Herfindahl-Index

The Herfindahl index ( Orris Clemens Herfindahl after, 1918-1972 ) also: Hirschman Index or Herfindahl -Hirschman index called (abbreviation: HHI, character: ), is the most commonly used indicator to measure the concentration (for example, in a market ).

When calculating the Herfindahl index is assumed that the distribution of objects to several groups: for example, about the total sales of a product in a given market shares on a certain number of producers on that manufacture the product. However, the sales usually not distributed evenly to all producers. About the degree of concentration of sales to one or a few suppliers now are the Herfindahl index information.

Calculation

HHI

The HHI is calculated as follows:

With

It denotes the -th (positive ) characteristic value.

In words, the HHI, the sum of squared market shares of competitors of a market. Mathematically, this value is between, where 1 corresponds to a monopoly. In economics, it is common to lose the percent sign (or to multiply the percentage market shares above 100 ), the resulting HHI can take values ​​between. The values ​​can be converted into each other by multiplying or dividing by 10,000.

The European Commission gives the following simplified example for better understanding: The HHI measures market concentration by summing the squared market shares of all suppliers in an industry. If keeping in a market, for example, five companies had a share of 20 %, the HHI is the HHI 400 400 400 400 400 = 2000. Higher for a particular market, the greater is the share of production, accounts for a small number of companies. In general, the market concentration in an HHI below 1000 may be referred to as low, from 1000 to 1800 as moderate and above 1800 as strong.

Normalized HHI

The normalized HHI is calculated as follows:

Or

This means the share attributable to producer paragraph.

The Herfindahl index is thus the normalized sum of the squared share values ​​and can take values ​​of up, with the minimum value at equal distribution of sales across all providers ( = minimum concentration ), the maximum value, however, at the maximum concentration (ie, when the entire paragraph on a single vendor is omitted) is achieved.

The Herfindahl index is not invariant with respect to the number of providers. If invariance with respect to the number of providers needed, offer itself as an alternative to other inequality measures.

Areas of application

The Herfindahl index is used mainly in the following areas:

• In economics and in the area of antitrust law for the detection of the dominant position of one or more provider: High values ​​of suggest that one or a few producers control large parts of the market, while stands for a monopoly.
• In market research as a measure of brand loyalty of a customer or group of customers: the higher, the stronger the customer focused its purchases on one or a few brands. Is always the same brand purchased is the same.
• In the operating system teaching when it comes to the fair distribution of resources.