Herfindahl hirschman index

What Is Herfindahl-Hirschman Index?

The Herfindahl-Hirschman Index (HHI) is a widely used measure of market concentration that helps assess the competitiveness of an industry. It is a key tool within market structure analysis, a branch of industrial organization, which examines how industries are structured and how firms behave within them. The HHI provides a single numerical value that reflects the distribution of market share among all firms in a given market, giving greater weight to larger firms. A higher HHI value typically indicates a more concentrated market and, consequently, less competition.

History and Origin

The concept behind what is now known as the Herfindahl-Hirschman Index emerged independently from two economists. The German economist Albert O. Hirschman introduced the idea in his 1945 book, National Power and the Structure of Foreign Trade, applying it to analyze the concentration of imports and exports. Five years later, in 1950, American economist Orris C. Herfindahl used a similar framework in his doctoral dissertation to analyze market concentration within the U.S. steel industry¹⁰. The measure gained significant prominence in antitrust law when the U.S. Department of Justice (DOJ) and the Federal Trade Commission (FTC) adopted it in the 1980s as a primary tool for evaluating the competitive impact of mergers and acquisitions (M&A)⁹.

Key Takeaways

• The Herfindahl-Hirschman Index (HHI) quantifies market concentration by summing the squares of individual firms' market shares.
• It is a crucial tool for regulatory bodies like the DOJ and FTC to evaluate the potential for anti-competitive outcomes from mergers and acquisitions.
• Higher HHI values indicate higher market concentration and lower competition, potentially leading to increased market power for dominant firms.
• The index ranges from near zero (highly competitive market with many small firms) to 10,000 (a complete monopoly).
• While widely used, the HHI has limitations, particularly concerning market definition and factors beyond market share that influence competition.

Formula and Calculation

The Herfindahl-Hirschman Index (HHI) is calculated by squaring the market share (expressed as a percentage) of each firm in an industry and then summing these squared values.

The formula is expressed as:

Where:

• (HHI) = Herfindahl-Hirschman Index
• (s_i) = the market share (as a percentage, e.g., 20 for 20%) of firm (i)
• (N) = the total number of firms in the market

For example, if a market has three firms with market shares of 50%, 30%, and 20%, the HHI would be calculated as:
((50^2) + (30^2) + (20^2) = 2500 + 900 + 400 = 3800)

Interpreting the Herfindahl-Hirschman Index

The value of the Herfindahl-Hirschman Index ranges from close to zero to 10,000. A lower HHI value suggests a highly competitive market with many small participants, while a higher HHI indicates a concentrated market with fewer, larger firms.

The U.S. Department of Justice and Federal Trade Commission use the HHI to classify markets and assess the competitive effects of mergers and acquisitions. Generally, the guidelines for interpretation are:

• HHI below 1,500: Indicates an unconcentrated, competitive market.
• HHI between 1,500 and 2,500: Indicates a moderately concentrated market.
• HHI above 2,500: Indicates a highly concentrated market.

Additionally, the change in HHI (ΔHHI) after a merger is a critical factor. Even in moderately concentrated markets, a significant increase in the HHI can raise antitrust concerns. For instance, recent guidelines state that a merger resulting in a post-merger HHI greater than 1,800 with an increase of more than 100 points is presumed to be unlawful.⁸

Hypothetical Example

Consider the market for online streaming services in a small country, where five major players currently operate:

• StreamFlix: 40% market share
• CineHub: 25% market share
• MovieMax: 20% market share
• SeriesSpot: 10% market share
• DocuWorld: 5% market share

To calculate the initial HHI for this market:

(HHI_{initial} = (40^2) + (25^2) + (20^2) + (10^2) + (5^2))
(HHI_{initial} = 1600 + 625 + 400 + 100 + 25)
(HHI_{initial} = 2750)

This initial HHI of 2750 indicates a highly concentrated market.

Now, imagine that CineHub proposes to acquire SeriesSpot. To determine the potential impact on market concentration, we first calculate their combined market share: (25% + 10% = 35%).

The new market shares would be:

• StreamFlix: 40%
• Combined CineHub/SeriesSpot: 35%
• MovieMax: 20%
• DocuWorld: 5%

The post-merger HHI would be:

(HHI_{post-merger} = (40^{2) + (35}2) + (20^{2) + (5}2))
(HHI_{post-merger} = 1600 + 1225 + 400 + 25)
(HHI_{post-merger} = 3250)

The change in HHI (ΔHHI) would be:

(ΔHHI = HHI_{post-merger} - HHI_{initial} = 3250 - 2750 = 500)

This hypothetical merger results in a post-merger HHI of 3250 and an increase of 500 points. Given that the post-merger HHI is well above 2,500 and the change exceeds 100 points, this proposed merger would likely face significant scrutiny from antitrust law enforcement agencies due to its potential to substantially lessen competition.

Practical Applications

The Herfindahl-Hirschman Index (HHI) finds several critical applications across finance, economics, and regulation:

• Antitrust Enforcement: The primary use of the HHI is by regulatory bodies such as the U.S. Department of Justice and the Federal Trade Commission to evaluate proposed mergers and acquisitions. It helps them determine whether a proposed combination of companies would create excessive market power or lead to a monopoly or tight oligopoly that harms consumers by reducing competition. T⁶, ⁷he Horizontal Merger Guidelines issued by these agencies provide clear thresholds for HHI values that trigger further investigation.
  *⁵ Market Analysis: Economists and industry analysts use the HHI to gauge the level of market concentration within various sectors. This analysis can inform strategic business decisions, investment analysis, and public policy discussions about industry structure.
• Portfolio Management: While less common than in market concentration, a modified form of the HHI can be applied in portfolio management to measure portfolio concentration. By squaring the proportion of each asset in a portfolio and summing them, investors can get a sense of how diversified their holdings are. A lower HHI for a portfolio indicates greater diversification.

Limitations and Criticisms

Despite its widespread use in antitrust law and market structure analysis, the Herfindahl-Hirschman Index (HHI) has several limitations and criticisms:

• Market Definition Challenges: The accuracy of the HHI heavily relies on the precise definition of the relevant market. Defining a market too broadly or too narrowly can significantly skew the HHI calculation, leading to misleading conclusions about market concentration and competition. For instance, an industry might appear competitive overall, but a specific product segment within it could be highly concentrated or even a monopoly. Geographic boundaries also play a crucial role; a national HHI might overlook regional monopolies.
• Ignores Product Differentiation and Innovation: The HHI solely considers market share and does not account for qualitative factors like product quality, innovation, brand loyalty, or consumer choice. A⁴ market with a high HHI might still be highly competitive if firms are constantly innovating or offering highly differentiated products.
• Doesn't Account for Potential Competition: The index reflects the current state of the market and doesn't explicitly factor in the threat of new entrants or the ease of entry (low barriers to entry). A concentrated market might remain competitive if potential entrants could easily enter and disrupt the market.
  *³ Static Measure: The HHI is a static snapshot and may not fully capture dynamic market forces or evolving industry landscapes, particularly in rapidly changing sectors like network industries. Critics argue that its application in such industries might lead to misjudgments regarding consumer welfare.
  *² Data Availability: Calculating the HHI requires accurate and complete market share data for all firms in the relevant market, which can be challenging to obtain, especially for privately held companies or niche markets. Some sources suggest that using HHI for comparisons of differences in concentration values may not be appropriate and caution should be exercised.

¹## Herfindahl-Hirschman Index vs. Concentration Ratio

The Herfindahl-Hirschman Index (HHI) and concentration ratio are both measures of market concentration, but they differ in their calculation and the insights they provide.

Confusion often arises because both aim to quantify market power. However, the HHI offers a more comprehensive picture of the entire market's competitive landscape by incorporating all firms and giving disproportionate weight to those with larger shares. For example, two markets could have the same 4-firm concentration ratio (CR4), but one might be dominated by a single very large firm (higher HHI), while the other has four similarly sized large firms (lower HHI, but still high). This distinction makes the HHI a preferred tool for antitrust authorities when evaluating potential anti-competitive effects from mergers and acquisitions.

FAQs

What does a high HHI mean?

A high Herfindahl-Hirschman Index (HHI) indicates that a market is highly concentrated, meaning a small number of firms control a significant portion of the total market share. This typically suggests less competition and potentially greater market power for the dominant firms, which can raise concerns for antitrust law enforcement.

Is HHI used in other areas besides antitrust?

While primarily known for its use in antitrust law and industrial organization, the underlying mathematical concept of squaring shares and summing them can be adapted. For example, a modified HHI can be used in portfolio management to assess the concentration of assets within a portfolio, helping to evaluate diversification levels.

How do government agencies use the HHI for mergers?

U.S. regulatory bodies like the Department of Justice (DOJ) and the Federal Trade Commission (FTC) use the HHI as a screening tool for proposed mergers and acquisitions. They calculate the HHI both before and after a merger. If the post-merger HHI is high (e.g., above 2,500) and the merger significantly increases the HHI (e.g., by more than 100 points), it triggers a presumption of anti-competitive harm, leading to a more in-depth investigation.