arkets vs Management 657 ather a remarkable agreement (see Table 4 for ent subsets of the data, or by considering differing a comparison of findings ) The agreement numbers of years in a longitudinal study. Com- gests, of course, had Schmalensee(1985) pounding this difficulty is the fact that there is more than I year's worth of data and, had he no unique measure for industry aver luded an SBU term in his equation, he might ages. We have described two possibilities: the well have arrived at a similar value for the time-series vs. cross-sectional methods amount of sBU variance accounted for as Rumelt Further, by analyzing industry averages, one (1991)found. (The comparison is clearly pointed implicitly suggests that the appropriate estimate out in Rumelt's, 1991, Table 4, p. 179) of the industry effect is the average of all uni Let us now focus our attention on the major within the industry. Such an implication leads to differences between Schmalensee (1985)and an erroneous conclusion. If the random effects Rumelt(1991) on their respective findings con- model is considered valid, then the industry aver cerning industry averages. Recall from Equation ages are inefficient estimates of industry effects 2 above, the equation for examining the average The appropriate estimates are the best linear profitability of industries. The percentage unbiased predictors (or BLUPs, see Searle, accounted for by industry effects was estimated Casella, and McCulloch, 1992) to be approximately 75 percent by Schmalensee Thus, to avoid the difficulties associated with (1985), but only 48 percent for Rumelt (Table choice of data base, choice of variance measure 5, 1991: 11). There are at least three possible for industry average, and choice of estimation of reasons for the discrepancy. ndustry effects themselves, we recommend the First, as indicated above, the industry term of decomposition of the actual Roa variance(the Schmalensee's (1985) model encompasses both rikr), rather than the variance of the industry the persistent and nonpersistent industry effects, averages, as the primary vehicle for assessing the i.e., includes the industry effects and industry by relative importance of factors. Such a decompo- year interactions of Rumelt's (1991)model, sition then may be used for determining decompo- Second, two sets of data were used which or time-series), or for other estimates (e.g yielded a different number of observations per BLUPs), if desired industry. The variance decomposition procedure is very sensitive to such differe Third, the two theorists calculated the industry THE CURRENT RESEARCH averages in a different way. Schmalensee(1985) computes the average return for all corporations We wanted not only to compare and contrast the in the given year, then considers a cross-sectional Schmalensee/Rumelt differences, but also to enter variance. Rumelt(1991)calculates the average the debate using a more up-to-date data base over all corporations and years, then considers while employing a variance components analysis variance of the time-series averages similar to Schmalensee (1985) and Rumelt It appeared that some of the difference might (1991). Thus, our mathematical model was as fol be due to the differing methods of average calcu- lows lations; thus, we examined Rumelt's(1991) find- gs on the decomposition of variance of industry r面k=+α1+阝k+Y:+δn+中+∈ Appendix 1 for a detailed, mathematical dis- where rikt represents the SBu ROa for a giver average calculations ). In conclusion, the discrep- are industry effects, B are the corporate effects, ancies between the 75 percent(Schmalensee) and y represent the year effects, 8 are the industry the 50 percent(Rumelt) may be the result of the by year interactions, represent the SBU effects, overall precision with which the industry effects and E represent error. are estimated. This precision may be more related Since we were conducting a longitudinal study, to a particular data base used than it is to the we expected to obtain results similar to rumelt actual ROA values-one can obtain drastically i.e., a high SBU effect, a low industry effect different variance decompositions through differ- and probably a zero or near zero corporate effect