By Phin Upham
Scholars often say that there are good firms and bad firms. Here Phin Upham looks at a seminal work which challenges some of these findings.
In Thomas H. Brush and Philip Bromiley’s What Does a Small Corporate Effect Mean? A Variance Components Simulation of Corporate and Businesses Effects, they analyze, reinterpreted, and retest Rumelt’s 1991 essay on corporate effects. In 1991, Rumelt had argues that the corporate effect on the variance of company performance is very small. This implies that strategy does not matter very much, since it makes so little difference. Brush and Bromiley argue that Rumelt did not interprets his statistical metrics well enough – that what he though he found was in fact not as telling or as robust as he believed. To prove this, they construct a simulation where there was important corporate effects and then used Rumelt’s “variance component analysis” metrics to test under what conditions we may get Rumelt-like results and what this means. This tact shows that value of researchers laying out their methods clearly, not only for later critiques but also for this kind of reproducibility and critical analysis.
Rumelt has taken up the gauntlet where Schmalensee (1985) had left off. Schmalensee had analyzed a variance model of firm performance studying firm, industry, and market share (for business units effects) and concluded that industry effects explained 19 percent of variance of rated of return and neither firm effects not market share are significant in explaining variance of return. Rumelt placed intra-firm level data into the analysis and decomposed the line of business profitability over time into corporate, business, industry, and other effects. He used variance components to estimate his model. Variance components are a tool in econometrics which, in order to control for some unknowable effect in each firm, assumes that each firm effect has an additional constant value u(i) randomly drawn form some population. This helps us to find the mean an and variance of u(i) as a population. But it is unclear how we ought to interpret the results we get from this strategy.
This variance components approach is used in genetics, but in this case special formulas and carefully designed experiments are used to ensure that this measure contributes rather than misleads. Rumelt uses variance components as a way to avoid dealing with model details, according to Brush and Bromiley, geneticists pay close attention to such factors.
Rumelt’s results are what has caused such a stir and provoked such an extensive rebuttal. He found that 46 percent of variance is explained by business unit effects, 8 percent is associated with industry effects and 1 percent with corporate effects. In short “if one business unit within a corporation is very profitable, there is little reason to expect that any of the corporation’s other business units will be performing at other than the norms set by industry, year, and industry-year effects.” (827). Rumelt is claiming that firms do not have any, or at least not much, ability to transfer success between product lines, in other words firms have few resources (in the RBV view) which can be applied internally to help them survive. This does not, it seems to me, contradict the possibility that a firm had an above average return or capability in some one division or another, only that a firm’s successes in one area do not transfer over (a strong version of Winter’s ideas on replication between product lines might be a consistent explanatory mechanism here).
But Brush and Bromiley have some very serious counter arguments to Rumelt’s conclusions. First, they argue that what his results appeared to say was not in fact what they necessarily meant. While the theory of variance components has been well developed, they argue, to interpret the effects of other variables, it is not as facile in actually measuring the relative importance of its estimates. In other words, Rumelt “makes statements of importance based on explained variance rather than an estimated parameter” (828). Brush and Bromiley take an unlikely, but ingenious, tact to establish their rebuttals to Rumelt. They construct a simulation in which they know there are significant firm effects and then they apply Rumelt’s analysis onto it. They are testing for two questions 1) the relative magnitude of a variance component as it relates to indicators of that particular effect. Rumelt is testing for some systematic advantage that is bestowed onto a division (say, by a manager) in virtue of being a part of a firm. Brush and Bromiley argue that this is too narrow a definition, a firm might have a unit performing less well in order to get extraordinary return in another unit, for example. This leads to question 2) how does shifting the number of business units influenced by corporate effects affect the measure of the variance component associated with corporate effect (829)? IN short, how does the size of the corporate effect pan out in the variance component and what might happen to the variance component if we don’t assume homogeneous corporate effects over business units.
Brush and Bromiley generate a simulation set of data and then measure scale (the difference between the performance of the top quartile of business units in a firm and the bottom quartile.). They believe that this will help them answer the first question above. To answer the second question they measure ROA for the top and bottom quartile and believe that this gets at the corporate affect on the business. They find that when scale is 1 (corporate and business unit effect identical) they get similar variance component measures, but when scale is .6, the variance component under represents this at .38, and when the scale is .2, the component variance is essentially zero at .03. this is the component variance Rumelt fount (1.5%). A scale of .20 implies, in Brush and Bromiley’s analysis, that the relevant importance of the corporation is 20 percent as important as the business unit. Thus, the authors conclude, variance component magnitudes do not reflect importance in a linear manner. Instead, variance components appear to be the square of importance.
Similarly, that the size of the industry variance components is 1/6 th that of the size of the business unit variance does not imply that the importance of the first is 1/6th the importance of the second. This means that the industry is 40 percent as important as the business unit. Lastly, the results vary significantly over simulations. Since the data is randomly drawn from the population, different draws get different results. This gives Brush and Bromiley yet another reason to question Rumelt’s conclusions. In conclusion, Brush and Bromiley say that Rumelt’s findings should be interpreted to mean that 1) corporate effect is not overwhelming and 2) corporate effect is significantly smaller than business unit effect (but not unimportant).
The authors have put much time and energy into critiquing the methods of a past scholar, whom they seem to nevertheless respect enormously. I personally question the use of “scale” as measures by the different between top and bottom quartiles because I think that this looses too much intra-firm information about profit, but I am not well versed enough in variance component methodology to critique the model or the model’s counter arguments fully. But I do admire the care and rigor of the authors. Whether right or wrong (I would love to see Rumelt’s response to this) they liven the debate in strategy and challenge a study they believe erroneous. I think the field would benefit from this sort of rigorous challenging of theories in order to synthesis and test results.
Phin Upham has studied at the Wharton School of Business, and is an investor specializing in macroeconomics and illiquid assets. Contact Phin Upham at PhinUpham.com.