A number of scholars have advanced arguments that accounting rates of return are systematically biased measures of true internal rates of return. Whatever the merits of this position, the purpose systematic biases in reported returns, the esti mated variance components will reflect these facts and, therefore, help in estimating their importance.
A VARIANCE COMPONENTS MODEL
In discussing the heterogeneity within industries the term 'firm' has an ambiguity that easily leads to confusion. In economics a 'firm' is usually an autonomous competitive unit within an industry, but the term is also often used to indicate a legal entity: a 'company' or 'corporation'. Because most empirical studies are of large corporations, and because most large corporations are substan tially diversified, legal or corporate 'firms' are, at best, amalgams of individual theoretical competitive units. Confusion can arise if one author uses the term 'firm effects' to indicate intra-industry dispersion among theoretical 'firms', and another author uses the same term to denote differences among corporations which are not explained by their patterns of industry activities.
To reduce the ambiguity in what follows I avoid the term 'firm'. Instead, I use the term business-unit to denote that portion of a company's operations which are wholly contained within a single industry. 12 I use the term corporation to denote a legal company which owns and operates one or more business-units. Thus, both industries and corporations are considered to be sets of business-units.
In this regard, note that Schmalensee (1985) used the term 'firm-effects' to denote what I call corporate effects. Thus, his first proposition, 'firm effects do not exist' (p. 349) refers to what are here termed corporate effects. Consequently, as he noted, finding insignificant corporate effects does not rule out the presence of substantial intra-industry effects. However, unless more than one year of data are analyzed, intra-industry effects pool with the error and cannot be detected.
Taking the unit of analysis to be the business unit, assume that each business-unit is observed over time and is classified according to its industry membership and its corporate ownership. Let r;k, denote the rate of return reported in time period t by the business-unit owned by corporation k and active in industry i. A particular business unit is labeled ik, highlighting the fact that it is simultaneously a member of an industry and a corporation. Working with this notation, I posit the following descriptive model