MODELLING FIRM SIZE DISTRIBUTION IN FOOD AND DRINK
PRODUCTS*
Patrick Paul Walsh and Ciara Whelan
Address for Correspondence:
Department of Economics,
Trinity College,
Dublin 2,
Ireland
[email protected]
[email protected]
Abstract
We model firm size distributions across 10 advertising intensive 5-digit food and drink products.
The presence of multiple independent 8-digit submarkets is empirically validated within
products. Sutton’s (1998) game theoretic bound approach to modelling the limiting firm size
distributions in the presence of submarkets is validated using a rich micro database. In addition,
we show how skew submarket sizes induce a tighter bound, approximated by the Simon model,
on firm size distributions.
Key words: Firm Size Distribution; Independent Submarkets; Food and Drink Products.
JEL Classification: D40
* Both authors are members of the Department of Economics, Trinity College, Dublin and LICOS,
Centre for Transition Economics, K.U. Leuven. Earlier drafts of the paper were presented to the
Department of Economics in K.U. Leuven in October 1998, the Dublin Economic Workshop in
February 1999, to an Economics of Market Structure workshop, sponsored by STICERD, L.S.E.,
May 1999 and the European Association for Research in Industrial Economics in September 1999.
We thank all participants for their comments. Special thanks are extended to AC Nielsen Ireland
for providing the rich data that made such research possible, and to John Sutton and Lennart
Hjalmarsson for valuable comments.
Introduction
Economists have long been consumed by the desire to identify and understand the
mechanisms driving skew firm size distributions, the cornerstone of Industrial Economics. This
strand of literature began with Gibrat [1931]. Using the mathematics of “stochastic processes”, he
postulates that the size growth relationship for active firms should generate size distributions
approximately lognormal in form.1 Hart and Prais (1956) and Iijri and Simon (1964,1977) took this
a step further by building in a stochastic entry process around Gibrats size growth relationship for
active firms. Unfortunately, their empirical work showed us that simple generalisations on the form
of firm size distributions, as outcomes of a historical stochastic processes, do not describe firm size
distributions observed across the general run of industries.
Researchers beginning with Dunne, Roberts and Samuelson (1988), using rich firm level
data, suggest that the relationship between firm growth and firm characteristics, including size and
age, is much more complex. Indeed theorists, such as Jovanovic (1982), that tried to give the sizegrowth relationship an economic foundation found the relationship to be sensitive to the details of
modelling. In general, the vast volume of empirical studies seem to agree that small firms grow
proportionately faster than large, even after correcting for the sample section process. The failure of
Gibrat’s law and the success of idiosyncratic firm and sector characteristics leaves us with a legacy
from the firm level studies that again fails to generalise on the form of firm size distributions across
the general run of industries at the empirical level (Schmalensee, 1989). These are the challenges
that we face in our empirical modelling of firm size distributions in this paper.
Sutton (1998) provides us with a new empirical approach to modelling firm size
distributions.2 Rather than looking for the “family of distributions that fit the data”, Sutton (1998)
derives a lower bound to firm size distributions within a game-theoretic model using a
deterministic entry process and in the presence of independent submarkets within products. The
1
game theoretic approach adopts the notion of a product market comprising of a number of
strategically independent submarkets, or islands, on the demand side. These islands may be defined
in terms of geographic locations or taste niches. Sutton’s approach predicts that the operation of
firms over multiple submarkets induces a lower bound to firm size distribution, which is shown to
hold over a broad cross section of 5-digit industries. We outline the Bounds approach and empirical
predictions in section I of the paper.
Our empirical analysis uses an extremely rich brand level panel database for 10 advertising
intensive 5-digit food and drink products. A detailed description of these data is outlined in section
II. One contribution of this paper is the empirical validation of the presence of 8-digit submarkets,
defined in terms of taste, rather than geographic location, within products at this very micro-level of
industry within food and drink sector. The submarkets given to us by official sources are shown to
be independent in that within Almost Ideal Demand Systems, submarket cross-price effects are
jointly insignificant in the determination of submarket consumer expenditures.
The presence of such independent submarkets and firms taking up of roles across
submarkets is shown to place Sutton’s mathematically predicted lower bound on the shape of firm
size distributions of our products. We also validate a second key result of the game-theoretic
model, that the nature of firm operations across submarkets override the details of any strategic
interactions that occur within submarkets. This analysis is undertaken in section III.
In section IV of the paper we document how the presence of skew submarket sizes within
products induce a tighter bound, approximated by the Simon model (to be outlined in section I), on
firm size distributions. Due to varying degrees of advertising intensity within submarkets, our
econometric work documents that larger submarkets, defined in monetary value, will host firms
with larger, more persistent and more equal sized roles, while smaller submarkets host smaller,
turbulent and more unequal sized roles. In addition, escalation in advertising in large submarkets
creates a history of a large role that generates positive spillovers for the firm in its ability to take-up
2
a role in smaller submarkets. Thus skewness in submarket sizes induces a historical escalation in
advertising in large submarkets that give firms a size advantage in the take-up of roles across
smaller submarkets, thereby inducing a tighter bound, on firm size distributions. Our analysis
illustrates the importance of submarkets in undertaking any analysis of market structure and in
addition provides valuable lessons for the “growth of firms” literature. Final comments and
conclusions are provided in section V.
I. Sutton’s Bound Approach
Sutton (1998) puts weak restrictions on the form of the entry process to model a lower
bound on the size distribution of firms in a market. Sutton (1998) outlines a benchmark stochastic
entry model in the tradition of Simon (Ijiri & Simon, 1964 and 1977). Using the mathematics of
stochastic processes, Sutton (1998) derives a lower bound on the limiting size distribution of firms
in a market. He departs from the Simon framework, or the traditional size growth relationship, by
abandoning Gibrats law in favour of the weaker restriction that the probability of an incumbent
firm taking up the next opportunity is non-decreasing in firm size.3 In the spirit of the Simon model
he assumes the probability of entry to be constant over time. Under these conditions the size
distribution of firms is restricted to a lower bound Lorenz curve that graphs the fraction of top
ranking firms k/N in the k-firm concentration ratio against their corresponding share of market
assets, Ck. It can be shown that the fraction of k opportunities accounted for by the k largest firms
satisfies,4
(1)
Ck ≥
k
N
(1 − ln Nk )
This defines the minimum degree of skewness in the size distribution of firms that one may
expect to hold across the general run of industries. In chapter 11, Sutton (1998) derives the same
lower bound within a game-theoretic model using a deterministic entry Symmetry Principle and in
the presence of independent submarkets within products. The game theoretic approach adopts the
3
notion of a product market comprising of a number of strategically independent submarkets, or
islands. These islands may be defined in terms of geographic locations or taste niches. Defined
product markets thus exhibit elements of strategic interdependence within submarkets, and
independence across submarkets. The chapter brings together these independence and strategic
effects within a game-theoretic model.
Within any submarket, a firm can only fill one role.5 A deterministic entry process with
game-theoretic foundations defines how firms take up roles across submarkets (or enters new
submarkets). This is where the Symmetry Principle comes in6. Its effect is to ensure that all
potential new entrants to a submarket are treated equally in their probability of taking up a role. The
take-up of a role in one submarket is unaffected by a firms history in the taking up of roles in other
submarkets. The effect of such an ‘equal treatment’ rule is to induce mixing at any node where a
new firm enters a submarket. This mixing generates an equal chance of any firm not active in the
submarket filling a new role.
To illustrate by way of example, we take the case where each submarket can only support
one firm or role. In addition, firms face a continuum of independent submarkets arriving. Consider
the simplest possible entry game where there are two potential entrants that may, by paying a small
sunk cost, produce a homogenous product at marginal cost. If one firm enters, it earns monopoly
profits. If both enter, Bertrand price competition ensures zero economic profits. There are only two
pure strategy Nash equilibria: firm one enters and firm two does not, or firm two enters and firm
one does not. A symmetric equilibrium in mixed strategies may also be calculated, where each
player has an equal probability of entering at each date and therefore have ‘equal treatment’. By
imposing a symmetry requirement on the strategy space of each subgame, all equilibria are
excluded except this mixed strategy equilibrium. Assuming that all submarkets are identical and
each supports a single role implies that all roles are of equal size in the product market. Firm size in
the product is simply equal to the sum of its roles, or total number of submarkets over which they
4
operate. Thus, unequal firm size distributions at the product level in this model can only be driven
by the heterogeneous take-up of roles across submarkets. In the limit, given the Symmetry
Principle, the game-theoretic model predicts a lower bound to the firm size distribution that is
identical to that of equation (1).
Such a setting clearly allows independence effects, or the operation of firms over
submarkets, to dominate strategic effects in the determination of size distributions and generate
outcomes equivalent to the adjusted Simon model outlined above. Yet even in a more general case
where there are many independent submarkets with each supporting multiple firms (roles), the
lower bound to the limiting firm size distribution, equation (1), is still shown to hold. The central
result of the game-theoretic model is that independence effects override the details of any strategic
interactions that occur within submarkets. This suggests an avenue along which one may
discriminate between the classical stochastic model and the game-theoretic model. While the gametheoretic model allows individual submarkets to have any type of structure as an outcome of
strategic effects, the overall size distribution is dominated by independence effects between
submarkets that override what is going on within submarkets.
The size of a firm in the limiting distribution can either be determined by a count in the
number of roles that it has taken up across submarkets, or the sum of the sizes of the roles that a
firm has taken up.7 A basic proposition in the theorem of majorisation states that the Lorenz curve
associated with the latter distribution will be further away from the diagonal than the former
(Marshall and Olkin, 1979). Since the size of roles within submarkets will be an outcome of
strategic competition within submarkets, strategic effects that create heterogeneity in the size of
roles can only induce outcomes inside the lower bound computed on the basis of equal sized roles
and the Symmetry Principle.
Finally, if the take-up of a role in one submarket is affected by a firm’s history in other
submarkets, then the probability of an incumbent firm taking up a new role in another submarket
5
can increase in firm size due to the presence of scope economies. This replaces the Symmetry
Principle with the stronger and more traditional restriction on firm size and growth. This will
enhance the degree of heterogeneity in the number of roles taken-up across submarkets by firms
over that generated by the Symmetry Principle. In the presence of scope economies, heterogeneity
in the size of roles within submarkets, an outcome of strategic competition, can lead to greater
heterogeneity in the take up of roles across submarkets. This will clearly induce outcomes inside
the lower bound computed on the basis of equal sized roles within and ‘equal treatment’ in the
take-up of roles across submarkets.
The main predictions of the game theoretic model can be summarised as follows:
Prediction 1: The presence of firms operating over independent submarkets in a product
places a lower bound on the shape of firm size distributions observed in the product market.
Prediction 2: While individual submarkets may have any type of size distribution in
submarket roles as an outcome of strategic effects, this will not lead to a violation of the lower
bound on the shape of firm size distributions observed in the product market.
Prediction 3: Heterogeneity in the size of roles as an outcome of strategic effects within
submarkets will induce the distribution of firm sizes observed in the product market to lie further
inside the lower bound.
Prediction 4: If the take-up of a role in one submarket is positively affected by a firm’s
history (size of roles) in other submarkets, due to scope economies, then heterogeneity in the size of
roles within submarkets will induce greater heterogeneity in the take-up of roles across submarkets.
This will induce the distribution of firm sizes observed in the product market to lie even further
inside the lower bound.
6
II. Data Description
AC Nielsen of Ireland provides the data used in our empirical analysis of submarkets and
the modelling of firm size distributions in this paper. This international marketing research
company has collated a very large panel database concerning key brand features in the Irish Food
and Drink sector. These data have been collected using a stratified quota sample of retail outlets
and shops that is skewed towards the largest shops and is said to contain a fair representation of
store locations for the Irish market8. The evolution of the grocery market from the early 1970s to its
present day structure is described in Walsh and Whelan (1999).9
The database provides bi-monthly data spanning October 1992 to March 1997 for 633
individual brands, identified for 93 firms, 232 firm roles over 52 submarkets, within 10 5-digit
product categories. The data record the retail activities of both Irish and foreign owned brands/firms
selling throughout the Irish owned shops and stores. In addition, within individual product
categories AC Nielsen identify various submarket taste niches within which brands with similar
product attributes are classified. These submarkets contain clusters of brands that are highly
substitutable on the demand side and tend not to compete with brands located in other submarkets
defined by different taste/packaging characteristics. In terms of consumption, the submarkets are
considered to be independent. No entry or exit of a submarket was observed for the time period of
the data. The 10 5-digit product categories and 52 associated 8-digit submarkets for which we have
brand level data are given in table I. These individual brand level data explain on average, 90
percent of total product sales in each category. Unavailable individual data accounting for the
remaining product sales usually relate to small fringe competitors in the market whose collective
influence is represented by ‘All Other’ brands.
Extensive brand i level information regarding sales, pricing, and distribution through shops
is provided. The following brand level data information is used in our study:
7
Pit : Brand i retail sale price in the bi-monthly period t, weighted by its sales share in the
shop and summed over all grocery shops selling the brand.
SLUit : Total sales units of brand i in the bi-monthly period t, aggregated over all grocery
shops selling the brand.
SLSit : Total sales value (in £000) of brand i in the bi-monthly period t, aggregated over all
grocery shops selling the brand.
S*it: Total sales value (in £000) of brand i in period t expressed as proportion of the total
product j sales value (in £000) in the shops that retail brand i (i.e. brand i market share in
the group of shops in which it sells).
Thus we have information on brand pricing, quantity and monetary sales, and distribution
coverage in terms of the number and size of the shops through which a brand i is retailed over the
bi-monthly period. These brand level data are identified by the supplying firm, f, and the associated
submarket m and product j to which the brand belongs. Our empirical analysis requires aggregating
these brand level data,
i)
Over all brands belonging to a firm in a submarket m, to yield information on the
firm Role in a submarket m.
ii)
Over all brands belonging to a firm f in a product, to yield information on the Firm
in the product market j.
iii)
Over all brands in a submarket m, to yield information on the Submarket at level m.
iv)
Over all brands in a product j, to yield information on the Product at level j.
Using these data, we empirically investigate firm size distribution in food and drink
products as we test the predictions of the approach outlined in the previous section. Further details
relating to the data and construction of the variables used in our empirical analysis are provided in
Appendix 1.
8
III: Testing Predictions 1 and 2
A central feature of the game-theoretic framework in Suttons deterministic model of firm
size distributions is the presence of independent submarkets within products. Firms operations over
these submarkets is predicted to place a lower bound on the shape of firm size distributions
observed in the product market, that is not violated by firm role heterogeneity induced by strategic
effects within submarkets. In this section we first test the presence of independent submarkets
within our 10 5-digit products in the retail grocery market, before turning our attention to the
predictions.
III.1: The Presence of Independent Submarkets
Submarkets describe a cluster of brands that compete closely with one another within the
wider definition of the market. Brands have been classified by an independent marketing research
company into their relevant submarket on the basis of their similarity in taste and packaging
characteristics. There is a high degree of substitutability on the supply side between all brands in a
defined product. Irrespective of the strategic positioning of brands in submarkets, firms can benefit
from economies of scope and scale by producing more brands in a product through lower per unit
production costs, advertising expenditures, and the costs of distributing through shops. On the
demand side, brands are considered to be highly substitutable within defined submarkets. Yet
brands in a given submarket are thought to be independent on the demand side from those
characterised by different taste or packaging features in other submarkets. Our analysis of
submarkets in this section empirically examines whether the subdivision of products into clusters of
closely competing brands is justified.
Product submarkets are defined on the basis of differential taste niches and in certain cases
additionally on the basis of differential packaging sizes as described in table I. The further
subdivision of taste submarkets on the basis of their packaging in the Chocolate, Carbonates and
Ready-to-Eat Cereals products is due to the differences they exhibit in their purchasing behaviour.
9
This is reflected in the concentration of sales for alternative sized packs in different shop types.
Irish consumers have a preference for ‘one-stop’ shopping with large chain stores and franchises
accounting for most of the grocery turnover in Ireland. The Irish Independent (‘corner shop’)
grocery market accounts for only 20 per cent of total turnover and has in excess of 8,000
independent shops with a highly fragmented distribution of grocery sales across these shops. This
fringe of shops in the market targets a ‘convenience’ niche. They have longer opening hours,
greater location convenience, and specialise in a particular set of goods. These include non-routine
items purchased by consumers on ‘impulse’ such as standard sized Chocolate items (bars, packets
of sweets), Carbonate Cans, and Crisps, or ‘top up’ items purchased in between regular visits to the
‘one-stop’ supermarket stores, such as small sized Cereals or Carbonates 1.5 litres. The high
proportion of sales that pass through small Independent (‘corner’) shops for these types of goods is
illustrated in figure I. This is in stark contrast to the share of sales that the ‘one-stop’ supermarket
chain stores attract for similar goods characterised by larger sized packaging. In figure I the large
sized and multi-pack Chocolate items, Carbonate 2 litre and multi-pack cans, and the standard and
large sized boxes of Ready-to-Eat Cereals are predominantly retailed through Multiples. These are
primarily ‘one-stop’ items whose purchase is confined to regular supermarket shopping.
Differential package sizes even within defined taste niches, thus are representative of products
located in different types of shop that are purchased by separate consumer bases with different
requirements. This provides a rationale for the additional subdivision of defined taste submarkets
by packaging in certain product categories.
We now empirically test the independence of the submarkets, defined on the basis of taste
and packaging attributes, for our 10 individual 5-digit product categories listed in table I. In
particular, we estimate the demand for each submarket m on the basis of an Almost Ideal Demand
System (AIDS), the general form for the mth equation being,
10
(2)
p mjt q mjt
I jt
⎛I
⎜ jt
= α m + β m Log ⎜
⎜ P jt
⎝
⎞ M
⎟
γ m Log p kjt
⎟+
⎟ k =1
⎠
∑
+ ε mt ,
where k = 1,…., M with M identifying the number of submarkets in the product and hence
the number of equations in the system for each product j, and t = 1,….27 bi-monthly periods. The
dependent variable describes the total expenditure (£000) share in of submarket m in product j,
where, Ijt is total expenditure on product j in period t. The explanatory variables include the log of
real consumer expenditure in product j, Ijt,/Pjt, , and a Paasche index, pkjt, of submarket prices.10
The M submarket regressions in a product are related insofar as the (contemporaneous)
errors associated with the dependent variables may be correlated. The system of M equations for
each of our 10 products was estimated using Generalised Least Squares. In order to test the
hypothesis of independent submarkets in product j, we wish to examine the extent to which the
cross-price effects are jointly significant in determining submarket expenditures. Hence, for Pk≠Pm,
we test the joint significance of each Paasche price coefficient across all M equations with the null
hypothesis γ1 = γ2 =….= γM = 0. This is a strong criterion since significance of a cross-price in only
a subset of the submarkets can lead to a rejection of the null. The results are presented for each of
the submarkets in our 10 products in table II. These illustrate for the majority of cases an
acceptance of the null hypothesis, which suggests that prices in submarket m do not systematically
determine the total value of expenditure in other submarkets within the 5-digit product market11.
III.2: Firms Operations Over Independent Submarkets
The operation of firms over independent submarkets in the 5-digit product markets allows
us to model firm size distributions within products using Suttons (1998) framework. Each firm has
only one role in each of the submarkets in which it is active. A count of roles in the product market
indicates the number of submarkets across which a firm operates. The percentage of submarkets
covered by firms within products is documented in table III. Within each product, firm operations
11
over submarkets ranges from 34 to 94 per cent on average. Moreover, while firms have taken-up
roles across submarkets within a product, we observe some degree of heterogeneity in the number
of submarket roles taken up by firms.
III.3: Prediction 1- Firm Size Distributions and the Lower Bound
The operations of firms over independent submarkets within a product market is
theoretically predicted to restrict the shape of firm size distribution observed for a product to a
Lorenz curve lying above the lower bound in (1). This is the minimal degree of skewness in firm
sizes that one can expect in the presence of firms operating over independent submarkets. Taking a
snapshot of our products in 1997, figure II illustrates what the size distribution of firms within
product markets has evolved into. This plots the fraction of top k ranking firms k/N against their
corresponding share of total product sales, where N is the total number of firms in the 5-digit
product j and Ck describes the k-firm sales concentration ratio. We do not observe a violation of the
predicted lower bound in our scatter of points in figure II. Thus this indicates the role of
independent submarkets in our products and the importance of independence effects in the
determination of firm size distributions across products. Empirical tests of this prediction in the
case of the Spanish retail banking sector (De Juan, 1999) and the Italian motor insurance industry
(Buzzacchi and Valletti, 1999) where submarkets are defined in terms of geographic location rather
than taste niches, replicate these findings.
III.4: Prediction 2- Role Size Distributions Within Submarkets and the Lower Bound
The size of roles, or firm size within submarkets, depends upon strategic effects within
submarkets. In the absence of very special conditions, not applicable to the Food and Drink sector,
Sutton (1998) places no theoretical restrictions on the shape of firm (or role) size distribution within
submarkets.12 Hence, the distribution of firm roles within submarkets can be either very skewed or
very equal. This outcome is illustrated in figure III, which shows the within submarket
12
heterogeneity of firm role size distributions that characterise our data. This depicts the percentage
of submarket m sales accounted for by the top k roles operating within that submarket, ranked in
ascending order of role size. We observe a scatter of points that lie very close to the diagonal, and
very skewed role distributions within submarkets where the scatter of points are positioned far
above the reference curve for the product market. Clearly then, independence effects have
dominated the details of any strategic interactions that occur within submarkets since the bound
holds in figure II, despite the within submarket heterogeneity of role sizes. This discriminates
between the classical stochastic model and the game-theoretic model of firm size distributions at
the product level.
IV: Testing Predictions 3 and 4
In the first part of this section we model heterogeneity in the size of roles within
submarkets. Since the size of roles within submarkets will be an outcome of strategic competition
within submarkets, strategic effects that create heterogeneity in the size of roles can only induce
outcomes inside the lower bound. Prediction 3, or the theory of majorisation in Sutton (1998),
implies that the more heterogeneity in roles, induced by strategic effects within submarkets, the
further the distribution of firm size in the product will lie from the lower bound. In Sutton (1998),
strategic effects can take any form. We model the key determinant of role size, role dynamics and
role inequality within submarkets in our data to be the monetary value of the submarket, among
other strategic factors. We find that while unequal submarket sizes do not violate the lower bound,
they systematically create heterogeneity in the size of roles within submarkets. This will induce the
distribution of firm sizes observed in the product market to lie inside the lower bound.
In the second part of this section we model heterogeneity in the take-up of roles across
submarkets. Prediction 4 states that if the take-up of a role in one submarket is positively affected
by a firm’s history (size of roles) in other submarkets, due to scope economies, then heterogeneity
in the size of roles within submarkets will induce greater heterogeneity in the take-up of roles
13
across submarkets. This will induce the distribution of firm sizes observed in the product market to
lie even further inside the lower bound.
Part I : Heterogeneity of Role Size Within Submarkets
To model the size of firm roles and their stability within submarkets we follow the
empirical agenda of the growth of firm literature, which has its roots in Gibrat (1931).13 Using rich
firm level panel data sets, this literature finds firm growth to be negatively related to firm size, or
the failure of Gibrat’s Law, across different sectors, countries, firm life cycles, business cycles, and
sample selection [Audretsch (1995) and Sutton (1997)].14 The failure of Gibrat’s law across all
sectors is usually motivated by the passive learning model of Jovanovic (1982) or an active
learning model of Ericson and Pakes (1995).15
We reconsider the growth of firm’s literature by taking into account the presence of
independent submarkets within a defined product market. In particular, we model the growth of
firm roles within submarkets. Our results show that submarket size will be a key determinant of
firm role sizes and dynamics within submarkets. As in Sutton (1991) we use submarket size as an
indicator of a historical “escalation mechanism” in advertising competition. As we increase
monetary size of submarket we will see a tendency for role sizes to increase and Gibrats law to
hold, while controlling for the nature of price, brand and distribution competition among other
strategic effects. In other words, we will not observe the co-existence of small and large roles in
larger submarkets or the ability of small roles to grow faster than larger roles over time. This will
be a key determinant of firm role heterogeneity within submarkets of products.
IV.1: Role Dynamics Within Submarkets
In order to examine the degree of turbulence in the size of roles within submarkets, we
allocate all roles within a submarket m into one of five different size classes. The cut-offs defining
the class boundaries are based on the average (normalised) size of roles within a submarket at the
14
initial date t0. Hence, the cut-off points for each class size are specific to the individual submarket
and constant over time. This ensures the dynamic movements over the entire cross section of roles
are accounted for. The classes are thus defined as follows, where role size in submarket m, RSizefm,
is equal to firm f’s total quantity sales in submarket m, normalised over all products by initial total
product j sales.
Class 1: RSizeR m t ≤ (0.05 × Ave. RSize m t0)
Class 2: RSizeR m t > (0.05 × Ave. Rsize m t0) and ≤ (0.20 × Ave. RSize m t0)
Class 3: RSizeR m t > (0.20 × Ave. RSize m t0) and ≤ (0.75 × Ave. RSize m t0)
Class 4: RSizeR m t > (0.75 × Ave. RSize m t0) and ≤ (1.50 × Ave. RSize m t0)
Class 5: RSizeR m t > (1.50 × Ave. RSize m t0)
These bands have been selected to ensure a relatively well-balanced sample of firm roles
across the alternative size classes for the pooled time-series and cross sectional data. The narrower
bands in the lower classes are used to capture the higher degree of turbulence expected among
smaller firm roles. We now examine the dynamics of roles for small (<£0.5mill), medium
(≥£0.5mill and < £1.5mill) and larger submarkets (≥£1.5mill) in tables IV(i),(ii) and (iii)
respectively. These provide information on the total number of transitions between the alternative
size classes over a bi-monthly period, as a proportion of total stock of firm roles in a defined size
class this period. This gives the hazard ratio, the average probability of a firm role moving or not to
an alternative size class from its initial state. Diagonal elements indicate no change in class status
two months later, while the probability of moving out of a class is equal to 1 minus the probability
given on the diagonal.
Overall, we observe greater stability of firm roles in larger submarkets. For the smaller size
classes, the probability of moving out of its initial size class over the next bi-monthly period
declines with the value of the submarket. The cumulative probability of roles positioned in any of
the bottom three size classes at date t moving to an alternative class at t+1 is 0.6, 0.55, and 0.36 for
small, medium, and large submarkets respectively. We clearly observe greater turbulence and role
15
movements in smaller submarkets compared with larger submarkets. One implication of this is that
Gibrat’s Law may be more likely to hold in bigger submarkets.
IV.2: The Growth of Firm Roles in Submarkets
In what follows we undertake a direct test of the above proposition as we model the growth
of role size within submarkets as an outcome of strategic effects.16 Since firms operate over
submarkets, a firms role is uniquely defined for each submarket m where they represent total
quantity sales of all firm f brands in that submarket. The total number of roles in our analysis is
232. We estimate the following using Robust Least Squares,
(3)
Growth Role fmt = α + β 1Subsizemt + β 2 RoleSize fmt − 2 + β 3 ⎛⎜ RoleSize fmt − 2 ⎞⎟
⎠
⎝
2
+ β 4 INTERFmt + β 5 INTRAFmt + β 6 RSpec fmt + β 7 RPPI fmt + ε mt
.
The dependent variable represents the growth of the firm role f within a submarket m over
the bi-monthly period t-1→t, where this is defined in appendix I. SubSizemt refers to the monetary
size of the submarket in terms of £000, which acts as an indicator for the intensity of advertising
competition in the submarket. To test Gibrats law we examine the relationship between lagged role
size (firm sales units in submarket m) at t-2 and its growth at t, in addition to the square of lagged
firm role size. We control for a number of strategic effects within submarkets using indices defined
in detail in Appendix I.17 The nature of brand competition in the submarket is controlled for using
the measures of inter-firm, INTERFmt, and intra-firm, INTRAFmt, brand submarket share rivalry.
Firm role characteristics include the degree of specialisation in distribution of submarket brands
through a subset of shops in the grocery market, RSPECfmt. Firm role pricing is measured using a
role paasche price index, RPPIfmt, which represents the firm price in submarket m at date t as a
proportion of the initial price in t0. In order to control for the size of the firm at the product level
and its ability to reap economies of scope and scale, and hence differences in firms underlying costs
16
or advertising levels, dummies are included for firm attachment in the product. Finally, Month,
Product, and Submarket dummies are included.
The results of the OLS regression, correcting standard errors for heteroskedasticity, are
presented in table V. Specification I is the basic regression in (3). The growth of roles is positively
related to the size of the submarket and is highly significant. Moreover, although not reported,
controls for firm attachment in the product are also highly significant in determining the growth of
roles within submarkets. The effect of lagged role size on growth illustrates a significant negative
effect. This is in keeping with the many empirical studies linking firm size to growth. However, as
found in the literature, for larger roles the empirical evidence suggests that growth is unrelated to
size. This is reflected in our positive significant effect that the square of role size has for the growth
of roles in submarkets. Submarkets that are characterised by higher levels of both inter- and intrafirm brand competition exhibit lower growth rates of roles. This suggests that brand proliferation
and competition does not expand submarket share, but rather ensures greater stability.18 Finally,
while the level of specialisation in a subset of shops in the submarket is not significant at the five
per cent level, pricing is seen to play a role in determining growth. An increase in the paasche price
index will reduce the growth of a role size.
We have already suggested that compared to smaller submarkets, large submarkets play
host to higher sunk costs outlays on advertising. This may not only create barriers to entry but in
addition may erect barriers to growth. On this basis, we interact each of the independent variables
with submarket size. The results for the second specification, correcting standard errors for
heteroskedasticity, are presented in the second column of table V. We find that the monetary size of
a submarket is crucial in augmenting the effects of our independent variables on growth. While role
size still exhibits a significant negative relationship with growth, its interaction with submarket size
is positive and significant. The effect of the square of role size on growth is positive and significant
but independent of submarket size. Smaller non-failing roles can have higher growth rates than
17
larger roles, but this effect diminishes with the size of the submarket and is offset in the larger
submarkets. Gibrat’s law holds in the bigger submarkets. In Appendix 2 we model the growth of
firms within 5-digit products using a standard analysis that does not control for the presence of
submarkets. From this, we show that the presence of many submarkets within products creates the
fallacy that Gibrats Law fails in mature advertising intensive products when in fact small firms can
only survive and grow in small submarket niches within the product.
In summary, one can expect larger roles in larger submarkets. In addition, the fact that
controls for firm attachment in the product are important determinants of the growth of roles within
submarkets is indicative of the importance of scope economies from operating over other
submarkets in the product. Finally, since Gibrats law holds in bigger submarkets, there is
persistence in the size of roles over time in larger submarkets. Given that submarket size is the key
determinant of role size and the persistence of roles within submarkets over time, we now examine
the relationship between role size inequality within submarkets and the size of the submarket.
IV.3: Modelling Inequality in Role Sizes Within Submarkets
The monetary size of submarkets is taken as a proxy for an induced historical escalation in
advertising competition. Submarkets with total sales value of less than £0.5 million are classified as
small, those exceeding £0.5 million and less than £1.5 million are classified as medium sized, while
all submarkets with sales value exceeding £1.5 million are considered large. The distribution of role
sizes for alternative sized submarkets are examined in figure IV. This figure clearly illustrates
greater inequality in role size within smaller submarkets.19 We model the role size inequality within
submarket m in the following random effect model,
(4)
RoleIneqmt = α + β1SubSizemt + β 2 (SubSizemt )2 + β 3 INTERFmt + β 4 INTRAFmt
.
+ β 5 SpecIneqmt 0 + β 6 PrIneqmt 0 + vm + ε mt
Appendix 1 provides a detail description of each of the variables used. The dependent
variable measures the inequality in role sizes within submarket m using a co-efficient of variation
18
in each bi-monthly period t. Submarket size, SubSizem, is given by the total value (£000) of
submarket m. The results for this model are presented in table VII. Equation 4 is estimated as a
random effect model, justified on the basis of the Hausman [1978] test. The presence of an autocorrelated error structure of order one in the GLS models led us to adopt a Prais-Winsten [1954]
transformation of the data to obtain the unbiased estimates of the coefficients presented for the
AR(1) model in columns 3 and 4 of table VII.20 Given the persistence estimated in size
distributions, particularly in larger submarkets, one might have expected this outcome. As indicated
in table VII, variation in role sizes within submarkets is apparent over time.
Submarket brand turnover, INTRAFm, within firms is not significant in determining role
inequality in the submarket. This is confirms our analysis on role dynamics, whereby brand
proliferation within submarkets creates stability and does not alter the size distribution within
submarkets. Inter-firm submarket share rivalry, INTERFm, and firm heterogeneity within
submarkets both in terms of specialisation of distribution in a subset of shops, SpecIneqmt0, and
retail pricing, PrIneqmt0, (using initial values to avoid endogeneity) are positively significant. The
nature of competition and differences in strategic activities, in terms of pricing and distribution, are
important determinants of the distribution of role sizes within a submarket. Yet, as estimated in
column 4 of table VII, the size of the submarket dictates a large proportion of the explanatory
power in the determination of role inequality within submarkets. We find that role inequality rises
with submarket size, but this effect diminishes and is offset for larger sized submarkets. Thus, for
submarkets exceeding a size of £2.5 million the submarket size actually has a negative effect on
role inequality.
IV.4: The Theory of Majorisation
By the theory of majorisation, prediction 3 of Sutton (1998) states that heterogeneity in the
size of roles at the product level will induce the distribution of firm sizes to lie inside the lower
bound given by equation 1. The main result of the previous section on role size and role inequality
19
within submarkets is that larger submarkets will host firms with larger, more persistent and more
equal roles. Smaller submarkets host smaller, turbulent and more unequal sized roles. More
unequal submarkets within a product will therefore increase the variance in role size in a product
level. Using the co-efficient of variation in submarket share within products, we segment products
into those exhibiting a low degree of submarket inequality (Group 1) and those with a more
unequal distribution (Group 2). On this basis, Chocolate, Crisps, Soup, and Mineral Water are
denoted Group 1, while Carbonates, Ready-to-Eat Cereals, Tea, Coffee, Cat foods and Dog foods
are classified as Group 2 products. Figure V documents the distribution of submarket shares over
the two groups of products in the initial period.
The distribution of roles within submarkets illustrated in figure III is redrafted in figure VI
to illustrate the dichotomy between group 1 and group 2 products. One should note the higher
variance in submarket role size distributions for group 2 products when compared to group 1. This
is a direct outcome of the fact that submarket sizes are more unequal in group 2 products compared
to group 1 as evidenced in figure V. This should, by prediction 3 and the theory of majorisation, be
a force that induces the distribution of firm sizes in the product to lie further inside the lower
bound. Before we examine distribution of firm sizes in the product by group 1 and group 2
products, we first document a complementary mechanism that induces the distribution of firm sizes
in the product to lie even further inside the lower bound.
Part II: Heterogeneity in the Take-Up of Roles Across Submarkets
In this section we model heterogeneity in the take-up of roles across submarkets. Prediction
4 states that if the take-up of a role in one submarket is positively affected by a firm’s history (size
of roles) in other submarkets, due to scope economies, then heterogeneity in the size of roles within
submarkets will induce greater heterogeneity in the take-up of roles across submarkets. This will
induce the distribution of firm sizes observed in the product market to lie even further inside the
lower bound. Given the impact of submarket size on role size within submarkets, with larger
20
submarkets hosting bigger roles, unequal submarket sizes may also determine the extent to which
roles are taken-up across submarkets and place an even tighter restriction on the shape of firm size
distributions observed at the product level. We previously estimated that the sizes of roles within
submarkets were systematically related to the firm attachment in the product. Clearly, firms are
able to reap economies of scope, in that the size of a role in one submarket benefits from the firm
operating in other submarkets. Unequal submarket sizes create a situation whereby the escalation in
advertising in large submarkets, creating a history of a large role, generates positive spillovers for
the firm in its ability to take-up a role in smaller submarkets. Thus the take-up of a role in one
submarket becomes positively affected by a firm’s history (size of roles) in other submarkets.
Figures VII(i) and (ii) describes the relationship between firms take-up of roles over
submarkets and their relative size in the product for group 1 and group 2 products respectively. In
the case of group 1 products, where submarket sizes are more equal, we observe that firms take-up
of roles over submarkets do not vary systematically with the rank of firm, in terms of their size in
the product. This contrasts with the operations of firms over submarkets within group 2 products,
where large and small submarkets co-exist. Within group 2 products, higher ranked firms, in terms
of their size in the product, clearly have an advantage in taking up roles across submarkets. This is
in violation of the Symmetry Principle used by Sutton (1998) in deriving the lower bound. For
group 2 products the traditional size growth relationship, whereby the probability of an incumbent
firm taking up the next opportunity is increasing in firm size, in line with the Simon model, may be
a more appropriate description of the data.
IV.5: Group 1 versus Group 2 and the Lower Bound to Firm Size Distributions
The above within and between submarket analysis suggest that, as in prediction 3 and 4,
unequal sized independent submarkets, via its impact on the role sizes within submarkets and on
the probability of accumulating roles across submarkets, should push outcomes further from the
reference lower bound in equation (1). Taking a snapshot of our products in 1997, figure VIII plots
21
the fraction of top k ranking firms k/N against their corresponding share of total product sales,
where N is the total number of firms in the 5-digit product j and Ck describes the k-firm sales
concentration ratio. In figure VIII (i) products are segmented into our group 1 and group 2. Group
1, Chocolate, Crisps, Soup, and Mineral Water display measures of firm size distribution that lie
very close to or on the Sutton’s theoretical lower bound. The second group of products exhibits
greater skewness in firm size, with the scatter of points positioned further away from Sutton’s
predicted lower bound. This group includes Carbonates, Ready-to-Eat Cereals, Tea, Coffee, Cat
foods and Dog foods. In group 2 products, higher ranked firms, in terms of their size in the product,
were shown to have an advantage in taking up roles across submarkets. In figure VIII (ii) we
observe the scatter of points for Group 2 to lie above the bound derived from the Simon Model in
Sutton (1998). Gibrats law seems to be an appropriate description of the data in terms of the takeup of roles across submarkets in group 2 products.
Such outcomes suggest a positive relation between the degree of firm inequality within a
product and the skewness of its inherited submarket structures. Using a regression approach we
model the relative importance of inherited submarket structures against other deterministic factors
that may be expected to determine the cross section variations in firm size distributions. We
empirically examine the relative importance of submarket structures across our 5-digit products in
the following random effect model,21
2
(5)
FrmIneq jt = α + β1ProSize jt + β 2 ⎛⎜ ProSize jt ⎞⎟ + β 3INTERF jt + β 4 INTRAF jt
⎝
⎠
.
+ β 5 SpecIneq jt 0 + β 6 PrIneq jt 0 + β 6 SubIneq jt 0 + v j + ε jt
Firm inequality is measured by the coefficient of variation in firm size in each bi-monthly
period t, for product j. Details of all variables are found in Appendix I. The coefficient of variation
in firm size is positively related to the degree of skewness in firm size in a product. This is
regressed on various product characteristics describing the market.
22
The regression variables are as in equation (4), but expressed at the level of the product j
rather than within submarket m. Firm size inequality may result from heterogeneity in the degree
to which firms brand proliferate, specialise their distribution of brands through a subset of shops in
the market, and their differences in prices or underlying differences in costs or vertical attributes.
These are controlled for in the initial value jt0 to prevent endogeneity. Controlling for the above
factors, month dummies, and unobservable random effects over the cross section of products, we
examine the impact that the initial structure of submarkets has on firm inequality in the product
with our variable SubIneqjt0. This coefficient of variation describes the inequality of submarket size
in the initial time period, where size is the submarket share of the total product j sales value.
Equation 5 is estimated as a random effect model, justified on the basis of the Hausman
[1978] test. The results are presented in table VIII. The presence of an auto-correlated error
structure of order one in the GLS models led us to adopt a Prais-Winsten [1954] transformation of
the data to obtain the unbiased estimates of the coefficients presented for the AR(1) model.
Examining results corrected for AR(1) indicates that only the structure of submarkets in terms of
the degree of heterogeneity in monetary size, has a significant effect on firm size distributions in
the product market. The inherited submarket structure is shown to be a key determinant of firm size
distribution across 5-digit products. In contrast, while controlling for other deterministic factors,
market size, and firm heterogeneity in pricing, distribution and brand proliferation are not
significant determinants of firm size distributions at this level of the market. This is consistent with
our empirical findings, where we observe in figure VIII greater inequality in firm size for products
classified in Group 2 as compared with Group 1, reflecting the relatively more heterogeneous sized
submarkets in Group 2.
Conclusion
The presence of many independent submarkets within product markets of the Irish Food
and Drink retail sector provides an ideal setting in which to empirically examine the role of
23
independent submarkets as a determinant of firm size distributions. Exploiting the extreme richness
of this brand level panel data, we validate Sutton’s (1998) game theoretic bound approach to
modelling firm size distributions. We demonstrate that the presence of firms operating over
independent submarkets places Sutton’s mathematical derived lower bound on the shape of firm
size distributions observed in 5-digit products. In addition, while individual 8-digit submarkets are
shown to have many forms of size distributions in submarket roles, as an outcome of strategic
effects, this does not lead to a violation Sutton’s lower bound on the shape of firm size distributions
observed in 5-digit products.
Our analysis also demonstrated that the historical evolution of skew submarket sizes
induced a tighter bound, approximated by the Simon model, on firm size distributions in six of
our 5-digit products. Sutton’s (1998) Theorem of Majorisation model predicts that heterogeneity
in the size of roles as an outcome of strategic effects within submarkets will induce the
distribution of firm sizes observed in the product market to lie inside the lower bound. Our
within submarket analysis of the data demonstrates that heterogeneity in the size of roles within
submarkets is mainly an outcome of the degree of advertising competition within a submarket,
while controlling for brand, distribution and price competition, among other factors. Larger
submarkets, defined in monetary value, will host firms with larger, more persistent and more
equal sized roles, while smaller submarkets host smaller, turbulent and more unequal sized
roles. This is one mechanism where skew submarket sizes, via heterogeneous advertising
environments, will induce the distribution of firm sizes observed in the product market to lie
inside the lower bound.
We also identify a second complementary mechanism. Sutton (1998) also predicts that if
the take-up of a role in one submarket is positively affected by a firm’s history (size of roles) in
other submarkets, this will also induce the distribution of firm sizes to lie inside the lower bound.
Our data analysis shows that escalation in advertising in large submarkets created a history of a
24
large role, and gave firms a size advantage in the take up of roles across smaller submarkets. This
identifies a complementary mechanism where skew submarket sizes will induce the distribution of
firm sizes observed in the product market to lie inside the lower bound. Our analysis demonstrates
that the historical evolution of skew submarket sizes induced a tighter bound, approximated by the
Simon model, on firm size distributions in six of our 5-digit products, while the other four 5-digit
products hosting more equal sized submarkets did not violate Sutton’s lower bound.
The presence of submarkets and the importance of submarket structure in terms of size
cannot be over-emphasised. At the brand level one can only see turbulence and absolute chaos in
the data. Yet all this bi-monthly micro-economic activity at the brand level leads to persistence and
stable firm size distributions at the product level that do not violate Sutton’s lower bound overtime. Sutton’s (1998) incorporation of independent (submarket) effects into game theory and
empirical work allows us to model and understand such an outcome.
Finally, the growth of firms literature should take into account the presence of independent
submarkets within a defined product market. Within submarkets we find a tendency for Gibrat’s
Law to hold as submarket size, or the intensity of advertising competition, increases. The observed
bi-monthly role dynamics do not create ongoing structural changes that prevents us from modelling
limiting firm size distributions across products. This contrasts strongly with findings at the product
level where the presence of independent submarkets are ignored. In such a case, like many of the
empirical firm level studies to date, we observe a failure of Gibrats law. This highlights the
importance of allowing for the presence of submarket niches, even at a 5-digit product level. The
presence of such, even at this very micro-level of industry, will create a fallacy that Gibrat’s Law
fails in advertising intensive sectors. In fact, in our data small firms can only survive and grow
within peripheral taste niches of a product. This ensures modelling firm size distributions as
outcomes of a long historical evolution as in Sutton (1998) is a legitimate and fruitful exercise.
25
Table I
Products, Submarkets, Firms and Brands Available
Product
No.
1
2
3
4
5
Name
Chocolate
Crisps
Min. Water
Soup
Carbonates
Submarket
No.
Name
Average over period
Including All
October 1992– March 1997 Entrants and Exits
Submarket
Size (£ Mill)
Submarket
Share
Number Number
of Firms of Brands
(Roles)
1
Filled Blocks Large
0.95
0.05
3
10
2
Filled Blocks
Std.
2.80
0.15
4
13
3
Moulded Items Large
0.51
0.03
4
8
4
Moulded Items Std.
8.46
0.44
6
43
5
Packets
1.46
0.08
3
13
6
Kiddies
1.81
0.09
4
15
7
Mpks/Treatsize
3.19
0.17
4
11
1
Potato Crisps
5.43
0.53
6
10
2
Tubes of Crisps
1.07
0.10
2
2
3
Snacks
3.72
0.36
4
11
1
Sparkling Mineral Water
0.93
0.60
11
13
2
Non-Sparkling Mineral Water
0.65
0.40
11
13
1
Packaged Soup
2.47
0.57
4
7
2
Instant Soup
0.84
0.19
4
13
3
Canned/Carton Soup
1.02
0.23
5
5
1
Cans Cola
2.58
0.11
4
12
2
Cans Orange
0.95
0.04
4
9
3
1.96
0.09
6
15
4
Cans Lemonade/Mixed
Fruit/Other
Std./1.5Ltr. Cola
2.46
0.10
4
21
5
Std./1.5Ltr. Orange
1.35
0.06
6
19
6
4.41
0.18
11
42
7
Std./1.5Ltr Lemonade/Mixed
Fruit/Other
2ltr.+ Cola
2.29
0.10
4
10
8
2ltr.+ Orange
1.45
0.06
4
7
9
4.99
0.21
7
16
10
2ltr.+ Lemonade/Mixed
Fruit/Other
Cans Mpks Cola
0.76
0.03
3
11
11
Cans Mpks Orange
0.15
0.01
3
5
12
Cans Mpks Lemonade/Mixed
Fruit/Other
0.19
0.01
1
5
i
Product
No.
6
7
8
9
Name
RTE Cereals
Tea
Coffee
Cat Food
10 Dog Food
Submarket
No.
Name
Average over period
Including All
October 1992– March 1997 Entrants and Exits
Submarket
Size (£ Mill)
Submarket
Share
Number Number
of Firms of Brands
(Roles)
1
Small Corn/Rice
0.31
0.04
1
11
2
Small Wheat/Bran
0.18
0.02
2
11
3
Small Museli
0.08
0.01
2
4
4
Small Sugar
0.23
0.03
1
9
5
Standard Corn/Rice
1.85
0.24
4
22
6
Standard Wheat/Bran
1.01
0.13
3
25
7
Standard Museli
0.38
0.05
5
14
8
Standard Sugar
0.42
0.05
3
14
9
Large Corn/Rice
1.67
0.22
1
10
10
Large Wheat/Bran
0.76
0.10
3
14
11
Large Museli
0.14
0.02
2
7
12
Large Sugar
0.39
0.05
1
5
13
All Other
0.25
0.03
4
6
1
Packaged Tea
1.26
0.18
8
8
2
Tea Bags
5.68
0.82
8
21
1
Regular Powder/Granules
3.07
0.78
8
20
2
Decaffeinated
0.24
0.06
5
8
3
Roast and Ground
0.42
0.11
10
13
4
Cappucino
0.13
0.03
5
5
5
Freeze Dried Coffee
0.08
0.02
4
3
1
Canned Cat Food
1.44
0.87
4
11
2
Packet Cat Food
0.19
0.13
4
7
1
Canned Dog Food
2.16
0.74
5
12
2
Mixers/Dog Biscuits
0.50
0.18
3
8
3
Comp. Dog Food
0.25
0.09
5
6
Overall Data Dimensions
Total Number of Products
10
Total Number of
Individual Submarkets
52
Total Number of
Individual Firms in the Product
93
Total Number of
Individual Firm Roles Across all Submarkets
232
Total Number of
Individual Brands
633
ii
Table II
Almost Ideal Demand Systems – Testing the Joint Significance of Submarket Price Coefficients
Chocolate
Mineral Water
Soup
Submarket
1 F(6,112) = 1.35 F(2,60) = 0.04
Paasche Price
Prob>F= 0.96
F(1,42) = 2.72
Prob>F= 0.11
F(2,60) = 1.621 F(11,132) = 3.67 F(12,130) = 1.41 F(1,42) = 2.90 F(4,90) = 3.14 F(1,42) = 9.67 F(2,60) = 3.36
Prob>F= 0.21
Prob>F= 0.001
Prob>F= 0.17
Prob>F= 0.10 Prob>F= 0.02 Prob>F= 0.01 Prob>F= 0.04
Submarket 2
F(6,112) = 1.79 F(2,60) = 1.16
Prob>F= 0.11 Prob>F= 0.32
F(1,42) = 1.63
Prob>F= 0.21
F(2,60) = 0.47
Prob>F= 0.63
F(11,132) = 3.64 F(12,130) = 6.16 F(1,42) = 2.54 F(4,90) = 1.65 F(1,42) = 1.30 F(2,60) = 1.77
Prob>F= 0.001
Prob>F= 0.00
Prob>F= 0.12 Prob>F= 0.17 Prob>F= 0.33 Prob>F= 0.18
F(2,60) = 0.68
Prob>F= 0.51
F(11,132) = 2.10 F(12,130) = 8.08
Prob>F= 0.03
Prob>F= 0.00
F(4,90) = 2.02
Prob>F= 0.10
Submarket
4 F(6,112) = 1.60
Paasche Price
F(11,132) = 5.53 F(12,130) = 9.33
Prob>F= 0.00
Prob>F= 0.00
F(4,90) = 0.81
Prob>F= 0.52
Submarket
5 F(6,112) = 3.36
Paasche Price
F(11,132) = 3.09 F(12,130) = 1.56
Prob>F= 0.001
Prob>F= 0.11
F(4,90) = 0.22
Prob>F= 0.93
Submarket
6 F(6,112) = 1.32
Paasche Price
F(11,132) = 1.30 F(12,130) = 9.33
Prob>F= 0.23
Prob>F= 0.00
Submarket
7 F(6,112) = 0.24
Paasche Price
F(11,132) = 1.80 F(12,130) = 4.80
Prob>F= 0.06
Prob>F= 0.00
Submarket
8
Paasche Price
F(11,132) = 0.70 F(12,130) = 2.62
Prob>F= 0.73
Prob>F= 0.01
Submarket
9
Paasche Price
F(11,132) = 3.68 F(12,130) = 5.31
Prob>F= 0.001
Prob>F= 0.00
Submarket
10
Paasche Price
F(11,132) = 2.18 F(12,130) = 3.54
Prob>F= 0.02
Prob>F= 0.00
Submarket
11
Paasche Price
F(11,132) = 2.08 F(12,130) = 3.55
Prob>F= 0.03
Prob>F= 0.00
Submarket
12
Paasche Price
F(11,132) = 0.86 F(12,130) = 2.98
Prob>F= 0.58
Prob>F= 0.01
Submarket
13
Paasche Price
F(12,130) = 5.85
Prob>F= 0.00
Prob>F= 0.24
Paasche Price
Submarket 3
Paasche Price
Crisps
F(6,112) = 2.08 F(2,60) = 0.46
Prob>F= 0.06 Prob>F= 0.64
Prob>F= 0.15
Prob>F= 0.01
Prob>F= 0.26
Prob>F= 0.96
Carbonates
RTE Cereals
Tea
Coffee
Cat Food
Dog Food
F(2,60) = 3.56
Prob>F= 0.04
iii
Table III
Firms Take-Up of Roles over Submarkets by Product: March 1997
% of Product Submarkets Firms Operate Over
No.
Submarkets
No. Firms
Chocolate
7
Crisps
Mean
Std. Dev.
Min.
Max.
6
67
37
28
100
3
8
46
17
33
67
Mineral Water
2
9
89
22
50
100
Soup
3
9
45
17
33
67
Carbonates
12
13
35
32
8
100
RTE Cereals
13
7
34
36
8
100
Tea
2
8
94
18
50
100
Coffee
5
13
43
30
20
100
Cat Food
2
6
67
26
50
100
Dog Food
3
8
54
31
33
100
Table IV
Transition Matrix for Firm Roles in Submarkets – Average Hazard Rates (Oct.’92-March ‘97)
(i) Small Submarkets: Total Value < £ 0.5 Mill
Class
1t+1
2 t+1
3 t+1
4 t+1
5 t+1
1t
0.79
0.05
0.03
0.00
0.00
2t
0.08
0.76
0.16
0.00
0.00
3t
0.01
0.06
0.85
0.08
0.00
4t
0.00
0.00
0.06
0.85
0.09
5t
0.00
0.00
0.00
0.05
0.95
(ii) Medium Submarkets: Total Value >= £ 0.5 Mill and < £ 1.5 Mill
Class
1 t+1
2 t+1
3 t+1
4 t+1
5 t+1
1t
0.82
0.11
0.01
0.00
0.00
2t
0.05
0.83
0.12
0.00
0.00
3t
0.00
0.09
0.80
0.10
0.00
4t
0.00
0.00
0.07
0.82
0.11
5t
0.00
0.00
0.00
0.08
0.91
(iii) Large Submarkets: Total Value >= £ 1.5 Mill
Class
1 t+1
2 t+1
3 t+1
4 t+1
5 t+1
1t
0.89
0.08
0.01
0.01
0.00
2t
0.06
0.84
0.09
0.01
0.00
3t
0.00
0.03
0.91
0.05
0.00
4t
0.00
0.00
0.10
0.82
0.08
5t
0.00
0.00
0.00
0.08
0.92
iv
Table V
Growth of Firm Roles in Submarket Regression
Summary of Regression Variables (fm = firm Role in submarket, t = bi-monthly period)
# Obs: 4923
(fm = 232)
Role Growthfmt
*
SubSizemt
**
RoleSizefmt
INTERFmt
INTRAFmt
RSPECf,mt
RPPIf mt
Mean
Std. Dev.
Min
Max
-0.007
0.02
0.07
0.02
0.02
0.33
1.08
0.34
0.03
0.14
0.04
0.04
0.12
0.24
-2
0.0001
0.00001
0
0
0.0001
0.11
+2
0.15
1.56
0.39
0.33
1.75
4.04
* note SubSizem t = SLS m t / Total SLS j t 0
Role Growth fmt
R2
CONSTANT
SubSizemt
RoleSizefm t –2
;
**
RoleSizef m t= SLU f m t / Total SLU m t0
I
OLSb
0.10
II
OLSb
0.11
0.14
(1.50)
6.52
(9.44)*
-0.45
(4.35)*
0.19
(1.89)
6.57
(4.09)*
-0.95
(4.71)*
8.86
(2.45)*
0.45
(2.12)*
-1.87
(0.33)
0.26
(1.34)
-1.21
(0.30)
0.09
(0.42)
-19.07
(2.65)*
-0.24
(1.49)
43.36
(3.67)*
-0.10
(2.34)*
0.57
(0.50)
Yes
Yes
Yes
Yes
4923
RoleSizefm t -2 X SubSizemt
(Rolesizefm t -2)²
0.27
(3.55)*
(Rolesizefm t -2)²X SubSizemt
INTERFmt
-0.33
(2.54)*
INTERFmt X SubSizemt
INTRAFmt
-0.32
(2.12)*
INTRAFmt X SubSizemt
RSPECf mt
0.22
(1.77)
RSPECf mt X SubSizemt
RPPIf mt
-0.12
(3.90)*
RPPIf mt X SubSizemt
Month Dummies
Product Dummies
Submarket Dummies
Firm in Product Dummies
Observations
Yes
Yes
Yes
Yes
4923
a
T-statistics in parenthesis
Model Corrected for Heteroskedasticity
* Significant at the 5% level
b
v
Table VI
Transition Matrix for Brands in Submarkets –Average Hazard Rates (Oct.’92-March’97)
(i) Small Submarkets: Total Value < £ 0.5 Mill
Class
1 t+1
2 t+1
3 t+1
4 t+1
5 t+1
1t
0.70
0.07
0.05
0.00
0.00
2t
0.15
0.66
0.16
0.01
0.00
3t
0.01
0.10
0.81
0.07
0.00
4t
0.00
0.00
0.07
0.83
0.09
5t
0.00
0.00
0.00
0.08
0.92
(ii) Medium Submarkets: Total Value >= £ 0.5 Mill and < £ 1.5 Mill
Class
1 t+1
2 t+1
3 t+1
4 t+1
5 t+1
1t
0.77
0.10
2t
0.10
0.78
0.02
0.00
0.00
0.12
0.00
0.00
3t
0.00
0.05
0.86
0.09
0.00
4t
0.00
0.00
0.12
0.78
0.10
5t
0.00
0.00
0.00
0.09
0.91
(iii) Large Submarkets: Total Value >= £ 1.5 Mill
Class
1 t+1
2 t+1
3 t+1
4 t+1
5 t+1
1t
0.85
0.09
0.01
0.00
0.00
2t
0.10
0.79
0.10
0.00
0.00
3t
0.00
0.06
0.88
0.06
0.00
4t
0.00
0.00
0.12
0.82
0.06
5t
0.00
0.00
0.00
0.07
0.93
vi
Table VII
Role Inequality in Submarkets Regression
Summary of Regression Variables (m = submarket, t = bi-monthly period)
# Obs: 1352
(m = 52; t = 27)
Mean
Std. Dev.
Min
Max
RoleIneqm,t
0.74
0.40
0
1.57
0.38
0.15
0
0
0.15
1.15
0.03
0.04
0.04
0.24
0.12
0.0001
0
0
0
0
0.15
0.39
0.33
1.05
0.53
I
GLS
II
GLS
I
AR(1)
II
AR(1)
0.10
0.75
0.66
0.11
0.42
0.37
0.19
0.70
0.52
0.17
0.39
0.32
CONSTANT
-0.06
(0.52)
0.44
(3.4)*
0.22
(3.97)*
0.43
(7.8)*
SubSizemt
9.2
(6.4)*
10.3
(7.0)*
4.96
(3.8)*
4.7
(3.6)*
(SubSizemt)²
-61.0
(5.4)*
-64.5
(5.6)*
-25.1
(2.6)*
-21.3
(2.2)*
INTERFmt
-0.15
(1.4)
-0.16
(2.3)*
INTRAFmt
-0.03
(0.2)
0.05
(0.63)
SpecIneqm t0
0.78
(5.5)*
0.38
(4.7)*
PrIneqm t0
1.04
(3.7)*
0.46
(2.8)*
Between Submarkets
Within Submarkets (T=27)
*
SubSizemt
INTERFmt
INTRAFmt
SpecIneqmt
PrIneqm,t
0.02
0.02
0.02
0.39
0.15
* note SubSizem,t = SLS(£000)m,t / Total SLS (£000) j t 0
RoleIneqm,t
R2
Within Submarkets
Between Submarkets
Overall
Product Dummies
Yes
Yes
Yes
Yes
Month Dummies
Yes
Yes
Yes
Yes
Observations
1352
1404
1352
1404
Hausman Spec.
χ2(29)=2.03
χ2(28)= 0.20
χ2(29)=0.96
χ2(28)= 2.35
Autocorr. AR1
χ2(1)=689.0
χ2(1)=722.6
χ2(1)= 1.4
χ2(1)= 1.5
Autocorr. AR4
χ2(4)=134.9
χ2(4)=138.9
χ2(4)=11.1
χ2(4)= 8.1
a
T-statistics in parenthesis
* Significant at the 5% level
vii
Table VIII
Firm Inequality in Products Regression
Summary of Regression Variables (j = product, t = bi-monthly period)
# Obs: 270
Mean
Std. Dev.
Min
(j = 10; t = 27)
Max
FrmIneqjt
1.35
0.35
0.70
2.11
0.33
0.14
0.90
0.82
2.02
1.70
0.12
0.02
0.03
1.48
0.41
0.76
0.11
0.03
0.03
0.55
0.32
0.32
0.01
0
0
0.72
0.08
0.06
0.49
0.21
0.20
2.41
1.21
1.51
I
GLS
II
GLS
I
AR(1)
II
AR(1)
0.40
0.62
0.58
0.34
0.49
0.46
0.67
0.68
0.68
0.64
0.49
0.59
CONSTANT
0.43
(1.51)
0.59
(4.62)*
0.48
(4.7)*
0.49
(9.1)*
ProSizejt
-1.57
(1.59)
-0.22
(0.35)
(ProSizejt ) 2
3.75
(2.57)*
-0.12
(0.12)
INTERFjt
-0.60
(1.97)*
-0.29
(1.96)
INTRAFjt
0.28
(0.94)
0.10
(0.65)
SpecIneqj t0
0.16
(0.99)
0.11
(1.37)
PrIneqj t0
0.05
(0.18)
0.01
(0.10)
SubIneqjt0
0.85
(6.45)*
0.82
(6.72)*
0.52
(4.7)*
0.51
(5.01)*
Yes
Yes
Yes
Yes
Between Products (j=10)
Within Products (T = 27)
*
ProSizejt
INTERFjt
INTRAFjt
SpecIneqjt
PrIneqjt
SubIneqjt
* note ProSizejt = SLSjt / Total SLSt0
FrmIneqjt
R2
Within Products
Between Products
Overall
Month Dummies
Observations
260
270
260
270
Hausman Spec.
χ2(30)=4.15
χ2(27)= 0.35
χ2(30)= 0.59
χ2(27)=0.5
Autocorr. AR1
χ2(1)=147
χ2(1)=182
χ2(1)=0.2
χ2(1)=1.0
Autocorr. AR4
χ2(4)=28.9
χ2(4)=51.5
χ2(4)=6.2
χ2(4)=1.0
a
T-statistics in parenthesis
* Significant at the 5% level
viii
Figure I
Average Share of Total Product Sales for Submarkets defined by Packaging:
October 1992-March1997
C h ain Store M ultiples
In depen den t Sh ops
100%
80%
% Share
60%
40%
20%
S ou rc e: A C N ie ls en
Large
ereals
RTE
C
RTE
Cerea
ls - S
tanda
rd
Small
ereals
RTE
C
K Ca
ns
- MP
onate
s
Carb
Carb
onate
s
- 2 ltr
.+
1.5ltr
.
- Std.
Carbo
nates
Carb
onate
s -C
ans
tanda
rd
Choc
olate
-S
Choc
olate
- Lar
ge &
MPK
S
0%
Figure II
Firm Size Distributions within Products and Suttons Lower Bound: March 1997
Ck of Top k/N Firms in Product j
1
.8
.6
.4
Line of Equality
.2
Predicted Lower Bound for Product
0
0
.2
.5
.75
1
Top k/N Firms in Product j
ix
Figure III
The Size Distribution of Roles within Submarkets and Suttons Lower Bound: March 1997
Ck of Top k/N Roles in Submarket m
1
.8
.6
.4
Line of Equality
.2
Predicted Lower Bound for Product
0
0
.25
.5
Top k/N Roles in Submarket m
.75
1
Figure IV
Distribution of Role Sizes in Different Sized (£ mill) Submarkets: March 1997
10 0 1
Sm all Subm arkets:
< £ 0. 5 m ill
M edium Subm arkets:
> = £ 0. 5 m ill & < £ 1. 5 mill
% of Roles
50
0
0
.5
1
1.5
Large Subm arkets:
> £ 1. 5 m ill
10 0
50
0
0
.5
1
1.5
R ole Size in Subm ark et m = SL U f m t / SL U
j t0
x
Figure V
Distribution of Submarket Size by Product Groups
Group 1
Group 2
60
40
20
0
0
.2
.4
.6
.8
Submarket
1
Size =
0
.2
.4
.6
.8
1
£000 Sales Submarket m t0
£000 Sales Product j t0
Figure VI
Role Size Distributions Within Submarkets by Group: March 1997
group1
Ck of Top k/N Roles in Submarket m
%
group2
1
.8
.6
.4
Line of Equality
.2
Predicted Lower Bound for the Product Market
0
0
.25
.5
.75
1
Top k/n Roles in Submarket m
xi
Figure VII (i)
Firms Operations Over Submarkets for Group 1 Products: March 1997
(Averaged over Pooled Cross Section of Products)
100
% Product Submarkets
80
60
40
20
0
2
1
4
3
6
5
8
7
9
Firm Sales Rank in Product
Figure VII (ii)
Firms Operations Over Submarkets for Group 2 Products: March 1997
(Averaged over Pooled Cross Section of Products
100
% Product Submarkets
80
60
40
20
0
1
2
3
4
5
6
7
Firm Sales Rank in Product
8
9
10
11
12
13
xii
Figure VIII (i)
Firm Size Distributions within Products by Group: March 1997
Suttons Lower Bound
group1
group2
Ck of Top k/N Firms in Product j
1
.8
.6
Line of Equality
.4
.2
Predicted Lower Bound for Product
0
0
.25
.5
.75
1
Top k/N Firms in Product j
Figure VIII (ii)
Firm Size Distributions within Products by Group: March 1997
Suttons Lower Bound and Simons Predicted Lorenz Curve for Entry Parameter 0.2
Group1
Group2
Ck of Top k/N Firms in Product j
1
.8
.6
Line of Equality
.4
Predicted Lower Bound for Product j
.2
Simons Predicted Lorenz Curve
0
0
.2
.4
.6
.8
1
Top k/N Firms in Product j
xiii
References
Audretsch, D., (1995), Innovation and Industry Evolution, Cambridge, MIT Press.
Bain, J., (1951), “Relation of Profit Rate to Industry Concentration: American Manufacturing,
1963-1940”, Journal of Economics, 65: 293-324.
Buzacchi, L. and T. Valetti, (1999), "Firm size distribution: testing the "independent
submarkets model in the Italian motor insurance industry", Discussion Papers Series
EI, STICERD, LSE.
Davis, S. and J. Haltwinger, (1992), “Job Creation and Destruction and Employment
Reallocation”, Quarterly Journal of Economics, 107:819-863.
De Juan, R., (1999), "The Independent Submarkets Model: An Application to the Spanish
Retail Banking Markets", Discussion Paper in Universidad Alcala de Henares.
Dunne, T., M. Roberts and L. Samuelson, (1988), “Patterns of Firm Entry and Exit in US
Manufacturing Industries”, Rand Journal of Economics, 18:1-16
Ericson R. and A. Pakes, (1995), “Markov-Perfect Industry Dynamics: A Framework for
Empirical Work”, Review of Industrial Economics, 35:567-581.
Gibrat, R., (1931), Les inégalitiés économiques; applications: aux inégalitiés des richesses, à la
concentration des enterprises, aux populations des villes, aux statistiques des familles,
etc., d’une loi nouvelle, la loi de l’effet proportionnel. Paris: Librairir de Receuil Sirey.
Harsanyi, J.C. and R. Selten, (1988), “Games with Randomly Distributed Payoffs: A New
Rationale for Mixed-Strategy Equilibrium Payoffs”, International Journal of Game
Theory, 2:1-23.
Hart, P. E. and S.J. Prais, (1956), “The Analysis of Business Concentration: A Statistical
Approach”, Journal of Royal Statistical Society (series A), 119:150.
Hausman, J.A., (1978), “Specification Tests in Econometrics”, Econometrica, 46:1251-1271.
Ijiri, Y. and H. Simon, (1964), “Business Firm Growth and Size”, American Economic Review,
54:77-89.
Ijiri, Y. and H. Simon (1977), Skew Distributions and Sizes of Business Firms, Amsterdam:
North-Holland Pub. Co.
Jovanovic, B., (1982), “Selection and the Evolution of Industry”, Econometrica, 50:649-70.
Marshall, A. and I. Olkin, (1979), Inequalities: Theory of Majorization and Its Applications.
New York: Academic Press.
Prais, S. and C. Winsten, (1954), “Trend Estimation and Serial Correlation”, Cowles
Commission Discussion Paper Number 383 Chicago.
Schmalensee, R., (1989), “Inter-Industry Studies of Structure and Performance”, in Handbook
of Industrial Organization Volume 2: 951-1009, Eds.: R. Schmalensee and R. Willig.
Oxford: North Holland.
Sutton, J., (1991), Sunk Costs and Market Structure: Price Competition, Advertising and the
Evolution of Concentration, Cambridge, MA: MIT Press.
Sutton, J., (1997), ‘Gibrat’s Legacy’, Journal of Economic Literature, 35:40-59.
Sutton, J., (1998), Technology and Market Structure, Cambridge, MA: MIT Press.
Walsh and Whelan (1999), “Modelling Price Dispersion as an Outcome of Competition in the
Irish Grocery Market”, The Journal Of Industrial Economics, XLVII:1-19.
Walsh, P.P. and C. Whelan, (1999), “A Rationale for Repealing the 1987 Groceries Order in
Ireland”, The Economic and Social Review, 30:71-90.
Walsh, P.P., (2000) “Sunk Costs and the Growth and Failure of Small Business”, Department
of Economics, Trinity Economic Papers, No. 2, 2000, Trinity College, Dublin.
APPENDIX 1
Further Details of the Data and the Construction of Variables
Role Size and Firm Size
•
The definition of a role size is the size of a firm in a submarket. The size of role is thus equal
to the sum of sales over all firm brands in a submarket m. Sales are measured either in total
number of units or monetary values (£000).
•
The definition of a firm size is sum of all the firms roles in a product. The size of firm is thus
equal to the sum of sales over all firm brands in a product market j. Sales are measured either in
total number of units or monetary values (£000).
Market Size
•
The total size of a submarket m, SubSizet, is equal to the sum of total sales over all brands in
a submarket at date t, where sales are measured in monetary values (£000) unless otherwise
stated.
•
The total size of a product market j, ProSizet, is equal to the sum of total sales over all brands
in a product, where sales are measured in monetary values (£000) unless otherwise stated.
Growth Rates
•
We calculate a discrete measure of growth over the bi-monthly period t-1 to t for the
individual brand i as
A1)
BrandGrowt h = git =
SLU it − SLU i t − 1
⎛⎜ SLU + SLU
⎞
it
i t − 1 ⎟⎠ 2
⎝
,
where SLUi is the total number of units of brand i sold. This measure incorporates both the entry
and exit of brands, adopting a value of +2 in the former case and –2 in the latter.
•
In a similar fashion, the growth of a role size in a submarket m can be computed as
A2)
•
RoleGrowth fmt =
SLU fm t − SLU fm
t −1
⎛
⎞
⎜ SLU fm t + SLU fm
⎟ 2
t −1⎠
⎝
And the growth rate of a firm f in a product market j, can be computed as
A3)
FrmGrowth fjt =
SLU fj t − SLU fj
t −1
⎛
⎞
⎜ SLU fj t + SLU fj
⎟ 2
t −1⎠
⎝
Inter-Firm and Intra-Firm Market Share Rivalry
•
In the Submarket m
Total brand turnover can be decomposed into the contributions made by the absolute net growth
in the submarket sales, sales switching between rival firms (inter-firm) and between brands
within firms (intra-firm) experienced in a submarket. The degree of intra-firm (INTRAFmt) and
inter-firm (INTERFmt) submarket share rivalry is computed by applying indices developed in
Davis and Haltwinger (1992) to our brand level data. INTERFj and INTRAFj control for the
nature of brand competition, inter-firm and intra-firm respectively, in the submarket m and are
computed as follows, where the growth rate is given as in equation A1.
(
A4)
)
N
POS mt = ∑ g imt × S imt
∀ g it > 0
i =1
N
NEG mt = ∑
g imt × S imt
∀ g it < 0
i =1
NET mt = POS mt − NEG mt
(
BT mt =
)
POS mt + NEG mt
⎡
⎤
BT mt = NET mt + ⎢ ∑ NET f mt − NET mt ⎥ + ∑ ⎡⎢ BT fmt − NET fmt ⎤⎥
⎦
⎢f
⎥ f ⎣
⎣ 4 4 442 4 4 4 43⎦ 1
4 4 4424 4 4 4
3
1
(
INTRAF
)
( INTERF mt )
mt
Weighting a brands growth by its sales (total number of units sold by brand i) share of total
submarket sales, Sim, the net growth of a submarket (NETm) is equal to the aggregate expansion
of brands (POSm) net of aggregate contracting brands (NEGm) in a submarket. Brand turnover
rate (BTm) is driven by the sum of all brand sales expansions and contractions in a submarket
over the defined period. Higher values of intra-firm competition is indicative of brand
proliferation by firms in the defined submarket, while inter-firm indicates the degree to which
brands compete head on with rival firms within submarkets.
•
In the Product j
Measures of Inter-firm (INTERFj) and Intra-firm (INTRAFj) in the product market j can be
computed as in equation A4 by substituting the subscript m for j. Thus, the growth of a brand i is
weighted by its sales share of total product j sales, Sij, allowing us to compute aggregate brand
expansions and contractions in the product market and to decompose the total brand turnover rate
in product market j into that driven by inter-firm and intra-firm product market share rivalry.
Inequality of Role and Firm Size
•
Role inequality within submarkets is measured by the coefficient of variation in role size in
submarket m for each bi-monthly period t, where role size refers to the firm share of submarket
sales (in terms of number of units sold). This is computed as,
A5)
RoleIneqmt =
2
Fm
∑ ⎛⎜ S fmt − S mt ⎞⎟ Fmt
⎠
f = 1⎝
S mt
where Sfmt represents firm f’s quantity share of total submarket m sales, i.e. role share. This
reflects the deviation of firm roles from the average role size, ⎯Sm, in a submarket m, normalised
by the number of firm roles, Fm, in that submarket, and expressed as a proportion of the mean
role size. The coefficient of variation in role size is positively related to the degree of skewness
in role size in a submarket.
•
Analogously, firm inequality within products is measured by the coefficient of variation in
firm size in product j for each bi-monthly period t, where firm size refers to the firm share of
product sales (in terms of number of units sold). This is computed as in A4, but at the product j
level rather than at the submarket m level.
A6)
FrmIneq jt =
2
Fj
F jt
∑ ⎛⎜ S fjt − S jt ⎞⎟
⎠
f = 1⎝
S jt
Firm Specialisation of Brand Distribution in a Subset of Shops
Not all brands are retailed through all shops in the Irish retail grocery market. Brands may
specialise their distribution, to varying degrees, through only a subset of retail shops. Total sales
value (£000) of brand i expressed as proportion of the product j sales value (£000) in the subset
of shops that retail brand i gives a measure S*ijt of brand i market share in the group of shops in
which it sells.
•
The degree to which brands specialise their sales in a subset of shops is indicated by the
difference between S*ijt, and Sijt, which is brand i share of total product market sales over all
shops in the grocery market. If S*ijt is equal to Sijt, then brand i is distributed in all shops and
there is no specialisation. The level of specialisation rises and tends to 1 with the differential
between the alternative measures of brand market share. Such a measure of brand specialisation
may be aggregated up to the firm role in a submarket level or firm in a product level to indicate
the degree to which firms specialise their distribution of submarket or product brands
respectively through a subset of shops.
•
The degree to which firms specialise distribution of their brands in a submarket m through a
subset of shops in the retail grocery market provides a measure of role specialisation,
RoleSpecfm. This is computed by weighting brand i specialisation by brand sales share of total
firm (role) sales in a submarket, Sifm, aggregating over all nm brands that a firm role has in a
submarket, and normalising for the number of brands. Thus,
A7)
•
nm
RSpec fmt = ∑ ⎡⎢⎛⎜ S *ijt − S ijt ⎞⎟ × S ifmt ⎤⎥ /n mt .
⎠
⎦
i = 1 ⎣⎝
The degree to which firms specialise distribution of their brands in a product j through a
subset of shops in the retail grocery market provides a measure of firm specialisation, FrmSpecfj.
This is computed by weighting brand i specialisation by brand sales share of total firm sales in a
product, Sifj, aggregating over all nj brands in that a firm has in a product, and normalising for
the number of brands. Thus,
A8)
nj
FrmSpec fjt = ∑ ⎡⎢⎛⎜ S*ijt − Sijt ⎞⎟ × Sifjt ⎤⎥ /n jt .
⎠
⎦
i = 1 ⎣⎝
Inequality in Role and Firm Specialisation
Heterogeneity in the degree to which firms specialise their distribution of submarket or product
brands through a subset of shops in the market are controlled for in the initial value of our
variables SpecIneqmt0 and SpecIneqjt0 respectively.
•
The initial degree of inequality in firm role specialisation within the submarket m is
measured by the coefficient of variation in the first period as
∑ (RSpec
2
Fm
A9)
SpecIneqmt 0 =
fmt 0
− RSpec mt 0
)
Fmt 0
f =1
RSpec mt 0
Using the measure of role specialisation, RSPecfm, in equation A7, this reflects the deviation of
firm roles from the average level of firm specialisation in the submarket m, normalised by the
number of firm roles Fm in that submarket, and expressed as a proportion of the mean role
specialisation. The coefficient of variation in role specialisation is positively related to the degree
of heterogeneity in the degree to which firms specialise their distribution of submarket brands
through a subset of shops.
•
The initial degree of inequality in firm specialisation within the product j is measured by the
coefficient of variation in the first period as in equation A9, but at the product j rather than the
submarket m level and using the measure of firm specialisation outlined in equation A8.
∑ (FrmSpec
2
Fj
A10)
fjt 0 − FrmSpec jt 0
)
F jt 0
f =1
SpecIneq jt 0 =
FrmSpec jt 0
Role and Firm Paasche Price Indices
•
The firm role price is simply the weighted sum of firms brand prices in submarket m, where
the weights equal brand share of total firm (role) sales in the submarket, Sifm. The Paasche index
of Role prices is obtained by dividing the current role price in period t by the initial value at t0.
Thus, the role price and Role Paasche Price Index, RPPIfm, for each firm in a submarket is
computed as,
A11)
nm
RolePrice fmt = ∑ ⎡ p imt × S ifmt ⎤
⎢
⎦⎥
i = 1⎣
Role Pri ce fmt
RPPI fmt =
Role Pri ce fmt 0
•
In a similar fashion, the firm price and the Firm Paasche Price index in a product j can be
computed, where brand price is weighted by brand share of total firm sales in the product
market, Sifj. Thus, re-writing equation A11 at the product j rather than the submarket m level,
A12)
nj
FrmPr ice fjt = ∑ ⎡ p ijt × S ifjt ⎤
⎢
⎥⎦
i = 1⎣
FrmPri ce fjt
FPPI fjt =
FrmPrice fjt 0
Inequality in Role and Firm Pricing
•
The degree of inequality in firm role pricing within a submarket is computed using the
coefficient of variation in the first period, where RolePricefm is measured as in equation A11, Fm
is the total number of roles in a submarket and ⎯ RolePrice m is the average role price in the
submarket.
∑ (RolePrice
2
Fm
A13)
PrIneqmt 0 =
fmt 0
− RolePricemt 0
f =1
RolePricemt 0
)
Fmt 0
.
The coefficient of variation in role pricing is positively related to the degree of heterogeneity in
firm pricing within submarkets.
•
The degree of inequality in firm pricing within a product can be measured as in A13, but at
the product j rather submarket m level, and using the measure of firm price provided in equation
A12. Thus,
∑ Frm(RolePrice
2
Fj
A14)
PrIneq jt 0 =
fjt 0
− FrmPrice jt 0
)
F jt 0
f =1
.
FrmPrice jt 0
Inequality in Submarket Size
The degree of inequality in the sizes of submarkets within a product j can be computed using a
co-efficient of variation in submarket size, where this is measured as the submarket m share of
total product j sales (£000). Hence,
∑ (SubSize
2
M
A15)
mt 0
SubIneq jt 0 =
− SubSize jt 0
m =1
)
M jt 0
.
SubSize jt 0
This reflects the deviation of submarkets from the average submarket size in product market j,
normalised by the number of submarkets, M, in product j expressed as a proportion of the mean
submarket size. More heterogeneity in the sizes of submarkets in a product market j is reflected
in higher values of SubIneqjt0.
APPENDIX 2
Firm Dynamics Within the Product Market: Explaining an Enigma
The firm dynamics and failure of Gibrat’s Law in industries characterised by higher
levels of Advertising and R&D expenditures is an enigma of the empirical literature to date. Why
do such industries with high barriers to entry have so much entry, leapfrogging and exit, and how
can so many small firms co-exist with extremely large ones in intensive competition
environments? In this appendix, we consider this issue in the context of our 10 5-digit
advertising intensive product markets in the Irish retail Food and Drink sector.
Following from our empirical analysis of firm role dynamics within the submarket in
Section IV.2, we now undertake a counterfactual exercise where we test Gibrat’s Law for the
product market without recognition of the presence of submarkets. The regression in (3) is
therefore redefined at the product j rather than the submarket m level. Hence, firm growth, size,
and all other variables are calculated at the product market j level. Table A2 presents the results
of this product level analysis. In column I of table A2 we observe that firm growth is negatively
related to size, but the effect diminishes for bigger sized firms. In column II this is shown to hold
irrespective of the monetary size of the market for the product. Gibrats law thus fails in our
advertising intensive product markets.
Comparing these results with those of the previous analysis of role growth within
submarkets sheds light on the empirical enigma that has surrounded firm dynamics in advertising
intensive markets. Once one corrects for the presence of submarket niches as in section IV.2, the
puzzle is resolved. Larger submarkets, where their size has triggered an “escalation mechanism”
in advertising with high barriers to entry do not exhibit leapfrogging and do not allow the coexistence of many small firms with extremely large ones. The presence of peripheral submarkets,
even at this very micro-level of industry, will create a fallacy that Gibrats Law fails in mature
endogenous sunk cost sectors. In fact, small firms can only survive and grow in peripheral taste
niches within the product category. In an analysis of small Irish business Walsh (2000)
highlights the importance of endogenous sunk costs in determining the growth and failure in
subcontracting niches of Irish manufacturing, and finds that Gibrats law holds in R&D industries
but not in homogenous good industries.
Table A2
Firm Growth in Product Regression
Summary of Regression Variables (fj = firm in product j, t = bi-monthly period)
# Obs: 1954
(fj = 93)
FrmGrowthfjt
*
ProSizejt
**
FrmSizefj t
INTERFjt
INTRAFjt
FSpecf jt
FPPIf jt
Mean
Std. Dev.
Min
Max
0.02
0.12
0.17
0.02
0.03
0.05
1.08
0.27
0.11
0.27
0.03
0.03
0.14
0.16
-1.8
0.01
0.00001
0
0
0.0001
0.42
1.99
0.49
1.67
0.21
0.20
1.75
2.48
* note ProSizej t = SLSj t / Total SLS t0
;
**
FrmGrowthfjt
R2
CONSTANT
ProSizejt
FrmSizefj t-2
FrmSizef ,j t= SLUf j t / Total SLU j t0
I
OLSb
0.17
II
OLSb
0.19
-3.90
(2.64)*
1.94
(5.76)*
-1.67
(3.48)*
-0.35
(1.81)
1.75
(2.0)*
-1.73
(2.93)*
-1.70
(0.64)
0.69
(2.36)*
2.48
(1.04)
0.01
(0.03)
-3.40
(1.25)
-0.12
(0.31)
-3.67
(1.56)
-0.24
(0.88)
24.47
(2.44)*
-0.33
(0.32)
0.04
(0.07)
Yes
Yes
Yes
1954
FrmSizefj t-2X ProSizejt
(FrmSizefj t-2) 2
0.74
(3.23)*
(FrmSizefj t-2) 2 X ProSizejt
INTERFjt
-0.32
(1.26)
INTERFjt X ProSizejt
INTRAFjt
-0.68
(2.77)*
INTRAFjt X ProSizejt
Fspecf j t
0.20
(1.04)
FSpecf j t X ProSizejt
FPPIf j t
-0.03
(0.31)
FPPIf j t X ProSizejt
Month Dummies
Product Dummies
Firm in Product Dummies
Observations
a
T-statistics in parenthesis
Model Corrected for Heteroskedasticity
*Significant at the 5% level
b
Yes
Yes
Yes
1954
ENDNOTES
1.
For a comprehensive review of this literature on firm size distributions, the reader is referred to
Sutton [1997].
2
. This builds on the Sutton [1991] Bounds approach where, in the Bain [1951] tradition, he uses
stage games to motivate differences in the lower bound to firm concentration that can be
expected to exist across advertising and non-advertising branches of 4-5 digit food and drink
products.
3.
This simply assumes that larger firms are not disadvantaged either on the cost side or through
strategic effects on the demand side, in the probability of capturing the next opportunity.
4
The structure of the Sutton model (1998) of firm size distributions takes the form of the Simon
model (Ijiri & Simon, 1964 and 1977). A sequence of discrete and independent investment
opportunities arise over time. Taking the setting in which each of the investment opportunities
are equal in size, the number of opportunities taken up measures the size of a firm. The stochastic
process of firm growth begins with a single firm of size 1, with each subsequent period involving
the take up of a new opportunity by an existing or a new firm. If the probability of entry is one,
these independent equally sized opportunities are taken up in succession by new firms. The
resultant size distribution will display perfect equality between firms. Allowing for opportunities
to be taken up by both incumbent and new firms under two conditions, Sutton (1998) predicts his
lower bound to size distribution that holds over a broad run of industries. Condition 1 replaces
Gibrats law with the weaker restriction that the probability of an incumbent firm taking up the
next opportunity, or one of the equally sized islands, is non-decreasing in firm size. Condition 2,
in the spirit of the Simon model (Ijiri & Simon, 1964 and 1977), assumes the probability of entry
to be constant over time. Hence, each new independent opportunity is taken up by a new entrant
with probability p and by one of the Nt firms already active in the market with probability (1-p).
The least skew limiting distribution consistent with Condition 1 is attained in the special case
where each active incumbent firm has an equal probability, (1-p)/Nt, of taking up the next
opportunity. The distribution of active firms in the market at date t, Nt, depends only on
Condition 2 and is simply a bi-nomial with mean 1+p(t-1). The number of firms of size i at time
t, i=1,2,3… is denoted nit. The expected value of nit conditional on Nt, E(nit | Nt), evaluated at
Nt=1+p(t-1) in the limit where t→∞, describes the size distribution of firms which is proxied by
a corresponding exponential distribution. It can be shown that the fraction of k opportunities
accounted for by the k largest firms satisfies equation (1).
5
The size of the role, or size of firm in a submarket, depends on the strategic effects within
submarkets. The size of a firm in the product is equal to the sum of its roles over all submarkets
in which the firm is active.
6
The Symmetry Principle is based on the Harsanyi and Selten (1988) concept of symmetry and
subgame consistency.
7
The size of a role can be measured by the total level of sales, either in terms of quantity or
value, that a firm has within a submarket.
8
A grocer is defined as a retail shop with 20 per cent or more of its turnover in groceries with no
larger proportion of turnover in any other commodity, unless it is one or a combination of the
following: off-licence trade, bakery goods, tobacco (if less than 70 per cent of sales).
9
All shops and outlets were Irish owned, by law, and market shares in terms of percentage of
retail turnover were stable throughout the period studied. The introduction of foreign competition
into the chain store market, which induced structural upheaval in the market, did not take place
until the end of 1998 with the introduction of EU single market reforms.
10
A submarket price is computed by taking each brands’ retail selling price, weighting by its
market share within submarkets, and aggregating over all brands in the defined submarket. The
Paasche index of prices is obtained by dividing the current submarket price by the initial value at
t0. The general price index, Pjt, is the sum of submarket Paasche price indices in a product,
weighted by submarket expenditure share of the product.
11
Although not reported, real income induces a significant amount of explanatory power in our
system of reduced form demand equations within products. The time-series movements in the
monetary values of our submarkets seem to be determined a great deal by product cycles induced
by factors such as the weather. This is an empirical validation of the presence of submarkets at
this very micro-level of industry
12.
Only under the special conditions of very weak competition and overlapping of submarkets,
where these define brands that are very close substitutes, can theory predict the shape that the
size distribution within submarkets must take. In this special case, which is not applicable to the
Irish Food and Drink sector, game theoretic analysis predicts an extremely fragmented outcome
so that the Lorenz Curve for each submarket must lie close to the diagonal [for an illustration,
see Sutton 1998, Chapter 12]
13.
For a comprehensive review of this literature the reader is referred to Sutton [1997]. Gibrat’s
Law states that the expected value of the increment to a firm’s size in each period is proportional
to the current size of the firm. Hence, proportionate growth rates are independent of firm size
and, assuming a fixed number of firms, generate a log normal size distribution.
14
However, when small firms are omitted from the sample, Gibrat’s Law holds. Firm growth
then becomes unrelated to firm size. This is consistent with our findings later, where small firms
are found to operate in different strategic niches.
15
These are conventional profit maximising theories of firm selection and industry evolution
under ex-ante uncertainty concerning ex-post performance of firms. A new firm does not know
its full relative efficiency before entering the market. This is only revealed through a process of
learning from its ex-post entry performance. The models explain why so many small firms can
exist with a large turnover, and why one should expect strong growth in small compared to large
firms. They predict a breakdown of Gibrat’s [1931] Law in theories of noisy selection.
16
The nature of the data set does not allow us to control for the age or life cycle of firm roles.
The data set does however, allow us to include a rich set of role specific control variables that
indicate the maturity of a role in a market. Our regression is not conditioned on the probability of
firm survival in a submarket. Over the four and half year period, entry and exit of roles is not a
big feature of this mature market. This if anything should bias the data to induce the faster
growth of non-failing small roles compared with large roles.
17
The indices used to control for strategic effects, such as the nature of brand competition and
specialisation in distribution of brands through a subset of shops were developed in Walsh and
Whelan’s (1999) empirical analysis of the nature of price dispersion in the retail grocery market.
18
One might have expected that innovation at the brand level should lead to more growth. To
understand why this is not the case we examine brand turbulence in submarkets in table VI using
the same methodology as for firms in table IV. Thus, we replicate the analysis by allocating
brands to the different size classes, with cut-offs this time being defined on the basis of average
brand size in submarket m at t0. The degree of brand turbulence is very large over bi-monthly
periods. Examining tables IV and VI we observe that the probabilities of a brand staying in its
size class are much lower compared to a role holding its market share within a submarket. This
suggests along with the econometric evidence that brand proliferation and competition does not
expand submarket share, but rather ensures greater stability.
19
Since our data relates to branded retail goods, there is a ‘quality window’ restriction (Sutton
1998) that may explain the decline in firm role inequality for larger submarkets. The lower
degree of firm inequality observed for larger submarkets can result from an escalation of
advertising competition induced by the monetary size of the submarket as described in Sutton
[1991]. Using the size of the market as a proxy for the degree advertising competition that has
evolved between firms within the submarket, this implies the presence of highquality/advertising firms in larger submarkets. The presence of advertising intensive competition
in larger submarkets makes it difficult for a ‘low-quality’ firm to survive. In bigger submarkets
therefore, the top-quality firm necessarily has a number of close rivals, while firms of lowquality do not survive due to the presence of a threshold level of quality required to earn positive
market share. When submarket firm concentration is low, the quality window is at its narrowest.
As C1→0, the top-quality firm necessarily has a large number of close rivals that do not allow
low quality firms to survive. Firm roles are more equal in size. In contrast, in low advertising
intensive environments the absence of a ‘quality window’ restriction allows both ‘high’ and
‘low’ quality firms to survive. Small firms can only survive and grow in peripheral taste niches
within the product market. As a result, this allows for a greater inequality in firm role size to
exist in smaller as compared with larger submarkets.
20.
Due to the flow nature of some or the inclusion of the initial period of other explanatory
variables, we do not expect hidden common factor effects or dynamics to drive the relationship.
21
The relationship between firm inequality and submarket inequality in the product is similar to
the C1 concentration and the h index (defining the share of the largest submarket within a
product) in Sutton (1998). In our case, this relationship is defined over the entire distribution of
firms and submarkets rather than focusing only on the right-hand tail of the distributions. Sutton
(1998) derives a joint restriction on C1, h, and endogenous sunk cost outlays. In the presence of
economies of scope, skewed submarkets can themselves be an outcome of the escalation
mechanism in endogenous sunk costs. We undertake our empirical analysis at a very mature
stage of the industry and hence, submarket structures have not changed over the period analysed.