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

mailto:[email protected]

mailto:[email protected]



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

15



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.

16



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

17



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(+

18



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

19



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

20



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).

21



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.

22



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 =++++

23



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)

24



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.

25



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%.

26



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).

27



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

28



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

29



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

30



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.

31



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37



-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

38



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

39



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

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