How To Calculate Hhi Index

Calculate the Herfindahl-Hirschman Index (HHI) to measure market concentration

Comprehensive Guide: How to Calculate the Herfindahl-Hirschman Index (HHI)

The Herfindahl-Hirschman Index (HHI) is the primary tool used by economists, antitrust regulators, and business strategists to measure market concentration. This comprehensive guide will explain what HHI is, how to calculate it, and how to interpret the results for antitrust analysis and market research.

What is the Herfindahl-Hirschman Index?

The HHI is a commonly accepted measure of market concentration that accounts for all firms in a market. It’s calculated by summing the squares of the market shares of each individual firm. The index ranges from 0 (perfect competition) to 10,000 (pure monopoly).

The U.S. Department of Justice and Federal Trade Commission use HHI as a screening tool for potential antitrust concerns in mergers and acquisitions. The index helps determine whether a market is:

• Unconcentrated (HHI below 1,500)
• Moderately concentrated (HHI between 1,500 and 2,500)
• Highly concentrated (HHI above 2,500)

Why HHI Matters in Antitrust Analysis

The HHI serves several critical functions in economic analysis:

1. Merger Review: Regulatory agencies use HHI to evaluate whether proposed mergers would significantly increase market concentration.
2. Market Structure Analysis: Economists use HHI to classify markets and study the relationship between concentration and performance.
3. Competitive Impact Assessment: Businesses use HHI to understand their competitive environment and potential regulatory scrutiny.
4. Policy Development: Governments use HHI data to develop competition policies and identify markets that may need intervention.

Step-by-Step Calculation of HHI

Calculating the HHI involves these key steps:

1. Define the Relevant Market:
   • Product market: What products/services are included?
   • Geographic market: What is the relevant geographic area?
   • Time period: What time frame are you analyzing?
2. Identify All Market Participants:
   • List all firms competing in the defined market
   • Include fringe competitors with small market shares
   • Consider both domestic and foreign competitors if relevant
3. Determine Market Shares:
   • Calculate each firm’s share of total market sales/revenue
   • Market shares should sum to 100% (or 1.0 if using decimals)
   • Use consistent measurement (units, revenue, or capacity)
4. Square Each Market Share:
   • Convert percentages to decimals (25% → 0.25)
   • Square each decimal (0.25² = 0.0625)
   • This gives more weight to larger firms
5. Sum the Squares:
   • Add up all the squared market shares
   • Multiply by 10,000 to get the HHI (if using decimals)
   • The result is your HHI score

HHI Calculation Example

Let’s calculate the HHI for a hypothetical market with five firms:

Firm	Market Share (%)	Market Share (decimal)	Squared Share
Firm A	30	0.30	0.0900
Firm B	25	0.25	0.0625
Firm C	20	0.20	0.0400
Firm D	15	0.15	0.0225
Firm E	10	0.10	0.0100
Total	100	1.00	0.2250

To get the HHI:

1. Sum of squared shares = 0.2250
2. Multiply by 10,000 = 2,250

This market has an HHI of 2,250, which falls in the “moderately concentrated” range according to U.S. antitrust guidelines.

Interpreting HHI Results

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

HHI Range	Market Concentration	Antitrust Implications
Below 1,500	Unconcentrated	Generally no antitrust concerns Mergers unlikely to raise issues Considered competitive market
1,500 to 2,500	Moderately Concentrated	Potential for competitive concerns Mergers that increase HHI by more than 100 may be scrutinized Possible need for further analysis
Above 2,500	Highly Concentrated	Significant antitrust concerns Mergers that increase HHI by more than 100 likely to be challenged Mergers that increase HHI by 50-100 may raise questions Presumptively anticompetitive

For merger analysis, regulators don’t just look at the post-merger HHI but also at the change in HHI (ΔHHI). The DOJ Horizontal Merger Guidelines provide specific thresholds for when mergers in concentrated markets are likely to enhance market power.

HHI in Merger Analysis

When evaluating mergers, antitrust authorities examine both:

1. Post-merger HHI: The concentration level after the merger
2. ΔHHI (Delta HHI): The change in HHI caused by the merger

The DOJ and FTC use these general standards:

• Mergers resulting in unconcentrated markets (HHI < 1,500) are unlikely to raise concerns
• Mergers resulting in moderately concentrated markets (1,500 < HHI < 2,500) that increase HHI by more than 100 points may raise concerns
• Mergers resulting in highly concentrated markets (HHI > 2,500) that increase HHI by:
  • More than 200 points are presumed likely to enhance market power
  • Between 100-200 points may raise significant competitive concerns
  • Less than 100 points are unlikely to raise concerns

Limitations of HHI

While HHI is a valuable tool, it has some limitations:

• Static Measure: HHI provides a snapshot but doesn’t account for market dynamics or potential entry
• Market Definition: Results are sensitive to how the market is defined (product and geographic scope)
• Barriers to Entry: Doesn’t consider ease of entry for new competitors
• Firm Behavior: Doesn’t account for competitive strategies or pricing behavior
• Quality Differences: Treats all market share as equal regardless of product differentiation
• Global Markets: May not fully capture international competition

For these reasons, HHI is typically used as an initial screen, with more detailed analysis following when potential concerns are identified.

Advanced HHI Applications

Beyond basic market concentration measurement, HHI has several advanced applications:

1. Merger Simulation:

   Economists use HHI in merger simulation models to predict post-merger pricing effects. These models combine HHI with demand elasticities and cost data to estimate likely price changes.

2. Market Power Analysis:

   HHI can be correlated with price-cost margins (Lerner Index) to study the relationship between concentration and market power. Research shows that higher HHI markets often have higher price-cost markups.

3. Regulatory Impact Assessment:

   Governments use HHI to evaluate the competitive effects of regulations. For example, occupational licensing requirements that raise HHI may face scrutiny.

4. International Comparisons:

   HHI allows for cross-country comparisons of market concentration, though differences in market definition can complicate interpretations.

5. Industry Studies:

   Academic researchers use HHI in studies of industry performance, innovation rates, and other economic outcomes.

HHI in Different Jurisdictions

While the basic HHI calculation is standard, different jurisdictions apply it differently:

• United States:

  DOJ and FTC use the thresholds mentioned above. The Horizontal Merger Guidelines provide detailed analysis frameworks.

• European Union:

  The European Commission uses HHI but with slightly different thresholds. Markets with HHI > 2,000 are considered concentrated, and mergers increasing HHI by > 250 in such markets may be problematic.

• Canada:

  The Competition Bureau uses HHI with thresholds similar to the U.S. but places more emphasis on the “substantial lessening of competition” test.

• Australia:

  The ACCC uses HHI but focuses more on the substantive assessment of competitive effects rather than rigid thresholds.

Calculating HHI with Market Share Data

When working with real-world data, you may need to:

1. Handle Missing Data:

   For markets with many small firms, you might group “other firms” into a single category. For example, if the top 5 firms have 80% share, you might treat the remaining 20% as one “fringe” firm.

2. Adjust for Different Measurement Bases:

   Market shares can be measured by revenue, units, capacity, or other metrics. Ensure consistency in your measurement approach.

3. Account for Vertical Integration:

   In some industries, you may need to adjust for vertical relationships that affect competitive dynamics.

4. Consider Geographic Markets:

   For products with limited shipping ranges (like cement), geographic markets may be very local. For digital products, markets may be global.

Practical Tips for HHI Calculation

• Use Consistent Data Sources: Ensure all market share data comes from the same time period and uses the same measurement method
• Include All Competitors: Even small firms should be included as their exclusion can understate concentration
• Document Your Methodology: Clearly explain how you defined the market and calculated shares
• Check Your Math: Verify that market shares sum to 100% before squaring
• Consider Sensitivity Analysis: Test how sensitive your results are to different market definitions
• Visualize the Results: Create charts showing firm shares and how they contribute to HHI

HHI and Digital Markets

Digital markets present special challenges for HHI analysis:

• Network Effects: Markets with strong network effects (like social media) can become highly concentrated very quickly
• Multi-sided Platforms: Traditional HHI may not capture the complexity of platforms serving multiple customer groups
• Dynamic Competition: Rapid innovation can change market shares quickly, making static HHI less predictive
• Zero-price Markets: Many digital services are “free,” requiring alternative measurement approaches
• Global Scale: Digital markets often span multiple countries, complicating geographic market definition

Regulators are developing new approaches to assess competition in digital markets, sometimes supplementing HHI with other metrics like:

• Number of significant competitors
• Barriers to entry and expansion
• Innovation metrics
• User switching costs
• Data advantages of incumbents

Academic Research on HHI

Extensive academic research has examined the relationship between HHI and various economic outcomes:

• Price Effects: Studies generally find that higher HHI is associated with higher prices, though the relationship varies by industry
• Innovation: Research shows an inverted-U relationship between concentration and innovation – moderate concentration may encourage R&D, but very high concentration can discourage it
• Product Quality: Some studies find that concentrated markets offer higher quality products, while others find quality declines with concentration
• Wages: Labor market concentration (measured by HHI) has been linked to lower wages in some studies
• Entrepreneurship: Highly concentrated markets may have lower rates of new business formation

For those interested in the academic literature, the National Bureau of Economic Research maintains a database of working papers on market concentration and HHI applications.

Conclusion

The Herfindahl-Hirschman Index remains the gold standard for measuring market concentration due to its simplicity and information richness. By squaring market shares, HHI gives more weight to larger firms, better capturing the potential for coordinated effects and unilateral market power.

While HHI has limitations and should be used alongside other competitive analysis tools, it provides a valuable first screen for identifying markets that may warrant closer scrutiny. For businesses, understanding HHI can help assess competitive positioning and potential regulatory risks in merger situations.

As markets evolve—particularly with the rise of digital platforms and global competition—the application of HHI continues to adapt. Regulators and economists are developing complementary metrics to address the unique challenges of modern markets while maintaining HHI as a fundamental tool in the antitrust toolkit.