Cautionary note about the Herfindahl-Hirschman index of market (industry) concentration

The Herfindahl-Hirschman index (HHI) appears to be the most widely used index of market or industrial concentration. It is a summary measure that indicates the degree of competition, market power, and efficiency within a market or an industry. The HHI is also used by government agencies when evaluating potential violation of antitrust laws and regulations. As emphasized in this paper, and in spite of its several desirable properties, HHI has one serious limitation: it lacks the value-validity property. Lacking this property, caution has to be exercised when using HHI in order to avoid invalid and misleading results and conclusions. A corrected index is developed as a simple reformulation of HHI. Since this new index formulation meets the conditions imposed by the valuevalidity property to a high degree of approximation, and has other desirable properties comparable to those of HHI, the corrected index can safely be used to make various types of comparisons that are true and valid representations of market (industry) concentration. Numerical data are provided to support and exemplify the use of the corrected index.