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:
- 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.
- 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.
- 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.’
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