How To Calculate Herfindahl Index

Calculate market concentration using the Herfindahl Index to assess competition levels

The Herfindahl-Hirschman Index (HHI) is the most commonly used measure of market concentration, employed by economists, antitrust regulators, and business strategists worldwide. This comprehensive guide explains how to calculate HHI, interpret its results, and apply it to real-world market analysis.

What is the Herfindahl-Hirschman Index?

The HHI is a statistical measure that evaluates the degree of competition in a market by calculating the sum of the squares of the market shares of all firms in that market. It ranges from 0 (perfect competition) to 10,000 (pure monopoly), with higher values indicating greater market concentration.

The index was developed independently by economists Orris C. Herfindahl and Albert O. Hirschman in the 1940s. Today, it’s the primary tool used by:

• The U.S. Department of Justice and Federal Trade Commission for merger reviews
• The European Commission’s competition authority
• Corporate strategists assessing competitive landscapes
• Economic researchers studying market structures

The HHI Formula

HHI = s₁² + s₂² + s₃² + … + sₙ²

Where:

• s = market share of each firm (expressed as a decimal)
• n = number of firms in the market

For example, if a market has three firms with shares of 50%, 30%, and 20%, the HHI would be:

(0.5)² + (0.3)² + (0.2)² = 0.25 + 0.09 + 0.04 = 0.38 or 3,800

Step-by-Step Calculation Process

1. Identify the relevant market

   Define the product market (what products/services) and geographic market (where they’re sold). This is crucial as HHI results vary dramatically based on market definition.

2. Determine market shares

   Collect data on each firm’s market share, typically measured by:

   • Revenue share
   • Unit sales share
   • Capacity share
   • Employment share (for labor markets)

   Shares should sum to 100%. For our calculator, enter percentages (e.g., 25 for 25%).

3. Convert to decimals

   Convert each percentage share to its decimal equivalent by dividing by 100.

4. Square each share

   Multiply each decimal share by itself.

5. Sum the squares

   Add up all the squared shares to get the HHI.

6. Multiply by 10,000 (optional)

   Some practitioners multiply by 10,000 to express the index as a whole number between 0 and 10,000. Our calculator automatically handles this conversion.

Interpreting HHI Results

The U.S. Department of Justice and Federal Trade Commission use these general guidelines for interpreting HHI values:

HHI Range	Market Type	Competition Level	Regulatory Implications
Below 1,500	Unconcentrated	High competition	Mergers unlikely to raise concerns
1,500 to 2,500	Moderately concentrated	Moderate competition	Mergers may raise concerns
Above 2,500	Highly concentrated	Low competition	Mergers likely to face scrutiny

For example, the U.S. wireless telecommunications market had an HHI of approximately 2,600 in 2023, indicating a highly concentrated market dominated by three major carriers (Verizon, AT&T, and T-Mobile).

Change in HHI (ΔHHI)

Antitrust authorities often examine the change in HHI (ΔHHI) resulting from proposed mergers. The general guidelines are:

• ΔHHI below 100: Unlikely to raise competitive concerns
• ΔHHI between 100-200: Potential concerns in concentrated markets
• ΔHHI above 200: Likely to raise significant competitive concerns

Effective Number of Firms (N)

The HHI can be converted to the “effective number of firms” (N) using this formula:

N = 1 / HHI

Where HHI is expressed as a decimal (divide by 10,000 if using the 0-10,000 scale).

For example:

• An HHI of 1,800 → N ≈ 5.56 (equivalent to 5-6 equal-sized firms)
• An HHI of 3,000 → N ≈ 3.33 (equivalent to 3 equal-sized firms)
• An HHI of 10,000 → N = 1 (monopoly)

Real-World Examples of HHI

Industry	Year	HHI	Dominant Firms	Regulatory Status
U.S. Wireless Telecommunications	2023	2,600	Verizon, AT&T, T-Mobile	Highly concentrated
U.S. Beer Production	2022	2,800	Anheuser-Busch, Molson Coors	Highly concentrated
U.S. Airline Industry	2023	1,800	American, Delta, United, Southwest	Moderately concentrated
U.S. Search Engines	2023	8,500	Google	Near monopoly
U.S. Coffee Shops	2023	1,200	Starbucks, Dunkin’, local shops	Unconcentrated

Limitations of the HHI

While the HHI is the standard measure of market concentration, it has several limitations:

1. Market definition challenges

   The HHI is highly sensitive to how the market is defined. Narrow definitions can overstate concentration, while broad definitions can understate it.

2. Ignores barriers to entry

   The HHI doesn’t account for how easy it is for new firms to enter the market, which can significantly affect competition.

3. Static measure

   It provides a snapshot but doesn’t show trends over time or potential future competition.

4. Assumes symmetry

   The HHI treats all firms symmetrically, not accounting for differences in cost structures or product differentiation.

5. Data requirements

   Accurate market share data can be difficult to obtain, especially in rapidly changing industries.

Alternative Measures of Market Concentration

While the HHI is the most commonly used measure, economists also use these alternatives:

• Concentration Ratio (CRₙ)

  The combined market share of the top n firms (typically CR₄ or CR₈). Simpler but less comprehensive than HHI.

• Lerner Index

  Measures market power by comparing price to marginal cost. Higher values indicate more market power.

• Rosenbluth Index

  Similar to HHI but gives more weight to smaller firms.

• Entropy Measure

  Uses information theory to measure concentration, sensitive to the number of firms.

Practical Applications of HHI

1. Merger Review and Antitrust Enforcement

The primary use of HHI is in merger review by competition authorities. The U.S. Horizontal Merger Guidelines use these thresholds:

• Safe Harbor: Mergers resulting in HHI below 1,500 are unlikely to raise concerns
• Potential Concerns: Mergers resulting in HHI between 1,500-2,500 with ΔHHI above 100
• Presumption of Anticompetitive: Mergers resulting in HHI above 2,500 with ΔHHI above 200

For example, when AT&T attempted to acquire T-Mobile in 2011, the deal was blocked partly because it would have increased the U.S. wireless HHI from about 2,500 to over 3,000.

2. Industry Analysis and Competitive Strategy

Businesses use HHI to:

• Assess the competitive intensity of markets they’re entering
• Identify potential acquisition targets that wouldn’t raise antitrust concerns
• Monitor changes in market structure over time
• Develop pricing strategies based on market power

3. Economic Research

Economists use HHI to study:

• The relationship between market concentration and innovation
• How concentration affects prices and consumer welfare
• The impact of regulation on market structure
• International comparisons of market concentration

Calculating HHI with Different Data Sources

The accuracy of your HHI calculation depends on the quality of your market share data. Common data sources include:

1. Government Statistics

   Agencies like the U.S. Census Bureau, Eurostat, or national statistical offices often publish industry concentration data.

2. Industry Reports

   Market research firms (IBISWorld, Statista, Nielsen) provide market share estimates for many industries.

3. Company Financial Reports

   Public companies disclose revenue figures that can be used to estimate market shares.

4. Trade Associations

   Industry groups often collect and publish market data for their members.

5. Survey Data

   For some markets, consumer or business surveys may be the best source of market share information.

Advanced HHI Applications

Weighted HHI

Some analysts use a weighted HHI where firms are weighted by additional factors like:

• Geographic presence
• Product line breadth
• Technological capabilities

HHI for Multi-Product Firms

For firms operating in multiple markets, you can calculate:

• Overall HHI: Treating all products as one market
• Product-specific HHIs: Calculating separately for each product market

Dynamic HHI Analysis

Tracking HHI over time can reveal:

• Trends in market concentration
• The impact of regulatory changes
• Effects of technological disruption

Common Mistakes in HHI Calculation

1. Incorrect market definition

   Too narrow or too broad market definitions can lead to misleading HHI values.

2. Using revenue instead of market shares

   HHI requires market shares (percentages), not absolute revenue figures.

3. Ignoring small firms

   Even firms with small market shares contribute to the HHI and should be included.

4. Double-counting affiliated firms

   Subsidiaries or affiliated companies should be treated as part of their parent company.

5. Using outdated data

   Market shares can change rapidly, especially in technology sectors.

Regulatory Frameworks Using HHI

United States

The U.S. Department of Justice and Federal Trade Commission use HHI as the primary screen for horizontal mergers. Their Horizontal Merger Guidelines provide detailed thresholds and analysis frameworks.

European Union

The European Commission uses HHI in its merger assessment guidelines, though it places more emphasis on qualitative factors than the U.S. approach.

Other Jurisdictions

Most developed countries use HHI in their competition analysis, including:

• Canada (Competition Bureau)
• United Kingdom (Competition and Markets Authority)
• Australia (Australian Competition & Consumer Commission)
• Japan (Japan Fair Trade Commission)

Case Studies in HHI Application

1. Blocked AT&T/T-Mobile Merger (2011)

The proposed $39 billion merger between AT&T and T-Mobile would have:

• Increased the U.S. wireless HHI from ~2,500 to ~3,000
• Reduced the number of national carriers from 4 to 3
• Resulted in a ΔHHI of over 800 points

The DOJ successfully blocked the merger, arguing it would “substantially lessen competition” in violation of the Clayton Act.

2. Approved Disney/Fox Merger (2019)

Despite creating a media giant, the Disney/Fox merger was approved because:

• The relevant markets (theatrical distribution, cable networks) had HHIs below 2,500
• ΔHHI increases were modest due to the presence of other major players (Netflix, Amazon, Comcast)
• Divestitures were required for certain assets

3. European Commission’s Google Cases

The EC has used HHI analysis in several cases against Google:

• Search market HHI exceeding 8,000 (near monopoly)
• Android mobile OS market HHI over 6,000
• Online advertising markets with HHIs between 2,000-4,000

These high concentration levels contributed to findings of dominance under EU competition law.

Calculating HHI for Different Market Structures

Perfect Competition

In a perfectly competitive market with many small firms:

• Each firm has a market share approaching 0%
• HHI approaches 0
• N approaches infinity

Monopolistic Competition

Markets with many firms selling differentiated products:

• Typical HHI: 500-1,500
• Example: Restaurants, retail clothing

Oligopoly

Markets dominated by a few large firms:

• Typical HHI: 1,500-3,000
• Example: Automobiles, airlines, telecommunications

Monopoly

Single-firm markets:

• HHI = 10,000
• N = 1
• Example: Local utilities, some patented drugs

HHI and Market Power

While HHI measures market concentration, economists often want to understand its relationship to market power. Key insights:

• HHI ≠ Market Power: High HHI suggests potential for market power but doesn’t prove its exercise
• Non-linear relationship: The impact of concentration on prices increases with HHI
• Threshold effects: Most price effects occur when HHI exceeds 1,800-2,000

Empirical studies suggest:

• An HHI increase from 1,000 to 1,800 is associated with price increases of 3-5%
• An HHI above 2,500 is associated with prices 5-10% above competitive levels

Software Tools for HHI Calculation

While our calculator provides a simple interface, professionals often use:

• Stata: Econometric software with HHI calculation commands

  // Stata code for HHI
  gen share_sq = share^2
  egen hhi = total(share_sq), by(market)
                      

• R: Open-source statistical software

  # R code for HHI
  hhi <- sum(market_shares^2)
                      

• Python: Using pandas for market analysis

  # Python code for HHI
  import pandas as pd
  df['share_squared'] = df['market_share']**2
  hhi = df['share_squared'].sum()
                      

• Excel: Simple spreadsheet calculations

  =SUM(A2:A10^2)  // Where A2:A10 contains decimal market shares
                      

Frequently Asked Questions

1. What's the difference between HHI and CR4?

The Concentration Ratio (CR4) simply adds the market shares of the top 4 firms. HHI considers all firms and gives more weight to larger firms (since squaring amplifies larger numbers). HHI is generally preferred as it uses more information and is more sensitive to market structure changes.

2. How often should HHI be recalculated?

For regulatory purposes, HHI is typically calculated annually. For business strategy, quarterly updates may be appropriate in fast-moving industries. Always recalculate after:

• Major mergers or acquisitions
• Entry/exit of significant competitors
• Regulatory changes affecting market structure

3. Can HHI be used for international comparisons?

Yes, but with caution. Differences in market definition across countries can make direct comparisons misleading. The OECD publishes harmonized HHI data for many industries to facilitate international comparisons.

4. What's a "good" HHI for consumers?

From a consumer welfare perspective, lower HHI values (below 1,500) are generally better as they indicate more competition, which typically leads to lower prices, better quality, and more innovation. However, some concentrated markets (HHI 1,500-2,500) can also deliver consumer benefits through economies of scale.

5. How does HHI relate to the Lerner Index?

The Lerner Index (L = (P-MC)/P) measures market power directly, while HHI measures the structural conditions that may lead to market power. Empirical studies find a positive correlation between HHI and Lerner Index values, though the relationship isn't perfect due to factors like cost structures and demand elasticity.

Conclusion

The Herfindahl-Hirschman Index remains the gold standard for measuring market concentration due to its comprehensive nature and sensitivity to market structure changes. Whether you're a business strategist assessing competitive landscapes, a regulator evaluating mergers, or an economist studying market dynamics, understanding how to calculate and interpret HHI is an essential skill.

Remember that while HHI provides valuable quantitative insights, it should be used alongside qualitative analysis of factors like:

• Barriers to entry and expansion
• Buyer power in the market
• Potential for disruptive innovation
• Regulatory environment

For the most accurate analysis, always use the most current and comprehensive market share data available, and consider consulting competition economics experts for complex market definitions or high-stakes decisions.