Calculate the Herfindahl-Hirschman Index (HHI) to measure market concentration and competition.
Highly Concentrated
This market is dominated by few firms. Mergers are likely to face significant antitrust review.
Department of Justice thresholds
< 1,500 — Unconcentrated
1,500 – 2,500 — Moderately concentrated
> 2,500 — Highly concentrated
If you've ever wondered how economists and regulators assess market competition, you've likely stumbled upon the Herfindahl-Hirschman Index, or HHI. This deceptively simple metric plays a central role in antitrust enforcement, merger reviews, and competitive analysis across the globe. Understanding HHI gives you insight into how markets function and why certain business combinations face regulatory scrutiny while others sail through approval.
The Herfindahl-Hirschman Index is a statistical measure of market concentration that quantifies how competitive an industry is by examining the market shares of all firms within it. The calculation involves squaring the market share of each firm and summing the results, producing a number that ranges from near zero (in a perfectly competitive market with countless tiny firms) to 10,000 (in a pure monopoly where one firm controls 100% of the market).
The index gets its name from two economists who independently developed the concept. Orris Herfindahl first proposed it in his 1950 doctoral dissertation on the concentration of the steel industry, while Albert Hirschman published a similar measure in 1945 in his book "National Power and the Structure of Foreign Trade." Though Hirschman's work technically came first, Herfindahl's application to industrial organization became more influential, leading to the dual naming.
What makes HHI particularly useful is how it weights market shares. By squaring each firm's share, the index gives proportionally greater weight to larger firms. A firm with 40% market share contributes 1,600 points to the HHI (40 squared), while a firm with 10% contributes only 100 points. This weighting reflects the economic reality that large firms have disproportionate influence on market dynamics compared to their smaller competitors.
The HHI serves as a foundational tool across multiple domains of economic analysis and policy:
Antitrust enforcement and merger review: The U.S. Department of Justice and Federal Trade Commission use HHI as a primary screening tool when evaluating proposed mergers and acquisitions. High concentration levels or significant increases in HHI trigger deeper investigation into whether a deal would harm competition. The European Commission, UK Competition and Markets Authority, and regulatory bodies worldwide employ similar approaches.
Market monitoring and regulation: Regulators track HHI trends over time to identify industries where competition may be deteriorating. Banking regulators, for instance, closely monitor HHI in local deposit markets to ensure adequate competition for consumers. Telecommunications authorities watch concentration levels in wireless markets. These ongoing measurements help policymakers intervene before markets become problematically concentrated.
Business strategy and competitive intelligence: Companies use HHI analysis to understand their competitive landscape. A firm considering market entry can assess whether they'll face a concentrated industry dominated by a few giants or a fragmented market with many competitors. Strategic planners use HHI to evaluate how acquisitions might change market dynamics and what regulatory obstacles they might encounter.
Investment analysis: Portfolio managers and investment analysts use HHI to assess industry risk. Highly concentrated industries may offer stable returns due to limited competition, but they also face regulatory risk and potential disruption if new entrants successfully challenge incumbents. Fragmented industries present different risk profiles, with more competitive pressure but potentially more acquisition opportunities.
Academic research: Economists use HHI extensively in empirical research on industrial organization, studying relationships between concentration and outcomes like pricing, innovation, wages, and productivity. The measure's simplicity and wide adoption make it valuable for cross-industry and cross-country comparisons.
The formula is straightforward:
Where:
When market shares are expressed as percentages (0 to 100), the HHI ranges from near 0 to 10,000. Some analysts express shares as decimals (0 to 1), producing an HHI between 0 and 1. The percentage approach is more common in U.S. regulatory practice.
Detailed calculation example:
Consider a market with four firms:
Calculate each firm's contribution:
Sum the contributions: 1,600 + 900 + 400 + 100 = 3,000
This HHI of 3,000 indicates a highly concentrated market.
Understanding the math: The squaring operation has important mathematical properties. It ensures HHI is always positive and gives more weight to unequal distributions. Compare two markets, each with four firms:
Though both markets have four competitors, Market Y is far more concentrated due to the dominant firm.
The U.S. Department of Justice and Federal Trade Commission established threshold guidelines in their Horizontal Merger Guidelines:
| HHI Level | Classification | Interpretation |
|---|---|---|
| Below 1,500 | Unconcentrated | Generally competitive market; mergers rarely challenged |
| 1,500 to 2,500 | Moderately concentrated | Mergers warrant scrutiny; outcomes depend on specifics |
| Above 2,500 | Highly concentrated | Significant market power concerns; mergers often challenged |
Beyond the absolute HHI level, regulators focus on the change in HHI (often called "delta") that a merger would cause:
These thresholds aren't rigid rules but starting points for analysis. Markets with low barriers to entry, rapid innovation, or strong buyer power might tolerate higher concentration. Conversely, markets with network effects, high switching costs, or regulatory barriers might raise concerns at lower HHI levels.
A useful way to understand HHI is through the concept of "numbers equivalent"—the number of equal-sized firms that would produce the same HHI. This equals 10,000 divided by the HHI.
| HHI | Numbers Equivalent |
|---|---|
| 10,000 | 1 firm (monopoly) |
| 5,000 | 2 equal firms |
| 2,500 | 4 equal firms |
| 2,000 | 5 equal firms |
| 1,000 | 10 equal firms |
| 500 | 20 equal firms |
Our earlier example with HHI of 3,000 has a numbers equivalent of about 3.3, meaning the market is as concentrated as if it had between three and four equal-sized competitors—even though it actually has four firms of varying sizes.
Let's walk through a complete merger analysis using our example market (HHI = 3,000).
Scenario: Firm C (20% share) proposes acquiring Firm D (10% share).
Step 1: Calculate post-merger market structure
Step 2: Calculate post-merger HHI
Step 3: Calculate the change (delta)
Step 4: Apply the guidelines
The post-merger HHI of 3,400 exceeds 2,500 (highly concentrated), and the delta of 400 points far exceeds the 200-point threshold that creates a presumption of anticompetitive harm. This merger would almost certainly face a detailed investigation and likely a challenge unless the parties could demonstrate offsetting efficiencies or other mitigating factors.
Shortcut for calculating delta: There's a quick formula for the HHI increase from a merger: Delta = 2 × (share of firm 1) × (share of firm 2). In our example: 2 × 20 × 10 = 400. This works because (a+b)² - a² - b² = 2ab.
Understanding HHI becomes more tangible when examining actual industries:
Commercial aviation: The U.S. domestic airline industry underwent significant consolidation in the 2000s and 2010s. Mergers including Delta-Northwest (2008), United-Continental (2010), Southwest-AirTran (2011), and American-US Airways (2013) substantially increased concentration. Today, four carriers control roughly 80% of domestic capacity. Many individual city-pair routes show HHI levels well above 2,500, though regulators approved these mergers after extracting concessions like gate divestitures at congested airports.
Wireless telecommunications: The U.S. wireless market has three major national carriers (AT&T, Verizon, T-Mobile) following the 2020 T-Mobile/Sprint merger. The DOJ approved this merger over objections, partly because Sprint was argued to be a weakening competitor. Pre-merger HHI was approximately 2,700; post-merger it approached 3,200 nationally, with higher levels in some regional markets.
Banking: Bank regulators apply HHI analysis to local deposit markets, typically defined as metropolitan statistical areas or rural counties. The general threshold considers HHI above 1,800 as concentrated for banking, lower than the standard DOJ thresholds. Major bank mergers often require branch divestitures in overlapping markets to keep local HHI below acceptable levels.
Internet search: Google's dominance of search advertising creates extremely high concentration. With roughly 90% U.S. search market share, the search market HHI exceeds 8,000—near-monopoly levels. This concentration has drawn antitrust scrutiny and litigation from the DOJ and multiple state attorneys general.
Beer brewing: After decades of consolidation, two companies (Anheuser-Busch InBev and Molson Coors) control approximately 65% of the U.S. beer market. When AB InBev sought to acquire Grupo Modelo in 2013, the DOJ required divestiture of Modelo's entire U.S. business to Constellation Brands to maintain competition.
While the U.S. originated modern HHI-based merger analysis, other jurisdictions have adopted similar approaches with variations:
European Union: The European Commission uses HHI but applies somewhat different thresholds. Markets with HHI below 1,000 are unlikely to raise horizontal competition concerns. Between 1,000 and 2,000, concerns arise if delta exceeds 250. Above 2,000, concerns arise if delta exceeds 150. The EU also places more emphasis on qualitative factors alongside HHI.
United Kingdom: The Competition and Markets Authority uses HHI as one factor among many, without rigid thresholds. UK practice tends to focus more on theories of harm and competitive effects than on concentration metrics alone.
Canada: The Competition Bureau uses HHI screens similar to U.S. practice, with 1,000 and 1,800 as key thresholds. Canadian analysis also considers import competition more explicitly given the country's trade-dependent economy.
Australia: The Australian Competition and Consumer Commission uses concentration ratios alongside HHI, with a safe harbor when the combined four-firm concentration ratio stays below 75% and HHI increases less than 100 points.
Japan: The Japan Fair Trade Commission uses HHI with thresholds at 1,500 and 2,500, similar to U.S. practice, but also maintains specific guidelines for particular industries like banking and telecommunications.
Despite its widespread use, HHI has important limitations that sophisticated analysts must consider:
Market definition challenges: HHI is only as good as the market definition underlying it. Define the market too narrowly, and HHI will overstate concentration. Define it too broadly, and HHI will understate competitive concerns. The "relevant market" for antitrust purposes includes products that consumers view as reasonably interchangeable and geographic areas where they can practically purchase. These boundaries are often contested in merger litigation.
For example, is the relevant market "premium electric vehicles" (where Tesla dominates) or "all passenger vehicles" (where Tesla has a small share)? The HHI differs dramatically depending on the answer.
Static versus dynamic competition: HHI captures market structure at a point in time but doesn't directly measure competitive dynamics. A concentrated market might still be competitive if:
Conversely, a less concentrated market might still have competition problems if:
Product differentiation: HHI assumes products are homogeneous or at least substitutable. In differentiated product markets, a merger between firms with similar products may harm competition more than the HHI change suggests, while a merger between firms with dissimilar products may be less problematic. Economists address this with more sophisticated tools like merger simulation models.
Multi-market contact: When firms compete across multiple markets, HHI in any single market may understate competitive concerns. Firms may refrain from aggressive competition in one market to avoid retaliation in another, even if single-market HHI looks acceptable.
Platform markets and two-sided competition: Digital platforms often serve multiple customer groups (users and advertisers, riders and drivers, buyers and sellers). HHI calculated on one side may not capture competitive dynamics on the other side or the feedback effects between them.
Economists have developed other concentration measures that complement or compete with HHI:
Concentration ratios (CR4, CR8): The four-firm or eight-firm concentration ratio simply sums the market shares of the largest firms. CR4 = s₁ + s₂ + s₃ + s₄. While simpler than HHI, concentration ratios ignore the distribution of shares among top firms and don't account for smaller competitors.
Lerner Index: Measures market power through the markup of price over marginal cost: L = (P - MC) / P. Unlike HHI, which measures structure, the Lerner Index measures outcomes. However, marginal cost is difficult to observe empirically.
Entropy measures: Information-theoretic approaches that measure the "uncertainty" about which firm a randomly selected customer would patronize. Higher entropy indicates more competitive markets.
Gross Upward Pricing Pressure Index (GUPPI): Specifically designed for differentiated product mergers, GUPPI measures the incentive to raise prices post-merger based on diversion ratios and margins. Unlike HHI, it directly addresses the economics of unilateral effects.
Willingness to pay analysis: For differentiated products, merger simulation based on estimated demand systems can predict price effects more precisely than HHI-based screens.
The rise of digital platforms has created new challenges for HHI-based competition analysis:
Winner-take-all dynamics: Digital markets often exhibit strong network effects where the value of a platform increases with its user base. These effects can lead to concentration that HHI captures but whose competitive implications differ from traditional industries. A platform with 70% market share might face different competitive constraints than a manufacturing firm with the same share.
Zero-price markets: Many digital services are free to consumers, with platforms monetizing through advertising or data. Traditional market share measures based on revenue may not capture competitive dynamics in these multi-sided markets.
Rapid change: Digital markets can shift quickly. MySpace once dominated social networking; Blackberry once led smartphones. High HHI might indicate temporary dominance rather than durable market power, though critics argue incumbents increasingly use acquisitions to eliminate nascent competitors before they can challenge the status quo.
Data as a competitive asset: Market shares in digital markets may understate competitive advantages when dominant firms control unique data assets that create barriers to entry and expansion.
These challenges don't mean HHI is useless for digital markets, but they suggest it must be applied thoughtfully alongside other tools and with attention to market-specific dynamics.
When conducting HHI analysis, keep these principles in mind:
Be rigorous about market definition: Before calculating HHI, carefully consider what products and geographic areas belong in the relevant market. Sensitivity analysis using alternative market definitions can reveal how conclusions depend on definitional choices.
Consider both levels and changes: Absolute HHI matters, but so does how much a transaction would change it. A merger that slightly increases an already concentrated market differs from one that transforms a competitive market into a concentrated one.
Don't stop at HHI: Concentration measures are screens, not verdicts. High HHI raises questions; answering them requires examining entry barriers, competitive dynamics, efficiency justifications, and likely competitive effects.
Account for market dynamics: Consider whether current market shares are stable or in flux. HHI based on today's shares may not reflect tomorrow's competitive conditions, especially in innovative industries.
Use appropriate data: Market share measurements should reflect economically meaningful metrics—revenue, capacity, volume, or other measures depending on the industry. Shares based on inconsistent or incomplete data will produce misleading HHI calculations.
The Herfindahl-Hirschman Index remains one of the most important tools in competition economics and antitrust policy, despite being developed over 70 years ago. Its elegance lies in its simplicity—a single number that captures the essential distribution of market power—while its value lies in its wide adoption and the accumulated experience regulators have developed in applying it.
Understanding HHI equips you to analyze competitive dynamics in any industry, anticipate regulatory scrutiny of transactions, and engage with economic policy debates about market power and concentration. Whether you're evaluating an investment, planning corporate strategy, or simply trying to understand why regulators blocked a merger in the news, HHI provides an essential analytical framework.
The index has limitations, and modern competition analysis increasingly supplements HHI with more sophisticated tools. But HHI remains the starting point—the first question regulators ask about any merger, and often the metric that determines whether further analysis is needed. Mastering this measure gives you insight into how markets work and how societies balance the benefits of scale against the risks of concentrated power.