Theory and Measurement of Common Ownership

By Matthew Backus, Christopher Conlon and Michael Sinkinson∗

The theory of common ownership posits sion (SEC) listing publicly traded securi- that investors, by taking non-controlling ties. These filings measure ownership at ownership stakes in competing firms, effect the level of a legal entity, which may or a partial merger. Azar, Schmalz and Tecu may not correspond to the level at which (2018) documented empirical evidence for decisions are made. These filings also suffer this claim in the US airline sector, evidence from additional shortcomings: short posi- that inspired a growing and controversial tion investments are not distinguished from empirical literature on common ownership. long ones; the entity that controls voting Backus, Conlon and Sinkinson (2019a) re- rights is often ambiguous; dual-class shares views that literature. Here, we focus on the complicate (or sometimes obviate) investor measurement of common ownership itself. influence for some firms; and reporting er- Differing approaches to measurement drive rors are common. controversy in the growing common owner- The commonly-used Thomson Reuters ship literature, as researchers describe his- database of 13(f) filings introduces a num- torical patterns, attempt to test the predic- ber of additional errors and coverage issues, tions of the model, and use it to generate which we document in Backus, Conlon and counterfactual predictions. Sinkinson (2019b). For the period 2000 to We consider three approaches, which are the present, we scraped data directly from sequentially nested by modeling structure. the SEC and have made our data available The first is descriptive; it measures owner- to the public. ship patterns and the extent to which in- Suppose each shareholder s ∈ S has a vestors overlap between firms. The second portfolio in which they own a fraction of maps ownership into primitives of the man- firm f ∈ F denoted by βfs. Measure- agers’ objective functions, which are as- ment of common ownership, then, is finding sumed to aggregate the preferences of their ways to characterize the potentially large investors. The third maps these primitives F ×S matrix β, which summarizes holdings into equilibrium outcomes of specific strate- across all shareholders and firms. A chal- gic settings, resulting in measures such as lenge of the descriptive approach is that one the “Modified Herfindal-Hirschman Index” must choose among the arbitrarily many (MHHI) of Bresnahan and Salop (1986). ways to reduce β, a high-dimensional object, to a reportable statistic. It is possible I. Measuring Investor Overlap to correlate ownership statistics of the form f(β) with various outcomes, but economi- In the United States, institutional in- cally meaningful claims require placing ad- vestors with over $100M in assets are re- ditional structure on the problem.1 quired to file quarterly 13(f) forms with the US Securities and Exchange Commis- II. Firm Objectives: Profit Weights

∗ Backus: Graduate School of Business, Columbia University, 3022 Broadway, Uris Hall With two additional assumptions, the 611, New York, NY 10027, CEPR and NBER, theory of common ownership maps overlap- [email protected]. Conlon: Stern School ping ownership positions as measured above of Business, New York University, 44 West 4th St, Kaufman Management Center 7-76, New York, NY 10012, [email protected]. Sinkinson: School of 1As an example of this approach, He and Huang Management, Yale University, 165 Whitney, Evans (2017) count the number of common blockholders who Hall Suite 3473, New Haven, CT 06511, and NBER, own βfs ≥ .05 and βgs ≥ .05 in both firms and correlate [email protected]. Any errors are our own. these measures with growth in market share. 1 2 PAPERS AND PROCEEDINGS MONTH YEAR into primitives of a firm’s objective func- Nearly any model of corporate gover- tion. nance (with or without agency frictions) can be written using Assumptions 1 and 2.4 ASSUMPTION 1: Investor returns/ port- P In other words, the controversy arises from folio values are given by: vs ≡ s βfsπf . the specific choice of γ and not Assumption 2 itself. Unfortunately, there is little guid- ASSUMPTION 2: Managers maximize a ance from the corporate governance litera- γ weighted average of investor returns: fs ture about how to measure or specify γ. Q ≡ P γ v (Rotemberg 1984). f s fs s One might be inclined to estimate γ from The first assumption defines investor data on market outcomes. As a general portfolios as the sum of corresponding cash- problem this is somewhat futile, as there are often many more investors S (several flow rights βfs ≥ 0, multiplied by the value thousand) than there are firms F (a hand- of each firm πf . The second assumption is more contro- ful) in an industry. Even if we knew the versial and states that managers maximize profit weights κ, we would not be able to a weighted average of their investor pay- recover the Pareto weights γ. offs. Because investors hold heterogeneous The empirical literature proceeds by as- portfolios, they may disagree about their suming γ = β, or “proportional control.” preferred objective for the firm. Managers In Backus, Conlon and Sinkinson (2019b) aggregate preferences of heterogeneous in- we consider a generalization to γ = βα for vestors using a set of Pareto weights γfs. α ∈ {1/2, 1, 2, 3}, a parameterization that Under these two assumptions one can re- offers some flexibility in the relative influ- arrange the manager’s objective such that:2 ence of large and small investors. Consider- ing the period 1980–2017, we found conver- X (1) Qf ∝ πf + κfg · πg, gence in the averages of pairwise κ across g6=f these specifications – by 2017 there is little difference – however α does matter for P ∀s γfsβgs measuring the frequency of extreme values where κfg ≡ . P (e.g., κfg > 1). ∀s γfsβfs With an assumption on γ, the primitives This implies that managers maximize their of the manager’s objective function are fully own profits π plus some κ weighted sum f fg specified, and those primitives may vary of the profits of other firms π . These κ g fg over time with changes in the observed own- terms are known as profit weights and have ership β. This variation across time and a long history in economics.3 pairs of firms provides a way to compare The Pareto weights γ stand in for the fs different assumptions on γ. influence of investors on firm decisions (e.g. corporate governance). Absent an assump- However, it is difficult to map κ to market outcomes without making additional as- tion on γfs the expression in (1) is suffi- ciently general to accommodate a host of sumptions on the nature of interactions be- behaviors. For example, the manager m tween firms (e.g. that they are horizontal might place weight on his own private ben- competitors engaged in selling substitutes). efit π with γ > 0 and potentially ignore Absent these assumptions, it may be pos- m fm sible to develop reduced form, correlation- his investors completely: γfs = 0; ∀s 6= m. Alternatively, the manager may place equal based tests, even though the magnitudes weight γfs = γfs0 > 0 on his largest two shareholders and ignore the rest; or place 4For example, the measure of common ownership equal weight on all shareholders γ = c; ∀s. and investor attention proposed by Gilje, Gormley and fs Levit (2019) can be shown to be mathematically equiva- lent to our Assumptions 1 and 2 under a formulation of 2 This expression first appeared as such in O’Brien γfs(βs) that places less weight on investors as they be- and Salop (2000). come more diversified. They rule out strategic interac- 3Dating as far back as Edgeworth’s “coefficients of tions among firms, which makes their measure inappror- effective sympathy”. priate for examining the common ownership hypothesis. VOL. VOL NO. ISSUE MEASUREMENT OF COMMON OWNERSHIP 3 of coefficients may not be interpretable. where the market shares depend on κ. For example, Gramlich and Grundl (2017) If the strategic game is something other don’t find a strong direct relationship be- than symmetric Cournot, there need not tween prices and functions f(κ) in the mar- be any relationship between MHHI(κ) and ket for retail banking (a setting similar to equilibrium outcomes. For example, if the Azar, Raina and Schmalz (2016)). These strategic game is Bertrand Nash-in-prices in reduced-form tests may not be as simple differentiated products so that Qf is a func- as they look. For example, O’Brien (2017) tion of p instead of q, then Qf (pf , p−f ) = P points out that equilibrium outcomes de- πf (pf , p−f ) + g6=f κfg · πg(pf , p−f ). This pend not only on κfg but on the entire F ×F gives a different first-order condition: matrix κ; the precise relationship depends (4) on the form of the strategic game.     III. Fully-Specified Strategic Games f  X  pf = cf + κfg Dfg (pg − cg) . f − 1    f6=g  If one begins with the firm’s objective | {z } function from (1) and fully specifies both PPI the Pareto weights γ and the form of the The bracketed expression is the Price Pres- strategic game played among all firms F , sure Index or PPI(κ): This relates prices it is possible to derive relationships be- to the own elasticity of demand f , and sub- tween common ownership and equilibrium stitution to rival’s products as measured outcomes such as prices, quantities, invest- by a “diversion ratio” Dfg (O’Brien and ment, and entry or exit. Salop 2000). Perhaps the most common example in Backus, Conlon and Sinkinson (2018) the literature is to assume that the firms show that mis-specifying the form of the engage in symmetric Cournot competition game can lead to spurious results. For ex- (simultaneous Nash-in-quantities) so that ample, regressions of prices on MHHI(κ) Q (q , q ) = π (q , q ) + P κ · f f −f f f −f g6=f fg can yield spurious positive or negative re- πg(qf , q−f ). When one solves for the first- sults when the strategic game is actually order-conditions of the resulting game, it Bertrand and there is no effect of common is possible to derive a relationship between ownership. share-weighted average markups and the Testing the theory of common ownership MHHI: by regressing prices on MHHI(κ) leads to

X pf − cf 1 additional challenges. First, the implied re- (2) sf = [MHHI(κ)] , lationship in (2) is between share-weighted pf f average markup and MHHI(κ), not prices and MHHI(κ). Second, any analyses (3) using MHHI require the researcher to X 2 X X MHHI(κ) = sf + κfgsf sg . compute market shares in addition to κ, f f g6=f thus introducing the myriad difficulties of | {z } | {z } 5 HHI ∆MHHI proper market definition. The PPI(κ) is hardly better, as it requires estimates of MHHI(κ) is not a measure of common the diversion ratios Dfg. Finally, because ownership, it is a modified concentration MHHI(κ) is a market-level measure, it is index and an equilibrium outcome itself. unable to exploit variation across firms. Scholars sometimes portray MHHI(κ) and the profit weights κ as different ways to 5This is further complicated when researchers con- measure common ownership, although they struct market shares from publicly available databases are not. The profit weights, κ, are a primi- such as COMPUSTAT which are limited to publicly tive object in the manager’s objective func- traded US firms. The MHHI(κ) measure implicitly requires the appropriate geographic and product market tion; while MHHI(κ) or ∆MHHI(κ) are as all products must be equally good substitutes within equilibrium outcomes of a Cournot game the relevant market. 4 PAPERS AND PROCEEDINGS MONTH YEAR

IV. The Role of Measurement the Ready-To-Eat Cereal Industry.” Un- published. The descriptive approach to measuring Backus, Matthew, Christopher Con- common ownership is limited by the lack lon, and Michael Sinkinson. 2019a. of interpretation. For this reason, Backus, “The Common Ownership Hypothesis: Conlon and Sinkinson (2019b), which mea- Theory and Evidence.” Brookings Work- sures common ownership in the US from ing Paper. 1980 to 2017, advocated for a focus on κ, Backus, Matthew, Christopher Con- the objective function of the firm. Because lon, and Michael Sinkinson. 2019b. it is generic to the formulation of firms’ in- “Common Ownership in America: 1980– teraction, there is no need for compromises 2017.” NBER Working Paper 25454. on market definition. Boller, Lysle, and Fiona Scott Mor- In Backus, Conlon and Sinkinson (2019b) ton. 2019. “Testing the Theory of Com- we also show that the key to testing the mon Stock Ownership.” Working Paper. theory of common ownership hypothesis is really the profit weights κ. While one Bresnahan, Timothy F., and might learn about κ through equilibrium Steven C. Salop. 1986. “Quantify- outcomes like MHHI(κ) or PPI(κ) or ing the Competitive Effects of Production other outcomes such as entry, R&D, or Joint Ventures.” International Journal of investment, testing common ownership — Industrial Organizatoin 4: 155–175. like testing collusion — is about the profit Gilje, Erik P., Todd A. Gormley, and weights firms put on each other. Doron Levit. 2019. “Who’s paying at- These reflections on measurement are tention? Measuring Common Ownership critical to structural testing, but can also and its Impact on Managerial Incentives.” guide reduced form work. For exam- Journal of Financial Economics. ple, seemingly innocuous financial market Gramlich, Jacob, and Serafin Grundl. transactions could have potentially large 2017. “Estimating the Competitive Effects impacts on product markets through κ. of Common Ownership.” FEDS Working Boller and Scott Morton (2019) provide Paper 2017-029. some encouraging evidence here. They find He, Jie, and Jiekun Huang. 2017. that when firms join stock indices, there “Product Market Competition in a World are pricing anomalies for the stock of rival of Cross-Ownership: Evidence from In- firms. These pricing anomalies are corre- stitutional Blockholdings.” The Review of lated with the theoretically-motivated κ — Financial Studies 30. consistent also with asymmetries of κ be- O’Brien, Daniel, and Steven Sa- tween firms — but not other, purely de- lop. 2000. “Competitive Effects of Partial scriptive overlap measures. Ownership: Financial Interest and Cor- porate Control.” Antitrust Law Journal REFERENCES 67(3): 559–614. Azar, Jose, Martin C. Schmalz, and O’Brien, Daniel P. 2017. “Price- Isabel Tecu. 2018. “Anti-Competitive Concentration Analysis: Ending Effects of Common Ownership.” Journal the Myth, and Moving Forward.” of Finance 73(4). https://ssrn.com/abstract=3008326. Accessed on 2020-01-08. Azar, Jose, Sahil Raina, and Mar- tin C. Schmalz. 2016. “Ultimate Rotemberg, Julio. 1984. “Fi- Ownership and Bank Competition.” nancial Transactions Costs https://ssrn.com/abstract=2710252. and Industrial Performance.” Accessed on 2020-01-08. http://hdl.handle.net/1721.1/47993. Accessed on 2020-01-08. Backus, Matthew, Christopher Con- lon, and Michael Sinkinson. 2018. “Common Ownership and Competition in