stationery— non EU imports, Perfumes & toilet preparations, Perfumes & toilet preparations— EU imports, Pharmaceutical preparations, Prepared
pet foods, Soap & detergents; (iii) Laundry goods, Health goods, Personal hygine goods. Meat:
(i a) Animal output, Crop output; (ii) Condiments & seasonings, Food products, Meat & poultry meat products, Other food products, Prepared meals & dishes, Preserved meat & meat
52
products, Processed & preserved …sh crustaceans & molluscs, Processed & preserved fruit &
vegetables, Processed & preserved potatoes, Food products— EU imports, Food products— non
EU Imports; (iii) Bread, Condiments, Dairy, Meat, Oils, Soup, Sugar, Vegetables, Other food.
Milk: as Dairy.
13
Appendix: Price Index Construction
References
[1] Amemya T (1974) Multivariate Regression and Simultaneous Equation Models when the
Dependent Variables Are Truncated Normal Econometrica Vol. 42, No. 6 (Nov., 1974),
pp. 999-1012
[2] Armstrong, M. and J. Vickers (2010) “Competitive Non-linear Pricing and Bundling,”
Review of Economic Studies, vol. 77(1), pages 30-60.
[3] Beggs A (1992) “Mergers and Malls” Journal of Industrial Economics vol. 42(4), pages
419-28
[4] Bell D R., Teck-Hua Ho and Christopher S. Tang (1998) Determining Where to Shop:
Fixed and Variable Costs of Shopping Journal of Marketing Research, Vol. 35, No. 3
(Aug., 1998), pp. 352-369
[5] Bliss C (1998) “A Theory of Retail Pricing”Journal of Industrial Economics Vol. 36, No.
4, pp. 375-391
[6] Chen Z. & P. Rey (2012). "Loss Leading as an Exploitative Practice," American Economic
Review 102(7): 3462-3482
[7] Competition Commission (2000) Supermarkets HMSO, London
[8] Competition Commission (2007) Groceries HMSO, London
[9] Dubin J. A. and D.L. McFadden (1984) “An Econometric Analysis of Residential Electric
Appliance Holdings and Consumption” Econometrica Vol. 52, No. 2 (Mar., 1984), pp.
345-362
[10] Dubois P and S Jodar-Rossell (2010) "Price and Brand Competition between Di¤erentiated Retailers: A Structural Econometric Model”CEPR Discussion Paper No DP7847.
[11] Economides, N (1989) “Desirability of Compatibility in the Absence of Network Externalities”American Economic Review 79(5):1165–1181 (September 1989)
[12] Farrell J. and C. Shapiro (2010) “Antitrust Evaluation of Horizontal Mergers: An Economic Alternative to Market De…nition”, The B.E. Journal of Theoretical
53
[13] Economics, Volume 10 (1)
[14] Gentzkow, M. (2007). “Valuing New Goods in a Model with Complementarity: Online
Newspapers”American Economic Review, 97(3): 713-744.
[15] Gould E, P Pashigian, and J Prendergast (2005) “Contracts, Externalities, and Incentives
in Shopping Malls” Review of Economics and Statistics August 2005, Vol. 87, No. 3,
411-422
[16] Gri¢ th R, E. Leibtag, A Leicester, & A Nevo (2008). "Timing and Quantity of Consumer
Purchases and the Consumer Price Index," NBER Working Papers 14433
[17] Haneman W M. (1984) "Discrete/Continuous Models of Consumer Demand" Econometrica 52:3 541-562
[18] Hendel I (1999) “Estimating Multiple Discrete Choice Models: An Application to Computerization Returns”Review of Economic Studies , 66, 423-446.
[19] Klemperer.P (1992) “Equilibrium Product Lines: Competing Head-to-Head May be Less
Competitive”American Economic Review, 82, 740–755.
[20] Lal, R and C Matutes (1994), “Retail Pricing and Advertising Strategies”. Journal of
Business, Vol 67 No 3
[21] Lal, R. and R. Rao (1997), “Supermarket Competition: The Case of Every Day Low
Pricing”Marketing Science 1997, 16, 60–80
[22] Matutes, C. and P. Regibeau (1988) “Mix and Match: Product Compatibiltiy without
Network Externalities”RAND Journal of Economics Vol 19 No 2 p221-234
[23] Nevo A (2001) "Measuring Market Power in the Ready-to-Eat Cereal Industry".Econometrica, Vol. 69, No. 2. pp. 307-342
[24] Schiraldi P, Seiler S, and H Smith (2012) Supermarket Choice with Multi-Store Shopping:
Measuring the E¤ect of Format Regulation Mimeo Oxford University
[25]
[26] Smith H (2004) “Supermarket Choice and Supermarket Competition”Review of Economic
Studies 71: 235-263
[27] Smith, H and D Hay (2005) "Streets Malls and Supermarkets" Journal of Economics &
Management Strategy, 14:1, pp. 29-59
[28] Smith H and J Thanassoulis (2008) "Oxford Milk Project"
[29] Smith H and O Thomassen (2012) “Multi-category demand and supermarket pricing”
International Journal of Industrial Organization, May 2012, 30:3 309-314
54
[30] Song I and P K. Chintagunta “A Discrete-Continuous Model for Multicategory Purchase
Behavior of Households”Journal of Marketing Research, Vol. 44, No. 4 (Nov., 2007), p
[31] Train K. E.: Discrete Choice Methods with Simulation, 2nd ed. p. 256.
[32] Villas-Boas, SB (2007) “Vertical Relationships between Manufacturers and Retailers: Inference with Limited Data”Review of Economic Studies 74:2 625-652
[33] Vroegrijk, Mark; Gijsbrechts, Els; Campo, Katia "Close Encounter with the Hard Discounter: A Multiple-Store Shopping Perspective on the Impact of Local Hard-Discounter
Entry" Journal of Marketing Research Volume: 50 Issue: 5 Pages: 606-626
[34] Wales T. J. and A.D. Woodland (1983) “Estimation of consumer demand systems with
binding nonnegativity constraints”, Journal of Econometrics 21:263-285.
[35] Wooldridge, J. M.: The Econometric Analysis of Cross-Section and Panel Data, 2nd ed
55