Using the H-Index of Concentration with Published Data - Schmalensee, Richard (The Review of Economics and Statistics, 1977)
N theoretical discussions industrial organization specialists often indicate a preference for comprehensive or summary concentration indices over the more readily available concentration ratios. Such indices consider the entire size distribution of sellers in a market, and they give weight to both fewness of sellers and inequality of market shares. The most popular such measure is probably the H index of Hirschman (1945) and Herfindahl (1950). (See Hart (1975) for a discussion of alternatives and a list of references.) Let P1 be the share of the largest firm in an industry, measured in terms of sales, employment, or whatever scale variable is considered most relevant, let P2 be the share of the second largest firm, and so on, in a market with N sellers. Then H is defined by