HHI Calculator (Herfindahl-Hirschman Index)
Calculate market concentration using real-world examples. Add firm market shares below.
Calculation Results
How to Calculate HHI (Herfindahl-Hirschman Index) with Real-World Examples
The Herfindahl-Hirschman Index (HHI) is the primary tool used by antitrust regulators to measure market concentration and evaluate potential competitive effects of mergers. This comprehensive guide explains how to calculate HHI with practical examples from different industries.
What is the Herfindahl-Hirschman Index?
The HHI is calculated by squaring the market share of each firm competing in a market and then summing the resulting numbers. The index can range from close to 0 (perfect competition) to 10,000 (pure monopoly).
HHI Calculation Formula
The formula for calculating HHI is:
HHI = s₁² + s₂² + s₃² + … + sₙ²
Where sₙ represents the market share of the nth firm expressed as a decimal (e.g., 25% = 0.25).
Step-by-Step Calculation Process
- Identify the relevant market – Define the product and geographic market boundaries
- Determine market shares – Calculate each firm’s percentage of total market sales
- Convert to decimals – Convert percentages to decimal form (divide by 100)
- Square each share – Multiply each decimal by itself
- Sum the squares – Add all squared values together
- Interpret the result – Compare against DOJ/FTC merger guidelines
Real-World Example: U.S. Wireless Telecommunications (2023)
| Company | Market Share (%) | Decimal | Squared Value |
|---|---|---|---|
| Verizon | 28.5 | 0.285 | 0.0812 |
| AT&T | 24.3 | 0.243 | 0.0590 |
| T-Mobile | 23.1 | 0.231 | 0.0534 |
| Dish Wireless | 8.2 | 0.082 | 0.0067 |
| Others | 15.9 | 0.159 | 0.0253 |
| Total HHI: | 0.2256 (2,256) | ||
Calculation: (0.285² + 0.243² + 0.231² + 0.082² + 0.159²) × 10,000 = 2,256
HHI Interpretation Guidelines
| HHI Range | Market Classification | Merger Implications |
|---|---|---|
| Below 1,500 | Unconcentrated | Mergers unlikely to raise concerns |
| 1,500 – 2,500 | Moderately Concentrated | Mergers may raise concerns if HHI increases by 100+ points |
| Above 2,500 | Highly Concentrated | Mergers likely to face scrutiny if HHI increases by 50+ points |
Industry-Specific Examples
1. U.S. Beer Market (2022)
- Anheuser-Busch InBev: 42% → 0.1764
- Molson Coors: 24% → 0.0576
- Constellation Brands: 10% → 0.0100
- Others: 24% → 0.0576
- Total HHI: 2,508 (Highly concentrated)
2. U.S. Search Engine Market (2023)
- Google: 83.8% → 0.7022
- Bing: 7.2% → 0.0052
- Yahoo: 2.8% → 0.0008
- Others: 6.2% → 0.0038
- Total HHI: 7,108 (Highly concentrated)
3. U.S. Smartphone Market (Q1 2023)
- Apple: 52% → 0.2704
- Samsung: 27% → 0.0729
- Others: 21% → 0.0441
- Total HHI: 3,876 (Highly concentrated)
Common Calculation Mistakes
- Incorrect market definition – Too broad or narrow geographic/product scope
- Using revenue instead of units – Can distort shares if price points differ significantly
- Excluding small firms – “Others” category should be included with combined share
- Not converting to decimals – Forgetting to divide percentages by 100
- Double-counting – Including both parent companies and subsidiaries
Advanced Considerations
For more sophisticated analyses:
- Post-merger HHI: Calculate the index after proposed mergers to assess competitive impact
- Delta analysis: Measure the change in HHI (ΔHHI) caused by a merger
- Local market HHI: Calculate for specific geographic areas when competition is local
- Weighted averages: For markets with different segments
- Dynamic analysis: Track HHI changes over time to identify trends
Regulatory Thresholds and Case Studies
The U.S. Department of Justice and Federal Trade Commission use HHI thresholds to evaluate mergers:
- Markets with HHI below 1,500 are considered unconcentrated
- Markets with HHI between 1,500-2,500 are moderately concentrated
- Markets with HHI above 2,500 are highly concentrated
- Mergers that increase HHI by more than 200 points in highly concentrated markets presumptively raise concerns
Notable cases where HHI played a key role:
- AT&T/T-Mobile (2011): Blocked due to HHI increase from 2,900 to 3,800
- Sysco/US Foods (2015): Abandoned after HHI analysis showed post-merger index would exceed 4,000
- Baker Hughes/GE Oil & Gas (2017): Approved with divestitures after HHI analysis
Alternative Concentration Measures
While HHI is the primary metric, economists also use:
- CR4 (4-Firm Concentration Ratio): Sum of top 4 firms’ market shares
- CR8 (8-Firm Concentration Ratio): Sum of top 8 firms’ market shares
- Entropy Index: Measures diversity of market shares
- Lerner Index: Measures market power through price-cost margins
Data Sources for HHI Calculations
When calculating HHI for real-world applications, reliable data sources include:
- Company annual reports (10-K filings for public companies)
- Industry trade associations (e.g., CTIA for wireless)
- Government statistics:
- U.S. Census Bureau Economic Census
- Bureau of Labor Statistics industry data
- Market research firms (Nielsen, IBISWorld, Statista)
- Securities filings (for public companies)
Limitations of HHI
While valuable, HHI has some limitations:
- Static measure: Doesn’t account for market dynamics or potential competition
- Ignores barriers to entry: High HHI might not indicate market power if entry is easy
- Geographic limitations: National HHI may mask local monopolies
- Product differentiation: Doesn’t account for quality differences between competitors
- Data quality issues: Market share data can be incomplete or outdated
Practical Applications
HHI calculations are used in:
- Merger review: By antitrust authorities to assess competitive impact
- Industry analysis: To identify oligopolistic markets
- Competitive strategy: To assess market positioning
- Regulatory impact analysis: For evaluating policy changes
- Academic research: In industrial organization studies
Calculating HHI in Excel
For quick calculations:
- List market shares in column A (as decimals)
- In column B, use formula =A1^2
- Drag the formula down for all firms
- Sum column B and multiply by 10,000
- Use conditional formatting to highlight concentration levels
Frequently Asked Questions
Why square the market shares?
Squaring gives more weight to larger firms, better reflecting their market power. A firm with 50% share contributes 2,500 to HHI (50²), while five firms with 10% each contribute only 500 total (5×10²).
How often should HHI be recalculated?
For regulatory purposes, HHI should be recalculated whenever:
- A significant merger occurs
- Market shares change by more than 5% for any firm
- New major competitors enter the market
- Annually for ongoing market monitoring
Can HHI be negative?
No, since HHI is the sum of squared market shares (all positive numbers), the minimum possible value is 0 (in a market with infinite firms each having 0% share).
How does HHI relate to the Lerner Index?
While HHI measures market concentration, the Lerner Index ((Price – Marginal Cost)/Price) measures actual market power. High HHI markets often have high Lerner Index values, but the relationship isn’t perfect due to factors like cost structures and demand elasticity.
Additional Resources
For more information on HHI calculations and antitrust analysis: