Herfindahl index

This article is about the economic measure; for the index of scientific proflicacy, see H-index.

In economics, the Herfindahl index, also known as Herfindahl-Hirschman Index or HHI, is a measure of the size of firms in relationship to the industry and an indicator of the amount of competition among them. It is defined as the sum of the squares of the market shares of each individual firm. As such, it can range from 0 to 1 moving from a very large amount of very small firms to a single monopolistic producer. Decreases in the Herfindahl index generally indicate a loss of pricing power and an increase in competition, whereas increases imply the opposite.

Example

The major benefit of the Herfindahl index in relationship to such measures as the concentration ratio is that it gives more weight to larger firms. Take, for instance, two cases in which the six largest firms produce 90 % of the output:

Case 1: All six firms produce 15%, and
Case 2: One firm produces 80 % while the five others produce 2 % each.

We will assume that the remaining 10% of output is divided among 10 equally sized producers.

The six-firm concentration ratio would equal 90 % for both case 1 and case 2, but in the first case competition would be fierce where the second case approaches monopoly. The Herfindahl index for these two situations makes the lack of competition in the second case strikingly clear:

Case 1: Herfindahl index of 0.1350
Case 2: Herfindahl index of 0.6420

This behavior rests in the fact that the market shares are squared prior to being summed, giving additional weight to firms with larger size.

Formula

$H =\sum_{i=1}^n(s_i^2)$

where s_i is the market share of firm i in the market, and $n$ is the number of firms.

The Herfindahl Index (H) ranges from 1/N to one, where N is the number of firms in the market. Equivalently, the index can range up to 10,000, if percents are used as whole numbers, as in $75$ instead of $0.75$ . The maximum in this case is $100^2 = 10,000$ .

A small index indicates a competitive industry with no dominant players. If all firms have an equal share the reciprocal of the index shows the number of firms in the industry. When firms have unequal shares, the reciprocal of the index indicates the "equivalent" number of firms in the industry. Using case 2, we find that the market structure is equivalent to having 1.55521 firms of the same size.

A H index below 0.1 (or 1,000) indicates an unconcentrated index.
A H index between 0.1 to 0.18 (or 1,000 to 1,800) indicates moderate concentration.
A H index above 0.18 (above 1,800) indicates high concentration^*.

There is also a normalised Herfindahl index. Whereas the Herfindahl index ranges from 1/N to one, the normalized Herfindahl index ranges from 0 to 1. It is computed as:

$H* = {\left ( H - 1/N \right ) \over 1-1/N }$

where again, N is the number of firms in the market, and H is the usual Herfindahl Index, as above.

Problems

The usefulness of this statistic to detect and stop harmful monopolies however is directly dependent on a proper definition of a particular market (which hinges primarily on the notion of substitutability).

For example, if the statistic were to look at a hypothetical financial services industry as a whole, and found that it contained 6 main firms with 15 % market share apiece, then the industry would look non-monopolistic. However, one of those firms handles 90 % of the checking and savings accounts and physical branches (and overcharges for them because of its monopoly), and the others primarily do commercial banking and investments. In this scenario, people would be suffering due to a market dominance by one firm; the market is not properly defined because checking accounts are not substitutable with commercial and investment banking.

Another typical problem in defining the market is choosing a geographic scope. For example, firms may have 20% market share each, but may occupy five areas of the country in which they are monopoly providers and thus do not compete against each other. A service provider or manufacturer in one city is not necessarily substitutable with a service provider or manufacturer in another city, depending on the importance of being local for the business—for example, telemarketing services are rather global in scope, while shoe repair services are local.

The United States uses the Herfindahl index to determine whether mergers are equitable to society; increases of over 0.0100 points generally provoke scrutiny, although this varies from case to case. The Department of Justice considers Herfindahl indices between 0.1000 and 0.1800 to be moderately concentrated and indices above 0.1800 to be concentrated. As the market concentration increases, competition and efficiency decrease and the chances of collusion and monopoly increase.

External links

US Department of Justice example and market concentration cutoffs.
Herfindahl-Hirschman Index Calculator. Web tool for calculating pre- and post-merger Herfindahl index.
Department of Justice and Federal Trade Commission Horizontal Merger Guidelines. More detailed information about mergers, market concentration, and competition (from the Department of Justice).

Intuition

In order to get a feel for the meaning of the index, it is often useful to look at the inverse of the index (or rather 10000 / Index). This can be interpreted as number of equally sized firms that operate in this market. Example: 5 companies that have a market share of 20% each lead to an index value of 0.2000 = 5 * 0.20^2. Dividing 1 through 0.2000 gives the original result of 5.

Decomposition

The index can be expressed as

H =\frac1n+n V

where n is the number of firms and V is the statistical variance of the firm shares, defined as

V=\frac{\sum_{i=1}^n\left(s_i-1/n\right)^2}n

. If all firms have equal (identical) shares (that is, if the market structure is completely symmetric, in which case s_i = 1/n for all i) then V is zero and H equals 1/n. If the number of firms in the market is held constant, then a higher variance due to a higher level of asymmetry between firms' shares (that is, a higher share dispersion) will result in a higher index value.