How To Calculate Hhi

Calculate market concentration using the standard HHI formula accepted by the U.S. Department of Justice and Federal Trade Commission.

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

The Herfindahl-Hirschman Index (HHI) is the primary tool used by antitrust regulators, economists, and business strategists to measure market concentration and assess competitive balance in an industry. This comprehensive guide explains everything you need to know about calculating and interpreting HHI values.

What is the Herfindahl-Hirschman Index?

The HHI is a commonly accepted measure of market concentration that accounts for:

• The number of firms in a market
• The distribution of market shares among those firms
• The relative size of each firm compared to the market

Unlike simpler concentration ratios (like the CR4 or CR8), the HHI considers the entire market structure by squaring each firm’s market share and summing those squares. This mathematical approach gives more weight to larger firms, making it particularly sensitive to market dominance by one or a few players.

The HHI Formula

The Herfindahl-Hirschman Index is calculated using this 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 market shares of 60%, 30%, and 10% respectively, the HHI would be calculated as:

(0.60)² + (0.30)² + (0.10)² = 0.36 + 0.09 + 0.01 = 0.46 or 4,600

Why the HHI Matters in Antitrust Analysis

The U.S. Department of Justice (DOJ) and Federal Trade Commission (FTC) rely heavily on HHI values when evaluating:

1. Potential mergers and acquisitions
2. Market dominance investigations
3. Competitive impact statements
4. Monopoly power assessments

DOJ/FTC HHI Thresholds for Merger Review (2023 Guidelines)

HHI Range	Market Concentration	Merger Implications
Below 1,500	Unconcentrated	Mergers unlikely to raise concerns
1,500 to 2,500	Moderately Concentrated	Potential concerns if HHI increases by 100+ points
Above 2,500	Highly Concentrated	Significant concerns if HHI increases by 50+ points

Step-by-Step Guide to Calculating HHI

Step 1: Define Your Market

Before calculating HHI, you must clearly define:

• Product market: Which products/services are included? (e.g., “carbonated soft drinks” vs. “all beverages”)
• Geographic market: Local, regional, national, or global? (e.g., “U.S. wireless carriers” vs. “global telecom”)
• Time period: Annual, quarterly, or other timeframe for market share data

Step 2: Identify All Market Participants

Create a comprehensive list of all firms operating in your defined market. For merger analysis, include:

• The acquiring firm
• The target firm
• All other significant competitors
• Fringe competitors (if they have meaningful market share)

Step 3: Determine Market Shares

Calculate each firm’s market share using one of these methods:

1. Revenue shares: Firm’s revenue ÷ Total market revenue
2. Unit sales shares: Firm’s units sold ÷ Total market units
3. Capacity shares: Firm’s production capacity ÷ Total market capacity

Pro Tip:

For merger analysis, use pre-merger market shares to calculate the baseline HHI, then calculate the post-merger HHI by combining the shares of the merging firms.

Step 4: Square Each Market Share

Convert each market share percentage to a decimal (e.g., 25% = 0.25) and square it. This squaring gives more weight to larger firms in the final index.

Step 5: Sum the Squares

Add up all the squared market shares to get your HHI value. The result will typically range from near 0 (perfect competition) to 10,000 (pure monopoly).

Step 6: Interpret the Results

Compare your HHI value to the DOJ/FTC thresholds:

• Below 1,500: Unconcentrated market (competitive)
• 1,500-2,500: Moderately concentrated (some competitive concerns)
• Above 2,500: Highly concentrated (significant competitive concerns)

Advanced HHI Applications

Delta Analysis for Mergers

When evaluating mergers, regulators calculate the HHI delta – the change in HHI resulting from the transaction. The DOJ considers:

• In moderately concentrated markets (1,500-2,500), deltas above 100 points may raise concerns
• In highly concentrated markets (>2,500), deltas above 50 points may raise concerns

Example Merger Analysis Using HHI Delta

Scenario	Pre-Merger HHI	Post-Merger HHI	Delta	Likely Regulatory Response
Small acquisition in competitive market	1,200	1,250	50	No concerns
Moderate acquisition in moderately concentrated market	1,800	1,950	150	Potential second request
Large merger in highly concentrated market	2,600	3,200	600	Likely challenge

HHI Variations and Extensions

Economists have developed several HHI variations for specific applications:

• Adjusted HHI: Accounts for import competition by treating imports as a separate “firm”
• Weighted HHI: Applies different weights to different market segments
• Dynamic HHI: Incorporates market share trends over time
• Network HHI: Used for two-sided markets (e.g., credit cards, ride-sharing)

Common Mistakes in HHI Calculation

Avoid these pitfalls when calculating HHI:

1. Incorrect market definition: Too narrow or broad geographic/product scope
2. Missing firms: Omitting small but significant competitors
3. Data errors: Using incorrect market share percentages
4. Double-counting: Including the same sales/revenue multiple times
5. Ignoring imports: Forgetting to account for foreign competition
6. Wrong time period: Using outdated market share data

Real-World Examples of HHI in Action

Case Study: AT&T/T-Mobile Merger (2011)

The DOJ blocked AT&T’s proposed $39 billion acquisition of T-Mobile after calculating:

• Pre-merger HHI: ~2,800 (highly concentrated)
• Post-merger HHI: ~3,200
• Delta: +400 points
• Result: DOJ lawsuit led to abandoned merger

Case Study: Anheuser-Busch InBev/SABMiller (2016)

The beer industry mega-merger required divestitures after analysis showed:

• U.S. beer market HHI would increase from 2,600 to 3,400
• Delta of +800 points in a already highly concentrated market
• Solution: Divestiture of SABMiller’s U.S. business (MillerCoors) to Molson Coors

HHI vs. Alternative Concentration Measures

Concentration Ratio (CRn)

Measures the combined market share of the top n firms (typically CR4 or CR8).

Pros: Simple to calculate and interpret

Cons: Ignores market share distribution beyond top firms

Lerner Index

Measures market power as (Price – Marginal Cost)/Price.

Pros: Directly measures pricing power

Cons: Requires cost data that’s often unavailable

Entropy Index

Measures market concentration using information theory.

Pros: Considers all firms equally

Cons: Less intuitive than HHI for regulators

When to Use HHI vs. Other Measures

The HHI is particularly valuable when:

• Evaluating horizontal mergers (between competitors)
• Assessing markets with many small competitors
• Comparing concentration across different industries
• Conducting antitrust investigations

Alternative measures may be better when:

• You need to measure pricing power directly (Lerner Index)
• Cost data is available for more precise analysis
• You’re analyzing vertical mergers (between suppliers and customers)

Limitations of the HHI

While powerful, the HHI has some important limitations:

1. Static measure: Doesn’t account for market dynamics or potential entry
2. No price effects: Doesn’t directly measure consumer harm
3. Market definition challenges: Results depend heavily on how the market is defined
4. Ignores efficiency gains: Doesn’t consider potential merger benefits
5. Data requirements: Requires accurate market share data

How Regulators Use HHI in Practice

The DOJ and FTC follow this general process when using HHI:

1. Define the relevant market (product and geographic)
2. Identify all market participants and their shares
3. Calculate pre-merger HHI
4. Calculate post-merger HHI
5. Determine the HHI delta
6. Apply the merger guidelines thresholds
7. Consider additional factors (entry barriers, efficiencies, failing firm defense)
8. Make enforcement decision (approve, challenge, or require remedies)

Calculating HHI for International Markets

While the HHI is widely used in the U.S., other jurisdictions have different approaches:

• European Union: Uses HHI but with different thresholds (typically concerns above 2,000)
• Canada: Similar to U.S. but with more emphasis on “substantial lessening of competition”
• China: Uses HHI but considers additional factors like technology impacts
• Australia: Uses HHI but with a stronger focus on potential competition

Tools and Resources for HHI Calculation

For professional analysis, consider these resources:

• DOJ HHI Calculator – Official government tool
• FTC Merger Guidelines – Current enforcement policies
• OECD Merger Analysis Compendium – International best practices

Frequently Asked Questions About HHI

What’s the highest possible HHI?

The maximum HHI is 10,000, which would occur in a pure monopoly (one firm with 100% market share: 1.0² × 10,000 = 10,000).

What’s the lowest possible HHI?

The minimum HHI approaches 0 in a market with perfect competition (infinite firms with infinitesimal market shares). For practical purposes, markets with HHI below 100 are considered highly competitive.

How often should HHI be recalculated?

For ongoing market monitoring, recalculate HHI:

• Annually for stable markets
• Quarterly for fast-changing industries
• Immediately after any significant merger or entry/exit

Can HHI be used for vertical mergers?

HHI is primarily designed for horizontal mergers (between competitors). For vertical mergers, regulators typically use other tools like:

• Upward Pricing Pressure (UPP) tests
• Input foreclosure analysis
• Customer switching costs assessment

How do regulators handle private data when calculating HHI?

When market share data isn’t publicly available, regulators may:

• Issue Civil Investigative Demands (CIDs) for company data
• Use industry reports and analyst estimates
• Conduct customer surveys
• Analyze public filings (10-K reports, etc.)

Conclusion: Mastering HHI for Competitive Analysis

The Herfindahl-Hirschman Index remains the gold standard for market concentration analysis due to its:

• Mathematical rigor in weighting firms by size
• Widespread acceptance by global regulators
• Ability to detect unilateral effects (single-firm market power)
• Usefulness in comparing markets across industries and countries

By mastering HHI calculation and interpretation, business strategists can:

• Anticipate regulatory challenges to mergers
• Identify attractive markets with healthy competition
• Assess competitive positioning relative to industry peers
• Develop strategies to navigate concentrated markets

For mergers and acquisitions, early HHI analysis can save millions by identifying potential antitrust issues before deals are announced. For competitive strategy, understanding your market’s HHI helps anticipate competitor behavior and regulatory risks.

Remember that while HHI is a powerful tool, it should be used alongside other competitive analysis methods for comprehensive market assessment. The most sophisticated analysts combine HHI with:

• Barriers to entry analysis
• Customer switching cost evaluation
• Innovation and R&D assessment
• Regulatory environment review