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8/9/2019 Structure Scale and Scope in the Global Compute
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,
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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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:
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
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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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