Archives For MHHI Delta

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.

In Antitrust & Competition, Federal Trade Commission, Justice Department, Merger Guidelines, Mergers & Acquisitions , , , , , ,
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The Case for Doing Nothing: The ‘Problem’ of Common Ownership

Michael Sykuta —  15 May 2018

As Thom previously posted, he and I have a new paper explaining The Case for Doing Nothing About Common Ownership of Small Stakes in Competing Firms. Our paper is a response to cries from the likes of Einer Elhauge and of Eric Posner, Fiona Scott Morton, and Glen Weyl, who have called for various types of antitrust action to reign in what they claim is an “economic blockbuster” and “the major new antitrust challenge of our time,” respectively. This is the first in a series of posts that will unpack some of the issues and arguments we raise in our paper.

At issue is the growth in the incidence of common-ownership across firms within various industries. In particular, institutional investors with broad portfolios frequently report owning small stakes in a number of firms within a given industry. Although small, these stakes may still represent large block holdings relative to other investors. This intra-industry diversification, critics claim, changes the managerial objectives of corporate executives from aggressively competing to increase their own firm’s profits to tacitly colluding to increase industry-level profits instead. The reason for this change is that competition by one firm comes at a cost of profits from other firms in the industry. If investors own shares across firms, then any competitive gains in one firm’s stock are offset by competitive losses in the stocks of other firms in the investor’s portfolio. If one assumes corporate executives aim to maximize total value for their largest shareholders, then managers would have incentive to soften competition against firms with which they share common ownership. Or so the story goes (more on that in a later post.)

Elhague and Posner, et al., draw their motivation for new antitrust offenses from a handful of papers that purport to establish an empirical link between the degree of common ownership among competing firms and various measures of softened competitive behavior, including airline prices, banking fees, executive compensation, and even corporate disclosure patterns. The paper of most note, by José Azar, Martin Schmalz, and Isabel Tecu and forthcoming in the Journal of Finance, claims to identify a causal link between the degree of common ownership among airlines competing on a given route and the fares charged for flights on that route.

Measuring common ownership with MHHI

Azar, et al.’s airline paper uses a metric of industry concentration called a Modified Herfindahl–Hirschman Index, or MHHI, to measure the degree of industry concentration taking into account the cross-ownership of investors’ stakes in competing firms. The original Herfindahl–Hirschman Index (HHI) has long been used as a measure of industry concentration, debuting in the Department of Justice’s Horizontal Merger Guidelines in 1982. The HHI is calculated by squaring the market share of each firm in the industry and summing the resulting numbers.

The MHHI is rather more complicated. MHHI is composed of two parts: the HHI measuring product market concentration and the MHHI_Delta measuring the additional concentration due to common ownership. We offer a step-by-step description of the calculations and their economic rationale in an appendix to our paper. For this post, I’ll try to distill that down. The MHHI_Delta essentially has three components, each of which is measured relative to every possible competitive pairing in the market as follows:

  1. A measure of the degree of common ownership between Company A and Company -A (Not A). This is calculated by multiplying the percentage of Company A shares owned by each Investor I with the percentage of shares Investor I owns in Company -A, then summing those values across all investors in Company A. As this value increases, MHHI_Delta goes up.
  2. A measure of the degree of ownership concentration in Company A, calculated by squaring the percentage of shares owned by each Investor I and summing those numbers across investors. As this value increases, MHHI_Delta goes down.
  3. A measure of the degree of product market power exerted by Company A and Company -A, calculated by multiplying the market shares of the two firms. As this value increases, MHHI_Delta goes up.

This process is repeated and aggregated first for every pairing of Company A and each competing Company -A, then repeated again for every other company in the market relative to its competitors (e.g., Companies B and -B, Companies C and -C, etc.). Mathematically, MHHI_Delta takes the form:

where the Ss represent the firm market shares of, and Betas represent ownership shares of Investor I in, the respective companies A and -A.

As the relative concentration of cross-owning investors to all investors in Company A increases (i.e., the ratio on the right increases), managers are assumed to be more likely to soften competition with that competitor. As those two firms control more of the market, managers’ ability to tacitly collude and increase joint profits is assumed to be higher. Consequently, the empirical research assumes that as MHHI_Delta increases, we should observe less competitive behavior.

And indeed that is the “blockbuster” evidence giving rise to Elhauge’s and Posner, et al.,’s arguments  For example, Azar, et. al., calculate HHI and MHHI_Delta for every US airline market–defined either as city-pairs or departure-destination pairs–for each quarter of the 14-year time period in their study. They then regress ticket prices for each route against the HHI and the MHHI_Delta for that route, controlling for a number of other potential factors. They find that airfare prices are 3% to 7% higher due to common ownership. Other papers using the same or similar measures of common ownership concentration have likewise identified positive correlations between MHHI_Delta and their respective measures of anti-competitive behavior.

Problems with the problem and with the measure

We argue that both the theoretical argument underlying the empirical research and the empirical research itself suffer from some serious flaws. On the theoretical side, we have two concerns. First, we argue that there is a tremendous leap of faith (if not logic) in the idea that corporate executives would forgo their own self-interest and the interests of the vast majority of shareholders and soften competition simply because a small number of small stakeholders are intra-industry diversified. Second, we argue that even if managers were so inclined, it clearly is not the case that softening competition would necessarily be desirable for institutional investors that are both intra- and inter-industry diversified, since supra-competitive pricing to increase profits in one industry would decrease profits in related industries that may also be in the investors’ portfolios.

On the empirical side, we have concerns both with the data used to calculate the MHHI_Deltas and with the nature of the MHHI_Delta itself. First, the data on institutional investors’ holdings are taken from Schedule 13 filings, which report aggregate holdings across all the institutional investor’s funds. Using these data masks the actual incentives of the institutional investors with respect to investments in any individual company or industry. Second, the construction of the MHHI_Delta suffers from serious endogeneity concerns, both in investors’ shareholdings and in market shares. Finally, the MHHI_Delta, while seemingly intuitive, is an empirical unknown. While HHI is theoretically bounded in a way that lends to interpretation of its calculated value, the same is not true for MHHI_Delta. This makes any inference or policy based on nominal values of MHHI_Delta completely arbitrary at best.

We’ll expand on each of these concerns in upcoming posts. We will then take on the problems with the policy proposals being offered in response to the common ownership ‘problem.’

 

 

 

 

 

 

In Antitrust & Competition, Banking, Corporate & Securities Law, Financial Regulation, Justice Department, Merger Guidelines , , , , , , , , ,
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