Herfindahl-Hirschman Index (HHI): Definition, Formula, and Example

What Is the Herfindahl-Hirschman Index (HHI)?

The Herfindahl-Hirschman Index (HHI) is a common measure of market concentration and is used to determine market competitiveness, often pre- and post-merger and acquisition (M&A) transactions.

The index measures the size of companies relative to the size of the industry they are in and the amount of competitiveness. The HHI is calculated by squaring the market share of each firm competing in a market and then summing the resulting numbers. It can range from close to zero to 10,000, with lower values indicating a less concentrated market.

Formula and Calculation of the Herfindahl-Hirschman Index (HHI)

The HHI is a commonly accepted measure of market concentration. It is calculated by squaring the market share of each firm competing in a market and then summing the resulting numbers. It can range from close to zero to 10,000. The U.S. Department of Justice uses the HHI for evaluating potential merger antitrust issues.

$\begin{aligned}&HHI=s^2_1+s^2_2+s^2_3+\dots s^2_n\\&\textbf{where:}\\&s_n=\text{the market share percentage of firm } n\\& \qquad\,\text{ expressed as a whole number, not a decimal}\end{aligned}$​HHI=s12​+s22​+s32​+…sn2​where:sn​=the market share percentage of firm n expressed as a whole number, not a decimal​

What the Herfindahl-Hirschman Index (HHI) Can Tell You

The closer a market is to a monopoly, the higher the market's concentration (and the lower its competition). If, for example, there was only one firm in an industry, that firm would have 100% market share, and the HHI would equal 10,000, indicating a monopoly.

If there were thousands of firms competing, each would have roughly 0% market share, and the HHI would be close to zero, indicating nearly perfect competition.

The U.S. Department of Justice considers a market with an HHI of less than 1,500 to be a competitive marketplace, an HHI of 1,500 to 2,500 to be a moderately concentrated marketplace, and an HHI of 2,500 or greater to be a highly concentrated marketplace.

As a general rule, mergers that increase the HHI by more than 200 points in highly concentrated markets raise antitrust concerns, as they are assumed to enhance market power under Section 5.3 of the Horizontal Merger Guidelines jointly issued by the Justice Department and the Federal Trade Commission (FTC).

The primary advantage of the HHI is the simplicity of the calculation needed to determine it and the small amount of data required for the calculation. The primary disadvantage of the HHI stems from the fact that it is such a simple measure that it fails to take into account the complexities of various markets in a way that allows for a genuinely accurate assessment of competitive or monopolistic market conditions.

Example of the Herfindahl-Hirschman Index (HHI)

The HHI is calculated by taking the market share of each firm in the industry, squaring them, and summing the result, as depicted in the equation above. Consider the following hypothetical industry with four total firms:

1. Firm 1 market share = 40%
2. Firm 2 market share = 30%
3. Firm 3 market share = 15%
4. Firm 4 market share = 15%

The HHI is calculated as:

$\begin{aligned}HHI &= 40^2 + 30^2 + 15^2 + 15^2\\ &= 1,600 + 900 + 225 + 225 = 2,950\end{aligned}$HHI​=402+302+152+152=1,600+900+225+225=2,950​

This HHI value is considered a highly concentrated industry, as expected because there are only four firms. However, the number of firms in an industry does not necessarily indicate anything about market concentration, which is why calculating the HHI is important.

For example, assume an industry has 20 firms. Firm 1 has a market share of 48.59%, and each of the 19 remaining firms has a market share of 2.71% each. The HHI would be exactly 2,500, indicating a substantially highly concentrated market. If Firm 1 had a market share of 35.82% and each of the remaining firms had a 3.38% market share, the HHI would be exactly 1,500, indicating a competitive marketplace.

Limitations of the Herfindahl-Hirschman Index (HHI)

The basic simplicity of the HHI carries some inherent disadvantages, primarily in terms of failing to define the specific market that is being examined in a proper, realistic manner.

For example, consider a situation in which the HHI is used to evaluate an industry determined to have 10 active companies, and each company has about a 10% market share. Using the basic HHI calculation, the industry would appear highly competitive.

However, within the marketplace, one company might have as much as 80% to 90% of the business for a specific segment of the market, such as the sale of one specific item. That firm would thus have nearly a total monopoly for the production and sale of that product.

Another problem in defining a market and considering market share can arise from geographic factors. This problem can occur when companies within an industry have roughly equal market share, but they each operate only in specific areas of the country, so that each firm, in effect, has a monopoly within the specific marketplace in which it does business.

For these reasons, for the HHI to be properly used, other factors must be taken into consideration, and markets must be very clearly defined.

History of the Herfindahl-Hirschman Index (HHI)

The concept behind the HHI initially emerged in a 1945 book by German economist Albert O. Hirschman titled "National Power and the Structure of Foreign Trade." The method proposed by Hirschman differed from existing measures of concentration by placing a more significant weighting on larger firms whose greater market share has a greater impact on the level of competitiveness in the market.

A few years after Hirschman outlined this system for measuring market concentration, American economist Orris C. Herfindahl repurposed the idea in his 1950 doctoral dissertation, "Concentration in the U.S. Steel Industry."

Whereas Hirschman applied the idea to the concentration of imports and exports on a countrywide basis, Herfindahl used the framework to analyze the competitiveness of the steel industry. Herfindahl refers to Hirschman's work in a footnote.

The Bottom Line

The Herfindahl-Hirschman Index (HHI) is used to determine market competitiveness. It measures the degree of concentration within a specific market. A market with an HHI of less than 1,500 is considered a competitive marketplace, an HHI of 1,500 to 2,500 is moderately concentrated, and an HHI of 2,500 or greater is highly concentrated.