Entropy Measure of Diversification and Corporate Growth

Abstract

During the past decade or more, a number of authors have proposed (and applied) a number of measures of corporate diversification. These have ranged from simple counts of the number of products to measures which assign various weights to the relative importance of each product within the corporation's total product mix.1 For the most part, these measures have direct counterparts in familiar measures of industrial structure. For example, Michael Gort [5] defined, as one measure of corporate diversification, the ratio of the firm's sales within the firm's primary industry to the firm's total sales. This is the equivalent (within the firm) of the primary product specialization ratio reported for 4-digit industries by the Bureau of the Census. A variation of Orris Herfindahl's index of industrial concentration-the sum of the squared shares of each product's contribution to the firm's total output-has been used by one of the authors of this paper [i], [2]. Others have suggested the application to corporate diversification of what has come to be called the entropy measure of industrial concentration.2 There is no axiomatic analysis or general model of diversification which suggests the advantage of any single index; at this stage it is therefore appropriate to ask which particular index performs best empirically. This note outlines a theme common to all these measures, identifies a major advantage of the entropy measure in the analysis of corporate diversification, and provides some comparative applications of the entropy measure and of the Herfindahl index to 460 of the largest US manufacturing corporations.