The Surprising Hybrid Pedigree of Measures of Diversity and Economic Concentration

Abstract

Measures of economic concentration, such as the k-firm concentration index and the Hirschman-Herfindahl Index (HHI) are commonly used to ascertain the competitiveness of a product market. Within a Cournot model industry equilibrium, it is known a relationship exists between the HHI and the gap between industry price and marginal cost, but the economic theory foundations and intuition underlying the HHI formula are seemingly arbitrary. Here we document that there are indeed powerful and intuitive theoretical foundations to the HHI, but those foundations emanate from outside economics, namely, ecology, where the HHI is known as Simpson’s Diversity Index. We discuss the origins of the HHI and Simpson’s Diversity Index, summarize other measures of concentration, and link them to common measures of inequality. Based on a priori reasoning, we conclude there is little on which to base a choice between the HHI and non-HHI measures of market concentration. We empirically illustrate the implementation of the HHI and other concentration indexes as the statin drug LipitorTM lost patent protection and faced generic competition in 2012; we find very similar empirical trends and high correlations among them. Our research provides support for the continued use of HHI as a measure of concentration, provided one recognizes its link to market power is equivocal.