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8/9/2019 Structure Scale and Scope in the Global Compute
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Structure, Scale, and Scope in the Global Computer Industry*
Matthew S. Bothner
University of Chicago, Graduate School of Business
Word count (including tables): 11,578
* For valuable comments, I thank Eric Anderson, Peter Bearman, Frank Dobbin, Stanislav Dobrev, Damon Phillips, Paul Ingram, Olav
Sorenson, Toby Stuart, and Harrison White. An earlier version of this paper received the Louis R. Pondy Award from the OMT
Division of the Academy of Management and the Newman Award from the Academy of Management for the best paper based on adissertation. Direct correspondence to Matthew Bothner, University of Chicago, Graduate School of Business, 1101 E. 58th Street,
Chicago, IL 60637, [email protected] 773-834-5953
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Structure, Scale, and Scope in the Global Computer Industry
Abstract: This article examines the effects of relative size and horizontal scope on rates of
firm growth. The contributions are twofold. The first is a fuller conception of the link
between size and future growth. Although a number of prior studies have sought to pinpoint
the effect of firm size, such efforts have been focused almost exclusively on absolute size,
thereby neglecting the ways in which a firm’s scale advantages with respect to its competitors
may independently determine its performance. This study extends current work in network
analysis, strategy, and organizational ecology by developing a localized measure of relative
size and showing that, over much of its distribution, relative size has a strong positive effect
on future growth, net of absolute size. The second contribution concerns the contingent
effects of the width of a firm’s horizontal position. Consistent with earlier ecological research
on specialist and generalist strategies, the results also show that although relatively large
firms grow by broadening in scope, their relatively smaller counterparts experience higher
growth when they narrow their focus on a particular section of the market. Consequently,
relative size affects firm growth directly as well as indirectly by shaping the effect of
horizontal scope.
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1. Introduction
Scholars in a variety of disciplines have long sought to clarify the determinants of the
growth rates of firms. Within this stream of research, much effort has been focused on identifying
the effects of absolute size, an emphasis that drew initial inspiration from Gibrat’s (1931) “law of
proportional effect.” Using the fact that size distributions in most industries are log-normal,
Gibrat posited that growth in absolute terms—of revenue, assets, or employees—was a function
of prior size multiplied by random error (see Sutton 1997 and Carroll and Hannan 2000:315–319
for reviews). Even if all firms were of equal size at an industry’s inception, small random
differences in growth could yield a highly skewed distribution in due time. Correspondingly, a
main mechanism thought to underlie Gibrat’s law is luck (Scherer 1970:125–130), in that some
firms enjoy better fortune than others and so end up larger over the long run.
Although this focus on absolute size and stochastic growth is elegantly simple, empirical
efforts to test its implications have brought forth mixed results, suggesting that new conceptions
of the size-growth link may be necessary for making theoretical progress. Very few studies,
except for Hart and Prais (1956), have confirmed Gibrat’s law by showing that absolute growth
results from prior size and random error, or equivalently, that proportional growth is independent
of size. Conversely, several studies have documented that smaller firms grow at a faster rate than
their larger counterparts (e.g., Mansfield 1962; Kumar 1985; Evans 1987; Barron, West, and
Hannan 1994; Dunne and Hughes 1994). Still others have shown the opposite, reporting that
larger firms grow at a faster rate (Samuels 1965; Singh and Whittington 1975; Prais 1976).
Consistent with these disparities in results, in a review of work arising in the wake of Gibrat’s
ideas, Sutton (1997) called attention to the absence of clear guidance for theorizing a general
relation between a firm’s absolute size and its rate of future growth.
Consequently, in light of the inability of prior research to yield consistent results, a
valuable approach to the size-growth link may be to characterize size differently. Specifically, it
may be useful to measure size in relative terms (Hannan et al. 1998; Carroll and Dobrev 2003),
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where an important predictor of growth is a chosen firm’s scale in relation to others occupying
similar positions in the market. In this way, the manner in which one firm’s performance hinges
on the scale (and corresponding advantages) of others near its position is accounted for,
potentially yielding a more realistic portrayal of growth processes. Using data on the growth rates
of computer firms, this article advances this approach. The main result of the analysis is that, over
much of its observed distribution, relative size has a strong positive effect on growth, holding
absolute size constant. Stated differently, as a chosen firm’s size relative to that of its
strategically closest rivals increases, that firm’s expected rate of future growth rises.
Using a localized measure of relative size, in which a firm’s size is placed over a weighed
average size of strategically similar competitors, extends current work on scale-based competition
in organizational ecology by combining it with earlier work in structural sociology and strategy.
Social network analysts have often construed structurally equivalent relations (Lorrain and White
1971; Burt 1976) as the social architecture out of which competition arises. Structurally
equivalent actors are seen as competitors by each other and by those with whom they interact.
Just as persons similarly tied to third parties view each other as rivals (Galaskiweicz and Burt
1991; Strang and Tuma 1993), or as economic sectors with analogous profiles of procurement
and sales compete with each other (Burt and Carlton 1989; Burt 1992), firms in the same industry
also compete in varying degrees as a function of how much they target the same classes of
buyers.
Contributors to the strategy literature have conceived of intraindustry competition in
similar ways. Social network imagery and methods have been used increasingly in this tradition
(see, e.g., Gulati, Nohria, and Zaheer 2000), and researchers have moved from industrywide to
firm-centered conceptions of rivalry. Within this line of work, theoretical perspectives inherent
in both resource based views of the firm (Penrose 1959; Wernerfelt 1984) and theories of
multipoint competition (Karnani and Wernerfelt 1985; Barnett 1993) have been extended to better
clarify the competitive pressure facing a focal firm. For instance, according to Chen’s (1996)
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model, a focal firm competes most intensely with firms endowed with similar resources and with
which market overlap is pronounced. Where the approaches of sociology and strategy converge
is on the central claims that incumbents of the same industry compete locally on the basis of
overlapping positions or attributes, and that the factors that pit firms together as rivals ought to be
harnessed in metrics of firms’ competitive positions.
Complementing the first aim of this paper, which is to extend prior research by clarifying
the effect of relative size on growth, a related second aim is to better understand how relative size
modifies the effects of intraindustry scope. Various scholars have long viewed horizontal scope
within a line of business as a central choice variable with significant performance-related
consequences (e.g., Abell 1980). Sparse attention has been given to the effects of competitive
scope (Porter 1980) or niche width (Freeman and Hannan 1983) on firm growth, however.
Choices about the allocation of outputs across market segments are likely to matter, but whether
or not moving toward a specialist or generalist strategy (Carroll 1984; 1985) yields higher rates of
growth remains an important question for theoretical and empirical researchers.
Earlier research suggests that a contingent view of horizontal scope may be well suited to
the task of modeling its effects on growth. Consequently, this paper develops the hypothesis that
relatively small firms grow by specializing (and thus matching the particular preferences of a
narrow set of consumers), whereas their larger counterparts grow by widening their reach across
market segments. The results of several within-firm models of firm sales growth support this
second hypothesis, as well as the first, baseline hypothesis that the main effect of relative size on
growth is positive.
To situate these hypotheses in the context of earlier research, section 2 reviews prior
empirical work on firm growth. After the main hypotheses are developed in section 3, section 4
describes the data and measures, and section 5 discusses a number of control variables. The
results appear in section 6, and section 7 discusses implications of the results for future research.
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2. Prior Empirical Research on Firm Growth
Empirical studies of firm growth span the literatures of industrial organization, strategy,
and organizational sociology. With few exceptions, these studies have proceeded in isolation,
along separate disciplinary pathways. Shared themes surface nonetheless, and may be viewed as
residing in one of three categories that reflect the kinds of findings reported. Specifically, some
studies (a) offer insights on the effects of firm-specific characteristics; (b) others document the
effects of industrywide environmental conditions; (c) still others offer insights on the effects of
time-varying conditions specific to a chosen firm’s position in the market, often using
information on the lagged conduct or performance of strategically similar firms to better clarify
the effects of localized industry structures.
With the exception of absolute size, whose effects were reviewed previously, firm age
has arguably attracted the most substantial attention among firm-specific covariates thought to
shape growth. Using data on manufacturing firms, Evans (1987), for example, found that growth
rates declined with age, an effect subsequently identified by other scholars among credit unions
(Barron 1999) and banks (Barnett and Sorenson 2002). Adjusting for absolute size, growth rates
typically fall with age, a pattern that researchers have often ascribed to processes by which a
firm’s routines either rigidify with age or fall increasingly out of step with the demands of its
competitive environment (Carroll and Hannan 2000:288–291).
Characteristics of founding team members, as well as shifts in strategic activities, have
also figured centrally among organization-specific predictors of firm growth. Eisenhardt and
Schoonhoven (1990), for instance, documented that semiconductor firms with large founding
teams (and thus greater chances for specialized decision-making) grew faster than their
counterparts. Studying the consequences of strategic shifts, Miller and Chen (1994) found that
the growth of airlines was positively related to inertia in strategic activities, especially when the
number of rivals faced and airports served were low. Using data on savings and loan
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organizations, Haveman (1992) reported the opposite effect, showing that higher rates of growth
typically followed strategic change.
Separate from firm-level results, insights related to large-scale environmental factors (a
second class of results) have also started to accumulate. Central in this area of work have been
efforts to identify the curvilinear effects of the total number of firms in an industry, or population
density (Hannan and Carroll 1992). Several scholars have found that firm growth rates initially
rise with density, but then fall after a certain number of firms are present in the industry (e.g.,
Barron, West, and Hannan 1994; Han 1998; Barnet et al. 2000). Other findings at the
environmental level shed light on the effects of industry-specific factors or trends, such as the
presence of war and the size of an industry’s overall client base (Ranger-Moore, Breckenridge,
and Jones 1995).
Closest to the approach of the present study is another, third class of findings, which have
relied on data on a firm’s strategically similar rivals to predict changes in size. Several scholars
have conceived of industries as stratified along a salient dimension (such as size, technology, or
kinds of labor inputs), and have therefore posited that the competitive pressure faced by a focal
firm (and thus its rate of growth) varies systematically with the conduct or performance of other
firms situated in close proximity. Work on size-localized competition is a prominent example of
this approach in organizational sociology (Hannan and Freeman 1977; Baum and Mezias 1992).
Consistent with the idea that size corresponds to the resources on which firms rely, Baum and
Mezias (1993) and Ranger-Moore, Breckenridge, and Jones (1995) found that size-localized
competition suppressed rates of organizational growth. Various extensions of this vein of
research have modeled growth as a function of crowding in other resource spaces, such as
patented technologies (Podolny, Stuart, and Hannan 1996) and executive labor markets (Sørensen
1999).
Keeping with such methods—where the properties of a firm’s market niche affect its
future performance—the next section develops two hypotheses pertaining to the effects of relative
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size: a main effect, in which relative size increases growth, and an interaction effect, in which
relative size modifies the effect of intraindustry scope. Subsequently, these hypotheses are tested
in two-way fixed effects panel models (Baltagi 1995:27-46) that control for the several factors—
age, founding conditions, strategic change, industry-level processes, and size-localized
competition—identified as important by the previously reviewed studies.
3. Hypotheses
Current work on the consequences of relative size offers partial motivation for expecting
relative size to affect growth positively (Bothner 2003). Until recently, ecologists had only used
measures of absolute size to estimate the performance-related consequences of small scale (e.g.,
Ranger-Moore 1997). Scholars have since distinguished between an organization’s ability to
persist in the face of environmental shocks (measured by absolute size) and its capacity to
compete head-to-head with rivals enjoying cost-advantages and greater bargaining power
(captured by relative size) (Dobrev and Carroll 2003; Hannan et al. 1998). The main insight of
this line of research, which thus far has focused primarily on survival, is that close coupling often
exists between shifts in the sizes of firms and the performance of their rivals, so that relative size
affects outcomes even when absolute size is kept fixed.
Hannan et al. (1998) estimated the effects of relative size on survival in the American,
British, French, and German automobile industries. Adjusting for absolute size, they
demonstrated that size relative to the largest firm in the industry reduced the likelihood of death
in all four national markets. Showing that firms in the U.S. beer industry with many larger
competitors were more likely to fail, Carroll and Swaminathan (2000) suggested that a relative
conception of size is most appropriate for contexts in which firms compete on scale. According to
this view, it is by virtue of their low position in a hierarchy defined by size that smaller, less
efficient organizations face a greater risk of extinction (Carroll and Swaminathan 2000; Dobrev
and Carroll 2003). Although survival and growth are clearly different outcomes, many
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researchers who have estimated the effects of specific covariates on survival and growth with the
same panel of firms have found that predictors of interest affected survival and growth in nearly
identical ways (e.g., Haveman 1992; Barron, West, and Hannan 1994; Henderson 1999; Sorenson
2003). Consequently, for research on relative size, an important task is to extend prior work by
clarifying as clearly as possible the link between relative size and rates of growth.
Carroll and Hannan (2000:313-14) offer material relevant to this task. They argue that
relative size should affect growth and delineate areas in which it is likely to do so. Consistent
with earlier work in economics and strategy, they suggested that gains in relative size may be
accompanied by greater influence or bargaining power over suppliers, cost advantages in
production, and greater influence over distributors, all of which in their view are likely to yield
higher rates of growth. Since the sections of the value chain in which scale advantages are most
consequential vary by industry, the responsibility resides with the researcher to determine the
causal mechanisms appropriate for the empirical context. Although the computer industry is
marked by scale advantages in production, at least at the left end of the size distribution (e.g.,
Scherer 1996:244–246), relative size matters most decisively as a source of power both in the
supply chain and in the downstream activities of the value chain.
Underpinnings of the claim that a firm’s capacity to influence suppliers rises with relative
size reside not only in scale-related etiologies of power in vertical relations (Porter 1980;
Ghemawat 2001), they also follow from statements concerning the relational consequences of a
firm’s share of its market. Specifically, relatively large firms can disproportionately affect their
suppliers’ routines and for the same cost extract further value or activities from them than their
smaller-scale counterparts can (Boulding and Staelin 1990:1160-1161). Underlying this
supposition is the premise that suppliers orient to buyers’ locations in a size-based ranking, at the
base of which suppliers’ compliance with buyers’ preferences is comparatively minimal.
Consequently, as a focal firm’s scale recedes further beneath that of its rivals, these rivals are in
turn likely to get inputs faster, and in a way that better matches their particular assembly routines
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(Nelson and Winter 1982), thereby impeding the focal firm’s growth opportunities in the product
space they collectively occupy.
Similarly, a number of prior investigations also support the contention that relative size
positively affects growth by virtue of the influence it affords over distributors and other actors
downstream. Just as comparably large firms are the priority of suppliers, they also enjoy greater
power over (and better access to) the many intermediaries who move goods to the end consumer
(Rivkin and Porter 1999). When a firm is relatively large, the implicit threat to push goods
through alternative routes is stronger, with the resulting better terms and access, that firm is likely
to enjoy higher rates of growth. Moving further ahead in the value chain, as a firm increases in
relative size, it is also poised to engage in better buyer selection and thus grow at a faster rate
(Porter 1980:108-109). Within the PC industry, as in many other contexts, buyers vary
considerably in their growth potential, and relatively size confers advantages in the contest to
secure high growth opportunities. Since relative size often signals a firm’s position an
unobserved quality distribution (Spence 1974; White 2002), increases in relative size will
enhance buyers’ perceptions of a firm’s products and services, thereby improving its access to the
outlets most conducive to growth in its target market.
Additionally, a related advantage of relative size is the capacity to preempt (Eaton and
Lipsey 1979; Ghemawat 1984; Judd 1985). With greater intangible and tangible resources than
its rivals, a relatively large firm can grow not only by virtue of better buyer selection; it can also
saturate certain areas of the market such that it dissuades the entry of its rivals and amplifies its
growth as a consequence. Greater relative size can thus deter the expansion of a focal firm’s
smaller competitors due to these smaller firms’ concerns about excess supply (Ghemawat 1984,
1986; Smith 1981), thereby enhancing the focal firm’s prospects for future growth. Collectively,
these earlier investigations converge on the hypothesis that, adjusting for absolute size, increases
in a firm’s size relative to its closest rivals will yield higher rates of future growth. When a firm
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increases in relative scale, it has greater influence throughout the value chain, positively affecting
its rate of future growth.
Hypothesis 1 (H1): Sales growth increases with relative size.
Several earlier studies suggest further that relative size plays another important role in the
growth process by modifying the effect of horizontal scope. Similar to research on relative size,
the body of existing work on the consequences of competitive scope or niche width has largely
been confined to survival analyses, mainly showing that firms having wider horizontal positions
are more likely to persist (Sorenson 2000; Barnett and Freeman 2001; Dobrev, Kim, and Hannan
2001). Nevertheless, at least one prior study has offered direct evidence to suggest that growth is
an increasing function of scope. Using multiyear sales data on workstation manufacturers,
Sorenson (2003) reported a substantively significant effect of product scope on rates of growth.
Consistent with this result, and with prior work on the advantages of developing a wider market
position, a plausible expectation is that of a positive effect of scope. When a firm broadens its
reach across segments of the market, it may grow faster by virtue of having extended its
capabilities (Montgomery and Wernerfelt 1988) in such a way that it realizes economies of scope
(Panzar and Willig 1981; Nguyen, Seror, and Devinney 1990) and potentially faces greater
opportunities to shift managerial efforts to those segments in which demand is currently greatest
(Hannan and Freeman 1989). Thus, prior research predicts that a firm’s growth rate will rise as it
efficiently shares its resources across more market segments and reduces its dependence on the
demand present in any one particular segment.
Conversely, prior research in organizational ecology and in related literatures predicts
that wider scope will not always yield positive changes in firm size. Specifically, the ecological
theory of resource partitioning (Carroll 1985; see Carroll, Dobrev, and Swaminathan 2002 for a
review) supports the contention that relatively small firms instead experience higher growth as
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they specialize. More precisely, the theory indicates that firms too small to compete on scale
grow by narrowing in scope, and that the benefits of targeting a delimited section of the market
rise with the distance in size between such firms and their larger counterparts. While large firms
possess the advantages of greater efficiency and bargaining power, they are less able (or less
likely) to tailor their goods or services to particularized consumer preferences, which in turn
generates growth opportunities for their smaller counterparts. Smaller firms in turn meet these
preferences by contracting in scope and optimizing their assembly and marketing routines for a
narrowly defined niche (Carroll 1985; Dobrev 2000). Without explicitly denying smaller firms’
ability to achieve scope economies, resource partitioning theory assumes that the most salient
consequence of smaller firms’ expansions in scope is the loss of differentiation from larger, scale-
competitive rivals, and thus diminished future performance (Carroll, Dobrev, and Swaminathan
2002). Additionally, the logic of the theory directly supports the prediction that the specialization
favors growth when a firm is relatively small. As a firm’s rivals get larger, these rivals are
increasingly unable to serve pockets of the market in which consumer tastes are nonstandard, thus
making available opportunities for the growth of their smaller counterparts to extent that they
narrow their focus on these specific segments.
Offering additional support for the claim that relatively small firms grow by focusing,
many earlier studies have indicated that strong matches between demand-side preferences and a
seller’s routines and capabilities are achieved under specialization (see Bruggeman 1997:203–
204). Specifically, prior work predicts that by specializing, a firm both makes products that are
more reliable (less variable) and refines a closely related set of capabilities (Hannan and Freeman
1984; 1989). Subsequent investigations also indicate that specializing renders a firm more adept
at harnessing the information produced by organizational search (Barnett, Greve, and Park 1994)
and discerning and satisfying particular customer tastes (Peli and Nootenboom 1999). Such
accounts concur with other views of sustainable advantage in the administrative and economics
literatures, according to which a firm thrives by constantly honing a narrow collection of coupled
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activities. For instance, in March’s (1991) account of exploitation-based (as opposed to
exploration-based) strategies, specialization is accompanied by incremental learning and efficient
execution. Similarly, specialization also enables a firm to align its routines and thus make more
valuable products (Siggelkow 2003). Such outcomes in turn contribute to growth in the
idiosyncratic segments of the market for which much larger firms are less well suited (Carroll
1985).
When considered together with work on resource partitioning, such conceptions of
specialization support the prediction that, although relatively large firms grow by widening in
scope, their relatively small counterparts grow faster by pursuing just the opposite tack. Through
specializing, comparatively small firms position themselves to exploit the market segments their
larger rivals find unattractive and raise their rates of growth as a result. Thus, a direct extension
of earlier lines of research is the following hypothesis:
Hypothesis 2 (H2): Sales growth rises with scope for relatively large firms, but increases with
specialization for relatively small firms.
4. Data and Measures
4.1 Data
The International Data Corporation (IDC) assembled the data used in this paper. IDC is
the largest data consultancy worldwide to IT firms and industries. With more than 575 analysts
and research centers in forty-three countries, IDC collected shipment and selling price data for
more than 400 vendors since the start of its quarterly tracking program. Although not complete,
its coverage of the global PC industry is highly comprehensive. The vendors tracked accounted
for 83 percent of the worldwide PC sales over the course of my observation window, which starts
with the first quarter of 1995 and ends at the first quarter of 1999. Most consumers of the data are
makers of PCs, who use the data to locate their positions relative to their rivals, follow trends in
specific segments, and make choices about market entry.
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IDC reports quarterly sales as well as breakdowns of units shipped for each vendor by
national market, technological emphasis, and channel. It tracked fifty-seven national markets,
ranging from Chile and Japan to the United Kingdom and Canada. This number includes five
aggregated regional markets, such as “rest of Latin America” and “rest of Asia Pacific” to deal
with areas in which demand is not individually tracked.
Combined with a firm’s presence in various national markets, its choice of “form-factor”
technology and channel defines its market position. These “form-factor” types (pertaining to the
“form,” or appearance, of the machine) are desktops, notebooks, sub-notebooks, and servers. IDC
also codes the units shipped by each firm as belonging to one of five channels: (1) direct inbound,
(2) direct outbound, (3) reseller, (4), retail, and (5) other.
Machines move through the direct inbound channel if the buyer commences the
transaction by phone, Internet, or a vendor-specific catalog. Conversely, the direct outbound
channel is characterized by the use of a sophisticated in-house sales force. When buyers need
highly specialized solutions, they frequently turn to the reseller channel, which is comprised of
dealers, system integrators, and value-added resellers. The retail channel consists of well-known
chains, such as Circuit City in the United States and Dixons in the United Kingdom. Finally, the
fifth channel (“other”) aggregates several distinct outlets, such as military exchanges and catalog
sales.
With IDC’s coverage of fifty-seven national markets, four form-factor categories, and
five channels, there are 1,140 possible segments in which vendors ship PCs. A virtue of this
dataset is that it includes time-varying information on each firm’s strategy. Such data are
sufficient for defining each firm’s unique set of closest competitors, which I do with the
techniques of social network analysis (Burt and Carlton 1989).
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4.2 Measures
The measure of relative size used in this analysis is a function of the level of structural
equivalence between firms having market contact. Market contact occurs between firms i and k at
time t if they “meet” by selling jointly in the same country. If they do not overlap in the same
national market, then I assume that they do not affect each other’s rates of growth and so exclude
the sales of non-overlapping firms from the measure. After defining market contact as a binary
outcome, the next step in quantifying relative size is to weight by the degree of structural
equivalence between firms i and k. Consequently, after collecting firms k with which i has
contact in at least one national market, the level of structural equivalence between i and k is
computed on the basis of their similarity in patterns of shipping computers across segments
defined by geography, channel, and technology.
Consider a well-known vendor, such as IBM, for illustration. IBM shares segments with
Compaq, which suggests that one’s level of sales at t affects the other’s rate of growth at t+1. But
IBM overlaps in segments with scores of other firms k at t —all of which are more or less
structurally equivalent to IBM than Compaq. Dell and Everex are also taken to bear on IBM’s
performance, for instance. Consequently, in quantifying IBM’s relative size, I follow a known
strategy in social network analysis (Burt 1987; Strang and Tuma 1993) by allowing the sales of
these firms k to receive weights proportional to their degree of equivalence to IBM.
The relative size of the ith firm at time t thus takes the form:
1
it
it
it K
ikt kt
k
S R
w S =
=
∑
(1)
where and S are the sales of the ith and k th firms. The integer is a time-varying count of
other firms with which i has market contact. The coefficient is the degree of structural
it S kt it K
ikt w
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similarity between firms i and k . Calculating first entails rescaling the shipment vectors of
each firm by dividing through by the maximum number of PCs a firm sells in any segment j at
time t (Burt and Carlton 1989). The second step is to compute a firm-by-firm matrix of Euclidean
distances, so that
ikt w
/ ( ijma
it d
max
(
1/ 221,140
1
) / ( )ikt ijt t kjt kjt
j
d Y x Y Y max Y =
= −
∑ ) (2)
where Y denotes the shipments of the ith firm in segment j at time t, and the maximum is taken
over j. I then convert each firm’s vector of distances into structural equivalence coefficients by
subtracting each vector from its maximum distance and making the weights on sum to unity.
ijt
kt S
1
( )
( )it
ikt ikt
K
it ikt
k
max d
d d =
w −
=
−∑ (3)
This measure of relative size has many desirable properties. It takes into account only
those firms that an ego firm meets tangibly in at least one national market and then weights those
alters by the extent of their structural similarity to ego. Since notions of size as a competitive
asset necessarily entail arguments about a firm’s standing in relation to others, this measure uses
similarity of strategy to define each firm’s set of rivals. The incumbents of this set are members in
gradations based on their strategic similarities with the ego firm. This measure is also sensitive to
strategic change, allowing a competitor’s influence on ego’s relative size to increase or decay
with time, depending on whether they get closer or more distant strategically.
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Consider the multidimensional scaling plot (Johnson and Wichern 1982) of the twenty-
five largest firms in figure 1, for a depiction of the stratification by strategy that marks the
computer industry.
(Figure 1 about here)
Closely positioned vendors, such as Gateway and Micron, followed similar strategies in the
fourth quarter of 1995. Specifically, they had comparable profiles of shipping computers across
market segments, which are defined by technology, geography, and method of distribution. I used
a matrix of Euclidean distances among normalized patterns of shipping PCs to generate this plot.
Gateway is close to Micron because they both majored in desktops in the United States through
the direct methods, but they are distant from Epson, which sold primarily through resellers and
retailers, and was almost as focused on Japan as it was on the United States. Consequently,
Gateway and Micron may be assumed to be competing more intensely with each other than they
are with Epson, Digital, or IBM.
I used the same data on shipments through market segments, again defined by form-
factor, channel, and national market, to measure firm scope. I constructed an entropy index of the
form:
∑=
+=it J
j
ijt ijt it P P scope1
)/1ln(1 (4)
where is the proportion of the ith firm’s shipments to market category j at t , and is a time-
varying count of the number of market categories in which i ships at t . I added unity to the
measure so that I could reduce its skewness by transforming it logarithmically. Social scientists
have used this measure, developed by Shannon (Shannon and Weaver 1949), to define an
economic actor’s scope in a number of fields, including network analysis (Coleman 1964),
economics (Jacquemin and Berry 1979), and ecology (Hannan and Freeman 1989). Advantages
of the measure include its ability to represent the scope or niche width of the firm in continuous
ijt P it J
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terms (Davis, Diekmann, and Tinsley 1994) and the simplicity of its properties (Coleman 1964;
see also Palepu 1985 and Kim 1989 for discussions of various measures of scope).1
5. Estimation and Control Variables
To test the preceding hypotheses, I used a standard power law framework to model
proportional growth of the form:
( ) 11 exp++
=it it it it it
S S S ε β α
X (5)
where represents the sales of firm i at t +1. After transforming (5) and adding further
covariates, the model may be estimated by OLS as:
1+it S
( ) ( ) 111 lnln+++
++++=it t iit it it it
eS S S τ γ β α X (6)
where contains covariates of interest, andit X β is a vector of parameters. Taking the log of the
dependent variable has the advantage of ensuring that the predicted rate of proportional growth
will be nonnegative (Barron, West, and Hannan 1994:408). Consistent with many earlier
dynamic panel models (Baltagi 1995:125-148), all continuous independent variables have also
been logged, which substantially improves the fit of the present models.
Moving to the fixed effects, the third term, γi , denotes a separate indicator variable for
each firm. Such effects absorb all time-invariant, firm-specific features, such as the time and
place of market entry, the characteristics of a firm’s founders, as well as managerial skill that
varies minimally over time. Statistically, this procedure also has the advantage of eliminating all
1 Coleman (1964:441-2) shows that entropy has a minimum of zero and a maximum of ln( where is the number of categories.
Thus, in the present context, the maximum number of categories, , equals 1,140, and so the measure of scope in equation (4)
cannot exceed 1 , which equals 8.039.
) N N
it J
)1140ln(+
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the autocorrelation arising from the unchanging features of firms that would otherwise bias the
estimates. I also included a set of quarter-specific indicator variables, 1t τ + , for all periods but the
second quarter of 1995. These terms adjust for temporal autocorrelation, controlling for the
macroeconomic features of each quarter, such as microprocessor costs, component supply
shortages, market size, technological changes, and the number of firms in the industry. When
fixed effects and time dummies are included jointly, the effects of firm age are entirely accounted
for. The error term, e , is then taken to conform to standard OLS assumptions of constant
variance and serial independence.
1+it
The matrix of covariates contains four additional control variables. The first is a control
for acquisitions. Over the four-year window of this study, a number of acquisitions took place,
including highly publicized events, such as Compaq’s purchase of Digital, but also less known
combinations, such as Gateway’s purchase of Advanced Logic Research, IBM’s purchase of
Lucky Gold Electronics, and Packard Bell’s acquisition of Zenith Data Systems, which was in
turn acquired by NEC. I created an indicator of a firm’s acquisition phase which I coded 1 for the
surviving firm if it made the acquisition final at time t +1, or if the acquisition had already
occurred, and 0 otherwise. This measure is thus a time-varying indicator variable. For example, in
the case of Gateway, it equals 1 only for and after the fourth quarter of 1996, which is the quarter
before which the sales of Gateway and ARL were no longer measured separately.
Second, I devised a measure of national market size. IDC reports the size of each of the
fifty-seven national markets in shipments across time. To compute a measure of national market
size for each firm, I used a weighted average by calculating a firm’s proportion of shipments to
each of the fifty-seven markets and using them as weights on these various sizes.2
2 Specifically, let wherent
n
int it U M ∑=
=57
1
π int is the proportion of the ith vendor’s shipments in market n andU is the size of
that market at time t .
nt
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Third, I constructed a measure of strategic or profile change. Changes in a firm’s
strategy, so that its focus at one time point differs significantly from its prior focus, may affect its
performance. To account for this possibility, I devised a Euclidean distance measure of strategic
change, capturing the difference between a firm’s shipment profile at t and t -1. 3
The fourth control is a measure of size-localized competition occurring between firms
meeting in the same national market. Extending Baum and Mezias’s (1993) analysis, I first
collected the sales of all firms k at time t with which firm i had market contact and which were
within a size window less than the size of firm i. Next, I weighted the squared size differences by
the structural equivalence of firms i and k . Then, these weighted distances were summed and the
square root taken.4 When this covariate increases, size-localized competition becomes less
intense, and so its effect on growth should be positive.
Table 1 reports descriptive statistics for these controls and other predictors included in
the analysis. Since I use a fixed-effects specification, table 1 reports within-firm standard
deviations and within-firm correlations.
(Table 1 about here)
6. Results
Table 2 shows results from seven regression models predicting firm sales growth. Before
turning to models that include a number of covariates, model 1 includes only lagged sales,
without fixed effects for firms or time periods. The estimate of -.029 on lagged sales is very close
to zero. Although significantly less than zero (-6.52 t -test), substantively the estimate is clearly
3 More formally, let profile change C where is the number of the ith firm’s
shipments to market segment j at time t , and the maximum is taken over j. The shipment profiles used to compute structuralequivalence distances are here being used to capture within-firm changes in strategy between the prior and the current quarter, which
in turn predict growth at t +1.
(
2/1140,1
1
2
11)max(/)max(/
−=
∑= −− j
ijt ijt ijt ijt it Y Y Y Y
) ijt Y
4 More precisely, the distance takes the form: ( )
2/1
2
−= ∑
≠
<−
ik
kt it ikt S S S it S S w Dit kt it
where is the sales of firm i in quarter t .
A number of prior analyses (not shown but available on request) revealed that the chosen size window is most appropriate for the
present panel.
it S
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not dramatically different. Thus, in this first model, proportional growth declines only
moderately with size, showing a small departure from Gibrat’s law, according to which the
estimate on lagged sales would equal zero.5
Nonetheless, in model 2, which adds fixed effects for firms and for time periods, it is
apparent that the coefficient on lagged sales drops substantially below zero. Therefore, when
unobserved differences in firms’ time-invariant capabilities and time-varying opportunities for
growth are swept out, the purely stochastic model proposed by Gibrat does not represent the
underlying process. Coefficients on the quarter dummies mirror the seasonal demand known to
mark the computer industry. Many of the fourth-quarter effects are especially pronounced,
reflecting the push of large-scale advertising, the pull of holiday consumer spending, and the
tendency for corporate buyers to drain capital budgets at the close of the year (Coyle 1996:18).
(Table 2 about here)
Model 3 then adds covariates identified as important in established studies of firm
growth. The adjustment for acquisitions is significant in light of the added physical, human, and
marketing-related resources a firm has in its possession after such events. Conversely, the
measure of strategic change, although positive, is insignificant at the standard level. Since the
measure of strategic or profile change requires data on two quarters, from t-1 to t , to predict
growth at t +1, entering this covariate reduces the number of observations. In addition, in model
3, the effect of size-localized competition is significant, while that of market size (although
5
Gibrat’s law of absolute growth resulting from prior size and random error may be represented as ,)( 11 ++ =− it it it it eS S S
where is the size of firm i at t +1and is a random error term. Solving for future size and rearranging terms yields
. Next, writing as the product of initial size, , and the firm’s history of stochastic growth results in:
. Under the assumption of short time periods (and thus small error terms), so
that , applying logs yields: . Collecting all except the last term on the
1+it S
1(= it S
1(0= iS
it e+1ln(
1+it e
)1+it
ln( it S
)11 ++ + it it eS
1)(11+ ++ iit eS
it e≅)
1+it S
1)( + e
0iS
2... +
1)...(2 + it i ee
1101 )ln() ++ +++= it it iii eeeeS
right hand side as ln( , the result is . Subtracting from both sides to get growth on the left)it S 11 )ln()ln( ++ += it it it eS S )ln( it S
brings the final expression to 11 )ln( ++ = it it it eS S . Consequently, when the estimate on the log of prior size predicting growth
equals zero, Gibrat’s law holds (see also Sutton 1997:40-41; Carroll and Hannan 2000:315-316).
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positive) is not. The significant effect of size-localized competition establishes that firms grow at
a slower rate the closer they are to others in the size distribution.
With the adjustments in model 3 offering a baseline, model 4 tests the hypothesis that a
firm’s rate of growth rises with its scale relative to that of its strategically proximate rivals.6 At
this juncture, before describing the effect of relative size, an important consideration is the extent
to which relative size discernibly improves the fit. With fixed effects for firms and time periods
as well as a number of other covariates, model 3 adjusts for many of the factors identified as
consequential in prior studies of firm growth, such as firm size, age, time-varying industry-level
factors, strategic change, and size-localized competition.7 Computing an F -test of the null
hypothesis that relative size does not incrementally improve the fit is useful for assessing whether
relative size advances the specification of growth. A comparison of the R2 values from models 3
and 4 strongly rejects the null, showing that relative size significantly increases the variance
explained ( F = 121.19 >> 3.00, the critical value for F 2,∞). 8
6 Supporting the current model specification, the results of a BIC (Bayesian Information Criterion) test for non-nested models (Raftery
1995) offers very strong support for the current version of model 4 over an alterative in which all continuous regressors (with the
exception of lagged size) enter linearly. The BIC for any model may be computed as -2(log likelihood) + ln( N ) p, where p is thenumber of parameters estimated. Calculating the difference between the BICs of two versions of a particular model yields information
about whether one specification exceeds another in accounting for the observed data. For model 4, this difference equals 257.335
(5024.754 for the model with linear covariates minus 4767.419 for the model containing logged covariates). Substantively, this
difference means that the probability of observing the data under model 4 is discernibly higher than under the alternative with linear
covariates. According to Raftery (1995), the factor by which the chances of observing the data are higher equals exp(BICdifference/2), and a difference in BICs greater than 10 constitutes “very stong” evidence in favor of the model with a lower (and thus
better) BIC. With 257.335 >> 10, model 4 was chosen over its alternative with considerable confidence. Similarly, all subsequent
models in Table 2 were also subjected to a BIC test, and in each case offered very strong support for the log-log specification.7 Although a two-way fixed effects model with the set of time-varying firm-specific measures described previously controls for themajor factors shown to affect growth in established studies, data collection constraints do not allow the inclusion of every measure
from models of growth across the different industries studied by earlier researchers. Nonetheless, with size-localized competition
capturing the degree of differentiation in a firm’s niche, and quarter dummies adjusting for competitive processes operating at the
industry level, the competition facing a given firm that is unrelated to relative size is stringently accounted for. Were it possible tocollect data available for studies of growth in other industries—for instance, on firms’ positions in technological networks (Podolny,
Stuart, and Hannan 1996) or in labor markets for executives (Sørensen 1999)—it is likely that the results of interest in the presentstudy would get marginally stronger, not weaker. Specifically, adding technology or labor market-related dimensions to the
conception of firms’ positions in the market could incrementally improve the measure of relative size, producing stronger effects. Yet
with IDC’s detailed reporting of shipments across sharply defined market segments, the data used in the present analysis are unusually
well suited to capturing the effects of size relative to a firm’s proximate competitors.
8 With representing the coefficient of determination for the model with new parameters, the appropriate F -test then assumes the
following form: , where is from the prior model,
new R2
]/)1/[(]/)[(222
, df R p R R F newold newdf p −−= old R2 p is the number of new
parameters, and equals n minus the number of parameters in the new model. When comparing models 3 and 4, the result is:df
19.121)]4203402/()3824.1/[(]2/)3322.3824[(.2982,2 =−−−= F , which exceeds the critical value of 3.00 at the .05 level of
confidence. The total number of parameters equals 420 because of the inclusion of fixed effects for firms.
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Similarly, coefficients on the linear and quadratic covariates measuring relative size are
positive and strongly significant. Linear and quadratic terms were entered to accommodate the
possibility that the effect of relative size depends on a firm’s place in the relative size distribution
(as the effect may rise with the level of relative size, or conversely may reveal diminishing
returns). Although casual inspection could yield the inference that growth rises explosively for
the relatively largest firms in the panel, the fact that logged growth rises faster than linearly with
the log of relative size is insufficient for such a process. Manipulating the terms of model 4 shows
that proportional growth is related to relative size in the following way:
( )it R
it it it RS S θ ∝+1 (7)
where ( ) ( )it it R R ln048.472. +=θ (8)
Although equation (8) does show that ( )it Rθ is increasing in relative size, ( )it Rθ never exceeds
unity over the range of the data, since the maximum value of relative size (shown in Table 1) is
only 47.26.9
To get a preliminary sense of how the effect of relative size changes with its level, it may
be useful to begin by considering the effect of a one within-firm standard deviation shift for a
firm at the mean of relative size.10 Using the descriptive statistics in Table 1 and the estimates of
model 4 in Table 2, at the mean of .65 such a shift (of 1.12 units) yields nearly a 62 percent
increase in the growth rate.11 Thus, PC makers at this point in the distribution enjoy substantial
returns to enhancing their relative size. Moving further out to relative size equal to 10 (Dell’s
9 which exceeds the observed maximum of 47.26.( ) ( )( ) 59,874048./471.1exp1 =−>⇔> it it R Rθ
10 Subsequently, the effects of relative size are again considered in light of the significant interaction between relative size and scopeidentified in model 6.11 This effect may be computed by arranging terms from model 4 to yield the following percentage change in the growth rate:
( ) ( )( ) ( ) ( )( ) 615.165.ln048.65.ln472.exp12.165.ln048.12.165.ln472.exp22 =++++
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value on the measure, in the first quarter of 1996), the same standard deviation increase now
yields a smaller 8 percent increase in the rate. And for relative size equal to 35 (Compaq’s
relative size in 1998 quarter 4), the effect is over 2 percent, showing that the effect of a standard
shift drops as firms move out to the right end of the distribution. Nevertheless, even a 2 percent
increase in the rate is substantively significant over the course of this observation window.
Imagine, for example, that firms z and k are fully comparable, except that z ’s quarterly growth
rate is 2 percent less than k ’s. Then, over the course of 16 quarters, z ’s size will be more than a
quarter less than the size of k (since [.98]16 = .72 < .75).
Before turning to a test of hypothesis 2, model 5 shows that scope has a positive but
insignificant main effect on sales growth. Consequently, if horizontal scope is to matter for the
growth of the firm, at least in this sample it can do so only in connection with another covariate,
such as relative size.
Model 6 adds interaction terms to test hypothesis 2, which posited that comparatively
large firms grow by expanding the width of their market positions, whereas relatively small firms
grow by specializing. This hypothesis followed from insights of the ecological theory of resource
partitioning, as well as a number of other prior works on the advantages of targeting a narrow
section of the market. The estimates in model 6 offer strong support for hypothesis 2. In addition
to the significant scope-by-relative size interaction effects (-3.19 and -6.94 t-tests), an incremental
F -test comparing models 4 and 6 shows that adding scope and its interactions with relative size
significantly advances the fit ( F = 21.35 >> 3.86 the critical value for F 3,∞ at the .05 level).
To clarify the nature of relative size-by-scope interaction, sales growth may be viewed as
a function of scope in the following way:
)(
1it R
it it it scopeS S Θ
+ ∝ (9)
where ( ) ( ) ( )2ln039.ln174.262. it it it R R R −−≡Θ (10)
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and( ) ( )
it
it
it
it
R
R
R
R ln078.174. −−=
∂
Θ∂ (11)
Setting (11) equal to zero and solving for relative size shows that scope has the greatest positive
effect when relative size equals .107. From equation (10), at this level of relative size, the
coefficient acting on scope, , equals .456. Using this result, it is straightforward to show
that a one within-firm standard deviation increase in scope from its mean raises the predicted
growth rate by 5 percent.12 Although this effect is considerable over the course of the panel, the
magnitude of this positive effect is substantively significant only within a narrow range on either
side of this maximum.
( it RΘ )
To examine the potentially stronger (negative) effects of scope for relatively small firms,
it is useful to begin by identifying where, in the relative size distribution, the effect of scope
switches sign. Using equation (10) further, it is apparent that the effect of scope is negative as
long as relative size is less than or equal to .0035. More than 30 percent of the panel’s
observations fall below this threshold where growth increases with specialization.13
Computing the effect of a typical shift in scope at the left end of the relative size
distribution clarifies how the magnitudes of the effects of specializing depend on a firm’s size
with respect to those of its strategically proximate competitors. To depict these effects, it is
useful to consider, across several points in the relative size distribution, the increase in the
predicted growth rate after a one within-firm standard deviation decrease in scope from its mean.
Calculating these various effects brings forward the fact that specialization is increasingly
beneficial as relative size falls. More precisely, this typical decrease in scope raises the growth
)
12 Using the descriptive statistics in Table 1, the increase in the rate of growth may be computed as follows:
( )( ) (( ) 05.192.1ln456.exp/229.92.1ln456.exp =+ . Clearly, an alternative means of interpreting the coefficient .456 is to note that a
1% increase in scope yields a .456% increase in growth, although in a firm growth model, it is more meaningful to consider the effect
of a standard change that a representative firm undergoes along a given covariate.13 Equation (10) also reveals that 4.6 percent of the observations exceed the relative size value of 3.28, where the effect of scope isagain negative. Although this range of the distribution of sparsely populated (by firms such as Compaq, IBM, and Dell), the empirical
pattern is nonetheless noteworthy. Specifically, it suggests that firms at the rightmost end of the relative size distribution may in fact
better their performance by contracting in scope, not widening their reach further.
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rate by 2% at the twentieth percentile of the relative size distribution, by 3% at the fifteenth
percentile, and by nearly 6% at the tenth percentile.14 Thus, the positive impact of specializing is
weak from the thirtieth to the twentieth percentile, strong over the next decile, and very strong in
the final decile. Substantively, this pattern of effects demonstrates that the benefits of targeting a
narrow segment of the market rise with distance from other firms on a size gradient, which is
consistent both with earlier research in organizational ecology and studies underscoring the
performance-related benefits of a focused strategy.
Before moving to the final model, it is important also to interpret the effect of relative
size as it depends on horizontal scope. Although the main objective of model 6 was to test the
hypothesis that the effect of scope hinges on relative size, clearly it also shows that scope
contours the effect of relative size. Collecting terms from model 6, it is possible to compute the
impact of relative size on growth for various levels of scope. Consider again the effect of a one
within-firm increase in relative size from its mean. Just as the estimates from model 4 showed
that this standard shift induced a considerable increase in the growth rate (an increase of 62
percent, as shown in note 11), here the effects are strong as well, but somewhat less so for firms
who are broad in scope. Specifically, at the average value of scope, an increase in relative size
(as described above) raises the predicted rate of growth by 46 percent, and by 22 percent for the
maximum level of scope observed in the panel.15 Consequently, the returns to relative size,
although still pronounced, are lower for firms occupying wide positions in the market. This result
14 Computing these increases in the growth rate first involves collecting the values of relative size for the three chosen points in thedistribution: At the 20th percentile, relative size equals .0020, and .00146 and .00088 are the values for the 15th and 10th percentiles
respectively. Next, from equation (10), the various coefficients acting on scope at these levels of relative size may be obtained.
Specifically, they are -.163,-.265, -.444 for each of the above values of relative size respectively. Finally, these coefficients (togetherwith the descriptive statistics in Table 1) in turn yield percentage increases in the growth rate. For example, at the 20th percentile of
the relative size distribution, the 2% effect reported above may be calculated as: ( )( ) ( )( ) 02.192.1ln163.exp/229.92.1ln163. =−−−exp 15 To compute the effect of a one within-firm increase in relative size at its mean, it is instructive to begin with the result when the log
of scope equals zero. Then, with the relative size-by-scope interaction terms dropping out, the effect (much as in note 11) is simply
the following ( ) ( )( ) ( ) ( )( ) 64.165.ln057.65.ln488.exp12.165.ln057.12.165.ln488.exp22 =++++
( )92.1ln039.− ( )
, showing a 64% increase in the
rate. Collecting and rearranging terms in model 6, it then follows that for the average value of scope (of 1.92, from Table 1), the
previously mentioned shift in relative size yields a 46% increase in the expected rate of growth. Setting
and ,
( )92.1ln174.488.1 −= β
057.2 = β ( )( ) ( ) ( )( ) 46.1=65.ln65.lnexp12.165.ln12.165.lnexp 212
21 ++++ β β β β 2 . Similarly, at the
maximum value of the scope vector, where ( ) and26.5ln174.488.1 −= β ( )26.5ln039.057.2 −= β , the rate goes up by almost 22%.
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carries an important equilibrium-related implication. Namely, the coefficients do not offer
support for the (empirically unlikely) cycle in which a single firm expands in relative size, widens
in scope, advances further in relative size, additionally extends its reach, and so on, until it fully
dominates the industry; instead, scope puts limits on the growth-related returns to relative size.
Moving to model 7, although the scale-by-scope interaction effect is statistically strong, a
potential concern is that it is an artifact of high correlation between the main and interaction
terms. Table 1 shows that these correlations are not especially high, but any argument based on
interaction effects calls for an assessment of their robustness. Multicollinearity does not yield
biased coefficients, but can produce estimates that are sensitive to small perturbations in the data.
An established method for evaluating the robustness of interaction effects is to mean-deviate each
of the terms involved. If interactions of globally demeaned terms show instability, far less
confidence may be placed in the results. In this case, I rescaled the scope and relative size terms
of the interactions by subtracting the overall mean from each and then using the products of these
demeaned terms as the two multiplicative covariates. However, model 7 shows that the estimates
are entirely unaffected by this procedure. The t-tests on the two relative size-by-scope terms are
exactly as they were in model 6. The only difference is a minor difference in the main effect of
scope due to the rescaling.16
Another potential concern is that the effect of relative size may in fact reflect relative age.
In this context, it is important to recall that the effect of (absolute) age is spanned by the time
16 Separate from the approach taken in model 7, four other procedures were followed to evaluate further the robustness of the results in
model 6. [1] To assess the potential effects of multicollinearity from another angle, I computed a condition index for the set of predictors used to generate the correlation matrix in Table 1, which shows moderate to strong pair-wise associations among some
covariates. The condition index equals the square root the ratio of the largest to the smallest eigenvalue of the correlation matrix.
Condition indices between 30 and 100 denote strong to severe collinearity (Belsey, Kuh, and Welsch 1980, p. 105). The condition
index for the present panel equals 14.4, indicating that multicollinearity is not problematic. [2] Confirming that the effects of interestare robust with respect to heteroskedasticity, all significant parameters in model 6 remain significant at the .05 level or better when the
standard errors in model 6 are estimated using White’s (1980) procedure (t -tests for the linear and quadratic effects of the relative size
terms and their interactions with scope are 3.93, 4.67, -2.00, and -3.49 respectively). [3] To check for effects of influential
observations, I compared Cook’s distance values against the percentiles of the F (p ,n-p) for model 6. Upon seeing that seven data pointshad corresponding Cook’s distance values above the 50 th percentile of the F 423,2979 distribution (beyond which threshold data points
may disproportionately affect the fit (Neter et. al. 1996:381-382)), I estimated an additional version of model 6 without these data
points. The parameters were virtually identical across specifications, with all coefficients of interest staying strongly significant (with
t -tests of 6.30, 11.83,-3.19, and -6.94 for relative size terms and their interactions with scope). [4] To check for first order
autocorrelation, I collected the residuals from model 6 and computed the correlation between them at t +1 and t , which was nearly zero(-0.0938). Additionally, I estimated a version of model 6 using Baltagi and Wu’s (1999) methods (implemented in STATA by the
xtregar command) for panel models in which the error term is autoregressive. This estimation procedure yielded the same pattern of
effects (with t -tests of 6.63, 11.27,-2.24, and -5.47 for relative size terms and their interactions with scope).
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dummies and the fixed effects. When calendar time is entered in place of the time dummies in
model 6, the effect (in a model not shown) is strongly negative and precisely the same if firm age
were entered in its place. This finding is consistent with the studies of aging and growth in the
economics and ecological literatures reviewed earlier, which have shown age to be a liability
once size is controlled for. Consequently, it is difficult to argue that by being older than its peers,
a firm develops a competitive advantage and can thus grow at a faster rate. Unfortunately, since
many of the firms in the panel are foreign and IDC does not collect date of entry data, it is not
possible to see if relative age has an effect. Nonetheless, even if such data were available, the
theoretical argument could not be that as a firm increasingly competes with younger rivals
(through strategic change and turnover), its growth rate rises.
7. Conclusions and Discussion
The focus of this paper has been on the determinants of firm growth, which has long been
an active area of empirical and theoretical inquiry in the social sciences. More broadly, to
understand the antecedents of the growth and decline of organizations is to grasp the main
determinants of market concentration, industry size, and the consolidation of social and economic
power (Blau 1977:229–234). In this paper, I built on prior work in the networks, strategy, and
ecology literatures by attending to the effects of each firm’s position in a system of competitive
relations induced by similarities in strategy. What is novel about this contribution to the growth
literature are the predictors that have been considered and the interactions that have been
identified among them. The present analysis showed that the properties of a firm’s market
position—specifically relative size and scope—affect future growth and, further, that the effect of
scope hinges on relative size in ways consonant with prior research.
Much of the earlier work on firm growth has given insufficient attention to the ways in
which changes in an organization’s size are affected by the performance of other incumbents
occupying similar roles in the market. Various scholars have instead directed considerable effort
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to understanding how a firm’s own individual characteristics shape its rate of growth, thus
implicitly reinforcing a conception of firms as isolates in which interdependencies figure only as
noise. Such an individualist approach of course has a long history. For instance, in an early paper,
Penrose (1952:808) noted: “We have every reason to think that the growth of a firm is willed by
those who make the decisions of the firm and are themselves part of the firm, and … no one can
describe the development of a given firm or explain how it came to be the size it is except in
terms of decisions taken by individual men.” Keeping with this orientation, even formal models
that cast size as an advantage in implicitly relative terms (e.g., Jovanovich and Rob 1987) have
yet to motivate relative conceptions of size in empirical specifications of firm growth.
Unlike firm-centered approaches, a central tenet of the strategy and sociological
literatures is that the properties of adjacent competitors substantially advance or constrain a firm’s
future performance. Correspondingly, the results of this study indicate that size relative to
neighboring rivals (with the concomitant advantage of greater power in vertical relations)
substantially affects growth, at least in the context of the computer industry. Consistent with the
network-based orientation of strategy and organizational sociology, this analysis in turn carries
implications for future research in at least two domains: Specifically, the effect of relative size
relates directly to models of organizational growth and industry evolution; and the contingent
effect of horizontal scope has relevance for the frequently considered topic of whether firms
benefit from achieving focus or by pursuing a wide section of the market.
Starting with implications for analyses of growth rates and industry structure, the results
suggest primarily that models of the size-growth link should be broadened beyond the earlier
(restrictive, if elegantly clean) focus on absolute size. Extending the focus of inquiry to include
an emphasis on relative size would of course entail changes at the levels of theoretical portrayals
and empirical measures. Although many of the theoretical statements related to growth arising
with the stochastic models of the last few decades have suggested the importance of positive
feedback between firm growth and relative advantages, such as innovative capabilities (Klepper
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1996) or the capacity to secure resources (Barron 1999), prior scholarship has given insufficient
attention to how advantages of scale differentially affect other rivals according to the extent of
their positional overlap. Since such feedback between growth and competitive advantage is often
accelerated or impeded by the growth or decline of strategically proximate firms, a more realistic
image of the growth process is likely to take shape as localized measures of relative size appear in
formal and statistical models.
While adding measures of relative size would complicate analytical and simulation-based
frameworks, doing so would also necessarily bring into focus the realistic processes of firms’
movements into and out of market segments and thereby their spatially and temporally varying
influence on the firms with which they overlap. Salient in many formal models of growth and
industry evolution is the exit of less efficient firms from the industry (e.g., Jovanovich 1982;
Barron 1999). Conversely, going back to the specialist-generalist distinction (Carroll 1985; Porter
1985) discussed earlier, it is easy to imagine adding to these models a decision rule according to
which declining firms select narrower strategic targets, and potentially recover instead of just
exiting the landscape entirely. Under that scenario, strategic change would figure as a central
process, and displaced firms would (more realistically) continue to affect outcomes in the
industry.
While the present paper only considered the width of each firm’s horizontal position as
predetermined via the lag structure, a direct implication of the relative size effect is that efforts to
deal systematically with processes clustered around firms’ market positions may yield richer
models of growth and therefore more accurate renditions of the micro-mechanisms underlying
industry evolution. Considering the primacy of firm growth equations in longitudinal models of
industry structure (e.g., Hannan and Ranger-Moore 1990; Barron 1999), it seems likely that
measures of relative size—together with equations predicting firms’ choices of horizontal
positions—could enhance the predictive value of industry-level models, yielding a better
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understanding of such topics as market concentration, the likelihood of shakeouts, and the
number of firms in the industry (Jovanovich and McDonald 1994; Carroll and Hannan 2000).
Just as the effect of relative size carries implications for analyses of industry evolution,
the manner in which relative size shapes the impact of horizontal scope has relevance for long-
studied question of whether firms should occupy a narrow or broad market position. Offering a
different angle from that of prior research, the present analysis implies that the local features of a
firm’s market role substantially affect the returns to contracting or widening in scope. Much of
the earlier research in this domain focused instead either on the turbulence of the larger
competitive environment or on firm-specific capacities. For example, early ecological work (e.g.,
Freeman and Hannan 1983) suggested that specialists outperform generalists in stable industries
and that the converse occurs in environments marked by substantial change. Standing at the other
end of the organization-environment continuum, Porter’s (1985) typology of generic strategies
implies that whether firms pursue focus or industrywide scope should result from a careful
calculus of their distinctive capabilities. Conversely, this analysis emphasized the properties of
firms’ immediate environments, showing that relatively small firms grow by specializing and that
their relatively larger counterparts enjoy higher rates of growth by expanding in scope. While
environmental change and firm-level capabilities will necessarily figure in future discussions of
scope and firm growth, the findings of this paper suggest that the local environment should
receive more careful attention in subsequent analyses. Consistent with work on resource
partitioning, the results suggest further that the match between the capabilities of a strategically
focused firm and its customers’ preferences may be enhanced by the distance between such firms
and their neighboring rivals on a size gradient. While analyses of growth in other industries are
necessary to assess the generality of this process, the result that the consequences of expansions
or contractions in scope depend on relative size bears both on research related to horizontal
positioning in particular and on models of the growth process more generally.
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-1.0 -0.5 0.0 0.5
- 1 .
0
- 0 .
5
0 .
0
0 .
5
Figure 1: Stratification by Strategy, Top 25 Firms in 1995Q4
Digital
Acer
HP
AST
Compaq
IBM
NCR
ZDS
Packard Bell
Unisys
Gateway
OlivettiTexas Instruments
Toshiba
Seimens
Vobis
Micron
Dell
Samsung Escom
Trigem
Epson
NEC
Hitachi
Fujitsu
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Table 1 Descriptive Statistics and Correlations for Variables in the Analysis
Variable Name Mean SD Min Max
Sales (S) 1.27e+08 1.67e+08 828 8.79e+09
Acquisitions (A) 0.0117179 0.0777147 0 1
Relative Size (R) 0.6505261 1.119512 9.17e-07 47.26079
Scope 1.92065 0.2287596 1 5.259388
Profile Change (C) 0.2269359 0.2812997 0 2.089277
Market Size (M) 963473.5 519424.8 4831.001 1.08e+07
Size-Localized Competition (D) 1.20e+08 1.70e+08 43.68463 8.61e+09
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
[1] ln(Salest+1/Salest)
[2] ln(Sales) -0.4499
[3] Acquisitions -0.0034 0.0617
[4] ln(Profile Change+1) 0.0041 0.0010 0.0188
[5] ln(Size-Localized Competition) -0.3684 0.8345 0.0526 0.0005
[6] ln(Market Size) -0.2476 0.3887 0.0810 0.0113 0.2816
[7] ln(Relative Size) -0.3446 0.9027 0.0482 -0.0051 0.7893 0.2333
[8] ln(Relative Size)2 0.4245 -0.8444 0.0076 0.0174 -0.7279 -0.1944 -0.9028
[9] ln(Scope) -0.0172 0.1435 0.0324 0.0989 0.1139 0.0158 0.1727 -0.1204
[10] ln(Scope)ln(Relative Size) -0.0596 0.2910 0.0609 -0.0717 0.2662 0.1131 0.3288 -0.1931 -0.7422
[11] ln(Scope)ln(Relative Size)2 0.1107 -0.3956 0.0237 0.0663 -0.3583 -0.1721 -0.4440 0.4018 0.6027 -0.8826
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Table 2: Regression Models Predicting ln(Sales t+1/Salest)
Variables 1+ 2 3 4 5 6 7++
ln(Sales) -.029 -.455 -.624 -.566 -.564 -.525 -.525
(.004)** (.015)** (.038)** (.057)** (.057)** (.057)** (.057)**
Acquisition .319 .114 .115 .214 .214(.110)** (.107) (.107) (.108)* (.108)*
ln(Profile Change+1) .050 .031 .021 .023 .023
(.052) (.050) (.050) (.050) (.050)ln(Size-LocalizedCompetition) .088 .079 .082 .066 .066
(.025)** (.025)** (.025)** (.025)** (.025)**
ln(Market Size) .066 .027 .033 -.031 -.031
(.041) (.040) (.040) (.041) (.041)
ln(Relative Size) .472 .455 .488 .387
(.054)** (.055)** (.077)** (.061)**
ln(Relative Size)2 .048 .047 .057 .035
(.003)** (.003)** (.005)** (.004)**
ln(Scope) .131 .262 .042
(.071) (.184) (.073)
ln(Scope)ln(Relative Size) -.174 -.174
(.055)** (.055)**
ln(Scope)ln(Relative Size)2
-.039 -.039(.006)** (.006)**
Period Indicators
95Q3 .067
(.051)
95Q4 .304 .252 .262 .259 .261 .261
(.050)** (.051)** (.049)** (.049)** (.049)** (.049)**
96Q1 .057 -.028 -.018 -.022 -.008 -.008
(.052) (.054) (.055) (.055) (.055) (.055)
96Q2 .121 .063 .053 .052 .059 .059
(.051)* (.055) (.054) (.053) (.053) (.053)
96Q3 .159 .060 .050 .049 .060 .060
(.051)** (.053) (.053) (.053) (.052) (.052)
96Q4 .325 .248 .243 .240 .246 .246
(.051)** (.053)** (.054)** (.054)** (.054)** (.054)**
97Q1 -.033 -.110 -.118 -.122 -.096 -.096(.054) (.057) (.064) (.064) (.064) (.064)
97Q2 .090 -.039 -.039 -.044 -.014 -.014
(.051) (.056) (.060) (.060) (.060) (.060)
97Q3 .105 .031 .042 .034 .060 .060
(.051)* (.054) (.057) (.057) (.057) (.057)
97Q4 .295 .208 .220 .210 .244 .244
(.051)** (.054)** (.058)** (.058)** (.058)** (.058)**
98Q1 -.087 -.201 -.170 -.181 -.147 -.147
(.052) (.058)** (.067)* (.067)** (.067)* (.067)*
98Q2 .010 -.113 -.108 -.118 -.080 -.080
(.050) (.055)* (.060) (.060) (.060) (.060)
98Q3 -.096 -.203 -.198 -.208 -.166 -.166
(.050) (.054)** (.059)** (.059)** (.059)** (.059)**
98Q4 .104 -.023 -.011 -.021 .030 .030
(.050)* (.055) (.062) (.062) (.062) (.062)
99Q1 -.229 -.379 -.372 -.385 -.332 -.332
(.051)** (.060)** (.072)** (.072)** (.072)** (.072)**Constant .446 7.124 8.449 8.950 8.677 8.879 9.005
(.072)** (.241)** (.548)** (1.119)** (1.128)** (1.139)** (1.126)**
N 4023 4023 3402 3402 3402 3402 3402
R 2 .0105 .3050 .3322 .3824 .3831 .3954 .3954
Standard errors in parentheses* significant at 5%; ** significant at 1%
+Model 1 omits fixed effects for firms. ++Model 7 reports results with interactions in which the terms for relative size and scope have been centered atth i