《Innovation, Diversity and Diffusion：A Self-Organisation Model》11 Brush-1998-Comparing Alternative Methods to Estimate Corporate and Industry Effects

ANOVA for showing that corporate effects are not significant, Rumelt primarily emphasizes his VCA findings. Rumelt argues that"it is only by estimating the variances of effects that relative importance can be assessed. (Rumelt, 1991: 173) Rumelt's results agree with Schmalensee in finding a very small corporate effect and modest industry effect, but Rumelt also finds a strong business effect which in Schmalensee (1985)was part of the error term. Rumelt finds that business effects are much larger than either the corporate or industry effects Rumelt(1991)discusses the small corporate effect as a conundrum. He finds it "surprising to find vanishingly ffects in these data" ne extent of literature on corporate strategy, corporate culture, the number of corporate management consulting firms, and the focus on senior corporate leaders in the business world(Rumelt, 1991: 182). While RumeIt's conclusion is formally based on the size of his estimated variance component, he suggests that corporate strategy may be relatively unimportant for explaining business unit performance In addition to more general concerns about vCA(see Brush bromiley, 1997), the small corporate effect in VCA may come from structural assumptions in Rumelt's(1991) variance components model. He decomposes the total variance of business unit profitability (or)into variance and covariance terms +2C in which o2, is the variance of stable industry effects, o? B is the variance of stable corporate effects, o2, is the variance of the year effect, o is the variance of the business effects, o?,is the variance of transient industry effects, o'e is the variance of transient corporate effects, and

Co is the covariance between a and B. The covariance term captures covariance between the corporation and the industry consistent with Schmalensee. This would be equivalent to the contribution from firms picking profitable industries(Schmalensee, 1985). However, Rumelt does not include the possibility that corporate effects may also covary with business effects in his model. Rumelt imposes the assumption that corporate and business unit effects are uncorrelated e, across corporations, corporate effects cannot correlate with business unit effects. Strategic management may argue for an association between business-unit and corporate effects if well-managed corporations both pick profitable businesses to enter and manage them well. For example, if high performance corporations achieve such performance by selecting high performance business units, this corporate effect might be masked as a business effect using VCA. While corporate strategy emphasizes activities that should create associations between business unit and corporate effects, VCA does not capture this correlation as part of its corporate effect. That is, if corporations differ in their ability to pick high performance business units, this capability will not necessarily be picked up as a corporate effect. Thus, one questions the underlying structural assumptions of using this model, without adjusting for this possibility More recent studies of industry, corporate and business effects use data from COMPUSTAT(Roquebert, et al, 1996; McGahan Porter, 1997a). COMPUSTAT provides more recent data on a larger sample of firms, but defines the"business"according to the accounting treatment of business segments rather than the Ftc's line of business approach Business segments tend to include business units with similar product lines. Given the size of the business segment, the use of business segments should produce a large business effect and reduce the corporate effect(McGahan& Porter, 1997a), yet these studies produce larger 8

corporate effects than Schmalensee's and Rumelt,'s. These studies result in a large range of corporate effects from 4%to 18%. To understand this range of effects, McGahan and porter (1997a)use sequential anova analysis entering industry before corporate effects and vice versa. When industry enters first, the corporate effect is 9.1% versus 11.9% when corporate enters first. James(1998) finds a similar issue between corporate and business effects. Corporate effects decline from 15% to 5% when entered last using continuous variables (James, 1988) Both VCA and ANova present problems. Researchers using VCA interpret the magnitude of the variance component as"importance". This contrasts with standard practice in other areas of management research in which researchers interpret estimated parameters (standardized beta)as importance rather than explained variance. In addition, the comparison of the size of the variance of each component may be misleading. Brush and Bromiley(1997)have shown that square roots of variance components more accurately reflect the relative importance of each component. Studies using variance components without taking the square root will obtain biased estimates and the biases increase with smaller effects(Brush Bromiley, 1997) Thus, while Schmalensee's industry effects explain 19% of the variance in business unit profitability, their relative importance is approximately 4.5% using the square root of the variance. Similar interpretation problems appear in all previous VCA analyses of this issue In addition to interpretation, Brush and Bromiley (1997) find that Vca does not provide very reliable estimates. They find that multiple runs of the same underlying model(simulated data with the same parameters)can result in a wide variance in estimates which means the technique is not reliable in any single application (Brush Bromiley, 1997) 9

ANova also has its pros and cons. On the positive side, management researchers understand its assumptions and interpretation better than VCA. On the other hand, order of entry matters because aNoVa allocates covariance effects to the first variable entered in the pair. Whether corporate effects enter before industry effects will influence which appears larger Furthermore, because business units(and segments )naturally nest within corporations and industries, corporations and industries must be entered before business units. In addition aNova uses many degrees of freedom. Thus, we are left with a conundrum of VCa giving us unreliable corporate effects and interpretations that underreport the relative size of smaller effects, with ANova giving us a range of corporate effects depending on the order of entr Simultaneous equations In addition to vCA and ANovA, some researchers have used regression models to measure the importance of one variable over another. Brush, Bromiley and Hendrickx (forthcoming) argue for continuous variable models which in this case implies a simultaneous equation system. Thus, they establish a simultaneous equations model that addresses the relative importance of corporate and industry effects. They also estimate these effects while controlling for business effects Brush and Bromiley's(forthcoming) simultaneous equation model allows for the influence of corporate profitability on business-unit profitability and the influence of business unit profitability on corporate profitability. The model avoids the problem of whether the corporation or industry term should enter first(ANOVA), or the imposition of orthogonality of estimated effects(VCA). They claim that the lower number of parameters should provide more reliable estimates of the magnitude of effects than VCA and ANOVa which use many more parameters 10