That is, the observed average industry return is the sum of µ, the industry effect a; and weighted averages of the business-unit effects and errors within that industry.
Working with sample A, it is a simple matter to compute y; for each of the 242 industries and to then calculate the sample variance s; among these industry returns. The result is s; = 61.90. How good an estimate is this of a;? Examining (8), it should be clear upon reflection that s; overestimates a;. The variance among industry returns will be a; plus terms in a and a;. That is, industry returns vary from one another because of industry effects and because of the random impact of business-unit effects and errors on computed industry returns. To develop an expression for Es; in terms of variance com ponents, first note that