Forthcoming, AER.
Market Share Dynamics and the ‘Persistence of
Leadership’ Debate
John Sutton
London School of Economics
j.sutton@lse.ac.uk
London School of Economics
Houghton Street
London WC2A 2AE
United Kingdom
Market Share Dynamics and the ‘Persistence of Leadership’ Debate
John Sutton∗
For how long does a typical ‘market leader’ in an industry maintain its position? This
question has attracted continuing attention in the Industrial Organization literature
over the past generation. Two rival views have emerged. The first, associated inter
alia with Alfred Chandler (1990), asserts that leadership tends to persist for a ‘long’
time. The rival view, sometimes labelled ‘Schumpeterian’, emphasises the transience
of leadership positions; an explicit version of this view is spelt out by Franklin Fisher,
John McGowan and Joel Greenwood (1983), in their model of ‘leapfrogging
competition’.
The central problem with this debate is that no benchmark is proposed relative to
which the duration of leadership might be judged ‘long’ or ‘short’. Thus, if it is
observed that the typical market leader stays in place for 20 years this can be
interpreted as ‘long’ by writers in the first group, and as ‘short’ by those in the
second.
This lack of an appropriate benchmark has not gone unnoticed by
contributors to the literature; an unusually full and frank acknowledgement of the
difficulty is set out by Dennis Mueller (1986).1
This paper introduces a formal model of market share dynamics, and uses it to provide
a benchmark case, corresponding to a ‘neutral’ situation in which neither positive
(‘Chandleran’) effects or negative (‘Schumpeterian’) effects are present2.
1
What degree of persistence should we expect on the basis of theory? The duration of
leadership in general will be affected by the width of the initial market share gap
between the leader and its (nearest) rival(s); by the volatility of market shares within
the industry; and by the nature of the process driving successive market share
changes.
Game-theoretic (‘strategic’) models offer little guidance either on the
determinants of volatility (which depends inter alia on firms’ immediate reactions to
rivals’ gains or losses) or on the nature of the process driving successive changes in
share (which depends inter alia on the temporal pattern of firms’ reactions to rivals
over successive periods).
The latter issue turns on the following consideration:
suppose the market share gap between the leader and its (nearest) rival narrows. Will
this tend to be followed by a further narrowing, or by a reversal which restores the
leader’s position? One (‘Chandlerian’) approach emphasises the (‘non-strategic’) role
played by the ‘dynamic capabilities’ of firms. On this view, market leadership is a
correlate (‘signal’) of superior capability, which is a slowly changing attribute. This
suggests a story in which a short-run narrowing of the market share gap between
leader and rival will tend to be followed by a reverse movement as the gap reverts to
the level corresponding to the firms’ relative capabilities. An alternative (‘strategic’)
approach leading to a similar outcome is described in Neil Ericsson and Ariel Pakes
(1995); here the leading firm may find it optimal to cease investing in R&D when its
lead is wide, (‘coasting’), while raising its effort level as its lead narrows, even
though this leads to a greater probability of its being leapfrogged by a rival.
How then can we define a useful benchmark? One way forward is to treat volatility
as an (industry-specific) given, and begin directly from the question: if the gap
2
between the leader and its (nearest) rival narrows, does this induce a
(‘Schumpeterian’) tendency for a further narrowing, or a (‘Chandlerian’) tendency for
a widening? The benchmark case proposed here is that in which neither of these
tendencies is present; instead, market share dynamics follow a simple random walk
(or first-order Markovian process). This model provides a benchmark against which
tendencies in either direction can be measured.
The idea that some kind of Markovian model might offer a useful first approximation
in modelling market dynamics is not new; indeed, within the different but related
‘growth of firms’ literature it has a substantial history, beginning from the seminal
contributions of Ian Little (1962) and Little and Anthony Rayner (1966).3 Yet such
models are often thought of as being unsatisfactory, on the grounds that they do not
treat changes in firms’ shares as an outcome of strategic interactions (maximizing
behaviour) in marketing, R&D, etc. but rather as the outcome of ‘stochastic shocks’.
Here, I defend the usefulness of such models on the following grounds: while
traditional discussions between and among ‘Chandlerians’ and Schumpeterians’
tacitly assume that there is some single mechanism driving (high or low) levels of
persistence, the central message of the game-theoretic literature in this area is that we
should not expect any single mechanism to play a dominant and systematic role in
driving market share dynamics. Many patterns of interaction may emerge between a
leader and its rivals, and these patterns will reflect various factors, some of which
(such as the beliefs of rival firms, for example), are very difficult to measure, proxy or
control for in empirical studies (Harris (1994) and Section IV below). What this
suggests is that, while it might be possible to build a satisfactory ‘structural’ model of
3
market share dynamics for a single industry, or even a group of cognate industries, it
is helpful in looking across the general run of industries to begin by examining the
data against the background of a more modest, low level representation of the kind
proposed here.
In developing a representation of this kind that might serve as a benchmark, we face
two technical difficulties. First, since market shares add to unity, shocks to different
firms’ shares are interdependent. Second, the (distribution of the) size of shocks to
each firm’s share might be expected to depend inter alia on that firm’s current share.
These two considerations imply that an appropriate model might be one in which the
distribution of shocks to each firm’s share would need to be conditioned on the full
vector of market shares in the current period. The analysis that follows rests on two
empirical features of the data that permit us to deal with these two central difficulties
in a relatively straightforward way.
The first key feature of the data is that, for all but four (highly concentrated) industries
among the 45 industries in the data-set, the shocks to the market shares of each
industry’s two leading firms display an extremely low degree of correlation, so that
we may impose, as a reasonable approximation, a model of ‘independent shocks’.
The second key feature of the data is that there is a simple ‘scaling relationship’
between a firm’s market share and the variance (or standard deviation) of its change
in market share. The nature of this scaling relationship is as follows: the variance of
the change ∆m in a firm’s market share m increases in direct proportion to m;
4
equivalently, the standard deviation of the fractional change in m, i.e. ∆m/m, falls
proportionally with 1 / m . We show in what follows that this implies that if we
measure market share by
m , rather than m, then we can treat all observations of
changes in share, measured as ∆ m , for any one industry as being drawn from the
same distribution (i.e. not conditioned on m). In what follows, we rely on the use of
Monte Carlo estimates for each industry in which we take successive draws from the
pool of all observations of ∆ m for the industry in question, avoiding the need to
condition directly on each firm’s current market share, a procedure which would not
be practicable using the ‘small’ data-set involved here.
Taking these two features together, the ‘duration of leadership’, i.e. the time elapsed
until the market leader is overtaken by some rival, can be modelled by reference to the
‘first passage times’ (or ‘crossing times’) in a simple Markovian model. The results
of this exercise are as follows:
i.
The cumulated number of losses of initial leadership among these 45
industries over the 23-year period is less than would be predicted under the
null hypothesis of Markovian behaviour;
ii.
This apparent departure from Markovian behaviour does not appear to reflect a
uniform tendency across all industries in the data-set. Rather, it appears that
there are some industries in which the Markovian model offers a good
representation of the frequency of losses in initial leadership, while for other
industries there appears to be a clear and significant ‘Chandlerian’ bias.
5
iii.
The characteristics of these two groups of industries do not appear to be linked
to any of the usual ‘industry characteristics’ familiar from the I.O. literature,
nor does any single ‘strategic’ mechanism appear to play a dominant role in
driving either the volatility of market shares of the nature of their dynamics.
Rather, a detailed examination of individual industries suggests a more
complex picture, in which a wide variety of strategic and non-strategic factors
are at work. A richer account of market share dynamics would require a move
from the present ‘low level’ representation of cross-industry patterns to a more
structured, industry-specific approach.
In what follows, we begin by describing the two key features of the data on which the
subsequent analysis rests (‘independence’ and the ‘scaling’ effect). We digress in
Section II to present a candidate interpretation of the scaling relationship, by reference
to a simple model, before turning to the empirical evidence on the duration of
leadership in Section III.
I. Two Key Features of the Data
The data-set consists of annual observations of market shares for leading firms in 45
narrowly defined industries in Japanese manufacturing over a 23 year period.
(Appendix B). These data were compiled using the annual volumes published by the
Yano company (Yano Keiza (1995)). This source covers a large number of industries,
but occasional changes in coverage and presentation occur, and it was possible to
construct fairly long and consistent series only for these 45 industries. The starting
6
date for this history is 1974 for the large majority of industries, but it is between 1975
and 1977 in a small number of cases. A series of interviews with selected companies
was used to check issues of interpretation and reliability of the data, and to record the
background facts pertinent to market share dynamics (see Section IV). Data of this
kind would be very difficult to compile for a broad cross-section of industries in other
countries; the availability of the Yano data was a primary reason for focussing on
Japan. The second, equally important, reason for this focus lies in the rarity of
mergers and acquisitions. For U.S. or U.K. data, for example, it would be difficult to
study the distribution of first passage times over an extended time period without
having to confront the confounding influence of M&A events. In the present data-set,
only one merger involving ‘leading’ firms occurs over the period of the study (and
this does not affect the pattern of leadership).
The level of aggregation in this data-set corresponds roughly to the 5-digit SIC
classification for the U.S.
The industries include, for example, motorcycles,
photographic film, beer and cash registers. The number of firms included in each
industry varies from two to five. Excluded firms generally have very small shares.
Their exclusion does not affect the computation of first-passage times, since if one of
these firms grows to become a leading supplier, it is incorporated in the data-set.
There are no instances in which such a ‘newly entered’ firm overtakes the market
leader during the period covered by the data.4
We begin with two key features of the data:
7
i.
Independence of shocks: labelling the top two firms in the initial year as ‘firm
1’ and ‘firm 2’ respectively, we examine the annual change in market share for
firm 1, versus the change for firm 2, in each year. The resulting scatter for the
pooled sample of all industries is shown in Figure 1 (a). The correlation
coefficient is 0.002. To explore this further, the exercise was repeated by
excluding successive groups of industries, using as a criterion the combined
market share of the top two firms in the reference year (panels (b) and (c)).
Only when the critical value of this combined market share was set to exclude
all but four industries did a clear negative correlation appear (panel (d))5.
Excluding these four industries from the analysis which follows has no
material effect on our conclusions. (See Section III).
ii.
The Scaling Relationship: to investigate the relationship between current
market share, mt, and the change in market share, ∆m t = m t +1 − m t , a pooled
sample of all pairs (m t , ∆m t ) was formed, over all firms and all time periods,
and partitioned into thirty equal sized groups (‘bins’) by market share, i.e. all
pairs (m t , ∆m t ) for which m k ≤ m t ≤ m k +1 fall in bin k, and so on. For each
bin, the mean value6 of m t and the standard deviation of ∆m t / m t were
calculated. The resulting scatter is shown on a log-log scale in Figure 2 (a). A
regression of ln σ(∆m t / m t ) against ln m t yields a slope of -0.584 (s.e. =
0.053); see Table 1. Reducing the number of bins leads to a sharper
characterization; for example, with five bins the slope coefficient is -0.521
(s.e. = 0.024). This suggests that the data is well represented by a power-law
8
relationship of the form σ = Am− c where c is (slightly greater) than ½ in
absolute value. This relationship is used directly in framing the empirical tests
that follow.7
II. A Digression: Interpreting the Scaling Relationship
It is natural to ask whether this ‘scaling’ relationship has any intuitive interpretation.
An examination of various standard product differentiation models indicates that the
only type of model that appears to exhibit this feature is a multi-product firm model
that combines a vertical product attribute of the standard kind with a horizontal
attribute of the locational (Hotelling) type.
In particular, this form of scaling
relationship does not arise either in ‘single attribute’ quality models, whether of the
‘vertical product differentiation’ type (Jean Gabszewicz and Jaques Thisse (1980),
Avner Shaked and John Sutton (1982)) or of the ‘stochastic quality jump’ type used
by Ericson and Pakes (1995) in their model of market share dynamics. In order to
provide an interpretation of the scaling relationship, we set out a deliberately simple
model that has this feature. The model is non-strategic, in that market shares are
driven by exogenous shocks to the quality of individual products.8 What drives the
scaling property in this model is that each product receives shocks of the same
absolute size, but the expected number of such shocks occurring in a given time
interval increases in proportion to the number of products owned by a firm, and so
with its size.
It is worth emphasising that the empirical analysis that follows rests
directly on the two empirical features of the data just noted, and does not depend on
the model that follows, which is offered simply as an aid to intuition.
9
The model is an extension of the standard “circular road” model: products are located
evenly around the circumference of a circle of unit diameter. Each (active) firm owns
a subset of these products. For simplicity, we confine attention to the case where no
firm owns two adjacent products; this allows us to obtain a simple characterization of
a Nash equilibrium in prices (it coincides with the price equilibrium for single product
firms).
We associate with each product a quality index u. Consumers are located uniformly
along the circle, the total size of the population of consumers being normalized to
unity. Each consumer buys exactly one unit of one of the goods on offer, the supplier
being chosen to maximize the consumer’s utility,
U(p, u) = u – p –td
where p is the price is the price of the chosen good and t is the (constant) unit cost of
transport along the circle. We set the firms’ production costs to zero for simplicity in
what follows, and the transport cost t equal to unity, and we seek a Nash equilibrium
in prices.
The range of u is restricted in what follows so as to ensure that the ‘marginal
consumers’ defining the left and right hand boundaries of product j’s clientele will lie
between product j and its immediate neighbours. The conditions defining the distance
from firm j to the marginal consumer on its right, which we label d j , is:
10
p j + u j + d j = p j+1 + u j+1+(1 / N − d j )
whence d j = 1 /(2 N) + [(p j+1 - p j ) - (u j+1 - u j )] / 2 and similarly for the firm on its left,
so the quantity sold by firm j becomes
(1)
q j = 1 / N + [(p j+1 + p j−1 − 2p j ) − (u j+1 + u j−1 − 2u j )] / 2
Given the assumption that no firm owns two adjacent goods, and that the quality
index is restricted so as to ensure that the marginal consumer always lies between two
adjacent products, it follows that each firm’s profit function is additively separable
into a number of functions, each corresponding to the profit of a single product. The
reaction function (optimal reply) defining the price set by the firm owning product j is
obtained by calculating the price pj which maximizes the profit earned from product j,
given the prices of its two neighbours and the qualities of the three products, viz9
(2)
p j = 1 / 2 N + (p j+1 + p j−1 )/ 4 − (u j+1 + u j−1 − 2u j )/ 4
Our focus of interest lies in examining the manner in which exogenous shocks to
(relative) quality levels of individual products impinge on the sales of the firm.
It is shown in Appendix A that a unit rise in the quality of product j, given equilibrium
price responses by all firms, leads to a rise in the quantity (sales volume) of product j
which we denote so, and which in the limit N → ∞ takes a value of 1 − 1 / 3 units.
The associated losses in the sales of other products decline geometrically as we move
11
away from product j; for the k-th product to the right or left of product j the change in
sales volume is denoted as sk ; in the limit N → ∞ this takes the value
(
)
k
− 2 − 3 / 3 . To ease notation, we confine attention to the case where the number
of products is even, whence k runs from –n to +n where N = 2n and s − n ≡ s n and we
note that
∑s
k
, taken over 0, ± 1, ± 2,... equals zero. (Appendix A). Given our
normalization of the total size of the population of consumers to unity, the (change in)
quantity sold by a firm equals its (change in) volume market share.10 We confine
attention throughout to the case where the number of products is large and each firm
owns only a small fraction of these products; and given the geometrically declining
size of impact, we approximate by neglecting all shocks beyond a certain radius viz.
the lth product on the left to the lth product on the right. This will allow us to
simplify the analysis that follows by neglecting multiple impacts on a single firm
consequent on a single shock to the quality of some product.
We restrict the range of quality to some interval 0 < u ≤ u ≤ u by setting
u t +1 = u if u t + ∆u > u , and u t +1 = u if u t + ∆u < u. We assume that the shocks to
quality are ‘small’ relative to this interval, so that the probability that u is on the
boundary of the interval in any period is small. Finally, we restrict this interval by
assuming that u − u < 1 / N; it follows from inspection of the reaction function (2)
above that all products then command positive prices at equilibrium, and so positive
sales, as was assumed above.11
We will not be directly concerned in what follows with the long run steady state
properties of the model;12 here, it suffices to remark that firm i’s expected market
12
share, conditional on its having n i out of N products, equals n i / N. We denote this
as µi in what follows.
We consider the impact on the pattern of market shares of a quality shock that affects
a single randomly chosen product.
It is intuitively clear that, in examining the
behaviour of the market share gap m1 − m 2 between the leading firm and its nearest
rival (or the gap µ1 − µ 2 which coincides with the expected value of m1 − m 2 ), that
there are two limiting cases of interest, viz. where µ1 + µ 2 << 1 so that firms 1 and 2
are ‘small’ and where µ1 + µ 2 is close to unity. In the latter case, there is a close
(negative) correlation between changes in the market shares of firm 1 and firm 2. In
the former case, (the ‘independence’ case) this correlation is close to zero and we can
approximate shocks to m1 − m 2 by treating m1 and m 2 as independent. We noted in
the previous section that the correlation between ∆m1 and ∆m 2 is very close to zero
in the present data-set. We focus accordingly on this case, where µ1 + µ 2 << 1. In
analysing the impact of a single shock to the quality of some randomly chosen good,
we represent the probability that the associated quantity shock of order k is received
by firm i as µ i , and ignore all multiple events impacting on firm i, as noted above. It
follows that the expected change in m i can be approximated as:
∑µ s
i k
k
= µi ∑ s k
k
13
where s k is the change in quantity (volume market share) for a product deriving from
a unit shock to the quality of a product at the k-th location to its right or to its left
associated with a shock of order k, and µ i is the share of products owned by firm i,
the sum being taken over k = −l,...,−1,0,1,..., l , and having a value of (approximately)
zero.
Now consider any (discrete) distribution of quality shocks: let f j denote the
probability that a shock of size ∆ j occurs. Then, recalling that the derived quantity
changes are directly proportional to the size of the quality shocks, and that the
expected change in m i is zero, the variance of changes to m i can be represented as
var (∆m i ) = µ i ∑
j
∑ (s ∆ ) f
2
k
j
j
k
Noting that the double sum in this last expression is a constant, independent of mi, the
variance of ∆m i is proportional to µ i , (the probability that a randomly chosen product
is owned by firm i) which we can approximate empirically by m i (the volume market
share of firm i).
It follows that the standard deviation of changes to market shares satisfies
σ(∆m i ) ≅ constant. m1 , whence
⎛ ∆m i
σ ⎜⎜
⎝ mi
14
⎞
constant
⎟⎟ ≅
mi
⎠
It follows that, if we replace our measure of market share m i by
m i , then for small
changes we may write
∆ mi ≅
1
2 mi
∆m i
Whence
(
)
σ ∆ mi ≅
1
σ (∆m i ) = constant.
2 mi
so that we have a measure of volatility that is constant over m i . It is this observation
that justifies the procedure used in Section III below, of pooling observations of
∆ m i for any single industry over all firms and all years.
A special case of interest arises in respect of losses of leadership to some specific rival
(such as the closest rival in the initial period, say). Again treating ∆m1 and ∆m 2 as
independent, we may measure the gap between firm 1 and firm 2 as
m1 − m 2 and
model the evolution of this gap as a random walk. If for example, the distribution of
shocks to
m i is normal with standard deviation σ , then changes to
are normal with standard deviation
σ 2 + σ 2 = 2σ .
‘normalized’ gap
m1 − m 2
2σ ( m i )
15
m1 − m 2
The evolution of the
can be modelled as a random walk, whose increments are drawn from the standard
normal distribution N(0,1).
III. Losses of Leadership
In order to predict the cumulated number of industries in which a loss of initial
leadership would be expected to have occurred by a given time, under the null
hypothesis, we proceed as follows: we generate Monte Carlo estimates for each
industry based on taking draws (with replacement) from all observations of ∆ m for
the industry in question.
(i.e. predicted crossings are estimated for each industry
separately, using the initial value of
m for each firm in that industry, and using
draws of ∆ m for that industry only.13 It is here that the usefulness of the scaling
relationship is evident: since the (standard deviation of the) distribution of ∆ m is
independent of m, we can pool observations for all firms and all time periods for the
industry in question. This provides a sufficiently large pool of observations for the
present purpose.
It also respects the fact that the (standard deviation of the)
distribution of ∆ m varies widely across industries.14
The results of this exercise are shown in Figure 3 (a). The cumulated number of
losses of leadership by the initial leader over the 45 industries in the data-set increases
to 18 by the end of the period, indicating that in the remaining 27 industries the leader
retains its lead over the whole period.
The predicted number, under our null
hypothesis, exceeds this actual number, and the actual number lies just below the 95%
confidence interval by the end of the 23 year period. This exercise is repeated,
beginning from alternative starting points (after five, ten and fifteen years have
16
elapsed, i.e. taking t = 6, 11 and 16 as our start dates). The results are shown in
Figure 3, panels (b), (c) and (d). In all cases the actual number of crossings falls
below the 95% confidence interval by the end of the period.
Since the ‘independence’ assumption is not justified for the seven most highly
concentrated industries (in none of which any crossing occurs), this exercise was
repeated for the 38-industry data-set that excludes these industries. The expected
number of crossings for the seven omitted industries is very small and the results for
the 38 industry data-set differ only slightly from those shown in Figure 3. (For
example, for the full 23 year period shown in panel (a), the expected number of
crossings by year 23 falls from 25.2 to 23.6 when these seven industries are omitted,
while the lower bound of the 95% confidence interval falls from 19.2 to 18.1).
It is of interest to repeat this exercise with reference to a special case, in which we
consider only crossings between the initial leader (firm 1) and its closest rival in the
initial period (firm 2). The reason this case is of interest is that, as we noted in the
preceding section, an implication of the independence property together with the
scaling relationship is that we can model these crossing times under the null
hypothesis by reference to a single random walk representing the value of the gap
between firms 1 and 2, measured as
m1 − m 2 . Here we take the successive draws
(with replacement) from a pooled set of all observations of ∆ ( m1 − m 2 ) for the
industry in question.15 The cumulative number of losses of initial leadership between
firms 1 and 2 over the 45 industries in the data-set are shown in Figure 4, together
17
with the number under the Markovian model. Again, the actual number (14) falls
below the expected number in the latter part of the 23 year period, but it lies within
the 95 percent confidence interval.16
These results, taken together, suggest the tentative conclusion that there may be a bias
in the ‘Chandlerian’ direction relative to Markovian behaviour. Such a bias might in
principle hold in a uniform way across the whole set of 45 industries (in which case
we might consider a modified Markovian model with some form of ‘drift’ to represent
the set of industries as a whole). Alternatively, it might be that this departure was
special to some subgroup of industries in which (varying degrees) of ‘Chandlerian’
bias are present, while for other industries, the Markovian model describes outcomes
well. To explore this, we turn to a second test of the null hypothesis. Under the null,
the firms’ current annual market shares constitute a sufficient statistic for what has
occurred in earlier periods. In particular, the presence or absence of changes in
industry leadership in past periods should not affect future changes in leadership. If,
on the other hand, some industries exhibit a departure from the benchmark model that
makes changes in leadership relatively rare, then the presence or absence of past
changes in leadership may be informative. With this in mind, we split the sample of
45 industries into two groups, according as a change in leadership has or has not
occurred over the first 5 years (i.e. by year 6); and we then repeat the above exercise
taking year 6 as the starting year, reporting results separately for the set of (10)
industries that experienced a change of leadership during periods 1-6, and the
remaining set of (35) industries in which the initial leader retains its leadership up to
period 6.
18
The results are shown in Figure 5, panels (a) and (b), and Table 3. The exercise was
repeated for successive 5-year intervals (i.e. for year 11 and year 16); the results are
shown in the panels (c) to (f) of Figure 5.
In all cases the cumulated number of first passage times for the group that
experienced earlier crossings lies wholly within the 95% confidence interval, whereas
the cumulated number of first passages for the group with no earlier change of
leadership lies in all cases below the 95% confidence interval by the end of the time
period. In interpreting these figures, it may be helpful to note what is expected if one
sub-group of industries conform to the null hypothesis of Markovian behaviour, while
the remaining industries are characterized by some ‘Chandlerian’ bias that makes
losses of leadership relatively rare.
In that setting, conditioning on losses of
leadership over some initial run of years would select a higher proportion of the
‘Markovian’ industries into the first set, and a higher proportion of ‘Chandlerian’
industries into the second. For a short initial test period, we would expect a relatively
high proportion of the industries in the first set to be ‘Markovian’, and for a long
initial test period, we would expect a relatively high proportion of industries in the
second set to be ‘Chandlerian’. This would imply that the Markovian model should
predict well in the first case (panel (a) of Figure 5) and that the number of crossings
observed should be very low in the latter case (panel (f) of Figure 5). An examination
of panels (a) and (f) indicate that the results are consistent with this pattern.
19
It is of interest to ask whether any clear split into ‘Markovian’ and ‘Chandlerian’
groups might be made by reference to observable industry characteristics;
and
whether the ‘Chandlerian’ bias might be traced to the presence of some specific
economic (or ‘strategic’) mechanism. The difficulties involved in doing this are
addressed in the next section. Here, we confine attention to a purely statistical
description of the nature of the departure from the Markovian model. In this sense, a
departure from the null hypothesis of Markovian behaviour can take one of three
forms:
(i)
The successive changes in the gap(s) between the leader and its nearest
rival(s)
(ii)
might exhibit serial correlation.
The distribution of changes in the market share gap between the leader and
its (nearest) rival(s) might be asymmetric about zero.
(iii)
The distribution of changes in the market share gap could fail to be
independent of the current value of the gap.17
In distinguishing between these possibilities, it is useful to consider a scatter plot of
the change in the market share gap between the two leading firms, against the current
value of that gap, for all time periods up to the first loss of leadership if any (Figure
6). Panel (a) refers to those industries where a change of leadership occurs in some
period; Panel (b) shows industries for which no leadership change occurs at any time.
A point below the -45o line corresponds to a change of leadership, so there are by
construction no such points in Panel (b). The absence of points below the -450 line is
consistent with (at least) three different patterns, corresponding to cases (i) – (iii)
above.
First, the presence of strong negative serial correlation can stabilize the
20
market share gap at some initial level; this would make possible, inter alia, a scatter in
panel (b) that had few observations for low values of the current gap. This does not
appear to be the case. A direct check suggests that the level of serial correlation is
low (the simple correlation coefficient between successive changes in the gap between
the industry’s two leading firms, for industries in which no change of leadership
occurs, is -0.097 (Table 4)). The second possible pattern involves an imbalance of
positive over negative values of the change in gap, for all values of the current gap;
this would imply a systematic tendency for the gap to widen over the 23 year period
(‘positive drift’). A third possibility is that the distribution of changes in the gap
varies with the current value of the gap, in the sense that the expected value of the
change in the gap is positive (resp. zero or negative) when the current gap is low
(resp. high). This third possibility appears to be consistent with the scatter shown in
Figure 6 (b): for values of the gap exceeding the median value, the asymmetry
between positive and negative values is small and runs in favour of negative values.18
The opposite is true at low values: when the gap becomes small in these industries,
there is a bias in favour of recovery in the leader’s relative position.19 It would be of
interest to pin down an economic explanation for this pattern; there are difficulties,
however, in doing this in a context of a cross-industry study of the present kind, a
point to which we turn in the next section.
IV. The Limitations of the Analysis
There are at least two candidate stories that might account for a ‘Chandlerian’ bias of
the kind found here (as noted in the introductory section above). It is natural to ask,
21
therefore, whether appealing to a richer structural model featuring appropriate
strategic factors might allow us to uncover the economic mechanism underlying this
bias. The present section strikes a cautionary note, regarding the difficulties inherent
in extending the present analysis in such a direction.
A strategic model would retain exogenous shocks to underlying ‘technology and
tastes’ parameters, but would extend firms’ reactions beyond the price-quantity
adjustments allowed for above, to deal with changes in marketing and/or R&D outlays
aimed at raising (perceived) quality, and with the entry and exit of products. In respect
of these adjustments, a series of case studies of individual industries in the present
sample indicates differences in experience across different industries which seem to
be driven by a wide range of factors. Some patterns of events are readily interpreted
by reference to standard game-theoretic models.20 Others however, appear to be
driven by factors – such as the beliefs of agents - which are very difficult to measure,
proxy or control for in empirical studies.
The effect of exogenous shocks on the pattern of market shares will depend crucially
on the speed and effectiveness of rivals’ responses. In this respect, different industries
display widely differing characteristics. In the cash register industry, for example,
technology
advanced
rapidly
over
the
23-year
period,
as
free-standing
electromagnetic registers were first replaced by electronic types, and as these
electronic types were in turn displaced by store-wide or company-wide computer
linked networks. The market share pattern was extremely volatile, as successive firms
gained a relative technical advantage (Figure 7). A contrasting pattern arises in the
22
margarine industry (Figure 7). Here, the industry was also characterized (perhaps
surprisingly) by a very rapid rate of introduction of new varieties (one manufacturer’s
1990 brochure contained scores of varieties, which differed in form of packaging,
choice of flavouring, hardness and texture, etc.). In spite of the high degree of new
product introductions, market shares remained remarkably stable, as each successful
innovation by any firm was immediately countered with a response by rivals, who
quickly imitated successful products.
The difference in the speed and effectiveness of rivals’ responses in these two
industries might simply reflect industry-specific differences in the ease with which
innovations can be imitated by rivals. It is interesting therefore, to examine events
within a single industry that exhibits different patterns of reactions at different periods
(Figure 7). The Japanese beer industry during the 1970s experienced a series of events
that came to be known in the industry as the ‘packaging wars’. Firms vied with each
other in introducing new forms of packaging (bottles and cans of new sizes; plastic
containers in odd and unusual shapes, and so on). Throughout this period, market
shares remained quite stable. During the 1980s on the other hand, a new product was
marketed by the Asahi company, then the industry’s fourth largest firm, under the
name ‘Asahi Dry’. Despite its initial success, rivals were slow to respond, apparently
because they failed to anticipate the success of the newly launched product, and
‘Asahi Dry’ propelled the Asahi company to second place in the industry. (The
market leader Kirin eventually imitated this strategy by marketing its ‘Kirin Dry’
product, whose sales remained below those of ‘Asahi Dry’ over the next decade). The
question raised by this is: if we constructed a ‘fully specified, strategic model’ of the
23
present set of industries, what variables accessible to the researcher could have
predicted the non-impact of the packaging wars on market shares, as against the
substantial impact of the ‘Dry beers’ marketing campaign? It would seem that the
speed and effectiveness of firms’ responses differed between the two cases because of
different beliefs on the part of the leader as to the probable effectiveness of its rivals’
strategies. What this suggests is that, just as the literature on dynamic oligopoly
implies, the size of the market share response will depend crucially on the beliefs of
agents – a factor that we must perforce treat as an unobservable in most settings.
The traditional ‘persistence of leadership’ debate has been conducted on the premise
that there might be some single key mechanism(s), either of a ‘Schumpeterian’ or
‘Chandlerian’ kind, that operate(s) across the general run of industries. What a study
of various industries in the present sample suggests is that there are many large and
systematic factors at work in driving market share changes, and some of these factors
are very difficult to control for in cross-industry studies. One implication of this is that
uncovering the mechanism(s) underlying the deviation from the Markovian model
reported in the preceding section by reference to a more fully developed ‘strategic’
model applicable at a cross-industry level may be very difficult. A second implication
is that the overall pattern of outcomes in any cross-industry study of market share
dynamics may be quite sensitive to the choice of sample of industries studied. It is in
this (rather cautious) spirit that the finding of an apparent ‘Chandlerian’ bias in the
present set of Japanese industries should be judged.
24
V. Conclusions
This paper makes three points. The first relates to the use of scaling relationships.
The recent literature on this topic has focussed on the description of such
relationships, and on differences in views as to candidate explanations (R. Michael
Stanley et al. (1996), Sutton (2002)). Little attention has been paid to the question of
whether the characterization of such relationships is empirically useful. Here, the
presence of a scaling relationship between a firm’s market share and the variance of
changes in market share permits a useful simplification in the modelling of market
share dynamics. More importantly, this scaling relationship provides a usefully sharp
criterion for model selection in the area of market share dynamics, as it is a feature of
only one of the several standard models in the current economics literature.
The second point relates to the ‘persistence of leadership’ debate. The empirical
evidence for the Japanese industries examined here is such as to suggest a degree of
persistence for at least one group of industries that is in excess of that predicted under
this benchmark model. It would be of interest to see whether a similar pattern holds
good for the general run of manufacturing industries in other countries.
The third point is a cautionary one: the statistical patterns reported here might suggest
the working of a single simple strategic mechanism in driving the pattern of market
share dynamics.
An examination of individual industries suggest, however, a
25
complex picture in which many strategic mechanisms are at work. Unravelling the
roles of these mechanisms in driving market share dynamics is a challenging task. In
this kind of setting, it can be useful to begin by developing a ‘low-level’ statistical
representation of cross-industry regularities of the kind attempted here.
26
Appendix A
Calculating the impact of a quality shock
We may take advantage of the fact that the system of equations (2) in the main text is
linear in the p j and u j to deduce that a unit change in u j will affect equilibrium prices
p j , p j+1 , p j , p j+ 2 , p j- 2 ,... by a constant amount, independently of the initial vector of
qualities. Hence we may ease the notational burden in what follows by taking as a
point of reference the case where all the u j are initially zero, so that all prices are
equal to 1/N. We now consider the impact on equilibrium prices of a unit rise in the
quality of some one good holding all other qualities constant.
We will confine the analysis in what follows to the case where the total number of
products is even (the odd case can be treated similarly). Label the good whose quality
has risen as good 0, its k-th neighbour to the right as good k, and k-th neighbour to the
left as good –k. Denote the total number of products by 2n; we then have that the
index k runs from -n to n, where good n is the same as good –n (Figure A1). We
denote the deviation of the quality-adjusted price (p k − u k ) from its initial level 1/N
by x k , viz x k = ∆ (p k − u k ) . We have from the symmetry of equations (2) that the
equilibrium price deviations satisfy x k = x −k for all k = 1, 2,…, n. It therefore
follows from (2) on writing ∆u 0 = 1, ∆u k = 0 for all k = ± 1, ± 2,... ± n, that the
deviations in quality-adjusted prices x k must satisfy the equations:
(A1)
x0 =
1 1
+ x1
2 2
27
(A2)
xk =
1
1
x k −1 + x k +1 , k = − (n − 1), − (n − 2),..., (n − 2), (n − 1).
4
4
(A3)
xn =
1
1
x n −1 + x −( n −1)
4
4
with the convention that x − n ≡ x n (Figure A1). Note that the x k correspond to price
changes for goods ±1, ±2, …, n ; but for good 0, whose quality has risen by 1 unit, the
change in price equals 1 − x 0 .
0
-1
1
-2
2
n-2
-(n-2)
-(n-1)
n-1
n(≡ −n)
Figure A1: Labelling the Products
Now from symmetry, x n −1 = x −( n −1) so (A3) implies that
28
(A4)
xn =
1
x n −1
2
while (A2) implies
(A5)
4 x n −1 = x n + x n − 2
Using (A4) to substitute for x n in (A5) and solving we have
(A6)
x n −1 =
1
1
4−
2
x n -2
We may now proceed iteratively to solve for the xk for any value of n. In the limit
n → ∞ , the solution can be expressed in terms of a repeated fraction, viz.
x n −i =
1
1
4−
4 − ...
x n −i−1 = (2 − 3) x n −i−1
Setting i = n - 1 in we have
(A7)
(
)
x1 = 2 − 3 x 0
Combining this with (A1) we obtain:
x0 = −
1
3
, x1 = −
2− 3
3
29
(2 − 3 )
k
, ... , x k = −
3
,...
We may interpret this intuitively as follows. Recall that x 0 = ∆(p 0 − u 0 ) = ∆p 0 − 1.
As the quality of product zero rises by 1 unit, its price rises by 1 −
quality-adjusted price falls by
1
3
1
3
units, so that its
units. There is a fall in the prices of all other
products, the size of this change falling off geometrically as we move away from good
zero.
To find the changes in quantities, we note that it follows from inspection of the
demand function (equation (1) of the main text) that
∆q 0 = ∆p1 − ∆(p 0 − u 0 ) = x 1 − x 0
∆q −1 = ∆q1 =
1
[∆(p 0 − u 0 ) + ∆p 2 − 2∆p1 ] = 1 [x 0 + x 2 − 2x1 ]
2
2
∆q −k = ∆q k =
1
[∆p k −1 + ∆p k +1 − 2∆p k ] = 1 [x k +1 + x k −1 − 2x k ]
2
2
whence we obtain, on substituting for x k −1 , x k and x k +1 that the volume market share
shocks s0 and sk introduced in Section II are given by
s 0 ≡ ∆q o = −
2− 3
1
1
+
= 1−
3
3
3
30
s k = s − k ≡ ∆q − k = ∆q k = −
(
and
∑
)
1
2 − 3 k,
3
s k = 0.
k =0±1,...
31
k ≥1
Appendix B
Industries in the Data-set
The 45 industries in the basic data-set are as follows: Sugar, Frozen Food, Regular
Coffee, Instant Coffee, Chocolate, Chewing Gum, Cola, Beer, Women’s Clothing,
Adhesives, Bath Soap, Toothpaste, Car Tyres/Tubes, Elevators, Escalators, Tin Cans,
Gas Stoves, Oil Stoves, Air Conditioners (Window), Air Conditioners (Package),
Cash Registers, English Typewriters, Pocket Calculators, Photocopiers, Refrigerators,
Washing Machines, Vacuum Cleaners, Colour TVs, Cars, Buses, Trucks,
Motorcycles, Optical Measuring Equipment, Analytical Equipment, Length and
Precision Measuring Equipment, Electric Meters, Gas Meters, Water Meters, 35mm
Cameras, Spare Lenses for Cameras, Black and White Film, Colour Film, Pencils,
Fountain Pens, Ball Point Pens.
An extended data-set incorporates nine additional industries for which non-trivial
gaps occur in some of the market share series; these are: Margarine, Baby Clothing,
Wood Furniture, Newsprint, Cement, Cast Iron Pipe, (Conventional) Lathes,
Numerically Controlled Machine Tools, Batteries.
32
Appendix C
Robustness
The Monte Carlo predictions assume that the mean (i.e. expected) change in market
share is zero. If this is not so, and if there is a decreasing (resp. increasing) relation
between the expected change in share, and the share, then incorporating this effect
will lead to a rise (resp. fall) in the expected number of crossings.
The best representation of the relation between the mean change, and the share, is in
the form of a linear spline; the results for 30 bins are:
E (∆ m )
=
0.0780
-
(s.e. = 0.1129)
=
-0.0352
(s.e. = 0.0107)
0.0054m
m< 21.8
(s.e. = 0.0051)
-
0.00022m
m ≥ 21.8
(s.e. = 0.00073)
(Here, units are percentage points, so m lies between 0 and 100, while
m lies
between 0 and 10.
When the Monte Carlo estimates are modified to incorporate this correction, the
predicted number of crossings over the full period, as reported in the final line of
Table 2, becomes 28.3, with a 95% confidence interval of 22.5 – 32.7.
33
References
Chandler, Alfred D. Jr. (1990), Scale and Scope: The Dynamics of Industrial
Capitalism, Cambridge, Mass.: Harvard University Press.
Ericson, Richard and Ariel Pakes, 1995, “Markov-Perfect Industry Dynamics: A
framework for Empirical Work; Review of Economic Studies, vol. 62, pp. 5382.
Feller, William (1967), An Introduction to Probability Theory and its Applications,
Vol. 1, (3rd ed.), New York, Wiley
Fisher, Franklin M., John J. McGowan and Joel E. Greenwood, (1983), Folded,
Spindled and Mutilated: Economic Analysis and U.S. v. IBM, Cambridge,
Mass.: MIT Press.
Gabszewicz, Jean Jaskold and Jaques Thisse (1980), ‘Entry (and Exit) in a
Differentiated Industry’, Journal of Economic Theory, vol. 22, pp. 327-338.
Harris, Christopher (1994), ‘Dynamic Models of Competition’, Review of Economic
Studies Lecture, 1995, unpublished working paper, Nuffield College, Oxford.
34
Little, Ian, (1962) ‘Higgledy Piggledy Growth’, Bulletin of the Oxford Institute of
Statistics, vol. 24.
Little, Ian M. D. and Anthony C. Rayner, (1966) Higgledy Piggledy Growth Again:
An Investigation of the Predictability of Company earnings and Dividends in
the U.K. 1951-1961, Cambridge, M.A.: Harvard University Press.
Mueller, Dennis (1986), Profits in the Long Run, Cambridge, Cambridge University
Press.
Shaked, Avner and John Sutton (1982), ‘Relaxing Price Competition through Product
Differentiation’, Review of Economic Studies, vol. 49, 91, pp. 3-13.
Stanley, R. Michael, L. A. N. Amaral, S. V. Buldyrev, S. Harlin, H. Leschorn, P.
Maas, M. A. Salinger, H. E. Stanley (1996), ‘Scaling Relationships in the
Growth of Companies’, Nature, vol. 319, pp. 804-806.
Sutton, John (1991), Sunk Costs and Market Structure, Cambridge, MIT Press.
Sutton, John (1998), Technology and Market Structure, Cambridge, MIT Press.
Sutton, John (2002), ‘The Variance of Firm Growth Rates: The Scaling Puzzle’,
Physica A , vol. 313, pp. 577-590.
35
Yano Keiza: Kenkyusho Co. Ltd. (1995), Nippon Market Share Jiten 1995 (Nippon
Market Share Dictionary 1995), Tokyo, Yano Institute of Economic Studies.
36
No. of bins
Dependent variable: l n σ(∆MSt ) / MSt
Constant
l n MS
R2
30
-0.295
(s.e. = 0.149)
-0.584
(s.e. = 0.053)
0.811
5
-0.452
(s.e. = 0.069)
-0.521
(s.e. = 0.024)
0.993
Table 1. The Scaling Relationship
37
Years Elapsed
Number of
Crossings
Predicted Number
95% Confidence
Interval
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
3
3
6
9
10
13
13
14
15
15
15
15
16
16
17
17
17
17
17
18
18
18
3.6
6.3
8.5
10.4
12.1
13.6
14.9
16.0
17.1
18.0
18.9
19.7
20.5
21.1
21.8
22.4
22.9
23.4
23.9
24.4
24.8
25.2
0.1 - 6.6
2 -9.9
3.6 - 12.7
5.3 - 14.8
6.8 - 16.7
8.1 - 18.3
9.3 - 19.6
10.3 - 20.8
11.3 - 21.9
12.2 - 22.9
13.1 - 23.9
13.8 - 24.7
14.5 - 25.4
15.2 - 26.0
15.8 - 26.7
16.3 - 27.3
16.9 - 27.8
17.4 - 28.3
17.9 - 28.8
18.3 - 29.1
18.8 - 29.6
19.2 - 29.9
Table 2
Actual and Predicted Numbers of Cumulated Losses of Initial
Leadership Over the 45 Industries by ‘years elapsed’ from Year 1.
(These results are illustrated in Figure 3(a)).
38
Industries with Leadership Change
Industries with no Leadership Change
between years 1 and 6
between years 1 and 6
All Industries
Years
Actual
Expected
95%
Actual
Expected
95%
Actual
Expected
95%
Elapsed
Number
Number
Confidence
Number
Number
Confidence
Number
Number
Confidence
1
1
2.3
Interval
0 - 4.4
3
2.2
Interval
0 - 4.7
4
4.5
0.7-7.9
2
2
3.6
0.4 - 5.9
3
4.1
0.4 - 7.1
5
7.7
3.1-11.8
3
4
4.6
1.2 - 6.9
4
5.7
1.6 - 9.2
8
10.3
5.2-14.7
4
5
5.3
2.0 - 7.7
5
7.1
2.8 - 10.8
10
12.4
7.0-16.9
5
6
5.8
2.3 - 8.0
5
8.3
3.7 - 12.1
11
14.1
8.5-18.8
6
6
6.2
2.8 - 8.5
5
9.3
4.6 - 13.1
11
15.6
10.0-20.3
7
6
6.6
3.2 - 8.8
5
10.3
5.3 - 14.1
11
16.9
11.1-21.6
8
6
6.9
3.4 - 8.9
6
11.1
6.2 - 15.0
12
18.0
12.2-22.6
9
6
7.1
3.8 - 9.0
6
11.8
6.9 - 15.8
12
18.9
13.1-23.6
10
6
7.3
4.1 - 9.3
7
12.5
7.5 - 16.5
13
19.8
14.0-24.5
11
6
7.5
4.2 - 9.5
7
13.1
8.1 - 17.0
13
20.6
14.8-25.2
12
7
7.7
4.4 - 9.6
7
13.6
8.5 - 17.6
14
21.3
15.4-25.9
13
7
7.8
4.5 - 9.6
7
14.1
9.1 - 18.1
14
21.9
16.1-26.5
14
7
7.9
4.7 - 9.7
7
14.6
9.5 - 18.7
14
22.5
16.7-27.0
15
7
8.0
4.9 - 9.7
8
15.0
10.0 - 19.0
15
23.0
17.3-27.5
16
7
8.1
5.1 - 9.8
8
15.4
10.4 - 19.5
15
23.5
17.8-28.0
17
7
8.2
5.1 - 9.8
8
15.8
10.7 - 19.8
15
24.0
18.3-28.4
Table 3.
Interval
Actual and Predicted Numbers of Cumulated Losses of Initial Leadership
over the 45-industries by ‘years elapsed from year 6’. These results are
illustrated in Figures 5(a) and (b), and in Figure 3(b).
39
Industry Group
Correlation Coefficient
All industries
Industries with Change of Leader
Industries without Change of Leader
Table 4
-0.078
-0.065
-0.097
No. of
Observations
945
378
567
Patterns of Serial Correlation between ∆m1 ( t ) - ∆m 2 ( t ) and
∆m1 ( t + 1) - ∆m 2 (t + 2) where firms 1 and 2 are the leading firms at
time t.
40
(b)
(a)
∆m1
20
∆m1
20
15
15
10
10
5
5
∆m2
0
-30
-20
-10
0
10
20
30
-20
-10
0
10
20
30
-5
-10
-10
-15
-15
-20
-20
(d)
(c)
∆m1
20
∆m1
20
∆m2
0
-30
-5
15
15
10
10
5
5
∆m2
0
-30
-20
-10
0
10
20
Figure 1
∆m2
0
-30
30
-20
-10
0
10
20
30
-5
-5
-10
-10
-15
-15
-20
-20
The annual change in percentage market share for the top ranking firm
(horizontal axis) versus the change for the second ranking firm (vertical axis).
The two firms are those ranked 1 and 2 in year 1 of the data-set). Panel (a)
shows the data for all 45 industries, while panels (b), (c) and (d) show data for
those industries in which the combined market share of the top 2 firms in year
1 exceeded 50%, 80% and 90% respectively.
41
lnσ(∆m/m)
0
-0.5
-1
-1.5
-2
-2.5
_
-3
lnm
-3.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
(a)
lnσ(∆m/m)
-1
-1.5
-2
-2.5
_
lnm
-3
1
1.5
2
2.5
3
3.5
4
4.5
5
(b)
Figure 2
The scaling relationship between current market share (horizontal axis) and
the standard deviation of proportional changes in share, on a log-log scale.
Panel (a) shows results for 30 bins , while panel (b) shows results for 5 bins.
42
Five Firms - All industries from t = 1
All industries from t = 6
35
30
30
25
frequency
frequency
25
20
15
10
20
15
10
5
5
0
0
1
3
5
7
9
11
13
15
17
19
21
1
2
3
4
5
6
7
8
t
10 11 12 13 14 15 16 17
t
(a)
(b)
All industries from t =16
All industries from t =11
30
25
25
20
20
frequency
frequency
9
15
10
15
10
5
5
0
0
1
2
3
4
5
6
7
8
9
10
11 12
1
2
3
t
5
6
7
t
(c)
Figure 3
4
(d)
Panel (a) shows the cumulated number of crossings (i.e. losses of initial
leadership over 45 industries by the leader in year 1, by the number of years
elapsed. Panels (b), (c) and (d) repeat this exercise, beginning from years 6,
11 and 16 respectively. The leader is defined as the largest firm in the chosen
‘initial year’. (Heavy line). The expected number of crossings, and the 95
percent confidence interval for the benchmark model, are also shown.
43
All Indus trie s from t=1
24
22
20
Cumulative Frequency
18
16
14
12
10
8
6
4
2
0
0
5
10
15
20
25
t12
Figure 4
The cumulated number of instances by year, over 45 industries, in which the
initial leader is overtaken by its closest rival in year 1 (heavy line). The
expected number of crossings and the 95 percent confidence interval are also
shown.
44
Group 1 (Industrie s with a crossing by t =6)
Group 2 (Industries with no crossing by t =6)
12
25
20
8
frequency
frequency
10
6
4
15
10
5
2
0
0
1 2
3 4
5 6
7 8
1
9 10 11 12 13 14 15 16 17
2
3
4
5
6
7
8
9
(a)
(b)
Group 2 (Industries with no crossing by t =11)
16
14
14
12
12
10
10
frequency
frequency
Group 1 (Industries with a crossing by t =11)
8
6
4
8
6
4
2
2
0
0
1
2
3
4
5
6
7
8
9
10
11
12
-2
1
2
3
4
5
6
7
(c)
12
10
frequency
8
6
4
2
0
3
4
5
6
7
t
11
12
10
9
8
7
6
5
4
3
2
1
0
-1
1
2
3
4
5
6
7
t
(e)
Figure 5
10
Group 2 (Industries with no crossing by t=16)
Group 1 (Industrie s with a crossing by t =16)
2
9
(d)
14
1
8
t
t
frequency
10 11 12 13 14 15 16 17
t
t
(f)
Panels (a) and (b) show the cumulated number of losses of leadership by the
leader in year 6, over the subsequent period, for the subsets of industries in
which a change of leadership has already occurred by period 6, (panel (a)),
and for the subset in which no earlier change has occurred (panel (b)). Thus
panels (a) and (b) provide a breakdown of the results for the set of all
industries shown in panel (b) of Figure 3. Panels (c) and (d) show the same
breakdown for a start date of year 11, while panels (e) and (f) correspond to a
start date of year 16.
45
(a)
30
∆gap
20
10
gap
0
0
10
20
30
40
50
60
70
80
90
100
-10
-20
-30
-40
(b)
30
∆gap
20
10
gap
0
0
10
20
30
40
50
60
70
80
90
100
-10
-20
-30
-40
Figure 6
A scatter of observations of the market share gap between the leading
firm and its nearest rival at time t (horizontal axis) and the change in
the market share gap between these two firms between t and t + 1.
Panel (a) pools observations for those (18) industries in which a loss of
initial leadership occurs in some year, for all years up to that year.
Panel (b) pools observations for those (27) industries in which no loss
of initial leadership occurs. The +450 and -450 lines are also shown.
46
Figure 7
Firms’ Market Shares by year for selected industries: Cash Registers,
Margarine, Beer.
47
Footnotes
∗
London School of Economics, Houghton Street, London WC2A 2AE, U.K. The
financial support of the Economic and Social Research Council is acknowledged. I
would like to thank Ciara Whelan and Chris Sutton for research assistance, and
Yoshiro Tamai, Daisuke Tsuruta and Kuniyoshi Saito for helping with data collection.
The comments of Tom Hubbard, my discussant at the 2002 Japan Project Meeting in
Tokyo sponsored by NBER, CEPR, CIRJE and EIJS were particularly helpful.
1
Mueller’s study relates to profit rates, while the present paper relates to market
shares; but the present point applies equally to both measures.
2
It may be of interest in this context to note the cautionary remarks by William Feller
(1957) regarding intuitive ideas as to the duration of leadership in the coin-tossing
game (simple random walk): “According to widespread beliefs a so-called law of
averages should ensure that in a long coin-tossing game each player will be on the
winning side for about half the time, and that the lead will pass not infrequently from
one player to the other …… contrary to popular notions, it is quite likely that in a long
coin-tossing game one of the players remains practically the whole time on the
winning side, the other on the losing side”. An exact analogy applies in the present
context: sustained periods of market leadership are consistent with an absence of any
bias relative to our Markovian benchmark, and do not necessarily reflect any
48
‘economic’ or ‘strategic’ mechanism at work; hence the need for a benchmark against
which to gauge the degree of persistence.
3
The tests used in the ‘growth-of-firms’ literature have been based on treating each
firm’s sales as an (independent) stochastic process, and examining correlations
between growth rates over successive periods. What is novel in the present paper,
relative to the standard approach, is the direct examination of the statistics of ‘first
passage times’, which leads to a more powerful and direct test of the relevant
hypothesis.
A more fundamental problem with using this standard approach in the present context
relates to the counterhypothesis against which the null is tested, viz. that the sales of
each firm form independent higher order Markov processes.
The economically
interesting counterhypotheses in the present ‘persistence of leadership’ context are
ones in which changes in the sales, or shares, of the firms depend inter alia on the
current difference in shares between the leader and its (nearest) rival(s).
4
The dataset contains missing values for some of the smaller firms in some years.
There are three instances affecting leading firms in which the Yano tables do not
report figures, or report figures based on a modified market definition, in which
supplementary information from company interviews was used to confirm
interpolated values. In all other cases affected by missing values, the industry in
question was deleted from the basic (45-industry) data set on which the following
analysis rests (Appendix B). An extended data-set that includes an additional nine
49
industries, in which there are some non-trivial problems with missing data, was also
constructed (Appendix B). An examination of results for the extended data-set does
not materially alter our conclusions.
5
For industries where the initial combined market share C2 exceeds 0.50 the simple
correlation coefficient is 0.060 (panel (b)); when C2 > 0.80 then r = 0.089 (panel (c)),
and when C2 > 0.90 then r = -0.889 (panel (d)).
It might seem surprising prima facie that the lack of correlation holds even in
moderately concentrated industries. If all firms experienced independent shocks to
their sales, then ∆m1 and ∆m 2 would be negatively correlated. The fact that the
correlation remains low even for moderately high values of m1 + m 2 suggests that the
(two) leading firms in these industries experience some common shocks to their sales
that do not affect lower-ranked firms.
6
The mean value is close to zero for all bins, but there is a (weak) tendency for the
mean change to be positive (resp. negative) for small (resp. large) values of market
share (“regression toward the mean”). We note the effect of allowing for this in
footnote 15.
50
7
To investigate the distribution of the size of shocks to market share we may appeal
to the scaling relationship to motivate an examination of the distribution of ∆ m t
which should be independent of mt (see Section II below). This indicates that the
distribution for the pooled sample of all industries, is well represented by a tdistribution with a coefficient of slightly over 1. The standard deviation
∆ mt
varies widely across industries, and a good characterization of the shape of the
distribution appropriate to a single industry cannot be attempted here, given the small
number of observations available for each industry.
8
Once strategic effects are introduced into the model, these will operate to place a
lower bound on the level of concentration that is sustainable as an industry
equilibrium (for example, Sutton (1991, 1998). This comes about as follows: suppose
we allow firms to choose the quality of their products optimally, subject to some fixed
cost schedule (which may or may not incorporate scope economies (Sutton 1998),
Chapter 4). Then, if the number of firms becomes sufficiently large, so that the
maximum market share falls below some critical level, it be optimal for one firm to
deviate by raising the quality of (at least one of) its products, so as to capture a greater
market share.
The idea behind the present model is that the number of firms that are active in the
market has been arrived at by some earlier (unmodelled) process of entry, and that this
number is not so large as to violate the ‘lower bound to concentration’. The focus of
51
interest here lies in asking, how do market shares fluctuate within the region permitted
by these bounds?
9
In the special case where all the u’s are equal, the set of equations defined by (2)
collapse to those of the standard circular road model: there is a symmetric Nash
equilibrium in prices, in which all firms set the same price p = 1/N.
10
We work for convenience in terms of volume market shares. The results for market
shares by value are similar, subject to an approximation.
11
An alternative formulation which leaves the results in the text unchanged, is to
assume that when the market share of any product falls to u it is deleted and replaced
by a new product of (initial) quality u, owned by any (non-neighbour) firm.
12
These will depend on the assumption made regarding product entry and exit
(footnote 10).
13
The scaling relationship is used to justify the pooling of these draws within each
industry. Ideally, the scaling relationship itself would be estimated for each industry
separately, but the number of observations required to pin down its slope far exceeds
the number available for any one industry. The present method relies on the argument
that the slope of the scaling relationship shown in Figure 2 is constant across
industries, though its level will vary, i.e. some industries have a higher (or lower)
level of σ(∆m / m) for any given m, than others. To check this, each industry was
assigned a volatility measure, equal to the mean absolute value of ∆ m ; and
52
industries were then divided into two groups (‘high’ and ‘low’ volatility) accordingly.
The scaling relationship was estimated separately for each group; the estimated slope
does not differ (at the 5% level) between the two groups. (For example, with five
bins, the slopes are -.546 (s.e. = .030) and -.591 (s.e. = .069) for high and low
volatility industries respectively).
14
An alternative (parametric) approach would involve fitting some standard
distribution to the observations of ∆ m t for each industry, and then taking random
draws from this fitted distribution. The number of observations for a single industry,
however, is too few to allow a good characterization of the fitted distribution,
especially at the tails. It is for this reason that the method described in the text has
been chosen, instead of a more parametric approach.
15
An additional advantage of this approach is that it does not rely on the first of the
two key features of the data on which we rely elsewhere, viz. the independence of
changes to m1 and m2.
Thus the breakdown of independence for the most
concentrated industries, noted above, is unproblematic here.
16
These Monte Carlo predictions are derived on the basis of an assumption that the
mean (i.e. expected) change in market share is zero for all values of market share. If
we modify the estimates by incorporating the (small) effect observed in the mean
changes, as described in footnote 6, then the predicted number of crossings after 22
years rises from 25.2 to 28.3, thus strengthening the above conclusion (Appendix C).
53
17
Cases (i) and (iii) are related, as follows: if the conditional expectation of the change
in the gap is decreasing in the current gap, then a process driven by successive
independent draws will show negative serial correlation, since a negative (resp.
positive) draw leads to a fall (resp. rise) in next period’s gap, and so to a rise (resp.
fall) in the expected value of the next change.
18
For values of the gap exceeding the median value, the change in the gap is positive
in 134 cases with a mean absolute value of 2.67, while it is negative in 163 cases, with
a mean absolute value of 3.28. For small values of the gap, the relevant asymmetry
can be gauged by comparing the number of observations below the -450 line (0 by
construction) with the number above the +450 line (10).
19
It is of some interest, in the light of this, to note that out of the 18 cases where a loss
of leadership occurs, seven lead to a takeover of leadership by the rival who then
retains leadership to the end of the data period; in eight cases the loss of leadership is
followed by a recovery that re-establishes the original leader up to the end of the data
period; while in the remaining three cases neither of these scenarios hold.
20
Among the ‘strategic mechanisms’ occurring in some of the industries, for
example, is one in which a challenge to the initial leader is followed by a rise in the
market shares of both leader and challenger, while other firms lose share. This pattern
emerges both in pocket calculators and photocopiers; for a strategic model with this
feature, see Sutton (1991), Chapters 3 and 5.
54