Identifying Price-Leadership Structures in Oligopoly
Paul W. Dobson, Sang-Hyun Kim and Hao Lan*
January 25, 2016
Abstract
Oligopoly can give rise to complex patterns of price interaction and price
adjustment. While firms in oligopolistic markets may divide into price leaders
and price followers, it is not inconceivable that some may take on dual roles,
being a leader to one group but a follower to a different group. Thus who leads
and who is led can be complicated and hierarchical. To help disentangle such
pricing relationships, this paper develops a method to empirically identify priceleadership structures in n-firm oligopolistic markets by generalizing the duopoly
method proposed by Seaton and Waterson (2013). Applying the method to UK
food retailing industry, our analysis finds that it has a three-tier structure in
which the two largest players (Tesco and Asda), tend to price-lead other retailers,
while the other two of the Big 4 major chains (Sainsbury and Morrisons) play
both follower (to the top two) and leader (to the smaller, premium/convenience
positioned supermarket chains).
Key words: Price leadership, oligopolistic markets, UK food retailing industry
JEL codes: D43, L13, L41, L81
* Author affiliations and contact details:
Paul W. Dobson, Norwich Business School, University of East Anglia - [email protected]
Sang-Hyun Kim, School of Economics, University of East Anglia - [email protected]
Hao Lan, Norwich Business School, University of East Anglia – [email protected]
1 Introduction
In contrast to the majority of theoretical models of price competition, markets in the real
world rarely operate as a simultaneous move game with price adjustments undertaken as
completely hidden actions until jointly revealed. Instead, firms post and alter their prices in
continuous time, responding to changes in production/operation costs and rivals’ posted
prices. While it is rather well understood that non-simultaneity of price changes can
facilitate coordination among competing firms, thus may detrimentally impact consumer
welfare, methods to empirically identify price leadership structures have been limited by a
lack of a clear, testable definition of price leadership applicable a wide range of competitive
circumstances. In confronting this challenge, Seaton and Waterson (2013, hereafter SW)
proposed a narrow, falsifiable definition of price leadership, and also a way to empirically
identify a price leader and a follower. However, as the authors admitted, the identification
strategy that they proposed has some limitations: one of which is that it can be used only
when a researcher restricts attention to just two firms. In this paper, we develop a
procedure to identify price-leadership structures when the market consists of more than
two significant players and when there is the possibility of quite complex patterns of pricing
dependencies across multiple firms.
We utilize SW’s method as a building block of the procedure. That is, we first test whether
there is a clear leader-follower relationship for each pair of firms. However, when there are
more than two firms, the pairwise test may identify a spurious relationship: company A may
be identified to have price-led company B although it actually did not, because A tended to
move more or less simultaneously with a real price-leader identified as company C. To rule
out such a spurious leadership, in the next step, we examine whether firm A alone could
lead B by focusing on the relationship among the three firms, A, B and C. By so doing, we can
rule out spurious leaderships and identify clear single-handed price leaderships. That is, we
use the tests involving more than two firms as a refinement method, and in this sense, our
identification strategy is conservative.
With more than two firms operating, more complicated relationships than a pair of one
leader and one follower may exist. For instance, two or more firms may hold a joint
leadership over one or more followers. In the procedure of identification, the existence of
joint leaderships is naturally tested. Also, there may exist an indirect influence of a price
leader, e.g. firm A price-leads B, and B leads C. Then although A and C do not have a direct
1
leader-follower relationship, we may want to say that there is an indirect price leadership of
A over C. We also test the indirect leadership by simply modifying the pairwise test.
To demonstrate our method at work, we explore the UK retail grocery market – a sector
regularly under the watchful gaze of competition authorities with concerns about ineffective
competition and price coordination – with particular focus here on fresh fruits and
vegetables. Our data have some advantages over other data used in previous studies. We
utilize the weekly observed price information of all 7 large mainstream supermarket retailers
– Tesco, Asda, Sainsbury, Morrisons, Marks & Spencer, Waitrose and Co-operative Food – for
7 years. Since we focus on the prices of fruits and vegetables, we can compare them easily
across retailers. Also, it is worth mentioning that these are regularly purchased items, thus
consumers should have good knowledge/recollection regarding the prices, reinforced by
their prominent instore display and being a key component of consumers’ grocery shopping
baskets.
Our analysis reveals that UK food retailing industry, at least in terms of these products, has a
three-tier structure where the major retailers can be categorized as either the leaders (Asda
and Tesco), the first followers (Sainsbury and Morrisons) or the second followers (Marks &
Spencer, Waitrose and Co-operative Food). The retailers in the leader group tend to pricelead all the other firms, but the followership by the first followers is more apparent. The first
followers are leaders as well with regard to the second followers (e.g. Sainsbury tends to be
followed by Marks & Spencer). It is noteworthy that there is no firm in the leader group
which follows a firm in the follower groups, nor is there a firm in the first follower group that
is led by a firm in the second follower group. In this sense, the three-tier structure is strictly
hierarchical, and the leader-follower relationship does not violate transitivity. Moreover, we
find that the leading retailers are not only directly but also indirectly followed by those in the
second follower group. That is, suppose that a firm in the leader group, say Tesco, is
followed by a firm in the first follower group, say Sainsbury, which is followed by a firm in
the second follower group, Marks & Spencer. We test whether Tesco price-leads Marks &
Spencer with a moderate time lag, and confirm the existence of indirect leadership of Tesco.
In contrast, we do not find any case of joint leadership by two or more firms.
To complement the main analysis, we also explore Granger-causal relationships among the
prices set by different retailers, which are arguably comparable to the price leader-follower
relationships. In particular, we run vector autoregression (VAR) for each product, and count
the number of products for which we found significant Granger-causal relationships.
2
Interestingly, the VAR analysis also finds the same three-tier structure in which the prices of
firms in a higher tier tend to Granger-cause the prices of those in a lower tier. Moreover, the
leader-follower relationships based on the VAR analysis largely overlap the leader-follower
relationships identified in our main analysis. We do not know which method is better in
identifying the true leadership structure. However, the consensus between the two may
suggest that the one identified in this paper indeed reflects the true structure.
In the literature, there are few papers that focus on a narrow, falsifiable perspective in the
manner of the SW paper. Similar approaches can be found in Wang (2009) and Lewis (2012)
but most of the empirical papers building on well-specified analytical models focus on the
gasoline retailing market and Edgeworth cycle patterns. Apart from these papers, the more
traditional empirical approach using Granger causality for identifying price interaction
patterns. In terms of grocery retailing, Lloyd (2008) applies such method to test price
leadership in the UK beef retailing market. Also, of more direct relevance to UK fresh
produce retailing, Revoredo-Giha and Renwick (2012), observe a strengthening price
interrelationship between Tesco and Sainsbury, where price responses tend to be more
strategic rather than straightforward direct competition. However, rather than just pairwise
comparisons, there might be merit in studying how a broader set of rivals interact on pricing,
which is the purpose of the study here. In addition, Berck et al. (2008) test sales promotion
leadership based on Granger causality using grocery scanner data of frozen and refrigerated
orange juice in the US. Accordingly, it will be interesting to examine how “temporary price
reductions” (“TPRs”) operate and whether they might be a means to avoid all-out price
competition to effect a degree of price co-ordination.
2 Method
2.1 Definitions
In this section, we first review the pairwise test proposed by SW, and then articulate the
spurious relationship problem, and propose our method. The definition of price leadership
proposed by SW is as follows: “price leadership occurs when one firm makes a change in a
price (or set of prices) that is followed within a predetermined short period by the other
(more generally, another) firm making a price change of exactly the same monetary amount
in the same direction on the same product(s), and doing so significantly more often than
3
would be expected by chance” (p. 392). This definition excludes simultaneous and some
sequential price changes such as those separated by a long time lag, those of similar but not
the same monetary amounts and those on similar but different products. This definition may
not be the best or the most comprehensive one. According to the authors, though, they
deliberately chose this tight definition to make it clearly falsifiable and to make a clear case
of leadership. Throughout the paper we follow this narrow definition.
To operationalize this definition, they restrict their focus on two firms (in their exercise, Asda
and Tesco) and fix the response time to 1 or 2 weeks. Then, they count leadership incidences
and simultaneous price changes of the same amounts on the same products. The formal test
is to check whether the leadership incidences are significantly more frequent than the
simultaneous price changes.
Formally, denote a change in a price of retailer X at week t by X(t) and let Y(t+1) be a price
change of the same amount by retailer Y in the next week or the week after the next week
(that is, within two weeks). The relevant events are then: {X(t), Y(t)}, {X(t), Y(t+1)}, {Y(t),
X(t+1)}. In words, X and Y simultaneously changed a price of the same product by the same
amount, X price-led Y or Y price-led X. When the events in the second category are
significantly more frequent than the first type of events, we say “X price-leads Y.” On the
other hand, if the third type of events are more frequent compared to the first events, it is
said that “Y price-leads X.” 1
When there are more than two (non-negligible) firms in the market, there are a few
conceptual and practical complications which do not exist in duopoly. First, the price leader
or the follower in the market may not exist at all. Instead, some price leaders may also be
followers at the same time, so leader-follower relationships must be defined within pairs or
subgroups of firms. Second, there may exist different types of leaderships such as joint
leaderships or indirect leaderships. Joint leadership indicates the following situation: two or
more firms none of which alone is a price leader may together lead another firm. On the
other hand, if X does not price-lead Z directly, but if X leads Y and Y leads Z, X may be able to
indirectly influence Z via Y. In this case, we can say that X has an indirect leadership over Z
via Y. In principle, the chain of influence can be as long as the number of firms in the market.
On more practical side, the pairwise test proposed by SW may produce misleading results:
even if X alone does not price-lead Y, it may appear so if X and one or more other firms are
1
In principle, X’s leadership over Y and Y’s leadership over X can co-exist. However, neither SW nor
we found such an incidence in the UK retail market data.
4
jointly price-leading Y. Or even if X itself does not lead Y in any sense, X may still appear to
lead Y because X changed its prices for sufficiently many times simultaneously with another
firm which price-leads Y. In other words, the pairwise test may identify spurious leadership
when there are more than two firms. Thus, we propose a refinement procedure to rule out
such leaderships and to make a clearer case of single-handed leaderships. While doing so,
we will be able to identify joint or indirect leaderships if there exists any.
2.2 Procedure
(i)
We start with the pairwise tests. For each pair (X,Y), we test both X’s and Y’s
leadership by comparing the numbers of incidences of {X(t), Y(t+1)} and {Y(t), X(t+1)}
to that of {X(t), Y(t)}. If for all price follower Y, Y is led only by X, that is, if each
follower has a single leader, the identification procedure stops, and we conclude:
the leaderships identified by the pairwise tests are genuine, single-handed
leaderships, and there does not exist a joint leadership.
(ii)
If a follower firm, say Z, turns out to be led by more than one leader firm, say X and Y,
then we conduct 3-group-wise test for each group of two leader firms and one
follower firm. To test X’s single-handed leadership, we test whether the incidences
of {X(t),Y(n),Z(t+1)} or {X(t),Y(t+1),Z(t+1)} are sufficiently more frequently observed
than those of {X(t),Y(t),Z(t+1)} where Y(n) indicates that the price of firm Y has not
changed at all or changed by a different amount during the period of interest. If X
passes the 3-group-wise tests with all the other leaders of Z, then X’s leadership is
confirmed. Otherwise, we regard X’s leadership over Z as a spurious one. The
refinement procedure for single-handed leaderships stops here.
(iii)
If in the 3-group-wise test, the incidences of {X(t),Y(t),Z(t+1)} turns out to be
sufficiently more frequent than both those of {X(t),Y(n),Z(t+1)} or {X(t),Y(t+1),Z(t+1)}
and those of {Y(t),X(n),Z(t+1)} or {Y(t),X(t+1),Z(t+1)}, that is, if neither X nor Y holds a
single-handed leadership and the joint leadership incidences are significantly more
frequent, we say that there may exist a joint leadership of X and Y over Z. If there is
no other firm which price-leads Z, then the joint leadership is confirmed, and the
procedure stops.
5
(iv)
If there is a firm other than X and Y which price-leads Z, then we repeat the
refinement procedure. In 4-group-wise test involving X, Y, Z and another leader A,
we compare {X(t),Y(t),A(t),Z(t+1)} to {X(t),Y(t),A(n),Z(t+1)} and {X(t),Y(t),A(t+1),Z(t+1)}.
Depending on the test result, we either confirm the joint leadership of X and Y or
move on to testing the joint leadership of X, Y and A. The procedure stops if there is
no more possible case of joint leadership or if the number of relevant observations
for the test is not large enough to give any conclusion. Otherwise, we keep
examining joint leaderships of n firms by (n+1)-group-wise tests.
(v)
If according to the pairwise test results, X leads Y and Y leads Z, we further test X’s
indirect leadership over Z by modifying the time lag from 1 or 2 weeks to 3 or 4
weeks. While doing so, we keep the other requirements (that is, of the same amount
on the same product) fixed. If there exists a longer chain of leader-follower
relationships, we also test those indirect leaderships by adjusting the response time
accordingly.
Note that we generalize the identification strategy of SW to eliminate spurious leadership
cases and to identify joint and indirect leaderships. Our method is conservative, so helps to
focus on the clearest cases. In the following sections, we apply this method to characterize
the leadership structure of the UK retail market using a dataset with a long time span. In
Section 5.4, we also estimate the responsiveness of prices to one another using vector
autoregression. Granger-causality is comparable to the price leadership, but is expected to
be noisier and more comprehensive because in VAR analysis not only the price changes of
the same amount but also of different amounts are considered.
3 UK food retailing industry
UK food retailing is recognised as one of the most concentrated and differentiated retail
grocery markets in the EU. For the past decade, the retail grocery sector in the UK has been
dominated by the so-called “Big 4” retailers – Tesco, Sainsbury, Asda and Morrisons –
operating predominantly from large-format superstores, followed by smaller chains with
more specialist appeal, including upmarket retailers like M&S and Waitrose focusing on
higher income consumers, convenience retailers like the Co-operative Food focusing on
neighbourhood retailing, or hard discount retailers, like Aldi and Lidl operating with limited
product ranges, mainly private label, sold at discount prices.
6
Even amongst the Big 4 retailers there is perceived differentiation in respect of product
ranges, services and consumer appeal. Sainsbury is seen as more upmarket than the others,
while Asda (owned by Walmart) is more price focused as an “everyday low price” (“EDLP”)
positioned retailer, with Morrisons value-oriented and the potential market leader, Tesco,
has taken the middle ground as the retailer having the broadest appeal. Nevertheless, they
are competing for the bulk of UK consumers, where they account for three-quarters of
grocery sales in the UK.
The other retailers are considerably smaller but still serve
consumers right across the demographic range and with national coverage. Accordingly, all
these retailers should be directly competing with each other and this should be evident in
perhaps the most staple product category of all represented by fresh fruit and vegetables.
The UK Competition Commission (2000; 2008) has twice investigated this retail sector in the
recent past and concluded that generally price competition has been working effectively.
Detailed analysis by Smith (2004; 2006) shows how the combination of store characteristics
and location affect consumer store choice and sales at the local level. However, while store
choice decisions are made at a local level, the prices that these chains set are generally
national, i.e., apply right across their supermarket networks. This feature is helpful in
examining retail price competition as conducted here, but also means that it is
straightforward for the retailers to monitor each other’s prices so could offer conditions
suitable for tacit price coordination.
Despite repeated sector inquiries by the UK competition authorities, there has continued to
be media interest and public concern about UK supermarkets profiteering and avoiding
intense price competition, with their tendency to focus on price promotions and engaging in
what many commentators see as phoney price wars with claims of slashing prices when
investigations have revealed that the price cuts have often been minuscule (Chakraborty et
al. 2014; 2015). Concerns have been particularly expressed about high prices on fruit and
vegetables, not least because of their importance for a healthy diet and worries about their
high prices resulting in low-income families eating insufficient amounts of fresh produce and
instead buying cheaper calorie-dense processed foods. For example, The Times (2011)
calculated the difference between retail and wholesale prices in two leading British
supermarkets and found that mark-ups are more than 100% in most fruits and vegetables
they investigated. It also reported comments from industry insiders with the claim that fresh
produce is one of the most profitable categories for UK supermarkets. The Grocer (2014)
extended coverage to investigate prices in the UK against those in other EU countries. It
found that prices are significantly higher in the UK than other EU countries even after
7
subtracting transportation costs and identified UK prices being inflated due to non-cost
reasons. In addition, promotional pricing has become to play a more pivotal role in modern
supermarket price competition (Hosken and Reiffen, 2004). In the UK, nearly 40% of all
grocery spending through supermarkets is attributable to price promotions, with accusations
that many of the promoted price discounts are not genuine but based on artificially inflated
prices (CMA 2015). Even for fruit and vegetables, traditionally a category with a relatively
low rate of price promotions, one observes a significant amount of price promotions, as our
data shows, and so they do form an important aspect of sequenced pricing moves, especially
for seasonal produce.
4 Data
Our supermarket retail prices are those reported weekly on a selection of fruits and
vegetables by the trade magazine “Horticulture Week” (“HW”) from October 2007 to April
2013 (288 weeks). The reported prices are those offered at each of the leading UK
supermarket retailers collected through store visits undertaken by price checkers from an
independent marketing agency, Market Intelligence Services.
For the purpose of constructing a panel dataset, we identified 26 products with regularly
reported prices each week across the full year for the leading seven UK supermarket
retailers. 2 In total, this HW retail price dataset provided a panel of 52,416 weekly prices. The
retailers cover the “Big 4” mainstream supermarket retailers – Tesco, Sainsbury, Asda and
Morrisons – which tend to operate with large format superstores, two “upmarket” retailers,
M&S and Waitrose, and the more convenience oriented (small supermarket format) retailer
Co-operative Food. Jointly these seven retailers account for over 90% of all supermarket
food sales in the UK. 3
2
The 26 common products identified were apples (cooking), apples (eating), aubergine, broccoli,
cabbage (savoy), carrots, cauliflower, celery (each), celery (hearts, pre-packed 2), courgettes,
cucumber (full), cucumber (half), leek, lettuce (gem), lettuce (iceberg), lettuce (round), onion (red),
onion (white), parsnip, pears (conference), radish, strawberries, swede, sweetcorn, tomatoes (loose)
and tomatoes (pre-packed 6). The products in the sample were matched across retailers on a like-forlike basis with any weight differences noted along with whether the goods were imported or
domestically grown.
3
There is also some price data available on a further retailer, the hard discounter Aldi, but the data
were only available on a far more limited number of products and for significantly shorter time
periods, so we have not included this retailer in our sample.
8
The data series have some missing values over the full time period, because the retail price
was not recorded by the price checker that week. In particular, we have retail prices missing
in the 2-3 weeks around Christmas and they are only bi-weekly collected since July 2012.
There is also a relatively long gap from the end of April to the beginning of June in 2008.
Here we interpolated the missing values following some pricing studies (e.g. Pesendorfer,
2002; SW, 2013) rather than leave them alone. Our approach has been to interpolate
missing values by applying a set of simple rules to minimise any distortions: (i) for one or two
consecutive missing values, based on either the previous or next value to them, not the
means between them; (ii) for more than three consecutive missing values, compare the
pattern of the identical products in other supermarkets; (iii) randomise the values according
to values in the previous and following weeks. Although we have this missing value problem,
our results are not affected much by it because our method (and also SW’s) relies on
counting the relevant sequential price changes as opposed to calculating some sort of
average.
Using fruit and vegetable supermarket prices, we are able to distinguish between regular
prices and temporary price reductions (TPR). As a result we define a TPR using the algorithm
proposed by Nakamura and Steinsson (2008). Specifically, we use a 10% or more price drop
that occurred for one to six weeks before reverting back to the previous price as a typical
TPR in the dataset. This definition is also consistent with the application of SW. Then, the
regular prices can be filtered out from original prices by removing TPRs. In our empirical
analysis, we focus on testing leadership using regular prices for a direct comparison to SW.
Furthermore, we are also interested in TPR leadership using TPRs on their own.
Table 1 shows the numbers of observations in each case. Among 4,593 changes in regular
prices, 1,639 changes (36%) were relevant for the analysis in the sense that before, after or
simultaneously with a change there was another price change by another firm of the same
amount. On the other hand, 245 of TPRs among 3,119 (8%) were sequentially started within
2 weeks. So it is easy to see that the regular price changes were much more sequentially
correlated in comparison with TPRs, which is consistent with what SW document in their
paper.
Table 1. The numbers of observations
All price changes
Up
Regular price
2460
TPR
9
Leadership-relevant
changes
Regular price
TPR
1065
Down
Total
2133
4593
3119
574
1639
245
5 Identifying the leadership structure in UK food retailing
5.1 Pairwise test of leadership
We first examine the price leadership between one and another retailers using the test
proposed by SW.
Following SW, we explore the price-up and the price-down cases
separately. For inference, we use exact binomial probability tests rather than the
approximation tests using the normal distribution which SW used in their paper. 4 Our key
results of the pairwise tests are summarized in Figure 1. The full results are reported in the
Appendix.
Figure 1. The upward (left) and the downward (right) leaderships identified by the pairwise
tests
An arrow from Y to X in Figure 1 represents the leadership of X over Y. In other words, the
arrow indicates that leadership incidences {X(t),Y(t+1)} are observed statistically significantly
(at 95% level) more often than the simultaneous price-change incidences {X(t),Y(t)}. The
panel on the left shows the upward price leaderships and the one on the right shows the
downward leaderships. In both panels, one can clearly see that there is a three-tier structure
in this industry. Among the “Big 4,” “the bigger 2,’” Tesco and Asda, turn out to lead the
other “smaller 2,” Sainsbury and Morrisons. But the smaller two are also leaders with
respect to non-Big 4 retailers, i.e. M&S, Waitrose and Co-operative Food. So we can group
them into three: the leaders (Asda and Tesco), the first followers (Sainsbury and Morrisons)
or the second followers (Marks & Spencer, Waitrose and Co-operative Food). This three-tier
4
As statistical theory suggests, if we had large sample size (N>30), it would not matter which test to
be used but binomial probability test is preferred with small sample size like ours.
10
structure is strictly hierarchical in the sense that no firm in the leader group follows a firm in
the follower groups. Also, neither is it the case that a firm in the first follower group is led by
a firm in the second follower group.
11
Table 2. Single-handed leadership refinement for group (X,Y,Z)
(T,A,S)
(T,S,MS),
(T,M,MS)
(S,M,MS)
(T,A,W)
(A,M,W)
(T,M,W)
(T,M,CP)
X leads up Z alone
Leadership incidences
Non-leadership incidences
Observed proportion
p value
17
15
0.531
0.43
28
4
0.875
0*
53
7
0.883
0*
22
9
0.71
0.015*
16
2
0.889
0.001*
28
3
0.903
0*
22
1
0.957
0*
Y leads up Z alone
Leadership incidences
Non-leadership incidences
Observed proportion
p value
45
15
0.75
0*
13
4
0.765
0.025*
10
7
0.588
0.315
9
9
0.5
0.593
14
2
0.875
0.002*
13
3
0.813
0.011*
13
1
0.929
0.001*
(T,S,W)
X leads down Z alone
Leadership incidences
Non-leadership incidences
Observed proportion
p value
45
3
0.938
0*
8
3
0.727
0.113
6
4
0.6
0.377
Y leads down Z alone
Leadership incidences
Non-leadership incidences
Observed proportion
p value
11
3
0.786
0.029*
42
3
0.933
0*
44
4
0.917
0*
Note: * means statistically significant at 95% or higher confidence level.
12
As shown in the left panel, Tesco appears to have an upward price leadership over all the other
retailers but Asda. In other words, when Tesco increases the price of a product, most of the other
retailers tend to increase the price of the same product by the same amount within two weeks. In
contrast, when Tesco lowers a price of a product, Morrisons and the Co-operative food tend not to
follow Tesco’s lead (see the right panel). On the other hand, Morrisons appears to exercise upward
leaderships over those in the second follower group. But similarly to Tesco’s case, none of the
second followers are led by Morrisons’ price cuts. The asymmetry between the upward and
downward leaderships may suggest that the retailers need to coordinate when increasing their
prices, but do not need it when they compete.
As noted above, however, the pairwise tests may have identified spurious leaderships, thus the
results above should be taken with caution. In particular, Sainsbury, M&S, Waitrose and Cooperative Food are led by more than one firm, so potentially, some of those leaderships may not be
a genuine single-handed leadership. Thus in the following subsection, we pick out such leaderships
using 3-group-wise tests.
5.2 Refinement
To focus on clearer cases of price leadership, we use 3-group-wise tests which involve two leader
firms and one follower firm. For instance, according to the pairwise test results, Sainsbury is led by
two firms, Tesco and Asda. In this case, it is ambiguous whether each of Tesco and Asda leads
Sainsbury single-handedly or they somehow jointly lead the follower. Or it is also possible that both
firms’ leaderships are spurious. To statistically examine whether Tesco’s leadership is genuine, we
compare the number of incidences that Tesco price-led Sainsbury without a help of Asda to the
number of incidences that Tesco and Asda jointly led Sainsbury. The results of this 3-group-wise test
are reported in Table 2. When Tesco passes this test, the price leadership of Tesco is confirmed.
However, if it does not pass a test with another leader, the leadership is regarded as spurious. Figure
2 shows the confirmed leaderships.
13
Figure 2. The upward (left) and the downward (right) leaderships refined by the joint tests
In comparison with the pairwise test results, Tesco’s leadership over M&S (for both upward and
downward cases), Asda’s leadership over Waitrose (for upward case), Morrisons’ leadership over
M&S (for upward case) and Tesco’s leadership over Waitrose (for downward case) turn out to be
spurious according to our criterion. However, many of the leader-follower relationships identified in
the pairwise test, for instance Tesco’s upward leadership over Sainsbury, Morrisons, Waitrose, and
the Co-operative food, are confirmed to be genuine. In total, 7 upward and 5 downward leaderships
are confirmed.
The three-tier structure that we observed in the original pairwise test results is still apparent in the
refined picture. Tesco tends to lead price-ups, and leaderships are less prevalent in price-down
cases. The first followers, Sainsbury and Morrisons, indeed play both roles of leader and follower.
One can also see that especially when the retailers cut their prices, Tesco has a greater influence
over those facing higher-end consumers, Sainsbury, M&S and Waitrose, while Asda’s prices influence
Morrisons’ which arguably appeals to more value-oriented customers.
5.3 Joint, indirect leaderships
When the incidences of simultaneous price changes are sufficiently more frequent in a 3-group-wise
test, we test further to confirm the presence of the joint leadership. However, as shown in Table 2,
in our sample, there is no such case. Thus, we conclude that there is no identifiable joint leader in
the industry, and we do not explore it further.
Nevertheless, there are quite a few potential indirect leadership cases. For instance, Tesco priceleads Sainsbury, and Sainsbury leads M&S both upward and downward. Therefore, Tesco may
14
indirectly lead M&S. Similarly, Tesco may indirectly price-lead Waitrose and the Co-operative food
via Morrisons, and Asda may indirectly lead M&S via Sainsbury. For upward leadership case, Tesco
may indirectly lead M&S and Waitrose. We test these potential indirect leaderships by modifying the
response time from 1-2 weeks to 3-4 weeks. The results are reported in Table 3.
Table 3. Indirect leadership test
Retailer pair X-Y using regular prices (3-4 weeks)
T-MS
T-W
T-CP
X leads up
Simultaneous up
observed proportion
p value
14
9
0.609
0.202
6
9
0.4
0.849
11
7
0.611
0.24
X leads down
Simultaneous down
observed proportion
p value
13
1
0.929
0.001*
12
2
0.857
0.006*
A-MS
A-W
8
2
0.8
0.055
5
3
8
0.625
Note: * means statistically significant at 95% or higher confidence level.
Table 3 shows that among seven potential indirect leadership cases, only two of them are
confirmed, both of which involve Tesco: Tesco indirectly leads M&S and Waitrose downward.
5.4 VAR approach
The method that we develop and apply in this paper, as well as that of SW, restricts the focus on the
price changes of the same amounts. On one hand, this strategy helps to put noisy price changes
aside and to focus on clear incidences. On the other hand, it may neglect relevant price responses of
different amounts. Thus, it is natural to let vector autoregression analysis complement the analysis
based on the tight definition of price leadership. Although in a typical VAR analysis, seemingly
irrelevant variables often appear to Granger-cause, that is to be useful in predicting, the variables of
our interest, if we impose more restrictions on the structure, we believe, it can provide useful
information. In particular, below we focus on price responses within two weeks, and judge the
presence of price leaderships of X over Y by examining for how many of the products, retailer X’s
price Granger-cause retailer Y’s. That is, only if X’s price-up predicts Y’s for sufficiently many
products, we will say that X holds a price leadership over Y. This strategy is in line with SW’s in that
we search for clear cases of leadership.
15
Formally, we estimate the following VAR(2) model:
Δp t = Φ1Δp t-1 + Φ 2 Δp t-2 + ΨDt + ε t
where Δp t is a (7 × 1) vector of jointly determined price changes, Dt is a ( d × 1) vector of other
exogenous variables (e.g. time fixed effects) and constant term. Φi and
Ψ
are (7 × 7) and (7 × d )
vector of coefficients to be estimated, and εt is a (7 × 1) vector of i.i.d disturbances with zero mean
and non-diagonal covariance matrix
Σ.
For the test of i’s leadership over j, we consider the null
hypothesis that (j,i) elements of both Φi are zero.
Note that this approach is slightly different from SW’s approach as in the former we compare price
changes to no change while the latter compares the leadership events to the simultaneous price
changes. Also, VAR estimates the effects of another retailer’s price controlling for all the others’.
Thus, we do not have to consider the other firms’ influence in separate analyses. We estimate the
VAR(2) model with 26 fresh fruit and vegetable products separately. In Table 4, we report the
percentage of products with significant Granger causality results. The numbers are the percentages
of products for which the null hypothesis is rejected at 99% confidence level. * indicates that for
more than 30% of products, the null is rejected. Figure 3 summarizes the results. The full results with
monthly and yearly fixed effects are reported in the appendix. While we use 2 week lags to follow
SW’s definition, one may wonder what the optimal lag length is according to the widely used
selection criteria such as AIC, BIC and HQIC. Obviously, the optimal lag length varies across different
products. The lag-length selection results are reported in the appendix.
Figure 3. The upward (left) and the downward (right) leaderships identified in the VAR analysis.
The thick arrows represent the leadership also identified in the main analysis
16
Table 4. Granger-causality results
Panel A: Price up
Tesco
Tesco
Asda
42.31*
Sainsbury
57.69*
Morrisons
34.62*
M&S
34.62*
Waitrose
34.62*
Co-op
34.62*
Panel B: Price down
Tesco
Tesco
Asda
7.69
Sainsbury
42.31*
Morrisons
23.08
M&S
3.85
Waitrose
11.54
Co-op
30.77*
Asda
Sainsbury
Morrisons
M&S
Waitrose
Co-op
11.54
7.69
15.38
23.08
23.08
11.54
15.38
11.54
15.38
7.69
11.54
11.54
26.92
23.08
34.62*
15.38
11.54
11.54
7.69
15.38
3.85
38.46*
19.23
23.08
19.23
26.92
23.08
34.62*
34.62*
26.92
23.08
15.38
15.38
19.23
15.38
23.08
Asda
Sainsbury
Morrisons
M&S
Waitrose
Co-op
23.08
3.85
7.69
15.38
11.54
30.77*
7.69
11.54
0.00
3.85
7.69
15.38
7.69
7.69
19.23
3.85
7.69
23.08
3.85
19.23
23.08
7.69
30.77*
3.85
11.54
15.38
15.38
34.62*
46.15*
19.23
15.38
23.08
15.38
15.38
26.92
7.69
Note: The numbers are % of products for which the column retailer’s price Granger-cause the row retailer’s at
99% confidence.
Note first that the three-tier structure found in the previous analysis is also observed here. Tesco
and Asda are price-leading the other firms, while Sainsbury and Morrisons follow the two large
retailers, and lead the other three. However, unlike in the leadership structure based on the tight
definition, here there are cases where a firm price-leads another firm in the same tier. In particular,
Tesco leads Asda up, and Morrisons leads Sainsbury down. Also, Waitrose leads M&S up. There still
is no case that a firm in a lower tier price-leads a firm in a higher tier. Nor there is a cycle. In this
sense, the two approaches agree on the hierarchical structure of leadership among the food
retailers.
Furthermore, many of the pairs with the percentage higher than 30% overlap the leader-follower
pairs identified in the previous subsections. In Figure 3, the thick arrows represent the leadership
identified both in the main and the VAR analyses. For example, Tesco’s upward and downward
leadership over Sainsbury is identified in the pairwise test, and confirmed in the refinement. In the
VAR analysis, for about 50% of products, Tesco’s prices turn out to Granger-cause Sainsbury’s prices.
Similarly, Sainsbury’s upward and downward leadership over M&S, Tesco’s upward leadership over
the Co-operative food, Sainsbury’s downward leadership over Waitrose, Asda’s downward
17
leadership over Morrisons are also identified in both analyses. As noted above, both approaches
have their own strengths and limitations, but the consensus between the two may suggest that the
one identified in this paper indeed reflects the true structure.
5.5 Temporary price reduction
Thus far, we have investigated the leadership structure among the retailers focusing on the regular
price. In this subsection, we turn our attention to the temporary price reductions. Due to the
limitation in the data, we do not find many TPR incidences not to mention TPR leadership
incidences. The only TPR leadership case in our dataset is between Sainsbury and Tesco where,
rather unexpectedly, Sainsbury leads Tesco. The full results are reported in the appendix.
We can reach a similar conclusion in the VAR analysis as shown in Table 4. With 30% threshold, there
is no significant leader-follower relationship.
With 20% threshold, however, there are a few
discernible leadership cases. In particular, sales by Tesco seem to lead those by the other Big 4
retailers, Sainsbury, Asda and Morrisons. Similarly, Asda’s sales Granger-cause Tesco’s. Rather
unexpected finding is that for about 27% of products, sales by Waitrose seem to trigger sales by
Asda. So we conclude that for TPRs, the three-tier structure is less clear.
Table 5. Granger-causality results for TPRs
Tesco
Tesco
Sainsbury
Asda
Morrisons
M&S
Waitrose
Co-op
26.92
23.08
23.08
7.69
3.85
11.54
Sainsbury
Asda
Morrisons
M&S
Waitrose
Co-op
15.38
26.92
19.23
3.85
7.69
11.54
3.85
3.85
7.69
0.00
15.38
15.38
26.92
11.54
15.38
7.69
7.69
15.38
0.00
3.85
3.85
15.38
7.69
15.38
15.38
15.38
15.38
15.38
3.85
7.69
3.85
11.54
23.08
11.54
15.38
3.85
Note: The numbers are % of products for which the column retailer’s price Granger-cause the row retailer’s at
99% confidence.
18
6 Conclusion
This paper, by generalizing the method of SW, develops an empirical method to identify priceleadership structure of oligopolistic markets. In particular, repeating tests involving more than two
firms, the procedure eliminates spurious leaderships, and identifies joint and indirect leaderships. In
application, we analyse the UK food retailing industry using data on fresh produce prices which we
identify as having a three-tier structure: Tesco and Asda tend to price-lead the other retailers, while
Sainsbury and Morrisons play both roles of leader and follower. We also find that more upward
leaderships are confirmed, which may suggest that the firms need to coordinate when increasing
their prices, but do not need it when lowering them. We also conduct VAR analyses to complement
the identification method based on the tight definition. In the VAR analyses, we again find the threetier structure of leadership and many overlapping leader-follower relationships.
Understanding the complexities of pricing interaction is important for industry players seeking to
maximise their profits by better understanding the dynamics of competition and how rivals lead and
respond on price moves. For antitrust authorities, their concern with price leadership is how it can
be used as a means to support tacit collusion and elevate prices. Equally, though, it is important to
appreciate that price leadership can be about bringing prices down, where a maverick or committed
discounter seeks to steal a march over rivals, which in turn obliges them to follow. Price leading can
also be asymmetric, where one firm might predominantly lead prices up while another has a
tendency to lead them down. For grocery retailing, even as we have seen with our small sample of
products, when viewed over a long time horizon that spans different economic conditions and with
different management teams running the different businesses, there may be some continuity to
leader-follower positions, and we find that firm size and price positioning serve as important factors
in shaping the three-tier structure we observe.
Nevertheless, things can change. Since our data series finished in early 2013, there has been
phenomenal growth of discount retailers in the UK, notably with the rapid expansion of the German
retailers Aldi and Lidl, and increasingly it these retailers, even though remain a fraction of the size
each of the Big 4 mainstream retailers, which appear to be acting as price leaders and responding to
them seems to be the main current preoccupation of Tesco and Asda (The Telegraph, 2014; 2015;
2016). Thus, it is not inconceivable that the UK might now be moving towards a four-layer price
leadership structure and it remains to be seen how stable this would be before there is shakeout or
positions flip. The method we propose here offers a means to monitor this development over time,
and equally look at other markets which are being transformed as power structures and market
positions shift.
19
References
Berck, Peter; Jennifer Brown; Jeffrey M. Perloff and Sofia Berto Villas-Boas. 2008. "Sales: Tests of
Theories on Causality and Timing." International Journal of Industrial Organization, 26(6), 1257-73.
Chakraborty, Ratula, Paul W. Dobson, Jonathan S. Seaton and Michael Waterson. 2014. "Market
consolidation and pricing developments in grocery retailing: a case study." In: Pietz M., Spiegel,Y.
(Eds.), Analysis of Competition Policy and Sectoral Regulation, World Scientific, Singapore, 3–29.
Chakraborty, Ratula, Paul W. Dobson, Jonathan S. Seaton and Michael Waterson. 2015. "Pricing in
inflationary times: The penny drops." Journal of Monetary Economics, 76 (November), 71–86.
CMA. 2015. Pricing Practices in the Groceries Market: Response to a super-complaint made by
Which? on 21 April 2015, Competition and Markets Authority, London, July 16, 2015
(https://assets.digital.cabinet-office.gov.uk/media/55a6c83540f0b61562000005/Groceries_Pricing_SuperComplaint_response.pdf).
Competition Commission. 2000. Supermarkets: A Report on the Supply of Groceries from Multiple
Stores in the United Kingdom, Cm 4842, TSO, London.
Competition Commission. 2008. The supply of groceries in the
(http://webarchive.nationalarchives.gov.uk/20140402141250/http://www.competition-
UK.
TSO,
London
commission.org.uk/assets/competitioncommission/docs/pdf/non-inquiry/rep_pub/reports/2008/fulltext/538.pdf).
Hosken, D. and D. Reiffen. 2004. "Patterns of retail price variation." The RAND Journal of Economics,
35 (1), 128–146.
Lewis, Matthew S. 2012. "Price Leadership and Coordination in Retail Gasoline Markets with Price
Cycles." International Journal of Industrial Organization, 30(4), 342-51.
Lloyd, Tim. 2008. "Price Leadership in Uk Food Retailing: Time Series Representation and Evidence,"
82nd Annual Conference of the Agricultural Economics Society, Cirencester, UK. Retrieved June. 2010.
Nakamura, Emi and Jón Steinsson. 2008. "Five Facts About Prices: A Reevaluation of Menu Cost
Models." The Quarterly Journal of Economics, 1415-64.
Pesendorfer, Martin. 2002. "Retail Sales: A Study of Pricing Behavior in Supermarkets." Journal of
Business, 75(1), 33-66.
Revoredo-Giha, Cesar and Alan Renwick. 2012. "Retailers Price Behavior in the Uk Fresh Fruit and
Vegetable Market." Agribusiness, 28(4), 451-68.
Seaton, Jonathan S. and Michael Waterson. 2013. "Identifying and Characterising Price Leadership
in British Supermarkets." International Journal of Industrial Organization, 31(5), 392-403.
The Grocer. 2014. "5-a-Day Would Cost Average Family an Extra £810 a Year," by Ian Quinn,
September 12, 2014 (http://www.thegrocer.co.uk/home/topics/health/5-a-day-would-cost-average-family-an-extra810-a-year/371549.article).
The Telegraph. 2014."Five numbers that show how Aldi has revolutionised grocery shopping." by
Graham
Ruddick,
September
29,
2014
(http://www.telegraph.co.uk/finance/newsbysector/retailandconsumer/11127811/Five-numbers-that-show-how-Aldi-hasrevolutionised-grocery-shopping.html).
The Telegraph. 2015. " Tesco, Sainsbury's and the like should be afraid - Aldi and Lidl can only get
bigger."
by
James
Quinn,
November
18,
2015
20
(http://www.telegraph.co.uk/finance/newsbysector/retailandconsumer/12001679/Tesco-Sainsburys-and-the-like-shouldbe-afraid-Aldi-and-Lidl-can-only-get-bigger.html).
The Telegraph. 2016. "Asda warns of more retail turmoil." by Ashley Armstrong, January 9, 2016
(http://www.telegraph.co.uk/finance/newsbysector/retailandconsumer/12090435/Asda-warns-of-more-retailturmoil.html).
The Times. 2011. "Can you afford to eat fruit?" by Helen Rumbelow, February 3, 2011
(http://www.thetimes.co.uk/tto/life/food/article2897351.ece).
Wang, Zhongmin. 2009. "(Mixed) Strategy in Oligopoly Pricing: Evidence from Gasoline Price Cycles
before and under a Timing Regulation." Journal of Political Economy, 117(6), 987-1030.
21
7 Appendix
7.1 Full test results of pairwise test
Retailer pair X-Y using regular prices
T-S
T-A
T-M
T-MS
T-W
T-CP
S-A
S-M
SMS
S-W
S-CP
A-M
AMS
A-W
A-CP
MMS
M-W
M-CP
MSW
MSCP
WCP
64
22
31
32
31
23
11
11
60
53
21
24
15
18
11
17
16
14
13
12
10
45
38
14
9
9
7
15
21
20
41
12
22
8
6
7
6
5
5
27
12
8
0.587
0.367
0.689
0.78
0.775
0.767
0.423
0.344
0.75
0.564
0.636
0.522
0.652
0.75
0.611
0.739
0.762
0.737
0.325
0.5
0.556
0.042*
0.986
0.008*
0*
0*
0.003*
0.837
0.975
0*
0.128
0.081
0.441
0.105
0.011*
0.24
0.017*
0.013*
0.032*
0.992
0.581
0.407
16
18
12
7
7
7
25
16
5
6
7
16
7
3
5
10
6
4
25
7
10
45
38
14
9
9
7
15
21
20
41
12
22
8
6
7
6
5
5
27
12
8
Observed
proportion
0.262
0.321
0.462
0.438
0.438
0.5
0.625
0.432
0.2
0.128
0.368
0.421
0.467
0.333
0.417
0.625
0.545
0.444
0.481
0.368
0.556
p value
1
0.998
0.721
0.773
0.773
0.605
0.077
0.838
1
1
0.916
0.872
0.696
0.91
0.806
0.227
0.5
0.746
0.661
0.916
0.407
X leads down
Simultaneous
down
48
9
19
11
10
5
5
11
45
48
7
23
6
6
3
6
8
5
13
4
5
15
15
13
1
2
2
3
13
9
13
6
9
2
3
1
6
6
4
12
2
2
Observed
proportion
0.762
0.375
0.594
0.917
0.833
0.714
0.625
0.458
0.833
0.787
0.538
0.719
0.75
0.667
0.75
0.5
0.571
0.556
0.52
0.667
0.714
p value
0
0.924
0.189
0.003*
0.019*
0.227
0.363
0.729
0*
0*
0.5
0.01*
0.145
0.254
0.313
0.613
0.395
0.5
0.5
0.344
0.227
Y leads down
Simultaneous
down
10
19
5
6
5
5
13
14
3
5
5
6
1
3
4
1
2
4
13
7
7
15
15
13
1
2
2
3
13
9
13
6
9
2
3
1
6
6
4
12
2
2
Observed
proportion
0.4
0.559
0.278
0.857
0.714
0.714
0.813
0.519
0.25
0.278
0.455
0.4
0.333
0.5
0.8
0.143
0.25
0.5
0.52
0.778
0.778
p value
0.885
0.304
0.985
0.063
0.227
0.227
0.011*
0.5
0.981
0.985
0.726
0.849
0.875
0.656
0.188
0.992
0.965
0.637
0.5
0.09
0.09
X leads up
Simultaneous
up
Observed
proportion
p value
Y leads up
Simultaneous
up
Note: * indicates statistical significance at 95% or higher confidence level.
22
7.2 Full results of VAR analysis with month and year fixed effects
Granger Causality results of price up (1% significance) - % of products
Eq. ΔPt
H 0 : Coefficients on ΔPt-1 and ΔPt-2 = 0
Tesco
Tesco
Sainsbury
Joint effect of time dummies
Sainsbury
Asda
Morrisons
M&S
Waitrose
Co-op
Month
Year
11.54
7.69
23.08
15.38
11.54
15.38
30.77*
7.69
15.38
23.08
11.54
11.54
11.54
15.38
11.54
11.54
15.38
26.92
11.54
30.77*
0.00
7.69
23.08
7.69
23.08
3.85
34.62*
15.38
7.69
3.85
3.85
3.85
19.23
0.00
3.85
42.31*
Asda
57.69*
38.46*
Morrisons
34.62*
19.23
23.08
M&S
34.62*
23.08
34.62*
23.08
Waitrose
34.62*
19.23
34.62*
15.38
19.23
Co-op
34.62*
26.92
26.92
15.38
15.38
23.08
Note: The numbers are the percentages of products for which the null hypothesis is rejected at 99% confidence level. * indicates that for more 30% of products, the null is rejected.
Granger Causality results of price down (1% significance) - % of products
Eq. ΔPt
H0: Coefficients on ΔPt-1 and ΔPt-2 = 0
Tesco
Tesco
Joint effect of time dummies
Sainsbury
Asda
Morrisons
M&S
Waitrose
Co-op
Month
Year
23.08
3.85
15.38
7.69
7.69
3.85
7.69
7.69
7.69
11.54
11.54
15.38
7.69
7.69
3.85
30.77*
0.00
7.69
23.08
3.85
7.69
3.85
7.69
3.85
15.38
7.69
19.23
19.23
7.69
3.85
23.08
3.85
3.85
3.85
3.85
Sainsbury
7.69
Asda
42.31*
7.69
Morrisons
23.08
30.77*
15.38
M&S
3.85
3.85
34.62*
15.38
Waitrose
11.54
11.54
46.15*
23.08
15.38
Co-op
30.77*
15.38
19.23
15.38
26.92
7.69
Note: The numbers are the percentages of products for which the null hypothesis is rejected at 99% confidence level. * indicates that for more 30% of products, the null is rejected.
23
7.3 AIC results of lag length selection
VAR lag selection
AIC
HQIC
BIC
Lag
Price up
Price down
Price up
Price down
Price up
Price down
0
0.00
19.23
26.92
50.00
69.23
84.62
1
15.38
7.69
19.23
19.23
19.23
11.54
2
26.92
23.08
42.31
11.54
11.54
3.85
3
11.54
19.23
0.00
11.54
0.00
0.00
4
46.15
30.77
11.54
7.69
0.00
0.00
Note: The numbers are % of products for which the indicated lag is optimal according to the criterion.
7.4 Full test results of TPR pairwise test
Retailer pair X-Y using TPR prices
T-S
T-A
T-M
TMS
T-W
T-CP
S-A
S-M
SMS
S-W
S-CP
A-M
AMS
A-W
ACP
MMS
MW
MCP
MSW
MSCP
WCP
27
10
10
4
3
2
2
4
5
8
1
20
2
2
0
2
1
3
2
0
1
3
8
13
0
1
1
2
4
5
5
2
12
2
1
0
1
2
0
4
0
0
0.9
0.556
0.435
1
0.75
0.667
0.5
0.5
0.5
0.615
0.333
0.625
0.5
0.667
.
0.667
0.333
1
0.333
.
1
0*
0.407
0.798
0.063
0.313
0.5
0.688
0.637
0.623
0.291
0.875
0.108
0.688
0.5
.
0.5
0.875
0.125
0.891
.
0.5
3
16
11
2
3
0
5
5
0
2
1
11
2
2
0
3
1
0
2
1
0
3
8
13
0
1
1
2
4
5
5
2
12
2
1
0
1
2
0
4
0
0
Observed
proportion
0.5
0.667
0.458
1
0.75
0
0.714
0.556
0
0.286
0.333
0.478
0.5
0.667
.
0.75
0.333
.
0.333
1
.
p value
0.656
0.076
0.729
0.25
0.313
1
0.227
0.5
1
0.938
0.875
0.661
0.688
0.5
.
0.313
0.875
.
0.891
0.5
.
X leads TPR
Simultaneous
TPR
Observed
proportion
p value
Y leads TPR
Simultaneous
TPR
Note: * indicates statistical significance at 95% or higher confidence level.
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