Concerns about market concentration and its effects on competition are at the heart of antitrust policy. Will Macheel explains the Herfindahl-Hirschman Index (HHI) as a common measure of market concentration, its implications for United States antitrust policy, and potential drawbacks of the measure. He closes the article by highlighting research on the HHI as a regulatory tool for screening mergers.

Measuring the distribution of economic power is often left to economists and lawyers. While it can seem like a technical, clouded process, the very statistics antitrust practitioners use to assess competition and the assumptions contained within them have downstream effects for the enforcement of antitrust policy and the healthy functioning of markets. This article explores the Herfindahl-Hirschman Index (HHI) as a measure of market concentration, its assumptions and limitations, its use by regulators, and recent research on how to gauge economic power. 

Market concentration is an indicator of the potential for anticompetitive harms in a given industry. A market in which one firm has the lion’s share of output may tend towards a monopoly, while a market concentrated into a few firms might be prone to collusive practices, such as price fixing. Either scenario may lead to higher prices, restricted output, and an overall reduction in consumer welfare. The effects of concentration on labor markets and rising monopsony power are another issue. Non-economic concerns have also been raised about market concentration, including threats to democracy and the control of information. 

How do we measure concentration?

The HHI is the main measure of market concentration. The index’s namesakes, Albert O. Hirschman and Orris C. Herfindahl, came up with the statistic independently. In 1945, Hirschmann used the square root of the HHI to examine trade patterns. A few years later, in 1950, Herfindahl employed the index to evaluate economic power in the U.S. steel industry for his Ph.D. dissertation at Columbia University. 

The HHI is simple to calculate—that is, if you have the right data. The HHI is the sum of the squares of each firm’s market share in the relevant market (such as an industry), usually defined as the firm’s share of all market revenue in a given time period. In essence, it is a statistical measure of both the number of firms in a market and the distribution of their market shares.

As an example, consider the following 10 firm market: one firm has a market share of 30%, three firms have a market share of 15% each, two firms with 10% each, and one firm with 5%. We would calculate the HHI as: 302 + (3 x 152) + (2 x 102) + 52 = 1,800. If there is only one firm in the market with a 100% market share, the HHI would rise to the maximum 10,000 points. Conversely, if there are many firms each with a near negligible market share, the HHI approaches its minimum value of zero. So, one way to measure the impact of a merger is to see how the merger between two firms would change the HHI. Using the above example, a merger between a firm with a 15% market share and a firm with a 10% market share would create an HHI of 2,100 for the market.

The HHI can also be estimated using market shares ranging from zero to one, although this is less commonly found in documents such as the Department of Justice and Federal Trade Commission’s Merger Guidelines. Under this derivation, a completely monopolized industry would have an HHI of one. One origin story behind the move from using fractional shares to whole numbers recounts that the squaring of fractions vexed DOJ officials, so the agency thus adopted whole numbers. 

An additional way of using the HHI is to measure the impact of a merger on an industry by calculating the change in HHI, or the DHHI (“D” stands for “delta”), pre- and post-merger. A naive approach to estimating the DHHI would simply sum the merging firms’ pre-merger market shares when estimating the DHHI for the post-merger market. This method assumes no changes to the market shares of the other firms in the industry post-merger. 

The HHI is directly related to a Cournot model of oligopolistic competition, in which firms compete on quantity, not price (the Bertrand oligopoly model has firms competing on the latter). Quantity is the key variable under Cournot competition because it is assumed firms make simultaneous output decisions, allowing for the examination of strategic commitments and their resulting effects on competition. Under Cournot competition, the HHI can be related to pricing power, as measured by profit margins (price minus marginal cost over price, also known as the Lerner Index). The ratio of the HHI over the price elasticity of demand—price elasticity is how much quantity demanded changes with an increase in price—is proportional to the weighted average of firm profit margins, with market shares serving as the weight. 

The Cournot model, however, is based on firms competing in an industry with homogenous products. This assumption does not mirror many actual markets in which firms sell differentiated goods and services. Additionally, firms or industries facing high fixed costs relative to variable costs would dilute the relationship between the HHI and the Lerner Index under the Cournot assumptions above. So, in certain scenarios, there is a connection between market power and the HHI—but the real world does not always match theory.

Does the HHI tell the whole story? 

Put simply, no. If HHI was both the necessary and sufficient predictor of anticompetitive conduct, the regulator’s job would be too simple. If a regulator identified and prevented an anticompetitive merger based only on the projected change in HHI post-merger, they would be missing other key data on the nature of competition in a given industry, such as margins, diversion ratios (i.e. the fraction of demand that shifts to a rival product due to a product price increase), and potential market entrants. 

The HHI is a crude measure of concentration that critically relies on market definition. Many antitrust cases involve parties disputing what defines the relevant market (e.g., what are the defining characteristics of the product market for Apple’s iphones: all mobile phones, all smartphones, or just smartphones of a certain caliber?). How one demarcates the relevant market will impact the HHI value—a more expansive definition might lower the HHI for a market or the DHHI for a merger, and vice versa. 

The rise of digital platform-based industries spurred on by network effects (how different services and products sustain and promote each other) has also affected the HHI’s usefulness. These industries demonstrate “winner-take-all” tendencies. In the case of two-sided digital markets, one firm may quickly capture the whole market due to the positive feedback loop that customers and sellers derive from having additional customers and sellers on either side of the platform (e.g., Amazon’s online marketplace). The HHI’s ability to capture accurately the concentration of these markets may therefore not keep up with their rapidly evolving and dynamic nature. 

How is the HHI used by regulators and the courts? 

One key policy arena in which regulators employ the HHI is for screening potential mergers. The antitrust agencies (the FTC and DOJ) infrequently update and publish merger guidelines. These guidelines include HHI thresholds for which a merger or acquisition will trigger a review by the agencies to determine whether the deal is anticompetitive and warrants legal action. 

Decreasing the HHI threshold for what is considered a concentrated market (or how much a merger changes the HHI) may result in enforcement actions that lead to Type I errors or “false positives,” in which procompetitive mergers are erroneously blocked. Conversely, increasing the HHI threshold beyond which a market is concentrated—essentially loosening the structural presumption—may result in more Type II errors or “false negatives,” whereby anticompetitive mergers are allowed. A focus on limiting false negatives, rather than false positives, is a hallmark of both the post-Chicago and Neo-Brandeisian schools of antitrust enforcement. The Biden administration’s 2023 Merger Guidelines took this approach, lowering the structural presumption for merger review with decreased HHI screening thresholds. Under the 2010 Horizontal Merger Guidelines, for example, the presumed anticompetitive concentration level was an HHI value of 2,500 after a merger along with a DHHI value of 200. The 2023 Merger Guidelines are much stricter in this regard, with an HHI threshold of 1,800 and DHHI of 100 for mergers.

As mentioned above, the HHI is not the one-size-fits-all solution to assessing the competitive nature of markets. Once cases are brought by the agencies or private plaintiffs, judges consider other indicators of the potential for anticompetitive harms, such as barriers to entry, market dynamics, and diversion ratios. 

The economics literature on the HHI is vast; this article does not attempt to comprehensively summarize the body of work on the topic. Instead, this section closes with two recent ProMarket articles summarizing research on the use of HHI thresholds in merger review.

Is U.S. antitrust policy too lenient? This is the question Vivek Bhattacharya, Gastón Illanes, and David Stillerman attempt to answer in their recent study. They review all significant U.S. retail mergers between 2006-2017, finding that “mergers with DHHI between 100 and 200 have overall price increases that are 2.9 percentage points larger than those with DHHI below 100, and those with DHHI above 200 are 5.1 percentage points larger.” The authors show that a lower threshold for merger review would result in blocking significantly more anticompetitive mergers, without greatly increasing the probability of blocked procompetitive mergers. 

Antitrust policy is not only concerned with the consumer effects of mergers but labor impacts as well. Kyle Herkenhoff and Simon Mongey model the effects of merger policy on U.S. labor markets and monopsony power—the idea being that more concentrated markets could lead to lower wages for workers. They compare the HHI thresholds from both the 1982/2023 and the 2010 Merger Guidelines, finding that stricter enforcement avoids significant wage losses for workers. 

What’s next for measuring concentration? 

The simplicity of the HHI is both a strength and a weakness. Scholars have long recognized this, proposing alternative measures of market power to more accurately capture the competitive status of markets. These alternative statistics include, but are not limited to, the Gross Upward Pricing Pressure Index (GUPPI) and the aforementioned Lerner Index.

Economists have also looked to the field of ecology for inspiration in deriving modified measures of concentration. For example, Kenneth Ahern, Lei Kong and Xinyan Yan have proposed a generalized concentration statistic that computes the number of “effective firms” in a given market, drawing on formulas from ecology that estimate the mathematical diversity of species or traits in an ecosystem.

The changing nature of the economy with the proliferation of the internet and digital services has led antitrust scholars and practitioners to acknowledge the limitations of the HHI. Other tools have and will continue to supplant its role in merger analysis. However, its simplicity will sustain it as an important tool among others in the enforcement agencies’ merger review toolkit.  

Articles represent the opinions of their writers, not necessarily those of the University of Chicago, the Booth School of Business, or its faculty.