What To Make of MHHI? A policy problem

Michael Sykuta —  27 August 2018

At the heart of the common ownership issue in the current antitrust debate is an empirical measure, the Modified Herfindahl-Hirschmann Index, researchers have used to correlate patterns of common ownership with measures of firm behavior and performance. In an accompanying post, Thom Lambert provides a great summary of just what the MHHI, and more specifically the MHHIΔ, is and how it can be calculated. I’m going to free-ride off Thom’s effort, so if you’re not very familiar with the measure, I suggest you start here and here.

There are multiple problems with the common ownership story and with the empirical evidence proponents of stricter antitrust enforcement point to in order to justify their calls to action. Thom and I address a number of those problems in our recent paper on “The Case for Doing Nothing About Institutional Investors’ Common Ownership of Small Stakes in Competing Firms.” However, one problem we don’t take on in that paper is the nature of the MHHIΔ itself. More specifically, what is one to make of it and how should it be interpreted, especially from a policy perspective?

The Policy Benchmark

The benchmark for discussion is the original Herfindahl-Hirschmann Index (HHI), which has been part of antitrust for decades. The HHI is calculated by summing the squared value of each firm’s market share. Depending on whether you use percents or percentages, the value of the sum may be multiplied by 10,000. For instance, for two firms that split the market evenly, the HHI could be calculated either as:

HHI = 502 + 502 = 5.000, or
HHI = (.502 + .502)*10,000 = 5,000

It’s a pretty simple exercise to see that one of the useful properties of HHI is that it is naturally bounded between 0 and 10,000. In the case of a pure monopoly that commands the entire market, the value of HHI is 10,000 (1002). As the number of firms increases and market shares approach very small fractions, the value of HHI asymptotically approaches 0. For a market with 10 firms firms that evenly share the market, for instance, HHI is 1,000; for 100 identical firms, HHI is 100; for 1,000 identical firms, HHI is 1. As a result, we know that when HHI is close to 10,000, the industry is highly concentrated in one firm; and when the HHI is close to zero, there is no meaningful concentration at all. Indeed, the Department of Justice’s Horizontal Merger Guidelines make use of this property of the HHI:

Based on their experience, the Agencies generally classify markets into three types:

  • Unconcentrated Markets: HHI below 1500
  • Moderately Concentrated Markets: HHI between 1500 and 2500
  • Highly Concentrated Markets: HHI above 2500

The Agencies employ the following general standards for the relevant markets they have defined:

  • Small Change in Concentration: Mergers involving an increase in the HHI of less than 100 points are unlikely to have adverse competitive effects and ordinarily require no further analysis.
  • Unconcentrated Markets: Mergers resulting in unconcentrated markets are unlikely to have adverse competitive effects and ordinarily require no further analysis.
  • Moderately Concentrated Markets: Mergers resulting in moderately concentrated markets that involve an increase in the HHI of more than 100 points potentially raise significant competitive concerns and often warrant scrutiny.
  • Highly Concentrated Markets: Mergers resulting in highly concentrated markets that involve an increase in the HHI of between 100 points and 200 points potentially raise significant competitive concerns and often warrant scrutiny. Mergers resulting in highly concentrated markets that involve an increase in the HHI of more than 200 points will be presumed to be likely to enhance market power. The presumption may be rebutted by persuasive evidence showing that the merger is unlikely to enhance market power.

Just by way of reference, an HHI of 2500 could reflect four firms sharing the market equally (i.e., 25% each), or it could be one firm with roughly 49% of the market and 51 identical small firms sharing the rest evenly.

Injecting MHHIΔ Into the Mix

MHHI is intended to account for both the product market concentration among firms captured by the HHI, and the common ownership concentration across firms in the market measured by the MHHIΔ. In short, MHHI = HHI + MHHIΔ.

As Thom explains in great detail, MHHIΔ attempts to measure the combined effects of the relative influence of shareholders that own positions across competing firms on management’s strategic decision-making and the combined market shares of the commonly-owned firms. MHHIΔ is the measure used in the various empirical studies allegedly demonstrating a causal relationship between common ownership (higher MHHIΔs) and the supposed anti-competitive behavior of choice.

Some common ownership critics, such as Einer Elhague, have taken those results and suggested modifying antitrust rules to incorporate the MHHIΔ in the HHI guidelines above. For instance, Elhague writes (p 1303):

Accordingly, the federal agencies can and should challenge any stock acquisitions that have produced, or are likely to produce, anti-competitive horizontal shareholdings. Given their own guidelines and the empirical results summarized in Part I, they should investigate any horizontal stock acquisitions that have created, or would create, a ΔMHHI of over 200 in a market with an MHHI over 2500, in order to determine whether those horizontal stock acquisitions raised prices or are likely to do so.

Elhague, like many others, couch their discussion of MHHI and MHHIΔ in the context of HHI values as though the additive nature of MHHI means such a context make sense. And if the examples are carefully chosen, the numbers even seem to make sense. For instance, even in our paper (page 30), we give a few examples to illustrate some of the endogeneity problems with MHHIΔ:

For example, suppose again that five institutional investors hold equal stakes (say, 3%) of each airline servicing a market and that the airlines have no other significant shareholders.  If there are two airlines servicing the market and their market shares are equivalent, HHI will be 5000, MHHI∆ will be 5000, and MHHI (HHI + MHHI∆) will be 10000.  If a third airline enters and grows so that the three airlines have equal market shares, HHI will drop to 3333, MHHI∆ will rise to 6667, and MHHI will remain constant at 10000.  If a fourth airline enters and the airlines split the market evenly, HHI will fall to 2500, MHHI∆ will rise further to 7500, and MHHI will again total 10000.

But do MHHI and MHHI∆ really fit so neatly into the HHI framework? Sadly–and worringly–no, not at all.

The Policy Problem

There seems to be a significant problem with simply imposing MHHIΔ into the HHI framework. Unlike HHI, from which we can infer something about the market based on the nominal value of the measure, MHHIΔ has no established intuitive or theoretical grounding. In fact, MHHIΔ has no intuitively meaningful mathematical boundaries from which to draw inferences about “how big is big?”, a fundamental problem for antitrust policy.

This is especially true within the range of cross-shareholding values we’re talking about in the common ownership debate. To illustrate just how big a problem this is, consider a constrained optimization of MHHI based on parameters that are not at all unreasonable relative to hypothetical examples cited in the literature:

  • Four competing firms in the market, each of which is constrained to having at least 5% market share, and their collective sum must equal 1 (or 100%).
  • Five institutional investors each of which can own no more than 5% of the outstanding shares of any individual airline, with no restrictions across airlines.
  • The remaining outstanding shares are assumed to be diffusely owned (i.e., no other large shareholder in any firm).

With only these modest restrictions on market share and common ownership, what’s the maximum potential value of MHHI? A mere 26,864,516,491, with an MHHI∆ of 26,864,513,774 and HHI of 2,717.

That’s right, over 26.8 billion. To reach such an astronomical number, what are the parameter values? The four firms split the market with 33, 31.7, 18.3, and 17% shares, respectively. Investor 1 owns 2.6% of the largest firm (by market share) while Investors 2-5 each own between 4.5 and 5% of the largest firm. Investors 1 and 2 own 5% of the smallest firm, while Investors 3 and 4 own 3.9% and Investor 5 owns a minuscule (0.0006%) share. Investor 2 is the only investor with any holdings (a tiny 0.0000004% each) in the two middling firms. These are not unreasonable numbers by any means, but the MHHI∆ surely is–especially from a policy perspective.

So if MHHI∆ can range from near zero to as much as 28.6 billion within reasonable ranges of market share and shareholdings, what should we make of Elhague’s proposal that mergers be scrutinized for increasing MHHI∆ by 200 points if the MHHI is 2,500 or more? We argue that such an arbitrary policy model is not only unfounded empirically, but is completely void of substantive reason or relevance.

The DOJ’s Horizontal Merger Guidelines above indicate that antitrust agencies adopted the HHI benchmarks for review “[b]ased on their experience”.  In the 1982 and 1984 Guidelines, the agencies adopted HHI standards 1,000 and 1,800, compared to the current 1,500 and 2,500 levels, in determining whether the industry is concentrated and a merger deserves additional scrutiny. These changes reflect decades of case reviews relating market structure to likely competitive behavior and consumer harm.

We simply do not know enough yet empirically about the relation between MHHI∆ and benchmarks of competitive behavior and consumer welfare to make any intelligent policies based on that metric–even if the underlying argument had any substantive theoretical basis, which we doubt. This is just one more reason we believe the best response to the common ownership problem is to do nothing, at least until we have a theoretically, and empirically, sound basis on which to make intelligent and informed policy decisions and frameworks.

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