By Duarte Brito, Einer Elhauge, Ricardo Ribeiro, Helder Vasconcelos

Expert Economist Helder Vasconcelos co-authored a paper with Duarte Brito, Einer Elhauge and Ricardo Ribeiro for the *International Journal of Industrial Organization*. The paper examines the objective function of managers in the presence of overlapping shareholding from both a theoretical and empirical perspective, with the findings showing that profit weights can (and should) be incorporated into the traditional indicators used to help predict anti-competitive effects.

###### Abstract

The objective function of managers in the presence of overlapping shareholding may differ from the traditional own-firm profit maximization, as they may internalize the externalities their strategies impose on other firms. The dominant formulation of the objective function in such cases has, however, been critiqued for yielding counter-intuitive profit weights when the ownership of non-overlapping shareholders is highly dispersed. In this paper, we examine this issue. First, we make use of a probabilistic voting model (in which shareholders vote to elect the manager) to microfound an alternative formulation of the objective function of managers, which solves the above-mentioned criticism. Second, we apply the two formulations to the set of S&P 500 firms. We show that ownership dispersion of non-overlapping shareholders is, in fact, a relevant empirical issue, which may induce an over-quantification of the profit

weights computed from the dominant formulation, particularly under a proportional control

assumption.

###### Introduction

The assumption of own-firm profit maximization is key, (at least) since Fisher (1930)’s separation theorem, to most literature in corporate finance and industrial organization. However, the validity of this assumption has been recently questioned due to the increase, documented for a multitude of industries and economies, particularly since 2000, of overlapping shareholding (Azar, Schmalz, Tecu, 2018, Newham, Seldeslachts, Banal-Estañol, Backus, Conlon, Sinkinson, 2021, Azar, Raina, Schmalz, 2022). The reason being that if firms impose externalities on one another, overlapping shareholding may imply a failure of the competitiveness condition, established by Hart (1979) to be essential for shareholders, regardless of their preferences, to unanimously agree on own-firm profit maximization. In order to see why, note, for example, that if firm A imposes a negative externality on firm B, a shareholder of firm A who also holds shares in firm B typically wants the manager of firm A to pursue a less aggressive strategy than the strategy desired by a shareholder with no holdings in firm B.

The managers of firms with overlapping shareholders, rather than maximizing own profit, may therefore weigh the eventual conflicting objectives of their shareholders. This implies that they may internalize (to some degree) the externalities their strategies impose on other firms (Rotemberg, Hansen, Lott, 1996). This internalization can alter the incentives to compete and can naturally impact market competition.1,2

In order to empirically examine the impact of overlapping ownership on market outcomes, we must quantify the above-mentioned induced internalization. To do so, the formulation of the objective function of managers is key.3 This formulation is, however, non-trivial. In order to see why, consider, for example, that firm A has four shareholders, each holding 25% of the firm, and that one of those shareholders also holds 20% of firm B. If firm A imposes an externality on firm B, what would the mathematical formulation of the objective function of the manager of firm A be? What weight would the manager of firm A assign to the profit of firm B?

The dominant formulation of the objective function of managers in the presence of overlapping shareholders is due to O’Brien and Salop (2000). Incorporating features from both Rotemberg (1984) and Bresnahan and Salop (1986), they assume that the manager of a firm with overlapping shareholders would decide the strategy of the firm to maximize a control-weighted sum of the expected returns of the firm’s shareholders. Azar, 2012, Azar, Azar, Brito et al. (2018a) and Moskalev (2019) show that this formulation can be microfounded through a voting model in which shareholders vote to elect the manager from two potential candidates, an incumbent and a challenger, with conceivably differing strategy proposals to the firm. This formulation, although heavily used in the literature, has also been critiqued for yielding counter-intuitive profit weights when the ownership of non-overlapping shareholders is highly dispersed (see, for example, Gramlich and Grundl, 2017, pages 9-13; O’Brien and Waehrer, 2017, pages 760-761; Crawford et al., 2018, supplementary material, pages 12-13).4 The argument can be generalized as follows. No matter how small the ownership of overlapping shareholders (and the corporate control induced from their voting rights) is in a firm, as the dispersion of the ownership of non-overlapping shareholders increases, the weight assigned by the manager to the profit of other firms (in which overlapping shareholders hold shares in) tends to reflect solely the interests of the (non-dispersed) overlapping shareholders. In other words, no matter how small the ownership of overlapping shareholders is, the dominant formulation yields that the manager would weigh solely the interests of the overlapping shareholders whenever the remaining ownership of the firm becomes diffuse, even if such dispersion does not yield overlapping shareholders the full control of the firm.

In this paper, we take the first step to examine this issue, from both a theoretical and empirical perspective. From a theoretical perspective, we make use of a probabilistic voting model (in the lines of Azar, 2012, Azar, Azar, Brito, Osório, Ribeiro, Vasconcelos, 2018; and Moskalev, 2019) to microfound an alternative formulation of the objective function of managers in the presence of overlapping shareholders in which the manager of a firm with overlapping shareholders would decide the strategy of the firm to maximize a control-weighted sum of the relative expected returns of the firm’ s shareholders. Under this proposed alternative formulation, the weight assigned by the manager to the profit of other firms (in which overlapping shareholders hold shares in) will never reflect solely the interests of the (the non-dispersed) overlapping shareholders, unless the dispersion yields overlapping shareholders the full control of the firm. As such, it solves the above-mentioned criticism regarding the dominant formulation. From an empirical perspective, we apply the two formulations to the set of S&P 500 firms (in the lines of Backus et al., 2021b; and Amel-Zadeh et al., 2022) from 2003 to 2019. We show that the theoretical issue noted above is indeed of empirical relevance for the set of S&P 500 firms.

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*This paper was originally published for International Journal of Industrial Organization here. The views expressed are those of the authors only and do not necessarily represent the views of Compass Lexecon, its management, its subsidiaries, its affiliates, its employees, or clients.*

*Duarte Brito, Einer Elhauge, Ricardo Ribeiro, Helder Vasconcelos, Modelling the Objective Function of Managers in the Presence of Overlapping Shareholding, International Journal of Industrial Organization (2022), doi: https://doi.org/10.1016/j.ijindorg.2022.102905 *