### Herfindahl-Hirschman Index Definition

The Herfindahl-Hirschman Index (HHI), also shortened to Herfindahl Index is a commonly accepted method of measurement of market concentration as a means to ascertain whether competitiveness exists within an industry or if market monopoly has set in. More often than not, the Herfindahl-Hirschman Index measures market concentration of the top 50 companies of an industry.

Economists calculate the Herfindahl-Hirschman Index (HHI) in an industry by squaring the market share of competing firms pertaining to that particular industry and then adding up the squares. The index is measured in points – any value above zero and up to 10,000 points is an acceptable value for the HHI.

### A Little More on What is the Herfindahl-Hirschman Index

Market monopoly stems from high market concentration and a significant reduction of competition. Any firm that has a monopoly in the market will have an HHI close to 10,000; in case the firm is the only player in its industry segment, it will have a 100% market share and thus, an HHI of 10,000. Conversely, if there were several thousand competing firms in an industry, each firm would have virtually 0% market share. In such an instance, the HHI would approach zero, signifying a scenario of perfect competition.

According to the U.S. Department of Justice, any industry with an HHI below 1,500 is considered a competitive industry. Similarly, an HHI value between 1,500 and 2,500 denotes a moderately concentrated industry. Finally, an industry with an HHI of 2,500 or more is designated a highly concentrated industry. Generally, any merger that raises the the Herfindahl-Hirschman Index by more than 200 points in extremely concentrated markets renders it vulnerable to antitrust issues.

### Herfindahl-Hirschman Index Example Calculations

The Herfindahl-Hirschman Index is calculated by squaring the market share of competing firms and then adding up the squares:

HHI = (market share 1)² + (market share 2)²+ (market share 3)² + … + (market share n)² , market share values with decimals being rounded off as whole numbers

Let us suppose there are four footwear manufacturers in an industry:

Manufacturer 1 market share = 30%

Firm two market share = 26%

Firm three market share = 24%

Firm four market share = 20%

The HHI calculation is as follows:

HHI = 30² + 26² + 24² + 20² = 900 + 676 + 576 + 400 = 2,552

In the above example, while the presence of only four firms in an industry anyhow depicts a highly concentrated industry, this depiction is reinforced by the HHI value of 2,552, which, according to the U.S. Department of Justice, corresponds to a highly concentrated industry. The HHI thus comes across as an invaluable and reliable index to measure market concentration.

### References for Herfindahl Index

- https://www.investopedia.com/terms/h/hhi.asp
- https://en.wikipedia.org/wiki/Herfindahl_index
- https://investinganswers.com/financial-dictionary/economics/herfindahl-index-1923

### Academic Research on Herfindahl Index

__The ____Herfindahl index ____in theory and practice__, Kwoka Jr, J. E. (1985). *Antitrust Bull.*, *30*, 915.

__A generalized interpretation of the ____Herfindahl index__, Kelly, W. A. (1981). *Southern Economic Journal*, 50-57.

__Adjusting the ____Herfindahl index ____for close substitutes: an application to pricing in civil aviation__, Lijesen, M. G. (2004). *Transportation Research Part E: Logistics and Transportation Review*, *40*(2), 123-134. This paper examines the wide usage and criticism of the Herfindahl–Hirschman index (HHI) as a well known concentration measure. The paper explores the shortcomings of the HHI especially its sensitivity for the relevant market definition, in terms of both geographical boundaries and in terms of product homogeneity. The paper develops an adjusted version of the HHI that accounts for close substitutes. The paper further suggests that the adjusted index generates better results than the traditional indicator.

__Using the ____Herfindahl Index ____to measure concentration__, Weinstock, D. S. (1982). Using the Herfindahl Index to measure concentration. *Antitrust Bull.*, *27*, 285.

__Harmony, statistical inference with the ____Herfindahl ____H ____index ____and C ____index__, Taplin, R. H. (2003). Harmony, statistical inference with the Herfindahl H index and C index. *Abacus*, *39*(1), 82-94. This paper examines the use of the Herfindahl H index and C index in meaures of harmony of accounting measurement practices by summarizing extent by which companies use the same accounting measures. It explores the absence of standard accounting errors of this system, and attempts to fill this gap in the past literatures by providing formulae to estimate the standard error of the H and C indices calculated from a sample.

__Aggregate industry cost functions and the ____Herfindahl index__, Dickson, V. (1994). Aggregate industry cost functions and the Herfindahl index. *Southern Economic Journal*, 445-452.

__Estimating the ____herfindahl index ____from concentration ratio data__, Michelini, C., & Pickford, M. (1985). Estimating the herfindahl index from concentration ratio data. *Journal of the American Statistical Association*, *80*(390), 301-305. This paper suggests that high concentration ratio Herfindahl (H) index correlations found in United States studies may be biased upward by using estimated H. Guided by income distribution studies, a new family of H estimators is proposed. The methodology for calculating the bounds from concentration ratio data is described, and the efficacy of various estimators is tested.

__An empirical investigation of the critical ____Herfindahl index ____in banking__, Daskin, A. J., & Wolken, J. D. (1989). An empirical investigation of the critical Herfindahl index in banking. *Journal of Economics and Business*, *41*(2), 95-105. This paper finds evidence of a critical Herfindahl index in the market for commercial and industrial loans using a 1985 data on unit banking states. The paper improves on earlier work on critical concentration in banking by using a superior switching regressions technique and data collected after the significant deregulation of depository institutions of the early 1980s.

__Hirschman–____Herfindahl index ____determination under incomplete information__, Nauenberg, E., Basu, K., & Chand, H. (1997). Hirschman–Herfindahl index determination under incomplete information. *Applied Economics Letters*, *4*(10), 639-642. This paper utilizes techniques from combinatorics to derive a closed form solution for an estimator of that portion of a Hirschman–Herfindahl index which measures concentration for that segment of the market with unattributed market share.

__Simulation of a Hirschman–____Herfindahl index ____without complete market share information__, Nauenberg, E., Alkhamisi, M., & Andrijuk, Y. (2004). Simulation of a Hirschman–Herfindahl index without complete market share information. *Health economics*, *13*(1), 87-94. This paper utilizes maximum likelihood methods to simulate a Hirschman-Herfindahl index (HHI) for markets in which complete market share information is unavailable or delayed. The paper suggests that with the development of this method, regulatory authorities monitoring health-care competition or health-care firms can now use market surveys–in which reliable recall is often limited to the largest three or four firms–to produce an on-the-spot measure of market concentration.

__Interval estimation of the ____Herfindahl____-Hirschman ____index ____under incomplete market information__, Naldi, M., & Flamini, M. (2014, March). Interval estimation of the Herfindahl-Hirschman index under incomplete market information. In *Computer Modelling and Simulation (UKSim), 2014 UKSim-AMSS 16th International Conference on* (pp. 318-323). IEEE. In this paper, an interval estimate is provided for the Herfindahl-Hirschman Index (HHI) when the knowledge about the market is incomplete, with just the largest market shares being known. Two rigorous bounds are provided for the HHI, without any further assumptions.

__A probabilistic approach of Hirschman-____Herfindahl Index ____(HHI) to determine possibility of market power acquisition__, Kanagala, A., Sahni, M., Sharma, S., Gou, B., & Yu, J. (2004, October). A probabilistic approach of Hirschman-Herfindahl Index (HHI) to determine possibility of market power acquisition. In *Power Systems Conference and Exposition, 2004. IEEE PES* (pp. 1277-1282). IEEE. This paper presents a probabilistic approach of the application of the Hirschman-Herfindahl Index (HHI) for the estimation of market concentration. A region of uncertainty in terms of the HHI is defined, the probability of any market participant acquiring market power is estimated, and a trend for this probability with the changes of HHI is identified by the analytical approach.