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I posted this originally on my own blog, but decided to cross-post here since Thom and I have been blogging on this topic.

“The U.S. stock market is having another solid year. You wouldn’t know it by looking at the shares of companies that manage money.”

That’s the lead from Charles Stein on Bloomberg’s Markets’ page today. Stein goes on to offer three possible explanations: 1) a weary bull market, 2) a move toward more active stock-picking by individual investors, and 3) increasing pressure on fees.

So what has any of that to do with the common ownership issue? A few things.

First, it shows that large institutional investors must not be very good at harvesting the benefits of the non-competitive behavior they encourage among the firms the invest in–if you believe they actually do that in the first place. In other words, if you believe common ownership is a problem because CEOs are enriching institutional investors by softening competition, you must admit they’re doing a pretty lousy job of capturing that value.

Second, and more importantly–as well as more relevant–the pressure on fees has led money managers to emphasis low-cost passive index funds. Indeed, among the firms doing well according to the article is BlackRock, “whose iShares exchange-traded fund business tracks indexes, won $20 billion.” In an aggressive move, Fidelity has introduced a total of four zero-fee index funds as a way to draw fee-conscious investors. These index tracking funds are exactly the type of inter-industry diversified funds that negate any incentive for competition softening in any one industry.

Finally, this also illustrates the cost to the investing public of the limits on common ownership proposed by the likes of Einer Elhague, Eric Posner, and Glen Weyl. Were these types of proposals in place, investment managers could not offer diversified index funds that include more than one firm’s stock from any industry with even a moderate level of market concentration. Given competitive forces are pushing investment companies to increase the offerings of such low-cost index funds, any regulatory proposal that precludes those possibilities is sure to harm the investing public.

Just one more piece of real evidence that common ownership is not only not a problem, but that the proposed “fixes” are.

regulation-v41n3-coverCalm Down about Common Ownership” is the title of a piece Thom Lambert and I published in the Fall 2018 issue of Regulation, which just hit online. The article is a condensed version our recent paper, “The Case for Doing Nothing About Institutional Investors’ Common Ownership of Small Stakes in Competing Firms.” In short, we argue that concern about common ownership lacks a theoretically sound foundation and is built upon faulty empirical support. We also explain why proposed “fixes” would do more harm than good.

Over the past several weeks we wrote a series of blog posts here that summarize or expand upon different parts of our argument. To pull them all into one place:

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.

The Federal Trade Commission will soon hold hearings on Competition and Consumer Protection in the 21st Century.  The topics to be considered include:

  1. The state of antitrust and consumer protection law and enforcement, and their development, since the [1995] Pitofsky hearings;
  2. Competition and consumer protection issues in communication, information and media technology networks;
  3. The identification and measurement of market power and entry barriers, and the evaluation of collusive, exclusionary, or predatory conduct or conduct that violates the consumer protection statutes enforced by the FTC, in markets featuring “platform” businesses;
  4. The intersection between privacy, big data, and competition;
  5. The Commission’s remedial authority to deter unfair and deceptive conduct in privacy and data security matters;
  6. Evaluating the competitive effects of corporate acquisitions and mergers;
  7. Evidence and analysis of monopsony power, including but not limited to, in labor markets;
  8. The role of intellectual property and competition policy in promoting innovation;
  9. The consumer welfare implications associated with the use of algorithmic decision tools, artificial intelligence, and predictive analytics;
  10. The interpretation and harmonization of state and federal statutes and regulations that prohibit unfair and deceptive acts and practices; and
  11. The agency’s investigation, enforcement and remedial processes.

The Commission has solicited comments on each of these main topics and a number of subtopics.  Initial comments are due today, but comments will also be accepted at two other times.  First, before each scheduled hearing on a topic, the Commission will accept comments on that particular matter.  In addition, the Commission will accept comments at the end of all the hearings.

Over the weekend, Mike Sykuta and I submitted a comment on topic 6, “evaluating the competitive effects of corporate acquisitions and mergers.”  We addressed one of the subtopics the FTC will consider: “the analysis of acquisitions and holding of a non-controlling ownership interest in competing companies.”

Here’s our comment, with a link to our working paper on the topic of common ownership by institutional investors:

To Whom It May Concern:

We are grateful for the opportunity to respond to the U.S. Federal Trade Commission’s request for comment on its upcoming hearings on Competition and Consumer Protection in the 21st Century. We are professors of law (Lambert) and economics (Sykuta) at the University of Missouri. We wish to comment on Topic 6, “evaluating the competitive effects of corporate acquisitions and mergers” and specifically on Subtopic 6(c), “the analysis of acquisitions and holding of a non-controlling ownership interest in competing companies.”

Recent empirical research purports to demonstrate that institutional investors’ “common ownership” of small stakes in competing firms causes those firms to compete less aggressively, injuring consumers. A number of prominent antitrust scholars have cited this research as grounds for limiting the degree to which institutional investors may hold stakes in multiple firms that compete in any concentrated market. In our recent working paper, The Case for Doing Nothing About Institutional Investors’ Common Ownership of Small Stakes in Competing Firms, which we submit along with these comments, we contend that the purported competitive problem is overblown and that the proposed solutions would reduce overall social welfare.

With respect to the purported problem, our paper shows that the theory of anticompetitive harm from institutional investors’ common ownership is implausible and that the empirical studies supporting the theory are methodologically unsound. The theory fails to account for the fact that intra-industry diversified institutional investors are also inter-industry diversified, and it rests upon unrealistic assumptions about managerial decision-making. The empirical studies purporting to demonstrate anticompetitive harm from common ownership are deficient because they inaccurately assess institutional investors’ economic interests and employ an endogenous measure that precludes causal inferences.

Even if institutional investors’ common ownership of competing firms did soften market competition somewhat, the proposed policy solutions would themselves create welfare losses that would overwhelm any social benefits they secured. The proposed policy solutions would create tremendous new decision costs for business planners and adjudicators and would raise error costs by eliminating welfare-enhancing investment options and/or exacerbating corporate agency costs.

In light of these problems with the purported problem and shortcomings of the proposed solutions, the optimal regulatory approach—at least, on the current empirical record—is to do nothing about institutional investors’ common ownership of small stakes in competing firms.

Thank you for considering these comments and our attached paper. We would be happy to answer any questions you may have.

Sincerely,

Thomas A. Lambert, Wall Family Chair in Corporate Law and Governance, University of Missouri Law School;
Michael E. Sykuta, Associate Professor, Division of Applied Social Sciences, University of Missouri; Director, Contracting and Organizations Research Institute (CORI)

Kudos to the Commission for holding this important set of hearings.

One of the hottest topics in antitrust these days is institutional investors’ common ownership of the stock of competing firms. Large investment companies like BlackRock, Vanguard, State Street, and Fidelity offer index and actively managed mutual funds that are invested in thousands of companies. In many concentrated industries, these institutional investors are “intra-industry diversified,” meaning that they hold stakes in all the significant competitors within the industry.

Recent empirical studies (e.g., here and here) purport to show that this intra-industry diversification has led to a softening of competition in concentrated markets. The theory is that firm managers seek to maximize the profits of their largest and most powerful shareholders, all of which hold stakes in all the major firms in the market and therefore prefer maximization of industry, not firm-specific, profits. (For example, an investor that owns stock in all the airlines servicing a route would not want those airlines to engage in aggressive price competition to win business from each other. Additional sales to one airline would come at the expense of another, and prices—and thus profit margins—would be lower.)

The empirical studies on common ownership, which have received a great deal of attention in the academic literature and popular press and have inspired antitrust scholars to propose a number of policy solutions, have employed a complicated measurement known as “MHHI delta” (MHHI∆). MHHI∆ is a component of the “modified Herfindahl–Hirschman Index” (MHHI), which, as the name suggests, is an adaptation of the Herfindahl–Hirschman Index (HHI).

HHI, which ranges from near zero to 10,000 and is calculated by summing the squares of the market shares of the firms competing in a market, assesses the degree to which a market is concentrated and thus susceptible to collusion or oligopolistic coordination. MHHI endeavors to account for both market concentration (HHI) and the reduced competition incentives occasioned by common ownership of the firms within a market. MHHI∆ is the part of MHHI that accounts for common ownership incentives, so MHHI = HHI + MHHI∆.  (Notably, neither MHHI nor MHHI∆ is bounded by the 10,000 upper limit applicable to HHI.  At the end of this post, I offer an example of a market in which MHHI and MHHI∆ both exceed 10,000.)

In the leading common ownership study, which looked at the airline industry, the authors first calculated the MHHI∆ on each domestic airline route from 2001 to 2014. They then examined, for each route, how changes in the MHHI∆ over time correlated with changes in airfares on that route. To control for route-specific factors that might influence both fares and the MHHI∆, the authors ran a number of regressions. They concluded that common ownership of air carriers resulted in a 3%–7% increase in fares.

As should be apparent, it is difficult to understand the common ownership issue—the extent to which there is a competitive problem and the propriety of proposed solutions—without understanding MHHI∆. Unfortunately, the formula for the metric is extraordinarily complex. Posner et al. express it as follows:

Where:

  • βij is the fraction of shares in firm j controlled by investor I,
  • the shares are both cash flow and control shares (so control rights are assumed to be proportionate to the investor’s share of firm profits), and
  • sj is the market share of firm j.

The complexity of this formula is, for less technically oriented antitrusters (like me!), a barrier to entry into the common ownership debate.  In the paragraphs that follow, I attempt to lower that entry barrier by describing the overall process for determining MHHI∆, cataloguing the specific steps required to calculate the measure, and offering a concrete example.

Overview of the Process for Calculating MHHI∆

Determining the MHHI∆ for a market involves three primary tasks. The first is to assess, for each coupling of competing firms in the market (e.g., Southwest Airlines and United Airlines), the degree to which the investors in one of the competitors would prefer that it not attempt to win business from the other by lowering prices, etc. This assessment must be completed twice for each coupling. With the Southwest and United coupling, for example, one must assess both the degree to which United’s investors would prefer that the company not win business from Southwest and the degree to which Southwest’s investors would prefer that the company not win business from United. There will be different answers to those two questions if, for example, United has a significant shareholder who owns no Southwest stock (and thus wants United to win business from Southwest), but Southwest does not have a correspondingly significant shareholder who owns no United stock (and would thus want Southwest to win business from United).

Assessing the incentive of one firm, Firm J (to correspond to the formula above), to pull its competitive punches against another, Firm K, requires calculating a fraction that compares the interest of the first firm’s owners in “coupling” profits (the combined profits of J and K) to their interest in “own-firm” profits (J profits only). The numerator of that fraction is based on data from the coupling—i.e., the firm whose incentive to soften competition one is assessing (J) and the firm with which it is competing (K). The fraction’s denominator is based on data for the single firm whose competition-reduction incentive one is assessing (J). Specifically:

  • The numerator assesses the degree to which the firms in the coupling are commonly owned, such that their owners would not benefit from price-reducing, head-to-head competition and would instead prefer that the firms compete less vigorously so as to maximize coupling profits. To determine the numerator, then, one must examine all the investors who are invested in both firms; for each, multiply their ownership percentages in the two firms; and then sum those products for all investors with common ownership. (If an investor were invested in only one firm in the coupling, its ownership percentage would be multiplied by zero and would thus drop out; after all, an investor in only one of the firms has no interest in maximization of coupling versus own-firm profits.)
  • The denominator assesses the degree to which the investor base (weighted by control) of the firm whose competition-reduction incentive is under consideration (J) would prefer that it maximize its own profits, not the profits of the coupling. Determining the denominator requires summing the squares of the ownership percentages of investors in that firm. Squaring means that very small investors essentially drop out and that the denominator grows substantially with large ownership percentages by particular investors. Large ownership percentages suggest the presence of shareholders that are more likely able to influence management, whether those shareholders also own shares in the second company or not.

Having assessed, for each firm in a coupling, the incentive to soften competition with the other, one must proceed to the second primary task: weighing the significance of those firms’ incentives not to compete with each other in light of the coupling’s shares of the market. (The idea here is that if two small firms reduced competition with one another, the effect on overall market competition would be less significant than if two large firms held their competitive fire.) To determine the significance to the market of the two coupling members’ incentives to reduce competition with each other, one must multiply each of the two fractions determined above (in Task 1) times the product of the market shares of the two firms in the coupling. This will generate two “cross-MHHI deltas,” one for each of the two firms in the coupling (e.g., one cross-MHHI∆ for Southwest/United and another for United/Southwest).

The third and final task is to aggregate the effect of common ownership-induced competition-softening throughout the market as a whole by summing the softened competition metrics (i.e., two cross-MHHI deltas for each coupling of competitors within the market). If decimals were used to account for the firms’ market shares (e.g., if a 25% market share was denoted 0.25), the sum should be multiplied by 10,000.

Following is a detailed list of instructions for assessing the MHHI∆ for a market (assuming proportionate control—i.e., that investors’ control rights correspond to their shares of firm profits).

A Nine-Step Guide to Calculating the MHHI∆ for a Market

  1. List the firms participating in the market and the market share of each.
  2. List each investor’s ownership percentage of each firm in the market.
  3. List the potential pairings of firms whose incentives to compete with each other must be assessed. There will be two such pairings for each coupling of competitors in the market (e.g., Southwest/United and United/Southwest) because one must assess the incentive of each firm in the coupling to compete with the other, and that incentive may differ for the two firms (e.g., United may have less incentive to compete with Southwest than Southwest with United). This implies that the number of possible pairings will always be n(n-1), where n is the number of firms in the market.
  4. For each investor, perform the following for each pairing of firms: Multiply the investor’s percentage ownership of the two firms in each pairing (e.g., Institutional Investor 1’s percentage ownership in United * Institutional Investor 1’s percentage ownership in Southwest for the United/Southwest pairing).
  5. For each pairing, sum the amounts from item four across all investors that are invested in both firms. (This will be the numerator in the fraction used in Step 7 to determine the pairing’s cross-MHHI∆.)
  6. For the first firm in each pairing (the one whose incentive to compete with the other is under consideration), sum the squares of the ownership percentages of that firm held by each investor. (This will be the denominator of the fraction used in Step 7 to determine the pairing’s cross-MHHI∆.)
  7. Figure the cross-MHHI∆ for each pairing of firms by doing the following: Multiply the market shares of the two firms, and then multiply the resulting product times a fraction consisting of the relevant numerator (from Step 5) divided by the relevant denominator (from Step 6).
  8. Add together the cross-MHHI∆s for each pairing of firms in the market.
  9. Multiply that amount times 10,000.

I will now illustrate this nine-step process by working through a concrete example.

An Example

Suppose four airlines—American, Delta, Southwest, and United—service a particular market. American and Delta each have 30% of the market; Southwest and United each have a market share of 20%.

Five funds are invested in the market, and each holds stock in all four airlines. Fund 1 owns 1% of each airline’s stock. Fund 2 owns 2% of American and 1% of each of the others. Fund 3 owns 2% of Delta and 1% of each of the others. Fund 4 owns 2% of Southwest and 1% of each of the others. And Fund 4 owns 2% of United and 1% of each of the others. None of the airlines has any other significant stockholder.

Step 1: List firms and market shares.

  1. American – 30% market share
  2. Delta – 30% market share
  3. Southwest – 20% market share
  4. United – 20% market share

Step 2: List investors’ ownership percentages.

Step 3: Catalogue potential competitive pairings.

  1. American-Delta (AD)
  2. American-Southwest (AS)
  3. American-United (AU)
  4. Delta-American (DA)
  5. Delta-Southwest (DS)
  6. Delta-United (DU)
  7. Southwest-American (SA)
  8. Southwest-Delta (SD)
  9. Southwest-United (SU)
  10. United-American (UA)
  11. United-Delta (UD)
  12. United-Southwest (US)

Steps 4 and 5: Figure numerator for determining cross-MHHI∆s.

Step 6: Figure denominator for determining cross-MHHI∆s.

Steps 7 and 8: Determine cross-MHHI∆s for each potential pairing, and then sum all.

  1. AD: .09(.0007/.0008) = .07875
  2. AS: .06(.0007/.0008) = .0525
  3. AU: .06(.0007/.0008) = .0525
  4. DA: .09(.0007/.0008) = .07875
  5. DS: .06(.0007/.0008) = .0525
  6. DU: .06(.0007/.0008) = .0525
  7. SA: .06(.0007/.0008) = .0525
  8. SD: .06(.0007/.0008) = .0525
  9. SU: .04(.0007/.0008) = .035
  10. UA: .06(.0007/.0008) = .0525
  11. UD: .06(.0007/.0008) = .0525
  12. US: .04(.0007/.0008) = .035
    SUM = .6475

Step 9: Multiply by 10,000.

MHHI∆ = 6475.

(NOTE: HHI in this market would total (30)(30) + (30)(30) + (20)(20) + (20)(20) = 2600. MHHI would total 9075.)

***

I mentioned earlier that neither MHHI nor MHHI∆ is subject to an upper limit of 10,000. For example, if there are four firms in a market, five institutional investors that each own 5% of the first three firms and 1% of the fourth, and no other investors holding significant stakes in any of the firms, MHHI∆ will be 15,500 and MHHI 18,000.  (Hat tip to Steve Salop, who helped create the MHHI metric, for reminding me to point out that MHHI and MHHI∆ are not limited to 10,000.)

A recent tweet by Lina Khan, discussing yesterday’s American Express decision, exemplifies an unfortunate trend in contemporary antitrust discourse.  Khan wrote:

The economists cited by the Second Circuit (whose opinion SCOTUS affirms) for the analysis of ‘two-sided’ [markets] all had financial links to the credit card sector, as we point out in FN 4 [link to amicus brief].

Her implicit point—made more explicitly in the linked brief, which referred to the economists’ studies as “industry-funded”—was that economic analysis should be discounted if the author has ever received compensation from a firm that might benefit from the proffered analysis.

There are two problems with this reasoning.  First, it’s fallacious.  An ad hominem argument, one addressed “to the person” rather than to the substance of the person’s claims, is a fallacy of irrelevance, sometimes known as a genetic fallacy.  Biased people may make truthful claims, just as unbiased people may get things wrong.  An idea’s “genetics” are irrelevant.  One should assess the substance of the actual idea, not the identity of its proponent.

Second, the reasoning ignores that virtually everyone is biased in some way.  In the antitrust world, those claiming that we should discount the findings and theories of industry-connected experts urging antitrust modesty often stand to gain from having a “bigger” antitrust.

In the common ownership debate about which Mike Sykuta and I have recently been blogging, proponents of common ownership restrictions have routinely written off contrary studies by suggesting bias on the part of the studies’ authors.  All the while, they have ignored their own biases:  If their proposed policies are implemented, their expertise becomes exceedingly valuable to plaintiff lawyers and to industry participants seeking to traverse a new legal minefield.

At the end of our recent paper, The Case for Doing Nothing About Institutional Investors’ Common Ownership of Small Stakes in Competing Firms, Mike and I wrote, “Such regulatory modesty will prove disappointing to those with a personal interest in having highly complex antitrust doctrines that are aggressively enforced.”  I had initially included a snarky footnote, but Mike, who is far nicer than I, convinced me to remove it.

I’ll reproduce it here in the hopes of reducing the incidence of antitrust ad hominem.

Professor Elhauge has repeatedly discounted criticisms of the common ownership studies by suggesting that critics are biased.  See, e.g., Elhauge, supra note 26, at 1 (observing that “objections to my analysis have been raised in various articles, some funded by institutional investors with large horizontal shareholdings”); id. at 3 (“My analysis of executive compensation has been critiqued in a paper by economic consultants O’Brien and Waehrer that was funded by the Investment Company Institute, which represents institutional investors and was headed for the last three years by the CEO of Vanguard.”); Elhauge, supra note 124, at 3 (observing that airline and banking studies “have been critiqued in other articles, some funded by the sort of institutional investors that have large horizontal shareholdings”); id. at 17 (“The Investment Company Institute, an association of institutional investors that for the preceding three years was headed by the CEO of Vanguard, has funded a couple of papers to critique the empirical study showing an adverse link between horizontal shareholding and airline prices.”); id. (observing that co-authors of critique “both have significant experience in the airline industry because they consulted either for the airlines or the DOJ on airline mergers that were approved notwithstanding high levels of horizontal shareholding”); id. at 19 (“The Investment Company Institute has responded by funding a second critique of the airline study.”); id. at 23-24 (“Even to the extent that such studies are not directly funded by industry, when an industry has been viewed as benign for a long time, confirmation bias is a powerful force that will incline many to interpret any data to find no adverse effects.”).  He fails, however, to acknowledge his own bias.  As a professor of antitrust law at one of the nation’s most prestigious law schools, he has an interest in having antitrust be as big and complicated as possible: The more complex the doctrine, and the broader its reach, the more valuable a preeminent antitrust professor’s expertise becomes.  This is not to suggest that one should discount the assertions of Professor Elhauge or other proponents of restrictions on common ownership.  It is simply to observe that bias is unavoidable and that the best approach is therefore to evaluate claims according to their substance, not according to who is asserting them.

Even if institutional investors’ common ownership of small stakes in competing firms did cause some softening of market competition—a claim that is both suspect as a theoretical matter and empirically shaky—the policy solutions common ownership critics have proposed would do more harm than good.

Einer Elhauge has called for public and private lawsuits against institutional investors under Clayton Act Section 7, which is primarily used to police anticompetitive mergers but which literally forbids any stock acquisition that substantially lessens competition in a market. Eric Posner, Fiona Scott Morton, and Glen Weyl have called on the federal antitrust enforcement agencies (FTC and DOJ) to promulgate an enforcement policy that would discourage institutional investors from investing and voting shares in multiple firms within any oligopolistic industry.

As Mike Sykuta and I explain in our recent paper on common ownership, both approaches would create tremendous decision costs for business planners and adjudicators and would likely entail massive error costs as institutional investors eliminated welfare-enhancing product offerings and curtailed activities that reduce agency costs.

Decision Costs

The touchstone for liability under Elhauge’s Section 7 approach would be a pattern of common ownership that caused, or likely would cause, market prices to rise. Elhauge would identify suspect patterns of common ownership using MHHI∆, a measure that assesses incentives to reduce competition based on, among other things, the extent to which investors own stock in multiple firms within a market and the market shares of the commonly owned firms. (Mike described MHHI∆ here.) Specifically, Elhauge says, liability would result from “any horizontal stock acquisitions that have created, or would create, a ∆MHHI of over 200 in a market with an MHHI over 2500,” if “those horizontal stock acquisitions raised prices or are likely to do so.”

The administrative burden this approach would place on business planners would be tremendous. Because an institutional investor can’t directly control market prices, the only way it could avoid liability would be to ensure either that the markets in which it was invested did not have an MHHI greater than 2500 or that its acquisitions’ own contribution to MHHI∆ in those markets was less than 200. MHHI and MHHI∆, though, are largely determined by others’ investments and by commonly owned firms’ market shares, both of which change constantly. This implies that business planners could ensure against liability only by continually monitoring others’ activities and general market developments.

Adjudicators would also face high decision costs under Elhauge’s Section 7 approach. First, they would have to assess complicated econometric studies to determine whether adverse price effects were actually caused by patterns of common ownership. Then, if they decided common ownership had caused a rise in prices, they would have to answer a nearly intractable question: How should the economic harm from common ownership be allocated among the investors holding stakes in multiple firms in the industry? As Posner et al. have observed, “MHHI∆ is a collective responsibility of the holding pattern” in markets in which there are multiple intra-industry diversified investors. It would not work to assign liability only to those diversified investors who could substantially reduce MHHI∆ by divesting, for oftentimes the unilateral divestment of each institutional investor from the market would occasion only a small reduction in MHHI∆. An aggressive court might impose joint liability on all intra-industry diversified investors, but the investor(s) from whom plaintiffs collected would likely seek contribution from the other intra-industry diversified investors. Denying contribution seems intolerably inequitable, but how would a court apportion damages?

In light of these administrative difficulties, Posner et al. advocate a more determinate, rule-based approach. They would have the federal antitrust enforcement agencies compile annual lists of oligopolistic industries and then threaten enforcement action against any institutional investor holding more than one percent of the stock in such an industry if the investor (1) held stock in more than one firm within the industry, and (2) either voted its shares or engaged firm managers.

On first glance, this enforcement policy approach might appear to reduce decision costs: Business planners would have to do less investigation to avoid liability if they could rely on trustworthy, easily identifiable safe harbors; adjudicators’ decision costs would fall if the enforcement policy made it easier to identify illicit investment patterns. But the approach saddles antitrust enforcers with the herculean task of compiling, and annually updating, lists of oligopolistic industries. Given that the antitrust agencies frequently struggle with the far more modest task of defining markets in the small number of merger challenges they file each year, there is little reason to believe enforcers could perform their oligopoly-designating duties at a reasonable cost.

Error Costs

Even greater than the proposed policy solutions’ administrative costs are their likely error costs—i.e., the welfare losses that would stem from wrongly deterring welfare-enhancing arrangements. Such costs would result if, as is likely, institutional investors were to respond to the policy solutions by making one of the two changes proponents of the solutions appear to prefer: either refraining from intra-industry diversification or remaining fully passive in the industries in which they hold stock of multiple competitors.

If institutional investors were to seek to avoid liability by investing in only one firm per concentrated industry, retail investors would lose access to a number of attractive investment opportunities. Passive index funds, which offer retail investors instant diversification with extremely low fees (due to the lack of active management), would virtually disappear, as most major stock indices include multiple firms per industry.

Moreover, because critics of common ownership maintain that intra-industry diversification at the institutional investor level is sufficient to induce competition-softening in concentrated markets, each institutional investor would have to settle on one firm per concentrated industry for all its funds. That requirement would impede institutional investors’ ability to offer a variety of actively managed funds organized around distinct investment strategies—e.g., growth, value, income etc. If, for example, Southwest Airlines were a growth stock and United Airlines a value stock, an institutional investor could not offer both a growth fund including Southwest and a value fund including United.

Finally, institutional investors could not offer funds designed to bet on an industry while limiting exposure to company-specific risks within that industry. Suppose, for example, that a financial crisis led to a precipitous drop in the stock prices of all commercial banks. A retail investor might reasonably conclude that the market had overreacted with respect to the industry as a whole, that the industry would likely rebound, but that some commercial banks would probably fail. Such an investor would wish to invest in the commercial banking sector but to hold a diversified portfolio within that sector. A legal regime that drove fund families to avoid intra-industry diversification would prevent them from offering the sort of fund this investor would prefer.

Of course, if institutional investors were to continue intra-industry diversification and seek to avoid liability by remaining passive in industries in which they were diversified, the funds described above could still be offered to investors. In that case, though, another set of significant error costs would arise: increased agency costs in the form of managerial misfeasance.

Unlike most individual shareholders, institutional investors often hold significant stakes in public companies and have the resources to become informed on corporate matters. They have a stronger motive and more opportunity to monitor firm managers and are thus particularly well-poised to keep managers on their toes. Institutional investors with long-term investor horizons—including all index funds, which cannot divest from their portfolio companies if firm performance suffers—have proven particularly beneficial to firm performance.

Indeed, a recent study by Jarrad Harford, Ambrus Kecskés, & Sattar Mansi found that investment by long-term institutional investors enhanced the quality of corporate managers, reduced measurable instances of managerial misbehavior, boosted innovation, decreased debt maturity (causing firms to become more exposed to financial market discipline), and increased shareholder returns. It strains credulity to suppose that this laundry list of benefits could similarly be achieved by long-term institutional investors that had no ability to influence managerial decision-making by voting their shares or engaging managers. Opting for passivity to avoid antitrust risk, then, would prevent institutional investors from achieving their agency cost-reducing potential.

In the end, proponents of additional antitrust intervention to police common ownership have not made their case. Their theory as to why current levels of intra-industry diversification would cause consumer harm is implausible, and the empirical evidence they say demonstrates such harm is both scant and methodologically suspect. The policy solutions they have proposed for dealing with the purported problem would radically rework an industry that has provided substantial benefits to investors, raising the costs of portfolio diversification and enhancing agency costs at public companies. Courts and antitrust enforcers should reject their calls for additional antitrust intervention to police common ownership.

Mike Sykuta and I have been blogging about our new paper responding to scholars who contend that institutional investors’ common ownership of small stakes in competing firms significantly reduces market competition and should be restricted.  (FTC Commissioner Noah Phillips cited the paper yesterday in his excellent prepared remarks on common ownership.)  Mike first described the purported competitive problem.  I then set forth some problems with the anticompetitive theory common ownership critics have asserted.

When confronted with criticisms of their theory, common ownership critics have pointed to the empirical evidence Mike mentioned. In the most high-profile study, researchers correlated changes in commercial air fares with changes in “MHHI∆”, an index designed to measure the degree to which common ownership has reduced the incentive to compete. They concluded that common ownership has increased airfares by three to seven percent. A similar study of the commercial banking industry correlated banking fees and interest on deposit accounts with “GHHI”, a metric similar to MHHI∆. That study concluded that common ownership has led to higher fees and lower interest rates for depositors.

Common ownership critics have treated these studies as a trump card. The authors of the airline study, for example, brushed off a criticism of their anticompetitive theory with the following retort: “This argument falls short of explaining why, empirically, taking into account shareholders’ economic interests does help to explain firms’ product market behavior.”

Of course, to demonstrate “empirically” that institutional investors’ “economic interests” influence their portfolio companies’ “product market behavior” (i.e., cause the companies to charge higher prices, etc.), researchers would need to (1) correctly identify institutional investors’ economic interests with respect to their portfolio firms’ product market behavior, and (2) establish that those interests cause firms to act as they do. On those crucial tasks, the airline and banking studies fall short.

In assessing institutional investors’ economic interests, the studies have assumed that if an institutional investor reports holding a similar percentage of each firm in a market—say, five percent of the stock of each major airline—then it must have an “economic interest” in maximizing industry rather than own-firm profits. Such an assumption is unwarranted. That is because each institutional investor’s reported holdings, set forth on forms it must submit under Section 13(f) of the Securities Exchange Act, aggregate its holdings across all its funds. Such aggregation paints a misleading picture of the institutional investor’s actual economic interest.

For example, while Vanguard’s Section 13(f) filing reports ownership of a similar percentage of American, Delta, Southwest, and United Airlines—suggesting an economic interest in industry profit maximization—the picture looks very different at the individual fund level:

  • Vanguard’s Value Index Fund (VIVAX) holds significant stakes in American, Delta, and United (0.46%, 0.45%, and 0.42%, respectively) but holds no Southwest stock. VIVAX does best if United, American, and Delta usurp business from Southwest.
  • Vanguard’s Growth Index Fund (VIGRX) holds a significant stake in Southwest (0.59%) but holds no stake in American, Delta, or United. Investors in VIGRX would prefer that Southwest win business from American, Delta, and United.
  • Vanguard’s Mid-Cap Index Fund (VIMSX) and Mid-Cap Value Index Fund (VMVIX) hold significant stakes in United (1.00% and 0.321%, respectively) but hold no stock in American, Delta, or Southwest. Investors in VIMSX and VMVIX would prefer that United win business from American, Delta, and Southwest.
  • Vanguard’s PRIMECAP Core Fund (VPCCX) holds stakes in all four major airlines, but its share of Southwest (1.49%) is twice its share of American (0.72%), nearly four times its share of United (0.38%), and seven-and-a-half times its share of Delta (0.198%). Investors in VPCCX would prefer that Southwest grow at the expense of American, United, and Delta. They would also prefer that American win business from United and Delta, and that United win business from Delta.

We could go on, but the point should be clear: Because returns to retail investors in the funds of Vanguard and similar institutions turn on fund performance, the competitive outcome that maximizes retail investors’ profits will differ among funds.

Proponents of restrictions on common ownership might respond that even if an institutional investor’s individual funds have conflicting preferences, the institutional investor as an entity must have some preference about whether to maximize industry profits or the profits of a particular company. Because it cannot honor all its individual funds’ conflicting preferences with respect to competitive outcomes, the institutional investor will settle on the compromise strategy that maximizes its individual funds’ aggregate returns: industry profit maximization.  Such a strategy would be the first choice of the institution’s funds holding relatively equal shares of all firms within a market.  And, while the first choice of the institution’s funds that are disproportionately invested in one firm would be to maximize that firm’s profits, those funds would do better with industry profit maximization than with the first-choice strategy of other of the institution’s funds, i.e., those that are disproportionately invested in a different firm.

But even if maximization of industry profits leads to the greatest aggregate returns for an institutional investor’s funds, such a strategy may not be the best outcome for the institutional investor itself. An institutional investor typically wants to maximize its profits, which will grow as it attracts retail investors into its funds versus those of its competitors and steers those investors toward the funds that earn it the greatest profits (fees less costs). To assess an institutional investor’s preferences with regard to the returns of its different funds, then, one must know (1) the degree to which each fund’s attractiveness vis-à-vis rivals’ similar funds turns on portfolio returns, and (2) the profit margin each fund delivers to the institutional investor.

For funds tracking popular stock indices, portfolio returns play little role in winning business from rival fund sponsors.  (For example, higher returns on the stocks in the S&P 500 are unlikely to attract investors to BlackRock’s S&P 500 index fund over Fidelity’s or Vanguard’s.) Moreover, the fees charged on such funds, and thus the institutional investor’s potential profit margins, are extraordinarily low. For actively managed funds, portfolio returns are far more significant in attracting investors, and management fees are higher. The upshot is that an institutional investor, in determining what competitive outcome it prefers, will attach little weight to the competitive preferences of passive index funds and more weight to the preferences of actively managed funds, with that weight growing as the funds provide the institutional investor with higher profit margins.

It is quite possible, then, for an intra-industry diversified institutional investor to prefer a competitive outcome other than the maximization of industry profits, even if industry profit maximization would maximize the aggregate returns of its individual funds. Consider, for example, an institutional investor that offers funds similar to the following Vanguard funds:

  • Vanguard’s 500 Index Fund (VFIAX) holds near equivalent interests in American, Delta, Southwest, and United and would thus do best with a strategy of industry profit maximization. Its expense ratio (annual fees divided by total fund amount) is 0.04 percent.
  • Vanguard’s Value Index Fund (VIVAX) holds similar stakes in American, Delta, and United but does not hold Southwest stock. Its expense ratio is 0.18 percent.
  • Vanguard’s PRIMECAP Core Fund (VPCCX) holds a much higher stake in Southwest than in the other airlines and has an expense ratio of 0.46 percent, 2.5 times as great as the no-Southwest VIVAX fund and 11.5 times as high as the fully diversified VFIAX fund.
  • Vanguard’s Capital Opportunity Fund (VHCAX) holds significantly higher shares of Southwest and United (1.74% and 1.55%, respectively) than of Delta and American (0.65% and 1.16%, respectively). Its expense ratio is 0.38, more than twice as great as the no-Southwest VIVAX fund and 9.5 times the fully diversified VFIAX fund.

This institutional investor’s Southwest-heavy funds (those resembling Vanguard’s VPCCX and VHCAX funds) charge much higher fees than its fully diversified index fund (the one resembling VFIAX, for which fund returns are unimportant) and significantly higher fees than its funds that are more heavily invested in airlines besides Southwest (those resembling VIVAX).  Thus, despite being intra-industry diversified at the institutional level, this institutional investor may do best if Southwest maximizes own-firm profits.

The point here is that discerning an institutional investor’s actual economic interest requires drilling down to the level of its individual funds, something the common ownership studies have not done. Thus, contrary to the assertion of the airline study’s authors, the common ownership studies have not shown “empirically” that “taking into account shareholders’ economic interests does help to explain firms’ product market behavior.” Indeed, they have never established what those economic interests are.

Even if institutional investors’ aggregated holdings accurately revealed their economic interests with respect to competitive outcomes, the common ownership studies would still be deficient because they fail to show that those economic interests caused portfolio firms’ “product market behavior.” As explained above, the common ownership studies employ MHHI∆ (or a similar measure) to assess institutional investors’ interests in competition-softening. They then correlate changes in that metric with changes in portfolio firms’ pricing behavior. The problem is that MHHI∆ is itself affected by factors that independently influence market prices. It is thus improper to infer that changes in MHHI∆ caused changes in portfolio firms’ pricing practices; the pricing changes could have resulted from the very factors that changed MHHI∆. In other words, MHHI∆ is an endogenous measure.

To see why this is so, consider the three-step process involved in calculating MHHI∆ (which Mike described). The first step is to assess, for every coupling of competing firms in the market (e.g., Southwest/Delta, United/American, Southwest/United, etc.), the degree to which the controlling investors in each of the firms would prefer that it avoid competing with the other. The second step considers the market shares of the two firms in the coupling to determine the competitive significance of their incentives not to compete with each other. (The idea is that reduced head-to-head competition by bit players matters less for overall market competition than does reduced competition by major players.) The final step is to aggregate the effect of common ownership-induced competition-softening throughout the overall market by summing the softened competition metrics for each coupling of competitors within the market.

Given this process for calculating MHHI∆, there are at least two sources of endogeneity in the metric. One arises because of the second step. To assess the significance to market competition of any two firms’ incentives to reduce competition between themselves, the market shares of those two firms must be incorporated into the metric. But factors that influence market shares may also influence market prices apart from any common ownership effect.

Suppose, for example, that five institutional investors hold significant and equal stakes (say, 3%) in each of the four airlines servicing a particular air route and that none of the airlines has another significant shareholder. The air route at issue is subject to seasonal demand fluctuations. In the low season, the market is divided among the four airlines so that one has 40% of the business and the other three have 20% each. The MHHI∆ for this market would be 7200. When the high season rolls around, demand for flights along the route increases, but the leading airline is capacity constrained, so additional ticket sales go to the other airlines.  The market shares of the airlines in the high season are equal: 25% each.

On these facts, the increase in demand causes MHHI∆ to rise from 7200 to 7500.  But the increase in demand is also likely to raise ticket prices. We thus see an increase in MHHI∆ that correlates with an increase in ticket prices, but the price change is not caused by the change in MHHI∆. Instead, the two changes have a common, independent cause.

Endogeneity also creeps in during the third step in calculating MHHI∆.  In that step, the “cross MHHI∆s” of all the couplings in the market—the metrics assessing for each coupling the extent to which common ownership will cause the two firms to compete less vigorously—are summed. Thus, as the number of firms participating in the market (and thus the number of couplings) increases, the MHHI∆ will tend to rise. While HHI (the market concentration measure) will decrease as the number of competing firms rises, MHHI∆ (the measure of common ownership pricing incentives) will increase.

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.

This is problematic, because the number of participants in the market is affected by consumer demand, which also affects market prices. In the market described above, for example, the third or fourth airline might enter the market in response to an increase in demand, and that increase might simultaneously cause market price to rise. We would see, then, a price increase that is correlated with, but not caused by, an increase in MHHI∆; increased demand would be the cause of both the higher prices and the increase in MHHI∆.

In the end, then, the empirical evidence of competition-softening from common ownership is not the trump card proponents of common ownership restrictions proclaim it to be.

Mike Sykuta and I have been blogging about our recent paper on so-called “common ownership” by institutional investors like Vanguard, BlackRock, Fidelity, and State Street. Following my initial post, Mike described the purported problem with institutional investors’ common ownership of small stakes in competing firms.

As Mike explained, the theory of anticompetitive harm holds that small-stakes common ownership causes firms in concentrated industries to compete less vigorously, since each firm’s top shareholders are also invested in that firm’s rivals.  Proponents of restrictions on common ownership (e.g., Einer Elhauge and Eric Posner, et al.) say that empirical studies from the airline and commercial banking industries support this theory of anticompetitive harm. The cited studies correlate price changes with changes in “MHHI∆,” a complicated index designed to measure the degree to which common ownership encourages competition-softening.

We’ll soon have more to say about MHHI∆ (admirably described by Mike!) and the shortcomings of the airline and banking studies.  (Look for a “Problems With the Evidence” post.)  First, though, a few words on why the theory of anticompetitive harm from small-stakes common ownership is implausible.

Common ownership critics’ theoretical argument proceeds as follows:

  • Premise 1:    Because institutional investors are intra-industry diversified, they benefit if their portfolio firms seek to maximize industry, rather than own-firm, profits.
  • Premise 2:    Corporate managers seek to maximize the returns of their corporations’ largest shareholders—intra-industry diversified institutional investors—and will thus pursue maximization of industry profits.
  • Premise 3:    Industry profits, unlike own-firm profits, are maximized when producers refrain from underpricing their rivals to win business.

Ergo:

  • Conclusion:  Intra-industry diversification by institutional investors reduces price competition and should be restricted.

The first two premises of this argument are, at best, questionable.

With respect to Premise 1, it is unlikely that intra-industry diversified institutional investors benefit from, and thus prefer, maximization of industry rather than own-firm profits. That is because intra-industry diversified mutual funds tend also to be inter-industry diversified. Maximizing one industry’s profits requires supracompetitive pricing that tends to reduce the profits of firms in complementary industries.

Vanguard’s Value Index Fund, for example, holds around 2% of each major airline (1.85% of United, 2.07% of American, 2.15% of Southwest, and 1.99% of Delta) but also holds:

  • 1.88% of Expedia Inc. (a major retailer of airline tickets),
  • 2.20% of Boeing Co. (a manufacturer of commercial jets),
  • 2.02% of United Technologies Corp. (a jet engine producer),
  • 3.14% of AAR Corp. (the largest domestic provider of commercial aircraft maintenance and repair),
  • 1.43% of Hertz Global Holdings Inc. (a major automobile rental company), and
  • 2.17% of Accenture (a consulting firm for which air travel is a significant cost component).

Each of those companies—and many others—perform worse when airlines engage in the sort of supracompetitive pricing (and corresponding reduction in output) that maximizes profits in the airline industry. The very logic suggesting that intra-industry diversification causes investors to prefer less competition necessarily suggests that inter-industry diversification would counteract that incentive.

Of course, whether any particular investment fund will experience enhanced returns from reduced price competition in the industries in which it is intra-industry diversified ultimately depends on the composition of its portfolio. For widely diversified funds, however, it is unlikely that fund returns will be maximized by rampant competition-softening. As the well-known monopoly pricing model depicts, every instance of supracompetitive pricing entails a deadweight loss—i.e., an allocative inefficiency stemming from the failure to produce units that create greater value than they cost to produce. To the extent an index fund is designed to reflect gains in the economy generally, it will perform best if such allocative inefficiencies are minimized. It seems, then, that Premise 1—the claim that intra-industry diversified institutional investors prefer competition-softening so as to maximize industry profits—is dubious.

So is Premise 2, the claim that corporate managers will pursue industry rather than own-firm profits when their largest shareholders prefer that outcome. For nearly all companies in which intra-industry diversified institutional investors collectively hold a significant proportion of outstanding shares, a majority of the stock is still held by shareholders who are not intra-industry diversified. Those shareholders would prefer that managers seek to maximize own-firm profits, an objective that would encourage the sort of aggressive competition that grows market share.

There are several reasons to doubt that corporate managers would routinely disregard the interests of shareholders owning the bulk of the company’s stock. For one thing, favoring intra-industry diversified investors holding a minority interest could subject managers to legal liability. The fiduciary duties of corporate managers require that they attempt to maximize firm profits for the benefit of shareholders as a whole; favoring even a controlling shareholder (much less a minority shareholder) at the expense of other shareholders can result in liability.

More importantly, managers’ personal interests usually align with those of the majority when it comes to the question of whether to maximize own-firm or industry profits. As sellers in the market for managerial talent, corporate managers benefit from reputations for business success, and they can best burnish such reputations by beating—i.e., winning business from—their industry rivals. In addition, most corporate managers receive some compensation in the form of company stock. They maximize the value of that stock by maximizing own-firm, not industry, profits. It thus seems unlikely that corporate managers would ignore the interests of stockholders owning a majority of shares and cause their corporations to refrain from business-usurping competition.

In the end, then, two key premises of common ownership critics’ theoretical argument are suspect.  And if either is false, the argument is unsound.

When confronted with criticisms of their theory of anticompetitive harm, proponents of common ownership restrictions generally point to the empirical evidence described above. We’ll soon have some thoughts on that.  Stay tuned!

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.’