Re-evaluating Diversity Measures: Calibrating for Scope to Capture the Distribution Effect

Abstract

This paper has practical implications in three areas of application in corporate management: strategy research corporate planning governmental regulation. The authors' review of the literature reveals a trend toward an increased use of the uncalibrated Herfindahl Index by regulators and of the uncalibrated Entropy measure by researchers. This trend involves considerable risks if it continues unabated into the new century. In the latter domain, the lack of discrimination power of current indices of concentration or diversification is becoming a major problem in that limit values specified by regulations are based on biased indicators. These are compounded when the Herfindahl Index becomes the sole anti-trust instrument for industry regulation as has been codified in the US by the guidelines jointly issued in 1992 by the Federal Trade Commission and the US Department of justice. Complementing the empirical investigations published in the research literature over the last ten years, this paper examines the existing measures of industry concentra- tion or product-line diversity on theoretical grounds and found them wanting in certain respects: There is a lack of calibration with respect to the effect of the number of product lines or scope variable n. Diversification studies are distorted by the fact that these diversity measures of firms with several product lines become unreliable and biased toward the high end of their range. There is a lack of sensitivity with respect to capturing intermediate load distributions Sbetween the two extreme cases of a single firm (or product) or of a very large number of them. This article presents clear criteria for designing diversity indices and gauging them. Industrial Organization (IO) economists appear to have been suspicious of these problems for a number of years, yet very little has been done to warn regulatory agencies and strategy researchers of the problems inherent in their increasing use of the uncalibrated indices. In contrast, this article develops two intrinsically calibrated indices, A1 and A2, for use by researchers, strategic planners, and industry regulators. An ideal composite measure should incorporate both the effect of cardinality or scope and the effect of shape or distribution. The existing indices bundle these two effects; the objective of this research is to ‘unbundle’ them. Most large North-American firms tend to be multi-product corporations for which the measurement of product-line diversity as well as social diversity will be affected by the above considerations. Chances are that the same holds true in the Indian context. However, this is partly an empirical question that could be further investigated by follow-up studies on databases such as Capital-Line and Prowess, leading to some useful information for strategic and legal considerations.