Herfindahl-Hirschman Index (HHI)

How can market power be quantified? The conventional method followed by competition authorities —although not the only one— consists of estimating market power indirectly through indicators of market share and market concentration.

These proxies are used to describe market structure and are considered a prima facie indicator of market power or the level of competition between companies. In general terms, market concentration reflects the number of participants and the relative market position achieved by each of them.

The Herfindahl Hirschman Index (HHI) is a measure used to determine market concentration levels and changes in it, based on models of competition in quantity with homogeneous products.

It is commonly used to analyze mergers and the changes they generate in market structure. Analysis through HHI generally goes along the following line of thought: (i) the greater the share achieved by a concentrated economic agent, (ii) the higher the concentration in the market, and (iii) the greater the variations resulting from the merger, (iv) the greater the probability of anti-competitive effects being generated (FNE, 2021).

This indicator consists of the sum of the squared market shares of all companies in the market (N companies).

HHI= \sum_{i=1}^{N}s_{i}^{2}

HHI varies between a lower limit of 0 and an upper limit of 10,000. As shown in Table 1, at one extreme, when there is a monopoly, the indicator takes the value of 10,000. On the contrary, when there are an infinite number of companies of equal size, the indicator takes a value very close to 0. Thus, the closer the HHI value is to 10,000, the more concentrated the industry is.

Table 1: Herfindahl-Hirschman Index

An advantage of the HHI is that it considers the relative size of companies in the market. Thus, it is not the same for two companies to have the same market share (HHI = 5,000) than for one company to have a 75% market share and another to have a 25% market share (HHI = 6,250).

In short, the HHI increases both as the number of companies in the market decreases and as the disparity in size between those companies increases (DOJ, 2018).

Agencies generally consider an HHI above 1,500 and below 2,500 corresponds to a moderately concentrated market. Markets that exceed 2,500 points are considered highly concentrated.

For the analysis of mergers, the Chilean competition authority, Fiscalía Nacional Económica (FNE), has established that it will rule out further analysis if, after the merger, the concentration indicator is:

• Lower than an HHI of 1,500.
• Higher than an HHI of 1,500 and lower than an HHI of 2,500 (moderately concentrated market), with a projected variation in the HHI of less than 200.
• Higher than an HHI of 2,500 (highly concentrated market), with a projected variation in the HHI of less than 100.

For example, if in scenario E in Table 1, companies 1 and 2 merge, the HHI increases from 2,500 pre-merger to 3,750 post-merger (scenario D), with a projected variation of 1,250.

For its part, the European Commission, in its Guidelines on the assessment of horizontal mergers, considers that it is unlikely that the Commission will find competition concerns in a merger that results in:

• An HHI between 1,000 and 2,000, with a variation of less than 250.
• An HHI greater than 2,000 and a variation of less than 150.

In any case, both the FNE and the European Commission will analyze in greater depth those mergers that, even if they do not exceed the thresholds, have exceptional traits. This may happen when:

• a potential entrant or a recently established operator with a small market share, also known as a killer or nascent acquisition;
• one or more of the parties to the concentration are important innovators in a sense that is not reflected in market shares;
• there is a high volume of cross-shareholdings;
• One of the companies participating in the concentration is a “maverick” company that is very likely to disrupt coordinated behavior;
• there are indications of coordination.
• there are significant consumer concerns regarding the effects of the merger.

Finally, the U.S. DOJ classifies markets into three categories —non-concentrated markets, moderately concentrated markets, and highly concentrated markets—. In its view, it is unlikely that a merger will give rise to adverse competitive effects and, generally, the following scenarios do not require further analysis:

• Mergers involving small changes in concentration (increase in HHI of less than 100).
• Mergers that result in non-concentrated markets (HHI of less than 1,500).

Conversely, the following scenarios raise significant competitive concerns and often warrant scrutiny:

• Mergers that result in moderately concentrated markets (HHI between 1,500 and 2,500) and involve an increase in the HHI of more than 100.
• Mergers that result in highly concentrated markets (HHI above 2,500) and involve an increase in the HHI between 100 and 200.

However, the HHI measure is not an absolute predictor of market power; rather, it is an indicator that allows for a preliminary analysis and to easily discard of transactions that are unlikely to have anticompetitive effects and therefore require less analysis.

For cases of partial acquisitions and/or joint ventures, the Modified Herfindahl-Hirschman Index (MHHI) is commonly used. In general terms, the MHHI considers the possibility that interdependence links may exist between companies, either through financial interest and the ability to exercise control or decisive influence. Thus, it quantifies the additional variation in the HHI resulting from cross-shareholdings.

On the one hand, financial interest refers to the acquiring company’s right to obtain a proportion of the acquired company’s profits. On the other hand, corporate control implies that the acquiring company could control or influence the competitive decision-making of the company (Salop & O’Brien, 2000).

The formula proposed by Salop and O’Brien (2000) is as follows:

MHHI=\sum_{k} \sum_{j} (\sum_{i} \gamma_{i j} \beta_{i k}/\sum_{i} \gamma_{i j} \beta_{i j}) s_{k} s_{j}

Or, alternatively:

MHHI=HHI+\sum_{j} \sum_{k \neq j}(\frac{\sum_{i} \gamma_{i j} \beta_{i k}}{\sum_{i} \gamma_{i j} \cdot \beta_{i j}}) s_{k} \cdot s_{j}

Where j y k  and  are company subscripts and i is a shareholder subscript, s_j and s_k are the market shares of companies, \gamma_{ij} is the degree of influence that shareholder i has over company j, and \beta_{ij} and \beta_{ik} correspond to the financial interest or equity participation of shareholder i in companies j and k, respectively (FNE Approval Report F219-2019).

Furthermore, the authors identify five situations associated with partial acquisitions and, for each of them, derive the formulas for the variation of the MHHI (FNE, 2013):

• Silent financial interest: acquiring and acquired firms continue to operate independently.

\Delta=\beta S_{a} S_{b}

• Full control of the acquired firm.

\Delta=(\beta+1 / \beta) S_{a} S_{b}

• Joint “Coasian” control: both firms jointly maximize their profits and then divide the profits according to a pre-established formula.

\Delta=2 S_{a} S_{b}

• Unidirectional control: the acquiring firm can make the acquired firm maximize joint profits. However, the acquiring firm maximizes its own profits.

\Delta=(1+\beta) S_{a} S_{b}

• Proportional control: companies do not maximize joint profits, but consider financial interests proportionally.

\Delta=(\beta+\beta /((1-\beta)^{2}+\beta^{2}))S_{a} S_{b}

When comparing the competitive effects in each of the scenarios, the authors conclude that the greater the financial interest, the greater the reduction in the company’s competitive incentives.

European Commission (2004) –  Directrices sobre la evaluación de las concentraciones horizontales

DOJ, EE.UU. (2010) – Horizontal Merger Guidelines

DOJ, EE.UU. (2018) – Herfindahl Hirschman Index

FNE (2013) – Participaciones minoritarias y directores comunes entre empresas competidoras

FNE (2021) – Guía para el Análisis de Operaciones de Concentración Horizontales

Salop, S. & O´Brien, D. (2000) – Competitive Effects of Partial Ownership: Financial Interest and Corporate Control