# Herfindahl index

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## Herfindahl-Hirschman Index

An index of market concentration the U.S. Department of Justice uses to determine whether a monopoly is forming. The scale goes from zero to 10,000, with 10,000 indicating that a single company controls 100% of the market share in a given industry. An HHI of less than 1000 indicates a market with little concentration, which the Justice Department prefers. Any merger or acquisition leading to an increase of more than 100 when the HHI was previously greater than 1,800 may lead to antitrust action against the company involved.
Fig. 83 Herfindahl index. The Herfindahl index (H) is the sum of the squared firm sizes, all measured as a proportion of total market size. In the figure, for market A, H = (0.12)2 X 5 + (0.08)2X 5 = 0.104. If all firms in the market are the same size, then the value of the index is equal to the reciprocal of the number of firms; thus, if there are 10 firms all of the same size, H = 0.1. The upper limit of the index is 1, which occurs when there is a monopoly. The figure shows that market B (H = 0.190), with a single dominant firm, is almost twice as concentrated as market A, despite the latter having fewer firms.

## Herfindahl index

a measure of the degree of SELLER CONCENTRATION in a MARKET that takes into account the total number of firms in the market and their relative size distribution (share of total market output). See CONCENTRATION MARKET.
Collins Dictionary of Economics, 4th ed. © C. Pass, B. Lowes, L. Davies 2005
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However, because the pluralism measure is based on a Herfindahl index, which is simply the sum of the squared shares, B&M's inclusion of both 1 - H and the shares introduces an odd quadratic specification in which the quadratic term for each share is constrained to have the same coefficient, Roman Catholicism enters only with the quadratic term and not an associated linear term, and the shares for Buddhists and Other Eastern Religions are constrained to have the same coefficient (since B&M combine these two in the share but not the Herfindahl calculation).
[HI.sub.it] The Herfindahl Index (sum of squared market shares) for industry i, year t is used to measure the market structure in each sector.
Public nonteaching hospitals are more likely to be located in a less competitive market, indicated by a larger Herfindahl index. (8) Public teaching hospitals are even more different from private hospitals.
Measuring inter-hospital competition within each hospital's county, a Herfindahl index was computed using bed size data for short-term general hospitals from the Area Resource File [USDHHS, 1998].
Previous research (Emmons and Schmid, 1999a) finds a link between the concentration of local commercial-bank deposit shares (as measured by the Herfindahl index) and indicators of credit-union efficiency (wage expense) and risk-taking (loan-loss allowances).
Patients living in the same MSA (or county for non-MSA residents) were all assigned the same value for facilities-per-square-mile and the Herfindahl index covariates (defined as the sum of squares of each facility's market share in the MSA or county).
Market growth and per capita income are the most important variables, but the Herfindahl index, a measure of market concentration, also plays a role after controlling for costs.
Herfindahl index is calculated as the sum of squares of the financial market shares of all Compustat firms in the Fama-French (1997) 48-industry classification.
The ratings on six P&I classes were affirmed because the transaction's key metrics, including Moody's loan-to-value (LTV) ratio, Moody's stressed debt service coverage ratio (DSCR) and the transaction's Herfindahl Index (Herf), are within acceptable ranges.
We adopt the Herfindahl index of the number of financial institutions as a proxy for the intensity of competition among financial institutions.
Although a Herfindahl index of 1 (indicating that 100% of ownership is concentrated in a single shareholder) leads to a decrease of 7.33% (the coefficient's marginal effect) in the likelihood of having a board, a Herfindahl index of 0.2 (the theoretical minimum for our measure, which indicates that the firm's equity is divided equally among the five largest shareholders) leads to a decrease of only 1.5% in the probability of having a board.

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