How To Calculate Hhi Index Example

Calculate the Herfindahl-Hirschman Index (HHI) for market concentration analysis

Comprehensive Guide: How to Calculate HHI Index with Examples

The Herfindahl-Hirschman Index (HHI) is the standard measure of market concentration used by economists, antitrust regulators, and business analysts worldwide. This metric helps determine whether a market is competitive, moderately concentrated, or highly concentrated—critical information for mergers, acquisitions, and market analysis.

HHI Formula:
HHI = Σ(s_i)² × 10,000
where s_i = market share of firm i (expressed as a decimal)

Why HHI Matters in Antitrust Analysis

The U.S. Department of Justice (DOJ) and Federal Trade Commission (FTC) rely on HHI to evaluate:

• Merger approvals — Will the combination reduce competition?
• Market power assessment — Do dominant firms exist?
• Barriers to entry — Is the market open to new competitors?
• Pricing behavior — Are firms likely to collude?

Step-by-Step Calculation Process

1. Define the relevant market

   Determine the product market (e.g., “smartphones”) and geographic market (e.g., “U.S. national market”). The DOJ provides guidelines on market definition.

2. Identify all market participants

   List every firm with ≥1% market share. For example, in the U.S. wireless telecom market (2023), this would include Verizon (39.3%), T-Mobile (30.1%), AT&T (24.6%), and others (6.0%).

3. Convert shares to decimals

   Divide each percentage by 100. Verizon’s 39.3% becomes 0.393.

4. Square each share

   0.393² = 0.1544, 0.301² = 0.0906, etc.

5. Sum the squares

   0.1544 + 0.0906 + 0.0605 + 0.0036 = 0.3091

6. Multiply by 10,000

   0.3091 × 10,000 = 3,091 HHI

Pro Tip: Always verify your market shares sum to 100%. Even a 0.1% discrepancy can significantly alter HHI results in concentrated markets.

HHI Interpretation Thresholds

HHI Range	Market Type	DOJ/FTC Merger Guidelines	Example Industries (2023)
< 1,500	Unconcentrated	Mergers unlikely to raise concerns	Fast food (HHI ~1,200), Generic pharmaceuticals (HHI ~980)
1,500–2,500	Moderately Concentrated	Mergers may require scrutiny if ΔHHI > 100	Automobiles (HHI ~1,850), Soft drinks (HHI ~2,100)
> 2,500	Highly Concentrated	Mergers presumed anticompetitive if ΔHHI > 200	Wireless telecom (HHI ~3,091), Domestic airlines (HHI ~2,780)

Real-World HHI Calculation Examples

Example 1: U.S. Beer Market (2023)

Company	Market Share (%)	Share²
Anheuser-Busch InBev	42.4	0.1798
Molson Coors	23.1	0.0534
Constellation Brands	12.8	0.0164
Others	21.7	0.0471
Total HHI		2,967

Interpretation: With an HHI of 2,967, the U.S. beer market is highly concentrated. The DOJ blocked the 2016 AB InBev/SABMiller merger partially due to HHI concerns (post-merger HHI would have exceeded 3,500).

Example 2: U.S. Search Engine Market (2023)

Company	Market Share (%)	Share²
Google	87.3	0.7621
Bing	7.2	0.0052
Yahoo	2.8	0.0008
Others	2.7	0.0007
Total HHI		7,686

Interpretation: An HHI of 7,686 indicates a near-monopoly. This aligns with the DOJ’s 2020 antitrust lawsuit against Google for maintaining illegal monopolies in search and advertising.

Common HHI Calculation Mistakes

• Excluding small firms — Even firms with <1% share contribute to HHI. Omitting them understates concentration.
• Using revenue vs. units — Ensure consistency. Mixing dollar-based and unit-based shares distorts results.
• Incorrect market definition — Too narrow (e.g., “premium smartphones”) or too broad (e.g., “all electronics”) skews HHI.
• Double-counting — Subsidiaries (e.g., T-Mobile/Sprint post-merger) must be treated as single entities.
• Ignoring imports — For global markets, exclude foreign firms at your peril (e.g., Toyota in U.S. auto HHI).

Advanced Applications of HHI

Beyond antitrust, HHI is used for:

1. Portfolio diversification

   Investors calculate “portfolio HHI” to measure concentration risk. A portfolio with 60% in tech stocks (0.6² = 0.36) and 40% in bonds (0.4² = 0.16) has an HHI of 5,200—indicating high sector risk.

2. Supply chain resilience

   Procurement teams assess supplier HHI. A manufacturer with 70% reliance on one chip supplier (HHI = 7,000) faces severe disruption risk, as seen in the 2021 semiconductor shortage.

3. Regulatory impact analysis

   The FCC uses HHI to evaluate media ownership rules. For example, the 2017 attempt to relax cross-ownership limits was abandoned after HHI models showed it would create local news monopolies in 80% of markets.

HHI vs. Alternative Concentration Metrics

Metric	Formula	Pros	Cons	Best Use Case
HHI	Σ(si)^2 × 10,000	Accounts for all firms DOJ/FTC standard Sensitive to large firms	Complex to calculate Requires precise shares	Antitrust analysis, merger reviews
CRn	Sum of top n firms’ shares	Simple to compute Easy to interpret	Ignores firms outside top n Less nuanced	Quick market overviews
Gini Coefficient	Lorenz curve area	Measures inequality Scale-independent	Not industry-specific Less intuitive for business	Income distribution studies

Frequently Asked Questions

Q: Can HHI exceed 10,000?

A: Yes, in a pure monopoly (100% market share), HHI = 10,000. Values above 10,000 are mathematically impossible since Σ(s_i) ≤ 1.

Q: How does the DOJ calculate ΔHHI for mergers?

A: ΔHHI = Post-merger HHI — Pre-merger HHI. The DOJ considers:

• ΔHHI < 100: Unlikely to raise concerns
• ΔHHI between 100–200: Potential scrutiny in moderately concentrated markets
• ΔHHI > 200: Presumed anticompetitive in highly concentrated markets

Q: Is HHI used outside the United States?

A: Yes. The EU Commission and UK CMA use HHI alongside other metrics. However, thresholds differ:

• EU: Markets with HHI > 2,000 may trigger “dominant position” investigations under Article 102 TFEU.
• Canada: Competition Bureau uses 1,800 as the “high concentration” threshold.
• Australia: ACCC considers HHI > 2,000 as concentrated, but examines case-specific factors.

Q: How often should HHI be recalculated?

A: Best practices recommend:

• Annually for stable markets (e.g., utilities)
• Quarterly for dynamic markets (e.g., tech, cryptocurrency)
• Pre/post major events (mergers, regulations, disruptions)

The FTC’s HSR Annual Reports show that 68% of second requests (in-depth merger investigations) involve markets where HHI changed by >15% in 2 years.

Tools and Resources for HHI Calculation

• DOJ HHI Calculator: Official tool with preloaded industry benchmarks.
• FTC Merger Guidelines: 2020 Vertical Merger Guidelines (see Section 4 for HHI applications).
• IBISWorld: Paid service providing HHI data for 1,300+ U.S. industries.
• Statista: Market share reports for global industries (requires manual HHI calculation).
• R/Python: Use the concentration package in R or pytimetk in Python for automated HHI calculations from datasets.

Expert Insight: For mergers involving private companies, the FTC often uses document requests (RFIs) to obtain internal data for HHI calculation, as public market share estimates may be unreliable. Always prepare detailed sales records if undergoing antitrust review.