Multifaceted Transactions and Organizational Ownership

Multifaceted Transactions and Organizational Ownership Abstract I provide a unified explanation for shareholder ownership, partnerships, mutuals, government ownership, cooperatives, and vertical and horizontal control: each ownership form constitutes a variation on a single underlying theme, the assignment of ownership to a subset of firm stakeholders. When not every facet of a transaction is contractible and high-powered incentives might divert investment toward the transaction’s contractible facets, to the overall transaction’s possible detriment, optimal organizational ownership allocates the right to set the power of managerial incentives to those stakeholders most affected by the noncontractible facets of the organization’s paramount transaction. Received August 3, 2016; editorial decision August 2, 2017 by Editor Uday Rajan. The owners of a firm are nearly always one or another subset of the firm’s patrons—that is, persons who have some transactional relationship with the firm, either as suppliers or customers, apart from their possession of the rights of ownership. Often, that transactional relationship is the supply of capital to the firm, in which case we have the conventional investor-owned firm. Not infrequently however, ownership of the firm is placed in the hands of another class of patrons. This is the case, for example, with producer cooperatives, consumer cooperatives, employee-owned firms, and governments (897).—Hansmann 2013 Hansmann’s intriguing observation suggests that investor ownership is not a uniquely distinct form of ownership. It is, instead, one of many possible variations on the single underlying theme that is the assignment of ownership to a class of firm patrons, a subset of the firm’s many stakeholders. The purpose of the present paper is to develop a formal model that accounts for Hansmann’s observation and to use that model to generate additional predictions that can be, in turn, compared with the extant empirical evidence.1 The central intuition of the model is perhaps best expressed by Holmstrom’s (1999, p. 76) statement that “ownership […] internalizes some of the contractual externalities that are present in markets.” More specifically, ownership confers the right to set the power of managerial incentives to those stakeholders who are most exposed to the (noncontractible) consequences of the firm manager’s actions. Ownership thereby provides these stakeholders with the ability to, at least partially, control the manager’s actions and determine the extent to which such actions affect the stakeholders.2 Contractual externalities generally arise when some, but not all, facets of a multifaceted transaction can be contracted (Barzel 1982, 1997). In this case, as noted by Barzel (2002, 2013), Hansmann (1996), Holmstrom (1999), and Holmstrom and Milgrom (1991, 1994), low-powered incentives for facets of the transaction that can be contracted may be necessary to avoid too large a distortion in facets that cannot be contracted. For example, a currency trader may need to be offered low- rather than high-powered incentives when the bulk of possible trading losses is borne by investors instead of the trader.3I argue that optimal organizational ownership allocates the right to set the power of managerial incentives to those parties that are most affected by the noncontractible facets of the organization’s paramount transactions. To make things concrete, consider a buyer and a supplier. Quality is important to the buyer; the supplier can trade off quantity and quality. Assume quantity is contractible but quality is not. If the cost of low quality is primarily borne by the buyer, then the supplier is expected to favor quantity over quality. The suppliers’ manager will do so more when his or her incentives are high powered: high-powered incentives make the supplier’s higher profit in part the manager’s too. By acquiring the supplier, the buyer gains the right to set the supplier manager’s incentives. He or she will set incentives at a lower level, consistent with the choice of higher quality.4 Quality is the contractual externality, which backward integration by the buyer internalizes; this is well known.5 What is perhaps less well known is that the same mechanism can provide an explanation for forms of ownership as diverse as partnerships, mutuals, and cooperatives. These correspond to different externalities involving different transacting parties, specifically the reputation of senior employees in the case of partnerships, the savings and premiums of depositors and policyholders in the case of mutual banks and insurance companies, the demand for labor in the case of worker cooperatives, the demand for farm products and the supply of farm implements in the case of farm marketing, processing and supply cooperatives, and the capital equipment of utilities in the case of customer and government ownership. Shareholder ownership corresponds to the case in which the paramount transaction concerns the noncontractible use of firm equity. Returning to the example of the currency trader, investors who are called on to provide the capital put at risk by the trader may do so only on the condition that they be granted the right to set the power of the trader’s incentives at a level consistent with properly accounting for investor capital in the choice of trading positions. That such right is conferred by ownership implies that investors are owners; this is shareholder ownership. I allow for ownership to be distinct from capital provision: in the example of the buyer integrating backward, the buyer need not provide the capital necessary for the acquisition of the supplier; he or she may, instead, rely on the issuance of nonvoting, preferred stock. The stock is nonvoting because only the owner, the buyer in the present case, has the right to set the power of managerial incentives; it is preferred, in the sense of mandating the payment of a fixed dividend, because the owner’s ability to manipulate profit precludes the issuance of common stock to investors called on to provide the capital necessary for the acquisition.6 I compare shareholder ownership, stakeholder ownership and stakeholder capital provision (stakeholder ownership), and stakeholder ownership and nonvoting preferred shareholder capital provision (stakeholder ownership combined with nonvoting preferred stock). Stakeholder ownership dominates when stakeholders have cost of capital close to that of specialized shareholders: stakeholder ownership allocates stakeholders, who are the party most affected by the externality, the right to set the power of managerial incentives at a level consistent with the recognition of the externality. As stakeholder cost of capital increases, however, eventually to become markedly larger than that of specialized shareholders, then the substitution of stakeholder by shareholder capital may be desirable. Such substitution may take two forms: (1) shareholders may become the owners, as the stakeholders’ high cost of capital transforms the provision of capital into the paramount externality, or (2) stakeholders may remain the owners but firm capital nonetheless be provided by specialized shareholders who, unlike in the case of shareholder ownership, do not acquire ownership in the sense of not acquiring the right to set the power of managerial incentives, which remains stakeholders’; the provision of capital fails to displace stakeholders’ externality as paramount in that case. Case (1) is that of shareholder ownership and case (2) that of stakeholder ownership combined with nonvoting preferred stock. I extend the analysis from ownership to integration: integration decreases capital requirements by allowing for the pooling of project capital; it precludes the tailoring of incentives to specific project characteristics. I establish the conditions under which the joint undertaking of two projects within a single integrated firm dominates their separate undertakings within two independent firms. The results suggest that projects that should be integrated within a single firm are those that (1) share similar characteristics, (2) are related by strong externalities, and (3) have weakly correlated payoffs. The requirements of strong externalities and similar characteristics are consistent with the observation that multiple-industry firms generally operate in related industries (Hoberg and Phillips 2017). I allow for partial contractibility of the externality, the use of capital, and investment. The first kind of contractibility increases the range of capital costs over which shareholder ownership dominates: stakeholder ownership is dominated by shareholder ownership absent the externality, because of shareholders’ lower cost of capital; the greater is contractibility, the lesser is the externality, and the lesser therefore is the need for stakeholder ownership. The second kind of contractibility increases the range over which stakeholder ownership is combined with nonvoting preferred stock: the greater is contractibility, the lesser is shareholders’ fear that the capital they provide be misused by stakeholders, and the more therefore are noncontrolling shareholders willing to leave ownership and control in the hands of the stakeholders. When stakeholders’ high cost of capital precludes stakeholder ownership, whether shareholder ownership or stakeholder ownership combined with nonvoting preferred stock dominates depends on whether the noncontractible part of capital provision displaces the noncontractible part of the externality as paramount. That it is probably easier to contract on a somewhat circumscribed externality than on the use of the generic resource that is capital may account for the relatively limited use of nonvoting preferred stock: it is easier for shareholders to commit through contract to account for the externality in their setting of managerial compensation than it is for stakeholders to commit to account for shareholder capital. The third kind of contractibility is similar to the first two in increasing the ranges over which shareholder ownership and stakeholder ownership combined with nonvoting preferred stock dominate. This is because contractible investment achieves indirectly what a contractible externality and contractible capital achieve directly: it is investment that causes the externality and requires capital; the more it can be contracted, the greater the—indirect—control that can be had on the externality and on the use of capital, the greater therefore the scope for shareholder ownership (externality) and for nonvoting preferred stock financing (capital). 1. Literature Review Barzel (1982, 1997) recognizes the multifaceted nature of most goods, assets, and transactions and the inability to contract every single such facet: contracting requires measurement, which generally can be done only with error and sometimes cannot be done at all. He analyzes the opportunities imperfect measurement provides for wealth transfers and identifies a wide variety of institutions intended to avoid such transfers. For example, regular investors in initial public offerings subscribe to every issue, thereby committing not to “pick and choose” among issues. Such commitment denies regular investors the incentive to produce information intended to distinguish between overpriced and underpriced offerings, information that benefits its holder but is a detriment to both the issuer and the other investors lacking the demand-side information that determines how well “received” an issue is. Regular investors are compensated for their commitment by being allocated a disproportionate share of issues that are, on average, underpriced.7 Observing that the desire to engage in wealth transfers is proportionate to the power of incentives, Barzel (2002, 2013) argues that within-firm transactions, by muting the power of incentives, correspondingly decrease the desire to exploit imperfect measurement to engage in wealth transfers. A supplier is thus less likely to skimp on quality when it is owned by its buyer than when it is independent. Transactions will therefore be within-firms when measurement of a valuable attribute is difficult or impossible; they will be in the market when it is not. Barzel (2002, 2013) develops a theory of firm boundaries on that basis.8 Hansmann (1996, 2013) considers a wide variety of ownership forms: investor- and employee-owned firms, agricultural cooperatives, customer- and supplier-owned firms, utilities, clubs, housing cooperatives and condominiums, nonprofits and mutuals. He provides a formal theory of ownership, based on the minimization of the combined costs of ownership and contracting. While Hansmann evaluates a broader range of explanations than I do, it is interesting to note that the basic mechanism in my model, ownership’s allocation of the right to set the power of managerial incentives to those stakeholders most affected by the noncontractible facets of an organization’s paramount transactions, can account for many of the ownership forms Hansmann considers. The model additionally makes possible an analysis of integration and the consequences of making investment and selected transaction facets contractible. Alchian and Demsetz (1972) present a theory of ownership based on the need for “metering” in case of team production: owners are those best able to meter—to measure and to apportion—input and output in joint production so as to avoid shirking and maximize output; they are incentivized to do so by being made residual claimants to output. If metering skills are viewed as endogenous, then my work may be viewed as complementing Alchian and Demsetz’s (1972) by identifying that subset of stakeholders who should optimally develop metering skills. Hart, Shleifer, and Vishny (1997) and Glaeser and Shleifer (2001) use the property rights theory of ownership (Grossman and Hart 1986; Hart and Moore 1990) to explain government ownership and nonprofits, respectively. That theory sees ownership as conferring residual control rights, which alter threat points and therefore payoffs in ex post bargaining, thereby affecting ex ante investment. My work is in the line of the property rights theory, from which it nonetheless differs in having ownership confer not the right to use assets but that to set managerial incentives. That right is residual, in the sense that owners can alter the power of incentives at all times, subject to satisfying the manager’s participation constraint. It is this last feature, the ability ex post to modify the terms of the compensation contract, that distinguishes my work from the incentives theory of ownership (Holmstrom and Milgrom 1991, 1994), which sees these terms as fixed.9 Despite this difference, my work is also in the line of the incentives theory, with which it shares a focus on managerial incentives. As a result, the managers are not the property rights theory’s “drone employees (who own nothing and hence, […], face no incentives and so do nothing)” (Gibbons 2005, p. 206); instead, the managers “face incentives, so they [do not] act like drones” (Gibbons 2005, p. 207). This implies that my analysis may be particularly appropriate for those organizations for which human capital is important: the manager in my model exercises judgement and enjoys discretion.10 2. Model Consider a firm that has resources B > 0 which it invests at time 0. The firm allocates resources L⩾0 to safe investment and B−L⩾0 to risky investment. The former has return a > 1 with probability 1, the latter return A > a with probability pr, 0<pr<1. Firm (gross) payoff K at time 1 has expectation E[K]=prA(B−L)+aL and variance var[K]=A2(B−L)2prpu, where pu=1−pr.11 Risky investment has higher expected return than does safe investment, prA>a, but it also involves costs that safe investment does not: (1) its prospects for success must be evaluated at a cost κ(B−L)2, (2) it imposes a negative externality −Θ(B−L), Θ>0, on one or many stakeholders of the firm, and (3) it requires capital.12 An example of a negative externality is the loss suffered by a customer when the quality of a firm’s products are somehow deficient; stakeholders are providers of capital, labor, or other supplies to the firm or are purchasers of firm products. Capital serves to bond the firm’s fulfillment of the numerous obligations that the undertaking of a project generally entails (Barzel and Suen 1997): employees’ salaries must be paid, suppliers’ bills honored, lenders’ loans serviced, and customers’ after-sales service provided.13 If the firm has little or no capital, low payoff realizations may jeopardize the firm’s ability to fulfill these obligations, possibly deterring potential stakeholders from transacting with the firm in the first place. I assume capital is proportional to the standard deviation of firm payoff sd[K]=A(B−L)prpu≡ρ(B−L): the wider is the range of possible payoffs, the greater is the extent to which firm payoff may fall short of firm obligations, the more capital is needed to make up for that shortfall.14 Assume that the firm’s owners are unable themselves to evaluate and make the investments L and B – L. They therefore hire a manager to do so on their behalf. Neither the evaluation nor the investment is contractible, in contrast to payoff, which is contractible to the owners and the manager.15 The manager therefore must be provided with payoff-dependent incentive compensation to be induced to evaluate and make investments. Let the manager’s compensation be β1K+β0, where the pay-for-performance parameter β1, β1>0, measures the power of incentives; β0 is the fixed component of compensation. I assume that both owners and the manager are risk-neutral; their concern with risk extends only in so far as it affects the cost of evaluating risky investment and the amount of capital to be provided. By analogy to the assumption that the evaluation and the making of investment are not contractible, I assume that the use of capital and the extent of the externality are not, either.16 Finally, I assume no wealth constraints. My purpose is to distinguish the identity of the owners of the firm from among the various stakeholders of the firm: shareholders when the stakeholders who should be owners are the providers of equity capital; workers when they are the providers of labor; suppliers when they are the providers of parts or other goods procured by the firm; and customers when they are the purchasers of firm products. What distinguishes owners from other stakeholders is that they, and they alone, have the right to determine the properties (β0,β1) of the manager’s compensation contract; this is true at all times, so that even a compensation contract initially agreed on subsequently can be altered by the owners, subject to satisfying the manager’s participation constraint. As will become apparent in Section 3 below, this provides the owners with an opportunity to profit at the expense of other firm stakeholders—an ex post benefit that generally must be paid for ex ante. Relatedly, only owners can contract firm payoff K with the manager. The rationale for allocating these privileges to owners alone is that ownership’s rights of control provide owners with the opportunity to manipulate both the parameters of the manager’s compensation contract and firm payoff, again subject to satisfying the manager’s participation constraint. An attempt on the part of nonowning stakeholders to condition a contract with the firm on the manager’s compensation contract or on firm payoff therefore will be manipulated by owners to their own advantage.17,18 Shareholders are stakeholders that are specialized in the provision of equity capital; that is all that they do, but they do it at a generally lower cost than other stakeholders. I denote Ψ, Ψ> 0, the cost of capital to shareholders, Φ⩾Ψ the cost of capital to other stakeholders.19 Unlike shareholders, other stakeholders may supply an input (other than equity capital) or purchase an output in addition to providing capital; that Φ⩾Ψ implies that (shareholder) specialization has both a benefit (shareholders provide capital at a lower cost than do other stakeholders) and a cost (shareholders provide only capital, unlike other stakeholders). Owners may but need not be providers of capital: it is possible for a firm to be owned by stakeholders other than shareholders, yet for shareholders to provide the equity capital; this is the case for a firm financed by nonvoting, preferred stock. The assumption that payoff is contractible only to the owners and the manager precludes the use of payoff-dependent common stock when shareholders are not the owners: owners would manipulate payoff K to minimize payments to common shareholders. Although manipulation is also possible in the case of preferred stock financing, manipulation likely serves to delay rather than to decrease payments to preferred shareholders: the fixed dividends of preferred stock are cumulative, unlike the variable dividends of common stock. Some formalism may help at this stage.20 Referring to stakeholders other than shareholders simply as stakeholders, I compare the objective functions of various classes of owners, distinguishing between the two cases where owners do and do not provide equity capital; I identify the corresponding externalities. I start with the case of first-best, in which the externality is taken into account and capital is provided by its lowest cost supplier, namely shareholders. The objective function in such case is   E[K]−Ψsd[K]−κ(B−L)2−Θ(B−L)=prA(B−L)+aL−Ψρ(B−L)−κ(B−L)2−Θ(B−L). (1) When shareholders are owners, the objective function is   E[K]−Ψsd[K]−(β1E[K]+β0)=prA(B−L)+aL−Ψρ(B−L)−κ(B−L)2, (2) where I have used the fact that the fixed component of compensation β0 serves to allocate the cost of evaluation to the owners.21 Shareholders do not take the negative externality −Θ(B−L) into account in maximizing their objective function, for that externality is not contractible. This does not mean that shareholders are not affected by the externality, for shareholders may need to compensate stakeholders for the externality as a condition for stakeholders to be willing to transact with the firm. What it does mean is that shareholders cannot commit to accounting for that externality in their setting of the manager’s compensation contract. When stakeholders are owners and provide equity capital, the objective function is   prA(B−L)+aL−Φρ(B−L)−κ(B−L)2−Θ(B−L); (3) this recalls the first-best, except in that stakeholders generally have a higher cost of capital than do shareholders: Φ⩾Ψ. Finally, when stakeholders are owners but capital is provided in the form of nonvoting preferred stock, the objective function is   prA(B−L)+aL−κ(B−L)2−Θ(B−L); (4) in a somewhat parallel fashion to the case of shareholder ownership, stakeholders do not take the cost of capital Ψρ(B−L) into account in maximizing their objective function. Preferred shareholders naturally require compensation for providing capital, but stakeholders cannot commit to accounting for capital provided in their setting of the manager’s compensation contract. I now turn to the formal analysis of the model. 3. Preliminary Results I start with the first-best. Risky and safe investments maximize (1)   MaxB−L,LprA(B−L)+aL−Ψρ(B−L)−κ(B−L)2−Θ(B−L), with the sum of these two investments equal to resources B. The maximization problem is equivalent to   MaxB−L(prA−a)(B−L)−Ψρ(B−L)−κ(B−L)2−Θ(B−L), (5) where I have removed the constant term aB. First-best risky and safe investment are22  (B−L)FB=prA−a−(Ψρ+Θ)2κ (6) and   LFB=B−(B−L)FB. The corresponding payoff is   VFB=aB+[prA−a−(Ψρ+Θ)]24κ; (7) the ratio with the quadratic term represents the value added by risky investment.23 I now introduce the agency problem. Recalling that only (gross) payoff K is contractible, the manager’s problem is   MaxB−L,Lβ1[prA(B−L)+aL]+β0−κ(B−L)2 (8)  ⇔MaxB−Lβ1[(prA−a)(B−L)+aB]+β0−κ(B−L)2; (9) it has solutions   B−L=β1(prA−a)2κ (10) and L the balance. Assuming owners have all bargaining power in their negotiations with the manager, and normalizing the manager’s reservation utility to zero, I have   β0=κ(B−L)2−β1[(prA−a)(B−L)+aB]. (11) Initially consider the case of shareholders ownership. As noted in Section 2, shareholders do not take the noncontractible externality −Θ(B−L) into account in maximizing their objective function (2); this is in contrast to the cost of the capital they provide. Shareholders solve   Maxβ1prA(B−L)+aL−β1[prA(B−L)+aL]−β0−Ψρ(B−L) (12)  ⇔Maxβ1(prA−a)(B−L)−Ψρ(B−L)−κ(B−L)2, (13) where I have substituted β0 from (11) and again removed the constant term aB. Using (10), I can solve for24 24 Specifically, I substitute (10) into (13) and solve for   β1SH=arg⁡max⁡β1β1(prA−a)22κ−Ψρβ1(prA−a)2κ−κ[β1(prA−a)2κ]2.  β1SH=1−ΨρprA−a, (14) with corresponding risky investment25  (B−L)SH=prA−a−Ψρ2κ. (15) The comparison of (15) with (6) reveals that shareholders incentivize the manager to make too large a risky investment. This is not without cost to shareholders, for stakeholders may not transact with the firm unless compensated for the negative externality −Θ(B−L)SH=−Θ(prA−a−Ψρ)/(2κ). Firm value under (specialized) shareholders’ ownership is   VSH=aB+[prA−a−Ψρ]24κ−Θ(prA−a−Ψρ2κ), (16) which can easily be shown to be lower than VFB in (7).26 26 Use (7) and (16) to write   VFB=[prA−a−(Ψρ+Θ)]24κ=[prA−a−Ψρ]24κ+Θ24κ−2Θ(prA−a−Ψρ)4κ>[prA−a−Ψρ]24κ−Θ(prA−a−Ψρ2κ)=VSH. Shareholders, who as owners are endowed with all bargaining power and thus receive all value created, are made worse off by their inability to commit to taking stakeholders’ externality into account. Investment is not contractible, and the compensation contract cannot be used as a commitment device toward stakeholders because shareholders in their capacity as owners are the only party able to negotiate with the manager over the terms of the compensation contract. Thus, a commitment, on the shareholders’ part, to incentivize the manager to make the first-best investment (B−L)FB in (6) by setting pay-for-performance parameter (PPP) β1FB=1−[(Ψρ+Θ)/(prA−a)] is not credible, because shareholders as owners can renegotiate the terms of the compensation contract (β0,β1) with the manager at all times, subject to satisfying the manager’s participation constraint. An initial setting of β1FB is increased to (14) by shareholders for whom the externality becomes a fixed cost following agreement with stakeholders on the payment of compensation Θ(B−L)FB for the externality. Three observations are in order at this point. First, including the compensation for the externality in the manager’s problem (8)—having him or her maximize β1[prA(B−L)+aL−Θ(B−L)SH]+β0−κ(B−L)2 instead of the objective function in (8)—fails to alter the manager’s choice of risky investment for the same reason as such inclusion fails to alter the owners’ choice of PPP β1: the externality is a fixed cost to both the manager and the owners. Second, whereas firm value is higher than the first-best under shareholder ownership if no compensation is paid to stakeholders for the externality, combined shareholder and stakeholder payoff is nonetheless lower.27 27 Formally,   aB+[prA−a−Ψρ]24κ>aB+[prA−a−(Ψρ+Θ)]24κ>aB+[prA−a−Ψρ]24κ−Θ(prA−a−Ψρ2κ). Optimal organizational ownership therefore does not depend on whether compensation is paid for the externality. Third, first-best could be achieved if payoff K were contractible to stakeholders too: a contract that sees shareholders compensate stakeholders for the externality through the payment of a payoff-dependent amount Θ(K−aB)/(prA−a) is equivalent to a contract on the externality.28 28 To see this, note that   E[Θ(K−aB)prA−a]=Θ{pr[A(B−L)+aL−aBprA−a]+(1−pr)[aL−aBprA−a]}=Θ{prA(B−L)+aL−aBprA−a}=Θ{(prA−a)(B−L)+aB−aBprA−a}=Θ(B−L). This, along with the earlier discussion in Section 2, motivates the assumption that payoff is contractible only to the owners and the manager. Stakeholder ownership naturally results in stakeholders taking the externality into account, which in fact no longer is “external” in this case, but payoff is decreased by stakeholders’ generally higher cost of capital Φ⩾Ψ in the case in which stakeholders also provide the capital. Firm value in such case is   VST=aB+[prA−a−(Φρ+Θ)]24κ: (17) analogous to (7) but with Φ replacing Ψ. The same holds true of risky investment (B−L)ST and PPP β1ST, which are29  (B−L)ST=prA−a−(Φρ+Θ)2κ (18) and   β1ST=1−Φρ+ΘprA−a. (19) This last case is that where stakeholders are owners but capital is provided by shareholders in the form of nonvoting preferred stock. The analysis is to some extent the mirror image of that of shareholder ownership: stakeholders’ externality is internalized, and shareholder capital provision becomes the externality, for stakeholders cannot commit to taking the use of capital into account in maximizing their objective function (4). I therefore have   β1ST,NV=1−ΘprA−a, (20)  (B−L)ST,NV=prA−a−Θ2κ, (21) and   VST,NV=aB+[prA−a−Θ]24κ−Ψρ(prA−a−Θ2κ). (22) The analogy with (14), (15), and (16), respectively, is immediate; the last term in (22) constitutes the dividend Ψρ(B−L)ST,NV paid to preferred shareholders, the analogue to Θ(prA−a−Ψρ)/(2κ)=Θ(B−L)SH in (16). I now wish to compare VSH, VST, and VST,NV. It is clear that all are smaller than VFB, with equality VST=VFB at Φ=Ψ.30 While VST is clearly larger than resources B, I assume this is also the case for VSH and VST,NV: a form of ownership that decreases firm value below initial resources B clearly is not considered. I first show31 Lemma 1. VSH>VST,NVif and only if Ψρ>Θ. The intuition for the result in Lemma 1 is simple. Both shareholder ownership and stakeholder ownership combined with nonvoting preferred stock introduce a distortion, due to the failure to account for stakeholder externality in the first case and for nonvoting shareholder capital in the second.32 When Ψρ>Θ, the second distortion is larger, and shareholder ownership dominates; when in contrast Ψρ<Θ, the first distortion is larger and stakeholder ownership combined with nonvoting preferred stock dominates. Lemma 1 implies that I need only compare stakeholder ownership to shareholder ownership when Ψρ>Θ, to stakeholder ownership combined with nonvoting preferred stock when Ψρ<Θ. I define the maximum cost of stakeholder capital consistent with positive risky investment by33 33 If Φ>Φmax⁡, then   (B−L)ST=prA−a−(Φρ+Θ)2κ<prA−a−(prA−a−Θρρ+Θ)2κ=0.  Φmax⁡≡prA−a−Θρ. I show Proposition 1. When Ψρ>Θ, there exists a Φ∗,SH, Ψ<Φ∗,SH<Φmax⁡, such that VSH≶VSTfor Φ≶Φ∗,SHif and only if Θ<Φmax⁡ρ−Ψρ; VSH<VST ∀Φ∈[Ψ,Φmax⁡]otherwise. When Ψρ<Θ, there exists a Φ∗,ST,NV, Ψ<Φ∗,ST,NV<Φmax⁡, such that VST,NV≶VSTfor Φ≶Φ∗,ST,NVif and only if Ψρ<Φmax⁡ρ−Ψρ; VST,NV<VST ∀Φ∈[Ψ,Φmax⁡]otherwise. The threshold costs of stakeholder capital Φ∗,SHand Φ∗,ST,NVboth increase in Θ. The intuition for the result in Proposition 1 is as follows. Firm value under stakeholder ownership VST is largest for Φ=Ψ, but decreases as the cost of stakeholder capital Φ increases toward Φmax⁡; whether VST eventually decreases below its value under alternative forms of ownership, shareholder ownership if Ψρ>Θ and stakeholder ownership combined with nonvoting preferred stock otherwise, depends on the importance of the distortion each of these two forms introduces relative to stakeholder ownership’s higher cost of capital. If Θ<Φmax⁡ρ−Ψρ, the distortion under shareholder ownership—the failure to account for stakeholder externality—is not overly high and there is a threshold cost of capital Φ∗,SH above which shareholder ownership dominates. If Ψρ<Φmax⁡ρ−Ψρ, the distortion under stakeholder ownership combined with nonvoting preferred stock—the failure to account for nonvoting shareholder capital—is not overly high and there is a threshold cost of capital Φ∗,ST,NV above which stakeholder ownership combined with nonvoting preferred stock dominates. Both Φ∗,SH and Φ∗,ST,NV increase in stakeholder externality Θ, reflecting stakeholder ownership’s better accounting for stakeholder externality: VST, VSH, and VST,NV all decrease in Θ, but VST decreases more slowly than do VSH and VST,NV. I now turn to the case of a positive externality, which I represent by Θ<0 as opposed to Θ>0 as has thus far been assumed; this makes the externality −Θ(B−L) positive as desired. An example of a positive externality provided by risky investment is the knowledge created by investment in research and development (R&D), which often profits not only the firm having conducted the R&D, but also other firms such as its customers and its suppliers. An important difference with the case of negative externality is that, whereas stakeholders previously required compensation for the (negative) externality in order to transact with the firm in the case of shareholder ownership, they are now willing to pay for the (positive) externality obtained from such transaction, −Θ(B−L)SH>0. From (20), I have β1ST,NV>1 for Θ<0. Despite such high-powered incentives being unrealistic, I allow the PPP β1ST,NV to be larger than one because I wish to maintain as much symmetry as possible between the analyses of the two cases of negative and positive externality. I thereby isolate the impact of the change from negative to positive externality to the sign of the term Θ in firm values VST, VSH, and VST,NV. Proposition 2. VSH>VST,NVif and only if Ψρ>−Θ. When Ψρ>−Θ, there exists a Φ∗,SH, Ψ<Φ∗,SH<Φmax⁡, such that VSH≶VSTfor Φ≶Φ∗,SH. When Ψρ<−Θ, there exists a Φ∗,ST,NV, Ψ<Φ∗,ST,NV<Φmax⁡, such that VST,NV≶VSTfor Φ≶Φ∗,ST,NVif and only if Ψρ<Φmax⁡ρ−Ψρ; VST,NV<VST ∀Φ∈[Ψ,Φmax⁡]otherwise. The threshold cost of stakeholder capital Φ∗,SHincreases in Θif and only if −Θ<Φ∗,SHρ−Ψρ; the threshold cost Φ∗,ST,NVincreases in Θ. The intuition for the results in Proposition 2 is similar, but not identical, to those in Lemma 1 and Proposition 1. The distortions introduced by shareholder ownership and stakeholder ownership combined with nonvoting preferred stock are still to be compared, but the former now involves a positive ( −Θ>0) rather than a negative ( −Θ<0) externality; this explains the transformation of the condition Ψρ>Θ in Lemma 1 into Ψρ>−Θ. That the externality is positive implies that stakeholders are willing to pay the firm in order to benefit from the positive externality transactions with the firm entail. This explains the unconditional existence of Φ∗,SH, where Proposition 1 required Θ<Φmax⁡ρ−Ψρ for Φ∗,SH to exist: there is no longer a payment to stakeholders to be compared to a differential in capital costs, but a payment from stakeholders to be added to the capital cost advantage of shareholder ownership.34 It also explains why the threshold cost of stakeholder capital Φ∗,SH is no longer monotone in the externality Θ. Although the intuition used in the case of negative externality applies when −Θ>Φ∗,SHρ−Ψρ, that is, when the externality is large, this is no longer the case when the externality is small, −Θ<Φ∗,SHρ−Ψρ. The lesser importance of accounting for a smaller externality increases the relative importance of the payment |Θ|(B−L)SH received for that externality under shareholder ownership; an increase in |Θ| increases that payment; it therefore increases the range [Φ∗,SH,Φmax⁡] over which shareholder ownership dominates; ∂Φ∗,SH/∂(−Θ)<0, that is, ∂Φ∗,SH/∂Θ>0, as a result. I conclude the present section by noting that the results are unchanged when the externality is associated with safe rather than risky investment; only the interpretation of the externality changes, in that a negative externality of risky investment becomes a positive externality of safe investment, and a positive externality negative.35 35 To see this, use (5) to write   arg⁡max⁡B−L(prA−a)(B−L)−Ψρ(B−L)−κ(B−L)2−Θ(B−L)=arg⁡max⁡B−L(prA−a)(B−L)−Ψρ(B−L)−κ(B−L)2−ΘB+ΘL=arg⁡max⁡B−L(prA−a)(B−L)−Ψρ(B−L)−κ(B−L)2+ΘL, where I have removed the constant term −ΘB. Contrast the minus sign preceding the externality of risky investment Θ(B−L) with the plus sign preceding that of safe investment ΘL. I associate externalities with risky rather than safe investment because this better describes the various settings I consider in Section 4. 4. Ownership Forms I now apply the results of Section 3 to provide a possible, unified explanation for a wide variety of ownership forms that are observed in practice. To a large extent, these correspond to various forms of the externality −Θ≶0 and its relation to stakeholder and shareholder costs of capital Φ and Ψ, respectively. Before doing so, I briefly recall the results of Section 3. Stakeholder ownership dominates for stakeholder cost of capital close to shareholder cost capital, Φ close to Ψ. As stakeholder cost of capital increases, stakeholder ownership may be replaced by shareholder ownership if the externality, positive or negative, is less important than is the shareholder cost of capital, |Θ|<Ψρ; stakeholder ownership is retained, possibly to be supplemented by outside equity in the form of nonvoting preferred stock, if the externality is more important than the shareholder cost of capital, |Θ|>Ψρ. 4.1 Founder, family, and dispersed ownership It is generally the case that founders, and their descendants to a perhaps lesser extent, derive valuable private benefits ( −Θ>0) from their control of the firms they or their forebears have founded.36 In countries where the possibly limited development of equity markets fails to decrease the cost of outside, public equity ( Ψ) markedly below that of private equity ( Φ), there may be little incentive to abandon private ownership for a public listing (Proposition 2). This may explain the prevalence of private ownership even among large firms across much of the world. Where the greatly increased size or riskiness of a firm makes recourse to outside, public equity unavoidable, founders and families that enjoy large private benefits ( −Θ>Ψρ) attempt to retain these by restricting outside shareholders’ voting rights (dual-class shares), or denying them altogether (nonvoting shares); these take the form of preferred shares in my model of noncontractible payoff K. Only where the cost of outside equity is of paramount importance ( −Θ<Ψρ) does a firm choose outside, dispersed shareholder ownership, with previously controlling shareholders relinquishing control, that of setting the properties of the manager’s compensation contract (β0,β1) in particular. Where control is relinquished through the unification of what were previously different classes of shares, the compensation often received by previously controlling shareholders in such case may be expected to be related to the decline in private benefits, from −Θ(B−L)ST,NV to −Θ(B−L)SH.37 37 That 0<−Θ<Ψρ implies that   (B−L)ST,NV=prA−a−Θ2κ>prA−a−Ψρ2κ=(B−L)SH, where I have used (15) and (21). 4.2 Partnerships Where tacit, noncodifiable knowledge makes important to a firm’s success the employees in whom such knowledge is embedded, like in some aspects of investment banking, for example (Morrison and Wilhelm 2007, p. 88), then disagreements may arise between the firm and the employees as to the use of the employees’ human capital.38 For example, when deciding which initial public offerings to underwrite and which to turn down, a decision that can have important reputational consequences (Morrison and Wilhelm 2007, p. 83), an investment bank will not necessarily arrive at the same conclusion as the investment bankers involved in the issue: the bankers’ reputation, however closely tied to that of the investment bank, is nonetheless distinct and will generally not be affected in the exact same way as that of the bank regardless of whether the issue succeeds or fails.39 There is therefore an externality −Θ≶0 pertaining to individual bankers’ reputation and affected by the bank’s decision of which issues to underwrite. Propositions 1 ( −Θ<0) and 2 ( −Θ>0) suggest ownership by investment bankers in such case if the cost of banker capital is markedly above that of specialized shareholder; this is the investment banking partnership. Where increased needs for capital raise its cost to investment bankers well above that to specialized shareholders, then the investment bank may abandon the partnership form for dispersed shareholder ownership or investment banker ownership combined with nonvoting preferred stock, depending on the relative importance of the externality and the cost of capital, |Θ|≶Ψρ (Lemma 1 and Proposition 2). Shareholder ownership involves compensation |Θ|(B−L)SH, to be paid to bankers in case of negative externality, by bankers in case of positive.40 Investment banker ownership with nonvoting preferred stock involves the payment of preferred dividend Ψρ(B−L)ST,NV. Much the same can be said of legal partnerships, with senior lawyers in place of senior investment bankers, and decisions about which court cases to take on or to turn down instead of decisions about new issues. That fewer legal partnerships have abandoned the partnership form than have investment banking partnerships attests to the lesser importance of (financial) capital to the former.41 4.3 Mutual banks and insurance companies By their very nature, banks are highly leveraged institutions; this gives rise to a risk-shifting problem, in which shareholders protected by limited liability may wish to engage in highly risky investment: the gains are mainly theirs because the interest on deposits is fixed, the losses are mainly depositors’ because of limited liability. Risky investment thus imposes a negative externality −Θ(B−L)SH, Θ>0, on depositors, for which they will of course require compensation for them to be willing to entrust their deposits to a bank. If the cost of capital Φ to depositors—the rate of return they require for providing the bank’s equity in addition to its deposits—is not markedly above that to shareholders Ψ, then Proposition 1 suggests that it is optimal for depositors to own the bank, that is, for the bank to be a mutual. Hansmann (1996, pp. 246–51) argues that this explains the ubiquity of mutually owned banks in the nineteenth century United States.42 He further notes (pp. 254–8) that improvements in bank regulation, which decreased the extent of the risk-shifting problem, account for much of the abandonment of the mutual form.43 A very similar argument can be made for savings and loans associations, building societies in Britain, and insurance companies (see O’Hara 1981; Valnek 1999; Mayers and Smith 1981, respectively), recalling that insurance policyholders’ claims are not unlike bank depositors’.44 4.4 Government and customer ownership The nineteen-eighties and nineties saw a wave of privatizations, not least in the United Kingdom, whose government under Prime Minister Margaret Thatcher can fairly be said to have both initiated and sustained that movement. Yet, by the first decade of the present century, many privatized utilities in the United Kingdom had reverted to some form of public ownership, either by a utility’s customers or by the government, the latter “essentially a form of consumer cooperative” (Hansmann 2013, p. 897). That reversal was in no small part the result of consumer dissatisfaction with the quality of the services provided by the privatized utilities, culminating with public anger over a number of fatal accidents that involved Railtrack, the then shareholder-owned, now defunct rail infrastructure (track, signaling, tunnels, bridges, railroad crossings, …) provider in the United Kingdom. Kay (2003, 2010) attributes the decline in service quality that followed privatization to a decrease in maintenance expenses. He argues that a judgment call is involved in determining the funds that a utility should allocate to maintenance and that a shareholder-owned utility will choose a different, lower level of maintenance expenses than would a utility owned by its customers or the government. This is because not all benefits of high maintenance, or costs of low maintenance, can be contracted by the utility and its customers; there is a negative externality −Θ<0 associated with the allocation of funds away from maintenance toward other uses. Unlike the externalities thus far considered, utilities’ negative externalities need not involve compensation to (captive) customers, because utilities generally are (local) monopolies. Using the notation of this model, maintenance expenses can be identified with safe investment L and funds allocated to other uses with risky investment B – L—it is allocation away from maintenance that gives rise to the risk of accidents. Further identifying customer and government ownership with ownership by stakeholders, (15) and (18) imply that (B−L)SH>(B−L)ST: more is allocated to other uses under shareholder ownership; maintenance expenses are consequently lower, LSH<LST.45 Where the cost of externalities is deemed excessive, Θ>Ψρ, Proposition 1 suggests that shareholder ownership is eschewed in favor of stakeholder ownership—customer or government ownership—when the cost of stakeholder capital is low, Φ<Φ∗,ST,NV, in favor of stakeholder ownership combined with nonvoting preferred stock when the cost of stakeholder capital is high, Φ>Φ∗,ST,NV. That the latter form rarely is observed suggests that, even at its maximum, the spread between stakeholder and shareholder cost of capital remains moderate, Φmax⁡ρ−Ψρ<Ψρ.46 46 Recall from Proposition 1 that a necessary condition for Φ∗,ST,NV to exist is that Φmax⁡ρ−Ψρ>Ψρ.,47 Summarizing, it is perhaps fair to say that the predictions of my model are consistent with the British experience of utilities privatization, regarding both decreased maintenance during and eventual abandonment of shareholder ownership. Further support for my model can be found in the controversy surrounding the compensation of privatized utilities’ managers, the so-called “fat cats.” As utilities’ profits soared in the wake of privatization, so did their managers’ compensation, a reflection both of these higher profits and of dramatically increased PPP. That privatization increased PPP is immediate from (14) and (19), recalling that I represent a negative externality by −Θ<0, Θ>0 in this model. That privatization increased profits requires comparing profits gross of the cost of the negative externalities—captive customers have no choice but to accept these—under both shareholder and stakeholder ownership. I therefore compare VSH+Θ(B−L)SH with VST+Θ(B−L)ST.48 The terms Θ(B−L)SH and Θ(B−L)ST represent the cost of the externalities in the two cases of shareholder and stakeholder ownership, respectively; they are added back because they are not in fact paid. It is easy to show that VSH+Θ(B−L)SH>VST+Θ(B−L)ST: profits are higher under shareholder ownership, an increase in part made possible by decreased maintenance expenses, LSH<LST.49 49 Formally, use (15), (16), (17), and (18) to write   VST+Θ(B−L)ST=aB+[prA−a−(Φρ+Θ)]24κ+Θ[prA−a−(Φρ+Θ)2κ]=aB+[prA−a−Φρ]24κ+Θ24κ−Θ[prA−a−Φρ2κ]+Θ[prA−a−(Φρ+Θ)2κ]=aB+[prA−a−Φρ]24κ−Θ24κ<aB+[prA−a−Ψρ]24κ=VSH+Θ(B−L)SH.,50 4.5 Worker cooperatives A situation of involuntary unemployment introduces a difference between the prevailing wage and the shadow cost of labor, with the former higher than the latter (Salanié 2000, p. 44). That difference introduces an externality to firms’ employment decisions: a firm’s decision to hire an involuntarily unemployed worker has a positive externality equal to the difference between the wage and the shadow cost, a firm’s decision to fire a worker in a situation of prevailing involuntary unemployment has a negative externality of the same magnitude. A shareholder-owned firm will not take such externalities into account, except in the unlikely case in which it can pay new hires a lower wage than paid to existing workers doing identical work, or make continued employment conditional on the lowering of existing wages only for those workers who would otherwise be fired. In contrast, a worker-owned firm is willing to accept the lower profits associated with higher employment because it recognizes the benefit from such policy accruing to workers, the externality that equals the difference between the wage and the shadow cost of labor. Where that externality is important, |Θ|>Ψρ, in regions with widespread un- or underemployment, one can expect workers to form cooperatives that will account for the externality. Whether these cooperatives’ capital will be provided by the workers themselves or by outside investors in the form of nonvoting preferred stock in such case depends on whether the cost of capital to workers Φ is below or above the threshold cost of capital Φ∗,ST,NV (Propositions 1 and 2). The relative paucity of worker cooperatives, even in times of difficult employment conditions, is not easy to reconcile with this model. It may be attributable to the heterogeneity of workers’ interests (Hansmann 1996, chapter 6): there is not one but many Θ’s, corresponding to different categories of workers, whose possibly diverging interests may compromise the optimality of worker ownership.51,52 4.6 Farm marketing, processing, and supply cooperatives Many agricultural products are sold to highly concentrated middlemen and processors, whose monopsony power, if exercised, keeps prices and production well short of welfare-maximizing levels (Hansmann 1996, pp. 122–3). This difference constitutes a positive externality ( −Θ>0) to raising prices and inducing production above their monopsony levels. Where that externality is important, −Θ>Ψρ, and in the absence of too large a cost of capital disadvantage to farmers, Ψ⩽Φ<Φ∗,ST,NV, Proposition 2 suggests that farmer ownership, in the form of farm marketing and processing cooperatives, dominates shareholder ownership. A very similar rationale can be provided for the existence of farm supply cooperatives, with monopsonistic purchase replaced by monopolistic supply (Hansmann 1996, pp. 150–1). 4.7 Vertical and horizontal control I have considered various forms of ownership, corresponding to different kinds of stakeholders, but have thus far neglected ownership of one firm by another firm, that other firm being the stakeholder of interest. It is to such ownership that I now turn, that is, to vertical and horizontal control. My starting point is Barzel’s (2002, 2013) observation that vertical integration serves to ensure product quality through the lowering of the power of supplier managerial incentives to a level consistent with the provision of that quality. More concretely, consider a supplier who can provide high-quality products that function in all circumstances, or lower quality products that function only with some probability. Such products may nonetheless be desired by the buyer if produced at lower prices or in higher quantities. Suppose there is a cost to determining the optimal level of quality and that, if the product fails to function as intended or at all, the cost of malfunction will in the first instance be borne by the buyer. Using the notation of this model, resources invested in providing the high quality alternative may be identified with L, those invested in developing the lower quality alternative with B – L, the probability that the lower quality products nonetheless function satisfactorily with pr, the cost of evaluating the trade-off between price/quantity and quality with κ(B−L)2, and the cost of product malfunction to the buyer with Θ(B−L), Θ>0. From (14), (15), (18), and (19), I know that an independent, shareholder-owned supplier sets managerial incentives β1SH=1−[(Ψρ)/(prA−a)] for resources invested in the high-quality alternative LSH=B−[(prA−a−Ψρ)/(2κ)], whereas the buyer having acquired control of the supplier with its own capital sets lower-powered incentives β1ST=1−[(Φρ+Θ)/(prA−a)]<β1SH, for higher resources invested in the high-quality alternative LST=B−[(prA−a−Φρ−Θ)/(2κ)]>LSH. If the buyer instead acquires control of the supplier with outside equity, raised in the form of nonvoting preferred stock, I know from (20) and (21) that the buyer sets incentives β1ST,NV=1−[Θ/(prA−a)] for resources invested in the high-quality alternative LST,NV=B−[(prA−a−Θ)/(2κ)].53 Whether vertical control is in fact desirable depends on the relative importance of quality and buyer and shareholder cost of capital. Lemma 1 and Proposition 1 together suggest that vertical control is chosen if either (1) Θ>Ψρ or (2) Θ<Ψρ and Φ<Φ∗,SH; vertical control is financed with nonvoting preferred stock if Θ>Ψρ and Φ>Φ∗,ST,NV, with buyer own capital otherwise.54 Condition (1) describes a situation in which quality is paramount and condition (2) one in which it is not, but the buyer’s cost of capital is sufficiently close to shareholders’ that buyer control and financing nonetheless dominate; this is because of buyer ownership’s better accounting for the externality, however modest that externality may be.55 I have assumed that the buyer is not itself shareholder-owned, Φ⩾Ψ. If it is, and has cost of capital Φ=Ψ, then it is clear from Proposition 1 that buyer control financed with own capital dominates, indeed attains first-best.56 Given the prevalence of shareholder ownership, at least among large firms, that vertical control attains first-best suggests widespread such control: the slightest externality in the relation between any two firms implies ownership of these firms by the same shareholders. Recognizing that competition generates what is perhaps the most widespread externality, competitors are owned by the same shareholders; this is horizontal control. Thus, if taken to the limit, this analysis suggests that all interacting firms are owned by the same shareholders who set the power of managerial incentives so as to minimize negative externalities, not least competition, among these firms.57 Before I deem such conclusion nonsensical, it is worth noting that both implications are partially borne out by the empirical evidence: many of the world’s large corporations are owned by a relatively small number of financial institutions (Vitali, Glattfelder, and Battiston 2011); at least some of these are believed to have directed their portfolio firms to settle lawsuits that pitted one firm against another (Hansen and Lott, 1996, p. 47) and to have incentivized portfolio firm managers in such manner as to soften competition among these firms (Azar, Raina, and Schmalz 2016; Azar, Schmalz, and Tecu 2016; Antón et al. 2016). I discuss this and related evidence in Section 7. Still, the world this model predicts in the case Φ=Ψ is not the one we observe. Why not? One possibility is that the coordination the preceding argument requires cannot be achieved simply through the setting of managerial incentives: it may be the case that accounting for externalities requires a level of coordination between firms that is so detailed as to require integration of these firms, vertical or horizontal.58 Section 5 thus turns to integration. 5. Integration Consider two projects that can be undertaken either separately by two independent firms or jointly by a single integrated firm. Integration has two benefits and one cost: (1) externalities can be accounted for, an option that may not be available to two independent firms and, in the case of competitive externalities in particular, may be illegal under antitrust law; (2) equity capital can be combined; this provides an opportunity to economize on costly capital as compared to the case of two independent firms; and (3) managerial incentives, for top management at least, must be provided at the level of the single integrated firm; this precludes the tailoring of incentives to the specific characteristics of each of the two projects, an option available to each of the two independent firms. I show in what follows that the desirability of integration depends on the net effect of these benefits and this cost. Index each project by i, i∈{1,2}, to write: Ai, ai, pr,i, pu,i, Bi, Li, κi, Θi, and ρi; denote ϱ the correlation between the two projects. When the two projects are undertaken jointly within the integrated firm, that firm’s payoff has variance   var[K1+K2]=ρ12(B1−L1)2+ρ22(B2−L2)2+2ϱρ1ρ2(B1−L1)(B2−L2), with capital required sd[K1+K2]. The variance of the payoff of project i undertaken separately by independent firm i is   var[Ki]=ρi2(Bi−Li)2. The total capital required for the purpose of undertaking the two projects in two independent firms is therefore   sd[K1]+sd[K2]=ρ1(B1−L1)+ρ2(B2−L2)=ρ12(B1−L1)2+ρ22(B2−L2)2+2ρ1ρ2(B1−L1)(B2−L2)⩾ρ12(B1−L1)2+ρ22(B2−L2)2+2ϱρ1ρ2(B1−L1)(B2−L2)=sd[K1+K2], with equality at ϱ=1: diversification across projects within a single firm decreases costly capital requirements; this is a first benefit of integration (Barzel and Suen, 1997). The parameter Θi, i = 1, 2, indexes the externality that project i imposes on project j, j = 1, 2, j≠i. The externality imposed by i on j is therefore Θi(Bi−Li). The two externalities Θ1(B1−L1) and Θ2(B2−L2) are accounted for by the single integrated firm, whose owners surely are mindful of the impact the risky investment made into one project has on the other, but they are not accounted for by the two independent firms: I assume coordination requires integration. This accounting for externalities is a second benefit of integration. The cost of integration is the inability to tailor the integrated firm’s incentives to the characteristics of each project. Formally, while each independent firm i sets PPP β1,i=1−Ψρi/(pr,iAi−ai) from (14), the integrated firm sets PPP β1,I to solve   Maxβ1,I∑i=1,2{(pr,iAi−ai−Θi)(Bi−Li)+aiBi−κi(Bi−Li)2}−Ψρ12(B1−L1)2+ρ22(B2−L2)2+2ϱρ1ρ2(B1−L1)(B2−L2), (23) subject to   Bi−Li=β1,I(pr,iAi−ai)2κi. (24) Note that the same PPP β1,I is used to induce the two risky investments B1−L1 and B2−L2. Substituting (24) into (23), the latter becomes   Maxβ1,Iβ1,I[(pr,1A1−a1)22κ1+(pr,2A2−a2)22κ2−Θ1(pr,1A1−a1)2κ1−Θ2(pr,2A2−a2)2κ2]−β1,I2[(pr,1A1−a1)24κ1+(pr,2A2−a2)24κ2]−Ψβ1,I2ρ12(pr,1A1−a1)2κ12+ρ22(pr,2A2−a2)2κ22+2ϱρ1ρ2(pr,1A1−a1)κ1(pr,2A2−a2)κ2. (25) Differentiating and solving for β1,I, I obtain   β1,I=1−Θ1(pr,1A1−a1)κ1+Θ2(pr,2A2−a2)κ2(pr,1A1−a1)2κ1+(pr,2A2−a2)2κ2−Ψ(pr,1A1−a1)2κ1+(pr,2A2−a2)2κ2ρ12(pr,1A1−a1)2κ12+ρ22(pr,2A2−a2)2κ22+2ϱρ1ρ2(pr,1A1−a1)κ1(pr,2A2−a2)κ2. (26) I introduce the need for tailored incentives by assuming   Ψρ2+Θ2pr,2A2−a2=γΨρ1+Θ1pr,1A1−a1, (27) 1⩽γ⩽γmax⁡≡(pr,1A1−a1)/(Ψρ1+Θ1).59 There is no need for project-specific incentives at γ = 1, for the two projects in such case involve an identical trade-off between excess return pr,iAi−ai on the one hand and cost of capital and externality Ψρi+Θi on the other; γ can be no larger than γmax⁡, for (B2−L2)FB=[pr,2A2−a2−(Ψρ2+Θ2)]/(2κ2)<0 if that were the case. The combined value of the two independent firms is, from (16) and (27),60 60 The derivation of (28), (29), and (30) uses the equalities   pr,2A2−a2=(Ψρ2+Θ2Ψρ1+Θ1)pr,1A1−a1γ and   (pr,2A1−a2−Ψρ2−Θ2)2=(Ψρ2+Θ2Ψρ1+Θ1)2(pr,1A1−a1γ−Ψρ1−Θ1)2.  Π12(γ)≡a1B1+(pr,1A1−a1−Ψρ1)24κ1−Θ2(pr,2A2−a2−Ψρ2)2κ2+a2B2+(pr,2A2−a2−Ψρ2)24κ2−Θ1(pr,1A1−a1−Ψρ1)2κ1=a1B1+(pr,1A1−a1−Ψρ1−Θ1)24κ1−Θ124κ1+a2B2+(Ψρ2+Θ2Ψρ1+Θ1)2(pr,1A1−a1γ−Ψρ1−Θ1)24κ2−Θ224κ2. (28) The value of the integrated firm is, from (25) and (27),   ΠI(γ,ϱ)=a1B1+a2B2+β1,I2(1−β1,I2)(pr,1A1−a1)2[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]−β1,I2(pr,1A1−a1)[Θ1κ1+Θ2γκ2(Ψρ2+Θ2Ψρ1+Θ1)+Ψρ12κ12+ρ22γ2κ22(Ψρ2+Θ2Ψρ1+Θ1)2+2ϱρ1ρ2γκ1κ2(Ψρ2+Θ2Ψρ1+Θ1)], (29) with   β1,I=1−1pr,1A1−a111κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2×[Θ1κ1+Θ2γκ2(Ψρ2+Θ2Ψρ1+Θ1)+Ψρ12κ12+ρ22γ2κ22(Ψρ2+Θ2Ψρ1+Θ1)2+2ϱρ1ρ2γκ1κ2(Ψρ2+Θ2Ψρ1+Θ1)]. (30) Remark 1. ∂ΠI(γ,ϱ)/∂ϱ<0from (29) and using the envelope theorem. Substituting (30) into (29), I obtain   ΠI(γ,ϱ)=a1B1+a2B2+(pr,1A1−a1)24[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]+[Θ1κ1+Θ2γκ2(Ψρ2+Θ2Ψρ1+Θ1)+Ψρ12κ12+ρ22γ2κ22(Ψρ2+Θ2Ψρ1+Θ1)2+2ϱρ1ρ2γκ1κ2(Ψρ2+Θ2Ψρ1+Θ1)]24[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]−(pr,1A1−a1)2[Θ1κ1+Θ2γκ2(Ψρ2+Θ2Ψρ1+Θ1)+Ψρ12κ12+ρ22γ2κ22(Ψρ2+Θ2Ψρ1+Θ1)2+2ϱρ1ρ2γκ1κ2(Ψρ2+Θ2Ψρ1+Θ1)]. (31) I show Lemma 2. Consider the case ϱ=1. If  −[κ1κ2(Ψρ2+Θ2pr,1A1−a1)21+κ1κ2(Ψρ2+Θ2pr,1A1−a1)2](pr,1A1−a1−Ψρ1−Θ1)2κ1+Θ12κ1+Θ22κ2<0, (32) then ∃γ∗, 1<γ∗<γmax⁡ such that ΠI(γ,1)⩽Π12(γ) if and only if γ∗⩽γ⩽γmax⁡. Proposition 3. If  −[κ1κ2(Ψρ2+Θ2pr,1A1−a1)21+κ1κ2(Ψρ2+Θ2pr,1A1−a1)2](pr,1A1−a1−Ψρ1−Θ1)2κ1+κ1κ2Ψρ2+Θ2pr,1A1−a11+κ1κ2(Ψρ2+Θ2pr,1A1−a1)2[Ψρ2κ2(Ψρ2+Θ2pr,1A1−a1)+pr,1A1−a1−Ψρ1−Θ1κ1](4Ψρ2)+Θ12κ1+Θ22κ2<0, (33) then ∃ Sγ,ϱ≡{γ|ΠI(γ,ϱ)⩽Π12(γ)}≠∅. Absent the need for tailored incentives (γ = 1), integration dominates separation because the former but not the latter accounts for externalities and, in the case ϱ<1, because it reduces costly capital requirements. However, as γ increases above 1 eventually to reach γmax⁡, the inability to provide tailored incentives constitutes so large a cost as possibly to offset the benefits of integration and reduced capital. This will be the case if (32) (when ϱ=1) or (33) (when ϱ<1) is true. It is worth interpreting the two LHS terms in (32) and (33). The two terms Θ12/κ1+Θ22/κ2 represent the benefit of integration in accounting for the externalities. The term   −FL(pr,1A1−a1−Ψρ1−Θ1)2/κ1, with   FL≡κ1κ2(Ψρ2+Θ2pr,1A1−a1)21+κ1κ2(Ψρ2+Θ2pr,1A1−a1)2, (34) represents the value lost due to the inability to tailor incentives to the characteristics of each project when γ=γmax⁡. It is expressed as a fraction of the value created by risky investment in project 1 alone, because risky investment in project 2 creates no value at γ=γmax⁡: it is easy to see from (27) that pr,2A2−a2=Ψρ2+Θ2 in such case. If the integrated firm could tailor the incentives it provides to the characteristics of each project, it would set the PPP at zero for project 2. Since the firm is unable to do so, it will distort the single PPP β1,I toward zero. The term FL represents the fraction of the value of project 1 that is lost because of that distortion. Observe that ∂FL/∂(κ1/κ2)>0: as the cost of project 1 increases relative to that of project 2, the latter project’s importance in the setting of incentives increases; this increases the distortion and the fraction of the value of project 1 that is lost FL. The same interpretation can be given of ∂FL/∂[(Ψρ2+Θ2)/(pr,1A1−a1)]>0, with (Ψρ2+Θ2)/(pr,1A1−a1) measuring relative returns rather than costs: (Ψρ2+Θ2)/(pr,1A1−a1) equals (pr,2A2−a2)/(pr,1A1−a1) at γ=γmax⁡ as pr,2A2−a2=Ψρ2+Θ2 in such case. As the return to project 1 decreases relative to that to project 2, the latter project’s importance in the setting of incentives increases. Finally consider the term that appears in (33) but not in (32): this is the value of diversification at ϱ=−1. Rewriting   1κ2Ψρ2+Θ2pr,1A1−a11κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2[Ψρ2κ2(Ψρ2+Θ2pr,1A1−a1)+pr,1A1−a1−Ψρ1−Θ1κ1](4Ψρ2)=11+κ1κ2(Ψρ2+Θ2pr,1A1−a1)2{[pr,1A1−a1−Ψρ1−Θ1+κ1κ2(Ψρ2+Θ2pr,1A1−a1)(2Ψρ2)]κ12−(pr,1A1−a1−Ψρ1−Θ1)2κ1}, I express the value of diversification as a fraction of the value gained by project 1 through reduced capital requirements. The first term of the product on the RHS equals 1−FL, with FL defined in (34); as FL is the fraction of value lost because of the distortion that is due to the inability to tailor incentives to the characteristics of each project, 1−FL is the fraction of value retained. The second term of the product is the increase in the value of project 1 made possible by reduced capital requirements; it is reflected in the term (κ1/κ2)[(Ψρ2+Θ2)/(pr,1A1−a1)](2Ψρ2). The fraction 1−FL decreases in (κ1/κ2) and in (Ψρ2+Θ2)/(pr,1A1−a1): increases in the relative importance of project 2 increase the distortion, thereby decreasing the fraction of value retained. That value, in contrast, increases in (κ1/κ2) and in (Ψρ2+Θ2)/(pr,1A1−a1): the greater is the relative importance of project 2, the more capital is allocated to that project relative to that allocated to project 1, the greater is the diversification benefit thereby provided to project 1. The same is true of project 2’s cost of capital Ψρ2: the higher is that cost, the more capital is allocated to project 2 relative to project 1, the greater is the diversification benefit thereby provided to project 1. Remark 1, Lemma 2, and Proposition 3 show that projects that should be integrated within a single firm are those that (1) share similar characteristics ( 1⩽γ≪γmax⁡), (2) are related by strong externalities ( |Θi| large), and (3) have weakly correlated payoffs ( −1⩽ϱ≪1).61 6. Contractibility I have thus far precluded contracting on the externality, the use of capital, and risky investment. While full contractibility is unlikely, except in the simplest of circumstances, the complete absence of contractibility is equally unlikely, except perhaps in the most complex of circumstances.62 I therefore consider the case where it is possible partially to contract, initially on the externality or the use of capital, then on risky investment. I examine the implications of contractibility for the optimal form of ownership. 6.1 Contractibility of the externality and of capital Suppose it is possible for the shareholder-owned firm to contract with stakeholders to an extent qΘ, 0⩽qΘ⩽1, on the externality Θ(B−L): the firm can commit to providing stakeholders with compensation qΘΘ(B−L). The now partially contractible externality naturally affects the objective functions of both the manager and the firm, the former becoming   MaxB−Lβ1[(prA−a)(B−L)−qΘΘ(B−L)]+β0−κ(B−L)2 (35) with solution   B−L=β1(prA−a−qΘΘ)2κ, (36) and the latter becoming   Maxβ1(prA−a)(B−L)−Ψρ(B−L)−qΘΘ(B−L)−κ(B−L)2 with solution   β1SH,qΘ=1−ΨρprA−a−qΘΘ (37) and corresponding risky investment   (B−L)SH,qΘ=prA−a−(Ψρ+qΘΘ)2κ. (38) The resulting firm value, from which the compensation (1−qΘ)Θ(B−L)SH,qΘ for that fraction of the externality not contracted must be subtracted, is   VSH,qΘ=aB+(prA−a−Ψρ−qΘΘ)(B−L)SH,qΘ−κ[(B−L)SH,qΘ]2−(1−qΘ)Θ(B−L)SH,qΘ=aB+[prA−a−(Ψρ+Θ)]24κ−[(1−qΘ)Θ]24κ. (39) Note that ∂VSH,qΘ/∂qΘ>0, with VSH,qΘ|qΘ=1=VFB. Contractibility increases payoff, and makes possible the attainment of first-best when it is possible fully to contract on the externality. This is intuitive as shareholder ownership’s departure from first-best was due to failure to commit to accounting for the externality, a failure partially or fully remedied by contractibility. I have Proposition 4. The threshold cost of stakeholder capital Φ∗,SH,qΘdecreases in qΘ. Contractibility increases the range of stakeholder capital cost [Φ∗,SH,qΘ,Φmax⁡] over which shareholder ownership dominates: the more contractible is the externality, the lesser is the disadvantage of shareholder ownership in accounting for the externality, the wider is the range over which shareholder ownership dominates. Remark 2. Contractibility decreases the power of incentives under shareholder ownership β1SH,qΘif and only if the externality is negative ( −Θ<0, Θ>0). Where the externality is negative and the power of incentives decreases, these nonetheless remain higher than under stakeholder ownership: β1SH,qΘ>β1STif −Θ<0. Shareholders can use contractibility partially or fully to commit to imposing a lower negative externality on stakeholders, or to providing a higher positive externality. They incentivize the manager to make the lower or higher risky investment that causes the now committed for externality by providing lower- or higher-powered incentives, respectively. As noted above, it is this ability to commit to accounting for the externality that makes the increases in firm value possible. Despite the lowering of the PPP provided by shareholders induced by contractibility in case of negative externality, the PPP remains higher than that provided under stakeholder ownership. This is true even if there is no differential cost of capital ( Φ=Ψ) and if full contractibility is possible ( qΘ=1). By making it possible to incorporate the externality into the manager’s objective function (35), contractibility lessens the need to rely on the lowering of the PPP to achieve that same effect; this is in contrast to stakeholder ownership.63 The case of positive externality is not entirely symmetrical, in the sense that the PPP under shareholder ownership with contractibility will not necessarily be lower than under stakeholder ownership, because the difference in the cost of capital, Φ>Ψ, may be so large as to keep the PPP under stakeholder ownership lower than under shareholder ownership.64 The analysis in the case of stakeholder ownership with nonvoting preferred stock proceeds along nearly identical lines. Suppose it is possible for the stakeholder-owned firm to contract with preferred shareholders to an extent qΨ, 0⩽qΨ⩽1, on the use of capital Ψρ(B−L).65 In a manner analogous to that used in the case of partially contractible externality, I can write   VST,NV,qΨ=aB+[prA−a−(Ψρ+Θ)]24κ−[(1−qΨ)Ψρ]24κ. (40) Comparing (39) and (40), I conclude that VSH,qΘ>VST,NV,qΨ if and only if (1−qΘ)|Θ|<(1−qΨ)Ψρ, that is, if the noncontractible fraction of the externality, whether positive of negative, imposes a lower cost than the noncontractible fraction of capital use. If one assumes that contracting on the externality is more feasible than contracting on the use of capital, because of the numerous influences on the latter, then qΘ>qΨ and, absent too large a differential between |Θ| and Ψρ, |Θ|/Ψρ<(1−qΨ)/(1−qΘ), shareholder ownership can be expected to dominate stakeholder ownership with nonvoting preferred stock financing. This result may explain the relative paucity of stakeholder ownership with nonvoting preferred stock observed in Section 4. 6.2 Contractibility of risky investment I introduce the contractibility of risky investment by assuming that the owner(s) of the firm can contract with stakeholders (whether the firm is shareholder owned) or with preferred shareholders (whether it is stakeholder owned but preferred shareholder financed) on a level of risky investment (B−L)C. Departure from that level is possible, (B−L)≠(B−L)C, but it imposes a cost δ[(B−L)−(B−L)C]2, δ>0, on the owner. I show in what follows that the contractibility of risky investment increases firm value under both shareholder ownership and stakeholder ownership with nonvoting preferred stock. I consider the former case first. The manager’s problem becomes   MaxB−Lβ1[(prA−a)(B−L)−δ[(B−L)−(B−L)C]2]+β0−κ(B−L)2. It has solution   B−L=β1[prA−a+2δ(B−L)C]2(κ+δβ1). (41) Shareholders’ problem is   Maxβ1(prA−a)(B−L)−Ψρ(B−L)−δ[(B−L)−(B−L)C]2−κ(B−L)2. I proceed in two steps to solve that problem: I first solve for the risky investment B – L that maximizes the objective function; I then determine the PPP that incentivizes the manager to make that investment by equating the obtained risky investment to (41). The solution to the first step is   (B−L)SH,δ=prA−a−Ψρ+2δ(B−L)C2(κ+δ); (42) equating with (41) and solving for β1, I obtain   β1SH,δ=prA−a−Ψρ+2δ(B−L)CprA−a+(δκ)Ψρ+2δ(B−L)C. (43) The corresponding firm value, with the compensation to be paid for the externality subtracted, is   VSH,δ=aB+[prA−a−Ψρ−Θ+2δ(B−L)C](B−L)SH,δ−(κ+δ)[(B−L)SH,δ]2−δ[(B−L)C]2=aB+[prA−a−Ψρ+2δ(B−L)C]24(κ+δ)−Θ[prA−a−Ψρ+2δ(B−L)C]2(κ+δ)−δ[(B−L)C]2. (44) Differentiating with respect to (B−L)C to obtain the value of risky investment to be contracted, I have   (B−L)C=prA−a−(Ψρ+Θ)2κ=(B−L)FB, (45) from (6). The parties find it optimal to contract on the first-best value of risky investment; this is despite the fact that this level will not be attained, risky investment being instead, substituting (45) into (42),   (B−L)SH,δ=(κ+δ)(prA−a−Ψρ)−δΘ2(κ+δ)κ=prA−a−Ψρ−(δκ+δ)Θ2κ>(B−L)C, if and only if Θ>0, with lim⁡δ→∞(B−L)SH,δ=(B−L)FB: when departure from the contracted value is infinitely costly, there is no such departure; risky investment equals its contracted value, which has been set to equal its first-best value. For δ finite, however, risky investment is above its first-best value if the externality is negative ( −Θ<0), below if it is positive ( −Θ>0): there is too much risky investment when such investment creates a negative externality, too little when the externality is positive. Substituting (45) into (44), I obtain   VSH,δ=aB+[(κ+δ)(prA−a−Ψρ)−δΘ]24(κ+δ)κ2−Θ2κ[prA−a−Ψρ−δΘκ+δ]−δ[prA−a−Ψρ−Θ]24κ2. (46) I show Proposition 5. Firm value VSH,δincreases in δ; the threshold cost of stakeholder capital Φ∗,SH,δdecreases in δ. The partial contractibility of risky investment imposes a cost δ[(B−L)−(B−L)C]2 to departures from contracted risky investment, which equals first-best investment. The higher is the cost δ per squared deviation, the higher is firm value under shareholder ownership. This naturally increases the range of stakeholder capital cost [Φ∗,SH,δ,Φmax⁡] over which shareholder ownership dominates. The analysis in the case of stakeholder ownership with nonvoting, preferred stock is very similar: Θ replaces Ψρ and vice versa in the various expressions. I therefore obtain   VST,NV,δ=aB+[(κ+δ)(prA−a−Θ)−δΨρ]24(κ+δ)κ2−Ψρ2κ[prA−a−Θ−δΨρκ+δ]−δ[prA−a−Ψρ−Θ]24κ2. (47) Comparing (46) and (47), I can write   VST,NV,δ−VSH,δ=[(κ+δ)(prA−a−Θ)−δΨρ]24(κ+δ)κ2−Ψρ2κ[prA−a−Θ−δΨρκ+δ]−[(κ+δ)(prA−a−Ψρ)−δΘ]24(κ+δ)κ2+Θ2κ[prA−a−Ψρ−δΘκ+δ]=(Ψρ−Θ)[2(κ+δ)(prA−a)−(κ+2δ)(Ψρ+Θ)]4(κ+δ)κ−12κ[(Ψρ−Θ)(prA−a)−δ[(Ψρ)2−Θ2]κ+δ]=Θ2−(Ψρ)24(κ+δ). (48) Thus, like in the case of noncontractibility of risky investment, δ = 0, whether stakeholder ownership with nonvoting preferred stock or shareholder ownership dominates depends on the relative sizes of Ψρ and |Θ| (Lemma 1 and Proposition 2): when the cost of equity looms larger in importance, Ψρ>|Θ|, then shareholder ownership dominates, for it is such ownership that better accounts for the use of capital; when in contrast it is the externality that is more important, then stakeholder ownership with nonvoting preferred stock dominates. 7. Empirical Evidence Vitali, Glattfelder, and Battiston (2011) consider 43,060 transnational corporations (TNCs) in an attempt to trace ownership and control links among these.66 They find that “nearly 4/10 of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of 147 TNCs” (Vitali, Glattfelder, and Battiston, 2011, p. 4); they report the top 50 control holders: all but 5 are classified as financial intermediaries. Azar, Raina, and Schmalz (2016, table 1) similarly report that the 6 largest US banks by deposits to a large extent share the same top 5 shareholders: Blackrock owns between 4.7% and 7.4% of each of J.P. Morgan Chase, Bank of America, Citigroup, Wells Fargo, U.S. Bank, and PNC Bank; Vanguard between 4.4% and 4.7%. Azar, Raina, and Schmalz (2016) find that the larger is the extent of common ownership, the higher are spreads, fees, and fee thresholds; Azar, Schmalz, and Tecu (2016) find a similar result in the airline industry, where common ownership increases ticket prices. In a somewhat different setting, Hansen and Lott (1996, p. 47) report that common ownership encourages the settlement of lawsuits. In the context of this model, if I identify (1) vigorous competition or aggressive litigation with risky investment, (2) the costs these strategies impose on competitors or defendants with a negative externality, (3) common ownership with stakeholder ownership, and (4) independent ownership with shareholder ownership, in that common ownership accounts for the externality but independent ownership does not, then the result from (15) and (18) that (B−L)ST<(B−L)SH if −Θ<0 even if Φ=Ψ can be viewed as being in agreement with the results reported in the preceding paragraph. That managers are incentivized to make lower risky investment by being provided with lower-powered incentives, β1ST<β1SH if −Θ<0 even if Φ=Ψ from (14) and (19), is consistent with the findings of Antón et al. (2016), who document a negative relation between managerial compensation and the product of common ownership and market value change: the rewards to increasing firm value are lower for the managers of those firms that are owned in common with their competitors. Proposition 4 has shown that there is an inverse relation between the ability to contract an externality and the desirability of stakeholder ownership. This result is consistent with corporate developments in the wake of the rise of mass production. Mass production made possible a dramatic decline in variable costs, but necessitated enormous investments which led to a very large increase in fixed costs.67 The substitution of fixed for variable costs introduced the need for demand and supply coordination (Piore and Sabel 1984, chapter 3): demand in excess of capacity could not easily be accommodated, demand below resulted in idle capacity. Initial attempts at coordination took the form of pools, “agreements among producers to fix prices or to limit output” (Piore and Sabel 1984, p. 55). Despite progressively increased sophistication, including “provisions for the exchange of production and sales data […] and fines for violations of the agreement ” as well as “provisions for the stronger producers to compensate the weaker ones for reducing production” (Piore and Sabel 1984, p. 55), pools, a form of contract, ultimately failed to achieve the desired coordination. That firms turned to integration through horizontal mergers rather than control through ownership is in accordance with the argument referred to at the end of Section 4 that coordination requires integration. Azoulay (2004) examines the decision by pharmaceutical companies to contract out clinical trials to Contract Research Organizations (CRO) or to conduct these “in-house.” Azoulay (2004, p. 1592) finds that “[t]he choice is […] between the hierarchy of the firm—in which subjective performance evaluations are combined with flat incentives—and the hierarchy of its subcontractor—whose virtue precisely stems from the ability to provide high-powered incentives on a narrow set of monitorable tasks.” Azoulay (2004, p. 1592) further finds that “knowledge-intensive projects are more likely to be assigned to internal teams,” with such knowledge arising from “[t]he unexpected and anomalous results of clinical experience[, which] pose new questions for basic biomedical research and enrich its ultimate payoff” (Gelijns, Rosenberg, and Moskowitz 1998, p. 693). In the context of this model, if I identify (1) clinical trials that allow for the careful investigation of unexpected results with safe investment, (2) the knowledge such investigation gives rise to with a positive externality, (3) in-house trials with stakeholder ownership in that the knowledge such trials produce is generally of much greater importance to a pharmaceutical firm than it is to a CRO, for it is the former that can make by far the most of it, (4) contracting with shareholder ownership, and (5) the ability to evaluate performance objectively and to monitor a task with contractibility, then the predictions of this analysis can be viewed as being in general agreement with Azoulay’s (2004) findings. Externalities favor stakeholder ownership (Proposition 1), whereas contractibility favors shareholder ownership (Propositions 4 and 5).68 Recalling that a positive externality of safe investment is a negative externality of risky investment (Footnote 35), the power of in-house incentives is lower than that of CRO incentives (Remark 2). Morrison and Wilhelm (2007, chapters 8 and 9) argue that the fundamental advances in financial economics that were made during the sixties and the seventies made possible the codification of much knowledge that had previously been only tacit: “[s]kills that previously could be acquired only though a long apprenticeship within a financial institution can now be learned in the classroom” (Morrison and Wilhelm 2007, p. 245). They further argue that codification caused “a drop in the relative importance of investment banker reputation in the markets where practice was most codified” (Morrison and Wilhelm 2007, p. 225), a development to which they attribute the gradual abandonment of the partnership form once quasi universal among investment banks. If I identify codification with the contractibility of risky investment, as some tasks which previously could be prescribed only with difficulty and monitored only imperfectly ceased being so, and if I associate the decline in the importance of reputation with a decrease in the (absolute) value of the externality, as reputation no longer was affected to the same extent by risky investment that could be at least partially contracted, then the predictions of this analysis can be viewed as being in agreement with Morrison and Wilhelm’s (2007) argument: the contractibility of risky investment diminishes the desirability of stakeholder ownership and capital provision (Proposition 5); the decline in the value of the externality favors the replacement of stakeholder by shareholder ownership rather than the combination of stakeholder ownership with non voting preferred shareholder capital provision (Equation (48) and the discussion that follows). 8. Conclusion I conclude by briefly discussing possible extensions to the model. The analysis here has assumed that total resources are fixed; the manager’s task has been limited to allocating resources between risky and safe investment. Yet resources are unlikely to be fixed, and an important task of the manager surely is to gather the resources necessary for investment. Put somewhat more formally, total resources B are unlikely to be exogenous but are instead endogenous. Endogeneity imparts a double role to the pay-for-performance parameter β1, which now induces resource gathering in addition to guiding resource allocation. Although this extension is not expected to affect optimal ownership, it may enrich the conclusions regarding the effects of contractibility, which now can encompass the contractibility of total resources in addition to that of risky investment. Preliminary analysis suggests that changes in contractibility may provide a combined explanation for the seemingly contradictory developments that have been the nineteenth and twentieth century rise in salaried employment (low β1) and the more recent rise in outsourcing (high β1). I leave this line of inquiry for future work. I am deeply grateful to Yoram Barzel, Josef Falkinger, Uday Rajan (the Editor), and an anonymous referee. I additionally thank, Øyvind Bøhren, Jos van Bommel, Dawei Fang, Peter Gruber, Ulf von Lilienfeld-Toal, Salvatore Miglietta, Bogdan Stacescu, and Alexander Wagner and seminar participants at the University of Gothenburg, the University of Lugano, the Luxembourg School of Finance, the CEPR First Annual Spring Symposium, the 15th Workshop on Corporate Governance and Investment at BI Oslo, and the IFABS 2015 Corporate Finance Conference at Oxford University for helpful comments and suggestions. Footnotes 1 Hansmann (1996, 2013) develops a formal theory of ownership, but he provides no model. I discuss the relation of my work to Hansmann’s in Section 1. 2 In Section 1, I place my work within the larger context of the theory of ownership. 3 Traders are generally acutely aware of their “trader’s option,” that is, the asymmetry in their gains and losses from taking large, risky positions. Profitable positions result in large bonuses, and unprofitable positions mean, at worse, job loss. 4 See Section 4.7 for a formal analysis. 5 See, for example, Gibbons (2005), Gibbons and Roberts (2013), Holmstrom (1999), and Holmstrom and Milgrom (1991, 1994). 6 I provide further justification in Section 2. I nonetheless acknowledge a limitation of the model in the failure to account for the issuance of dual-class, common shares to noncontrolling shareholders, as opposed to that of nonvoting, preferred shares. 7 See Barzel, Habib, and Johnsen (2006), Cornelli and Goldreich (2001), Gondat-Larralde and James (2008), and Jenkinson and Jones (2009). 8 For an extended discussion of firm boundaries and vertical integration, see Bresnahan and Levin (2013) and Hart (1995) and the references therein. 9 For a superb comparative analysis of various theories of the firm and the role of ownership therein, see Gibbons (2005). 10 Specifically, the manager evaluates a risky investment opportunity and decides how much to invest; see the formal analysis. 11 The present model is a much simplified version of Falkinger (2014). 12 Section 3 analyzes the case of a positive externality. 13 The prototypical example is probably bank capital, which serves to bond the value of bank deposits against possible declines in the value of bank assets. 14 I set the proportion between capital and standard deviation to one for simplicity. I use the standard deviation, rather than the variance, to keep the analysis tractable. 15 The next paragraph, as well as Section 3 present the reasons for this qualification. 16 I allow for partial contractibility of investment, the use of capital, and the externality in Section 6. 17 Limiting owners’ discretion to alter (β0,β1) or K is not realistic: changes in circumstances that are entirely unrelated to any attempt on the part of owners to exploit firm stakeholders may require a change in the parameters of the compensation contract; changes in circumstances may alter firm payoff, regardless of any attempt at stakeholder exploitation. I do not model these changes. 18 Conditioning on the compensation contract, if feasible, amounts to making investment contractible, thereby making the original problem moot. I thank the anonymous referee for alerting me to this result. 19 In Sections 4.7 and 5, I consider the case in which the other stakeholders are themselves shareholder owned. 20 Section 3 provides the exact derivations. 21 See Section 3 for details. 22 I assume prA−a⩾Ψρ+Θ for (B−L)FB⩾0. 23 Substitute (6) into (1) rewritten as (prA−a)(B−L)+aB−Ψρ(B−L)−κ(B−L)2−Θ(B−L) to obtain (7). 25 Substitute (14) into (10) to obtain (15). 29 I assume prA−a⩾Φρ+Θ for (B−L)ST⩾0. 30 I have shown in Footnote 26 that VSH<VFB; a very similar argument shows that VST,NV<VFB. That VST⩽VFB with equality at Φ=Ψ is immediate from (7) and (17). 31 The appendix provides all proofs. 32 Failure is apparent from (2) and (4). 34 There is still a distortion, however; this is why stakeholder ownership dominates for low cost of stakeholder capital Φ<Φ∗,SH. 36 That Google has “a world-class research team working on all sorts of moonshot projects, from self-driving cars to healthcare” (Bort 2015), for example, may at least in part reflect the eclectic interests of its founding and controlling shareholders. The description of research projects as “moonshots” accords well with the identification of risky investment as giving rise to positive externalities. 38 As an example of the importance of such employees, consider the following description of Michael Milken’s role at Drexel, Burnham, Lambert (Bruck 1989, p. 57): “He [Milken] had the issuers. He had the buyers. He had the most trading capital of any firm. He had the knowhow. He had the best incentive system for his people. He had the history of data—he knew the companies, he knew their trading prices, probably their daily trading prices going back to at least 1971. He had boxed the compass.” 39 As for Google’s “moonshot” projects discussed in Footnote 36, it is risky investment—those issues for which success or failure is most uncertain—that creates the externality. 40 Payment to the bank generally takes the form of lower salaries: firms that are viewed as increasing an employee’s human capital often pay lower wages, ceteris paribus, than do firms that provide no such positive externality. 41 It may also attest to the perhaps greater codifiability of at least of parts of investment banking knowledge (Morrison and Wilhelm 2007, pp. 244–6); codifiability is an issue I return to in Section 7. 42 Somewhat misleadingly, though, mutual savings banks in the United States are actually nonprofit organizations as opposed to despositor-owned banks (Hansmann 1996, pp. 246–7). I do not consider nonprofits in this paper but note that nonprofits share with mutuals the characteristic of controlling the risk-shifting problem: there are no shareholders to benefit fron risky investment at the expense of depositors. 43 This is an instance of the contractibility of investment, an issue I analyze in Section 6.2. 44 Building societies are the British equivalent to savings and loans associations. 45 Recall that safe and risky investment must add up to total resources B, a constant. 47 Section 6.1 provides a further explanation for the relative paucity of stakeholder ownership combined with nonvoting preferred stock. 48 I proxy profits by firm value. 50 Total payoff is not, however; this explains the reversal to government ownership in some cases, the adoption of customer ownership in others. 51 For an example of the difficulties posed by heterogeneous worker interests in a context of difficult employment conditions, consider the turbulent relations between United Airlines’ pilots and machinists in the run-up to the 1994 employee buyout (Hansmann 1996, pp. 117–8) and prior to the 2003 bankruptcy (Gordon 2003, p. 4). 52 In the investment banking and legal partnerships considered in Section 4.2, and the farmer cooperatives considered in Section 4.6, a single category of workers appears to be paramount, at least as concerns the externality. 53 I show below that β1ST,NV<β1SH and LST,NV>LSH under the conditions in which the buyer finances its acquisition with nonvoting preferred shares. 54 That Θ>Ψρ establishes β1ST,NV<β1SH and LST,NV>LSH. 55 Recall the discussion that follows Proposition 1. 56 Recall from Section 3 that VST=VFB at Φ=Ψ. 57 Hansen and Lott (1996, p. 43) put it very nicely: “[a]ny kind of externality, pecuniary or nonpecuniary, vertical or horizontal, suffices.” Hansen and Lott’s (1996) focus is on the incentive for portfolio value maximization induced by common ownership, mine is on the incentive for choosing common ownership in the first place. 58 Besanko, Dranove, and Shanley (1996, pp. 89–90) and Milgrom and Roberts (1992, pp. 556–8) argue that one purpose of vertical integration is to make possible the coordination a product’s multiple “design attributes” (Milgrom and Roberts 1992, p. 91) require. 59 I interchange the indices 1 and 2 if γ⩽1. 61 That (33) is more restrictive than (32) is consistent with a positive role for low or negative correlation in favoring integration: the condition is less likely to hold, and integration therefore more likely to dominate, when ϱ=−1 (condition (33)) than when ϱ=1 (condition (32)). 62 See Bolton and Dewatripont (2005, Chapter 12) and the references therein for a detailed analysis of contractibility. 63 Note that there is no need for contractibility under stakeholder ownership, for the externality is fully accounted for by stakeholders in setting the power of incentives. 64 Formally, β1SH,qΘ>β1ST if (and only if) (Φ−Ψ)ρ(prA−a)>−Θ(prA−a−qΘΦρ−qΘΘ), with −Θ>0. 65 For comparability with my previous analysis, I continue to assume that the manager cannot contract with the owner on the use of capital. 66 Distinguishing between ownership and control links changes their findings only little. 67 To illustrate the tremendously increased scale of manufacturing, consider Chandler’s (2002, p. 249) observation that a mere fifteen cigarette-making machines “could fill the total demand for cigarettes in the United States in 1880.” 68 I appeal to the analysis of Section 5 to explain why the phamaceutical firm might wish to contract out some clinical trials, despite itsef likely being shareholder-owned. 70 Failure to establish the monotonicity of 4[ΠI(γ,−1)−Π12(γ)] in γ precludes establishing the result that Sγ,−1 consists of a single interval. 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CrossRef Search ADS PubMed  Appendix Proof of Lemma 1: Use (16) and (22) to write   sign{VSH−VST,NV}=sign{[prA−a−Ψρ]24κ−Θ(prA−a−Ψρ2κ)−[prA−a−Θ]24κ+Ψρ(prA−a−Θ2κ)}=sign{[prA−a−Ψρ]2−[prA−a−Θ]2−2Θ(prA−a−Ψρ)+2Ψρ(prA−a−Θ)}=sign{[prA−a−Ψρ+prA−a−Θ](Θ−Ψρ)−2(Θ−Ψρ)(prA−a)}=−sign{(Ψρ+Θ)(Θ−Ψρ)}=+1, if and only if Ψρ>Θ. Proof of Proposition 1: Initially consider the case Ψρ>Θ and define   F(Φ)≡VST−VSH=[prA−a−(Φρ+Θ)]24κ−[prA−a−Ψρ]24κ+Θ(prA−a−Ψρ2κ); it is clear that F′(Φ)<0 for Φ<Φmax⁡ and, from Footnote 30, that F(Ψ)>0. In contrast   F(Φmax⁡)=−[prA−a−Ψρ]24κ+Θ(prA−a−Ψρ2κ); it has sign   sign{F(Φmax⁡)}=sign{−(prA−a−Ψρ)+2Θ}=sign{−Φmax⁡ρ+Ψρ+Θ}=−1, if and only if Θ<Φmax⁡ρ−Ψρ. By the intermediate value theorem, there exists a Φ∗,SH, Ψ<Φ∗,SH<Φmax⁡, such that F(Φ∗,SH)=0; F(Φ)=VST−VSH>0 for Φ<Φ∗,SH and F(Φ)=VST−VSH<0 for Φ>Φ∗,SH. To establish ∂Φ∗,SH/∂Θ>0, define F∗,SH≡F(Φ∗,SH)=0, note that ∂F∗,SH/∂Φ∗,SH<0 from F′(Φ)<0 and   ∂F∗,SH∂Θ=−prA−a−(Φ∗,SHρ+Θ)2κ+prA−a−Ψρ2κ=Φ∗,SHρ+Θ−Ψρ2κ>0, where the inequality is true by Φ∗,SH>Ψ, and use the implicit function theorem to write   ∂Φ∗,SH∂Θ=−∂F∗,SH∂Θ∂F∗,SH∂Φ∗,SH>0. The results for the case Ψρ<Θ can be obtained in a very similar manner. Define   G(Φ)≡VST−VST,NV=[prA−a−(Φρ+Θ)]24κ−[prA−a−Θ]24κ+Ψρ(prA−a−Θ2κ) and note that   G(Φmax⁡)=−[prA−a−Θ]24κ+Ψρ(prA−a−Θ2κ) has sign   sign{G(Φmax⁡)}=sign{−(prA−a−Θ)+2Ψρ}=sign{−Φmax⁡ρ+2Ψρ}=−1, if and only if Ψρ<Φmax⁡ρ−Ψρ. Further note that   ∂G(Φ∗,ST,NV)∂Θ=−prA−a−(Φ∗,ST,NVρ+Θ)2κ+prA−a−Θ2κ−Ψρ2κ=Φ∗,ST,NVρ−Ψρ2κ>0. Proof of Proposition 2: I have   sign{VSH−VST,NV}=−sign{(Ψρ+Θ)(Θ−Ψρ)}=sign{Ψρ+Θ}=+1, if and only if −Θ<Ψρ; the first equality uses the derivation in the proof of Lemma 1, the second uses Θ<0. Following the reasoning used in the proof of Proposition 1, I write   sign{F(Φmax⁡)}=sign{−(prA−a−Ψρ)+2Θ}=sign{−Φmax⁡ρ+Ψρ+Θ}=−1, where I have used Φmax⁡>Ψ and Θ<0; the existence of Φ∗,SH, Ψ<Φ∗,SH<Φmax⁡, is now unconditional. Again following the reasoning used in the proof of Proposition 1, I write   ∂F∗,SH∂Θ=−prA−a−(Φ∗,SHρ+Θ)2κ+prA−a−Ψρ2κ=Φ∗,SHρ+Θ−Ψρ2κ>0, if and only if −Θ<Φ∗,SHρ−Ψρ; ∂Φ∗,SH/∂Θ>0 in such case. The results for Φ∗,ST,NV are similar to those in the case Θ>0. Proof of Lemma 2: Substituting ϱ=1 into (31), I obtain   ΠI(γ,1)=a1B1+a2B2+14(pr,1A1−a1)2[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]+14(Ψρ1+Θ1)2([1κ1+1γκ2(Ψρ2+Θ2Ψρ1+Θ1)2]21κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2)−12(Ψρ1+Θ1)(pr,1A1−a1)[1κ1+1γκ2(Ψρ2+Θ2Ψρ1+Θ1)2]. To compare the values of the single integrated and the two independent firms, I compute   4[ΠI(γ,1)−Π12(γ)]=(pr,1A1−a1)2[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]+(Ψρ1+Θ1)2([1κ1+1γκ2(Ψρ2+Θ2Ψρ1+Θ1)2]21κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2)−2(Ψρ1+Θ1)(pr,1A1−a1)[1κ1+1γκ2(Ψρ2+Θ2Ψρ1+Θ1)2]−(pr,1A1−a1−Ψρ1−Θ1)2κ1+Θ12κ1−(Ψρ2+Θ2Ψρ1+Θ1)2(pr,1A1−a1γ−Ψρ1−Θ1)2κ2+Θ22κ2=(Ψρ1+Θ1)2([1κ1+1γκ2(Ψρ2+Θ2Ψρ1+Θ1)2]21κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2)−(Ψρ1+Θ1)2κ1+Θ12κ1−(Ψρ2+Θ2)2κ2+Θ22κ2=−(Ψρ2+Θ2)2κ1κ21κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2(1−1γ)2+(Θ12κ1+Θ22κ2). This is positive at γ = 1; it decreases in γ for γ>1; it equals the LHS of (32) at γ=γmax⁡. Thus, if (32) holds, then ∃ γ∗, 1<γ∗<γmax⁡, such that ΠI(γ,1)⩽Π12(γ) if and only if γ∗⩽γ⩽γmax⁡. Proof of Proposition 3: Set ϱ=−1; if I can establish Sγ,−1≡{γ|ΠI(γ,−1)⩽Π12(γ)}≠∅, then I will have established Sγ,ϱ≡{γ|ΠI(γ,ϱ)⩽Π12(γ)}≠∅ because ΠI(γ,ϱ)<ΠI(γ,−1) for −1<ϱ⩽1 from ∂ΠI(γ,ϱ)/∂ϱ<0 in Remark 1. Consider the two limits γ = 1 and γ=γmax⁡ in turn. At γ = 1, use Remark 1 and Lemma 2 to write 4[ΠI(1,−1)−Π12(1)]>4[ΠI(1,1)−Π12(1)]>0. At γ=γmax⁡, substitute ϱ=−1 and γmax⁡=(pr,1A1−a1)/(Ψρ1+Θ1) into (28) and (31) to obtain69 69 Rewrite ΠI(γ,ϱ) in (31) as   ΠI(γ,ϱ)=a1B1+a2B2+1411κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2×{(pr,1A1−a1)[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]−[Θ1κ1+Θ2γκ2(Ψρ2+Θ2Ψρ1+Θ1)+Ψρ12κ12+ρ22γ2κ22(Ψρ2+Θ2Ψρ1+Θ1)2+2ϱρ1ρ2γκ1κ2(Ψρ2+Θ2Ψρ1+Θ1)]}2 for the calculation that follows.  4[ΠI(γmax⁡,−1)−Π12(γmax⁡)]=11κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2×{(pr,1A1−a1)[1κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2]−[Θ1κ1+Θ2κ2(Ψρ2+Θ2pr,1A1−a1)+Ψρ12κ12+ρ22κ22(Ψρ2+Θ2pr,1A1−a1)2−2ρ1ρ2κ1κ2(Ψρ2+Θ2pr,1A1−a1)]}2−(pr,1A1−a1−Ψρ1−Θ1)2κ1+Θ12κ1+Θ22κ2=11κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2×{(pr,1A1−a1)[1κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2]−[Ψρ1+Θ1κ1+Θ2−Ψρ2κ2(Ψρ2+Θ2pr,1A1−a1)]}2−(pr,1A1−a1−Ψρ1−Θ1)2κ1+Θ12κ1+Θ22κ2=11κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2{pr,1A1−a1−Ψρ1−Θ1κ1+2Ψρ2κ2(Ψρ2+Θ2pr,1A1−a1)}2−(pr,1A1−a1−Ψρ1−Θ1)2κ1+Θ12κ1+Θ22κ2, which is the LHS of (33). If it is negative, then the intermediate value theorem and continuity together imply the existence of a nonempty set Sγ,−1={γ|ΠI(γ,−1)⩽Π12(γ)}.70 Proof of Proposition 4: Define   F(Φ)≡VST−VSH,qΘ=[prA−a−(Φρ+Θ)]24κ−[prA−a−(Ψρ+Θ)]24κ+[(1−qΘ)Θ]24κ, and F∗,SH,qΘ≡F(Φ∗,SH,qΘ)=0. Using F′(Φ)<0 for Φ<Φmax⁡ to obtain ∂F∗,SH,qΘ/∂Φ∗,SH,qΘ<0 and   ∂F∗,SH,qΘ∂qΘ=−(1−qΘ)Θ22κ<0, I conclude using the implicit function theorem that   ∂Φ∗,SH,qΘ∂qΘ=−∂F∗,SH,qΘ/∂qΘ∂F∗,SH,qΘ/∂Φ∗,SH,qΘ<0. Proof of Remark 2: The first part of the remark is immediate from (37). The second part is proved by contradiction. Assume   β1SH,qΘ<β1P⇔ΨρprA−a−qΘΘ>Φρ+ΘprA−a⇔Ψρ(prA−a)>(Φρ+Θ)(prA−a−qΘΘ)⇔0>(Φ−Ψ)ρ(prA−a)+Θ(prA−a−qΘΦρ−qΘΘ), (49) which is false if −Θ<0. Proof of Proposition 5: Differentiate (46) with respect to δ to obtain   ∂VSH,δ∂δ=−[(κ+δ)(prA−a−Ψρ)−δΘ]24(κ+δ)2κ2+2[(κ+δ)(prA−a−Ψρ)−δΘ][prA−a−Ψρ−Θ]4(κ+δ)κ2+Θ22(κ+δ)2−[prA−a−Ψρ−Θ]24κ2. The first, second, and fourth term equal   14(κ+δ)2κ2{−[(κ+δ)(prA−a−Ψρ)−δΘ]2+2(κ+δ)[(κ+δ)(prA−a−Ψρ)−δΘ][prA−a−Ψρ−Θ]−(prA−a−Ψρ−Θ)2(κ+δ)2}=14(κ+δ)2κ2{−(κ+δ)2(prA−a−Ψρ)2−(δΘ)2+2(κ+δ)(prA−a−Ψρ)δΘ+2(κ+δ)2(prA−a−Ψρ)2−2(κ+δ)2(prA−a−Ψρ)Θ−2(κ+δ)(prA−a−Ψρ)δΘ+2(κ+δ)δΘ2−(κ+δ)2(prA−a−Ψρ)2−(κ+δ)2Θ2+2(κ+δ)2(prA−a−Ψρ)Θ}=14(κ+δ)2κ2{−(δΘ)2+2(κ+δ)δΘ2−(κ+δ)2Θ2}=−Θ24(κ+δ)2. Combining with the third term, I obtain   ∂VSH,δ∂δ=Θ24(κ+δ)2>0. (50) Define   F(Φ)≡VST−VSH,δ and F∗,SH,δ≡F(Φ∗,SH,δ)=0. Using F′(Φ)<0 for Φ<Φmax⁡ to obtain ∂F∗,SH,δ/∂Φ∗,SH,δ<0 and   ∂F∗,SH,qΘ∂δ=−∂VSH,δ∂δ<0, from (50), I conclude using the implicit function theorem that   ∂Φ∗,SH,δ∂δ=−∂F∗,SH,δ/∂δ∂F∗,SH,δ/∂Φ∗,SH,δ<0. © The Author 2017. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Review of Corporate Finance Studies Oxford University Press

Multifaceted Transactions and Organizational Ownership

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Oxford University Press
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© The Author 2017. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
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2046-9128
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10.1093/rcfs/cfx019
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Abstract

Abstract I provide a unified explanation for shareholder ownership, partnerships, mutuals, government ownership, cooperatives, and vertical and horizontal control: each ownership form constitutes a variation on a single underlying theme, the assignment of ownership to a subset of firm stakeholders. When not every facet of a transaction is contractible and high-powered incentives might divert investment toward the transaction’s contractible facets, to the overall transaction’s possible detriment, optimal organizational ownership allocates the right to set the power of managerial incentives to those stakeholders most affected by the noncontractible facets of the organization’s paramount transaction. Received August 3, 2016; editorial decision August 2, 2017 by Editor Uday Rajan. The owners of a firm are nearly always one or another subset of the firm’s patrons—that is, persons who have some transactional relationship with the firm, either as suppliers or customers, apart from their possession of the rights of ownership. Often, that transactional relationship is the supply of capital to the firm, in which case we have the conventional investor-owned firm. Not infrequently however, ownership of the firm is placed in the hands of another class of patrons. This is the case, for example, with producer cooperatives, consumer cooperatives, employee-owned firms, and governments (897).—Hansmann 2013 Hansmann’s intriguing observation suggests that investor ownership is not a uniquely distinct form of ownership. It is, instead, one of many possible variations on the single underlying theme that is the assignment of ownership to a class of firm patrons, a subset of the firm’s many stakeholders. The purpose of the present paper is to develop a formal model that accounts for Hansmann’s observation and to use that model to generate additional predictions that can be, in turn, compared with the extant empirical evidence.1 The central intuition of the model is perhaps best expressed by Holmstrom’s (1999, p. 76) statement that “ownership […] internalizes some of the contractual externalities that are present in markets.” More specifically, ownership confers the right to set the power of managerial incentives to those stakeholders who are most exposed to the (noncontractible) consequences of the firm manager’s actions. Ownership thereby provides these stakeholders with the ability to, at least partially, control the manager’s actions and determine the extent to which such actions affect the stakeholders.2 Contractual externalities generally arise when some, but not all, facets of a multifaceted transaction can be contracted (Barzel 1982, 1997). In this case, as noted by Barzel (2002, 2013), Hansmann (1996), Holmstrom (1999), and Holmstrom and Milgrom (1991, 1994), low-powered incentives for facets of the transaction that can be contracted may be necessary to avoid too large a distortion in facets that cannot be contracted. For example, a currency trader may need to be offered low- rather than high-powered incentives when the bulk of possible trading losses is borne by investors instead of the trader.3I argue that optimal organizational ownership allocates the right to set the power of managerial incentives to those parties that are most affected by the noncontractible facets of the organization’s paramount transactions. To make things concrete, consider a buyer and a supplier. Quality is important to the buyer; the supplier can trade off quantity and quality. Assume quantity is contractible but quality is not. If the cost of low quality is primarily borne by the buyer, then the supplier is expected to favor quantity over quality. The suppliers’ manager will do so more when his or her incentives are high powered: high-powered incentives make the supplier’s higher profit in part the manager’s too. By acquiring the supplier, the buyer gains the right to set the supplier manager’s incentives. He or she will set incentives at a lower level, consistent with the choice of higher quality.4 Quality is the contractual externality, which backward integration by the buyer internalizes; this is well known.5 What is perhaps less well known is that the same mechanism can provide an explanation for forms of ownership as diverse as partnerships, mutuals, and cooperatives. These correspond to different externalities involving different transacting parties, specifically the reputation of senior employees in the case of partnerships, the savings and premiums of depositors and policyholders in the case of mutual banks and insurance companies, the demand for labor in the case of worker cooperatives, the demand for farm products and the supply of farm implements in the case of farm marketing, processing and supply cooperatives, and the capital equipment of utilities in the case of customer and government ownership. Shareholder ownership corresponds to the case in which the paramount transaction concerns the noncontractible use of firm equity. Returning to the example of the currency trader, investors who are called on to provide the capital put at risk by the trader may do so only on the condition that they be granted the right to set the power of the trader’s incentives at a level consistent with properly accounting for investor capital in the choice of trading positions. That such right is conferred by ownership implies that investors are owners; this is shareholder ownership. I allow for ownership to be distinct from capital provision: in the example of the buyer integrating backward, the buyer need not provide the capital necessary for the acquisition of the supplier; he or she may, instead, rely on the issuance of nonvoting, preferred stock. The stock is nonvoting because only the owner, the buyer in the present case, has the right to set the power of managerial incentives; it is preferred, in the sense of mandating the payment of a fixed dividend, because the owner’s ability to manipulate profit precludes the issuance of common stock to investors called on to provide the capital necessary for the acquisition.6 I compare shareholder ownership, stakeholder ownership and stakeholder capital provision (stakeholder ownership), and stakeholder ownership and nonvoting preferred shareholder capital provision (stakeholder ownership combined with nonvoting preferred stock). Stakeholder ownership dominates when stakeholders have cost of capital close to that of specialized shareholders: stakeholder ownership allocates stakeholders, who are the party most affected by the externality, the right to set the power of managerial incentives at a level consistent with the recognition of the externality. As stakeholder cost of capital increases, however, eventually to become markedly larger than that of specialized shareholders, then the substitution of stakeholder by shareholder capital may be desirable. Such substitution may take two forms: (1) shareholders may become the owners, as the stakeholders’ high cost of capital transforms the provision of capital into the paramount externality, or (2) stakeholders may remain the owners but firm capital nonetheless be provided by specialized shareholders who, unlike in the case of shareholder ownership, do not acquire ownership in the sense of not acquiring the right to set the power of managerial incentives, which remains stakeholders’; the provision of capital fails to displace stakeholders’ externality as paramount in that case. Case (1) is that of shareholder ownership and case (2) that of stakeholder ownership combined with nonvoting preferred stock. I extend the analysis from ownership to integration: integration decreases capital requirements by allowing for the pooling of project capital; it precludes the tailoring of incentives to specific project characteristics. I establish the conditions under which the joint undertaking of two projects within a single integrated firm dominates their separate undertakings within two independent firms. The results suggest that projects that should be integrated within a single firm are those that (1) share similar characteristics, (2) are related by strong externalities, and (3) have weakly correlated payoffs. The requirements of strong externalities and similar characteristics are consistent with the observation that multiple-industry firms generally operate in related industries (Hoberg and Phillips 2017). I allow for partial contractibility of the externality, the use of capital, and investment. The first kind of contractibility increases the range of capital costs over which shareholder ownership dominates: stakeholder ownership is dominated by shareholder ownership absent the externality, because of shareholders’ lower cost of capital; the greater is contractibility, the lesser is the externality, and the lesser therefore is the need for stakeholder ownership. The second kind of contractibility increases the range over which stakeholder ownership is combined with nonvoting preferred stock: the greater is contractibility, the lesser is shareholders’ fear that the capital they provide be misused by stakeholders, and the more therefore are noncontrolling shareholders willing to leave ownership and control in the hands of the stakeholders. When stakeholders’ high cost of capital precludes stakeholder ownership, whether shareholder ownership or stakeholder ownership combined with nonvoting preferred stock dominates depends on whether the noncontractible part of capital provision displaces the noncontractible part of the externality as paramount. That it is probably easier to contract on a somewhat circumscribed externality than on the use of the generic resource that is capital may account for the relatively limited use of nonvoting preferred stock: it is easier for shareholders to commit through contract to account for the externality in their setting of managerial compensation than it is for stakeholders to commit to account for shareholder capital. The third kind of contractibility is similar to the first two in increasing the ranges over which shareholder ownership and stakeholder ownership combined with nonvoting preferred stock dominate. This is because contractible investment achieves indirectly what a contractible externality and contractible capital achieve directly: it is investment that causes the externality and requires capital; the more it can be contracted, the greater the—indirect—control that can be had on the externality and on the use of capital, the greater therefore the scope for shareholder ownership (externality) and for nonvoting preferred stock financing (capital). 1. Literature Review Barzel (1982, 1997) recognizes the multifaceted nature of most goods, assets, and transactions and the inability to contract every single such facet: contracting requires measurement, which generally can be done only with error and sometimes cannot be done at all. He analyzes the opportunities imperfect measurement provides for wealth transfers and identifies a wide variety of institutions intended to avoid such transfers. For example, regular investors in initial public offerings subscribe to every issue, thereby committing not to “pick and choose” among issues. Such commitment denies regular investors the incentive to produce information intended to distinguish between overpriced and underpriced offerings, information that benefits its holder but is a detriment to both the issuer and the other investors lacking the demand-side information that determines how well “received” an issue is. Regular investors are compensated for their commitment by being allocated a disproportionate share of issues that are, on average, underpriced.7 Observing that the desire to engage in wealth transfers is proportionate to the power of incentives, Barzel (2002, 2013) argues that within-firm transactions, by muting the power of incentives, correspondingly decrease the desire to exploit imperfect measurement to engage in wealth transfers. A supplier is thus less likely to skimp on quality when it is owned by its buyer than when it is independent. Transactions will therefore be within-firms when measurement of a valuable attribute is difficult or impossible; they will be in the market when it is not. Barzel (2002, 2013) develops a theory of firm boundaries on that basis.8 Hansmann (1996, 2013) considers a wide variety of ownership forms: investor- and employee-owned firms, agricultural cooperatives, customer- and supplier-owned firms, utilities, clubs, housing cooperatives and condominiums, nonprofits and mutuals. He provides a formal theory of ownership, based on the minimization of the combined costs of ownership and contracting. While Hansmann evaluates a broader range of explanations than I do, it is interesting to note that the basic mechanism in my model, ownership’s allocation of the right to set the power of managerial incentives to those stakeholders most affected by the noncontractible facets of an organization’s paramount transactions, can account for many of the ownership forms Hansmann considers. The model additionally makes possible an analysis of integration and the consequences of making investment and selected transaction facets contractible. Alchian and Demsetz (1972) present a theory of ownership based on the need for “metering” in case of team production: owners are those best able to meter—to measure and to apportion—input and output in joint production so as to avoid shirking and maximize output; they are incentivized to do so by being made residual claimants to output. If metering skills are viewed as endogenous, then my work may be viewed as complementing Alchian and Demsetz’s (1972) by identifying that subset of stakeholders who should optimally develop metering skills. Hart, Shleifer, and Vishny (1997) and Glaeser and Shleifer (2001) use the property rights theory of ownership (Grossman and Hart 1986; Hart and Moore 1990) to explain government ownership and nonprofits, respectively. That theory sees ownership as conferring residual control rights, which alter threat points and therefore payoffs in ex post bargaining, thereby affecting ex ante investment. My work is in the line of the property rights theory, from which it nonetheless differs in having ownership confer not the right to use assets but that to set managerial incentives. That right is residual, in the sense that owners can alter the power of incentives at all times, subject to satisfying the manager’s participation constraint. It is this last feature, the ability ex post to modify the terms of the compensation contract, that distinguishes my work from the incentives theory of ownership (Holmstrom and Milgrom 1991, 1994), which sees these terms as fixed.9 Despite this difference, my work is also in the line of the incentives theory, with which it shares a focus on managerial incentives. As a result, the managers are not the property rights theory’s “drone employees (who own nothing and hence, […], face no incentives and so do nothing)” (Gibbons 2005, p. 206); instead, the managers “face incentives, so they [do not] act like drones” (Gibbons 2005, p. 207). This implies that my analysis may be particularly appropriate for those organizations for which human capital is important: the manager in my model exercises judgement and enjoys discretion.10 2. Model Consider a firm that has resources B > 0 which it invests at time 0. The firm allocates resources L⩾0 to safe investment and B−L⩾0 to risky investment. The former has return a > 1 with probability 1, the latter return A > a with probability pr, 0<pr<1. Firm (gross) payoff K at time 1 has expectation E[K]=prA(B−L)+aL and variance var[K]=A2(B−L)2prpu, where pu=1−pr.11 Risky investment has higher expected return than does safe investment, prA>a, but it also involves costs that safe investment does not: (1) its prospects for success must be evaluated at a cost κ(B−L)2, (2) it imposes a negative externality −Θ(B−L), Θ>0, on one or many stakeholders of the firm, and (3) it requires capital.12 An example of a negative externality is the loss suffered by a customer when the quality of a firm’s products are somehow deficient; stakeholders are providers of capital, labor, or other supplies to the firm or are purchasers of firm products. Capital serves to bond the firm’s fulfillment of the numerous obligations that the undertaking of a project generally entails (Barzel and Suen 1997): employees’ salaries must be paid, suppliers’ bills honored, lenders’ loans serviced, and customers’ after-sales service provided.13 If the firm has little or no capital, low payoff realizations may jeopardize the firm’s ability to fulfill these obligations, possibly deterring potential stakeholders from transacting with the firm in the first place. I assume capital is proportional to the standard deviation of firm payoff sd[K]=A(B−L)prpu≡ρ(B−L): the wider is the range of possible payoffs, the greater is the extent to which firm payoff may fall short of firm obligations, the more capital is needed to make up for that shortfall.14 Assume that the firm’s owners are unable themselves to evaluate and make the investments L and B – L. They therefore hire a manager to do so on their behalf. Neither the evaluation nor the investment is contractible, in contrast to payoff, which is contractible to the owners and the manager.15 The manager therefore must be provided with payoff-dependent incentive compensation to be induced to evaluate and make investments. Let the manager’s compensation be β1K+β0, where the pay-for-performance parameter β1, β1>0, measures the power of incentives; β0 is the fixed component of compensation. I assume that both owners and the manager are risk-neutral; their concern with risk extends only in so far as it affects the cost of evaluating risky investment and the amount of capital to be provided. By analogy to the assumption that the evaluation and the making of investment are not contractible, I assume that the use of capital and the extent of the externality are not, either.16 Finally, I assume no wealth constraints. My purpose is to distinguish the identity of the owners of the firm from among the various stakeholders of the firm: shareholders when the stakeholders who should be owners are the providers of equity capital; workers when they are the providers of labor; suppliers when they are the providers of parts or other goods procured by the firm; and customers when they are the purchasers of firm products. What distinguishes owners from other stakeholders is that they, and they alone, have the right to determine the properties (β0,β1) of the manager’s compensation contract; this is true at all times, so that even a compensation contract initially agreed on subsequently can be altered by the owners, subject to satisfying the manager’s participation constraint. As will become apparent in Section 3 below, this provides the owners with an opportunity to profit at the expense of other firm stakeholders—an ex post benefit that generally must be paid for ex ante. Relatedly, only owners can contract firm payoff K with the manager. The rationale for allocating these privileges to owners alone is that ownership’s rights of control provide owners with the opportunity to manipulate both the parameters of the manager’s compensation contract and firm payoff, again subject to satisfying the manager’s participation constraint. An attempt on the part of nonowning stakeholders to condition a contract with the firm on the manager’s compensation contract or on firm payoff therefore will be manipulated by owners to their own advantage.17,18 Shareholders are stakeholders that are specialized in the provision of equity capital; that is all that they do, but they do it at a generally lower cost than other stakeholders. I denote Ψ, Ψ> 0, the cost of capital to shareholders, Φ⩾Ψ the cost of capital to other stakeholders.19 Unlike shareholders, other stakeholders may supply an input (other than equity capital) or purchase an output in addition to providing capital; that Φ⩾Ψ implies that (shareholder) specialization has both a benefit (shareholders provide capital at a lower cost than do other stakeholders) and a cost (shareholders provide only capital, unlike other stakeholders). Owners may but need not be providers of capital: it is possible for a firm to be owned by stakeholders other than shareholders, yet for shareholders to provide the equity capital; this is the case for a firm financed by nonvoting, preferred stock. The assumption that payoff is contractible only to the owners and the manager precludes the use of payoff-dependent common stock when shareholders are not the owners: owners would manipulate payoff K to minimize payments to common shareholders. Although manipulation is also possible in the case of preferred stock financing, manipulation likely serves to delay rather than to decrease payments to preferred shareholders: the fixed dividends of preferred stock are cumulative, unlike the variable dividends of common stock. Some formalism may help at this stage.20 Referring to stakeholders other than shareholders simply as stakeholders, I compare the objective functions of various classes of owners, distinguishing between the two cases where owners do and do not provide equity capital; I identify the corresponding externalities. I start with the case of first-best, in which the externality is taken into account and capital is provided by its lowest cost supplier, namely shareholders. The objective function in such case is   E[K]−Ψsd[K]−κ(B−L)2−Θ(B−L)=prA(B−L)+aL−Ψρ(B−L)−κ(B−L)2−Θ(B−L). (1) When shareholders are owners, the objective function is   E[K]−Ψsd[K]−(β1E[K]+β0)=prA(B−L)+aL−Ψρ(B−L)−κ(B−L)2, (2) where I have used the fact that the fixed component of compensation β0 serves to allocate the cost of evaluation to the owners.21 Shareholders do not take the negative externality −Θ(B−L) into account in maximizing their objective function, for that externality is not contractible. This does not mean that shareholders are not affected by the externality, for shareholders may need to compensate stakeholders for the externality as a condition for stakeholders to be willing to transact with the firm. What it does mean is that shareholders cannot commit to accounting for that externality in their setting of the manager’s compensation contract. When stakeholders are owners and provide equity capital, the objective function is   prA(B−L)+aL−Φρ(B−L)−κ(B−L)2−Θ(B−L); (3) this recalls the first-best, except in that stakeholders generally have a higher cost of capital than do shareholders: Φ⩾Ψ. Finally, when stakeholders are owners but capital is provided in the form of nonvoting preferred stock, the objective function is   prA(B−L)+aL−κ(B−L)2−Θ(B−L); (4) in a somewhat parallel fashion to the case of shareholder ownership, stakeholders do not take the cost of capital Ψρ(B−L) into account in maximizing their objective function. Preferred shareholders naturally require compensation for providing capital, but stakeholders cannot commit to accounting for capital provided in their setting of the manager’s compensation contract. I now turn to the formal analysis of the model. 3. Preliminary Results I start with the first-best. Risky and safe investments maximize (1)   MaxB−L,LprA(B−L)+aL−Ψρ(B−L)−κ(B−L)2−Θ(B−L), with the sum of these two investments equal to resources B. The maximization problem is equivalent to   MaxB−L(prA−a)(B−L)−Ψρ(B−L)−κ(B−L)2−Θ(B−L), (5) where I have removed the constant term aB. First-best risky and safe investment are22  (B−L)FB=prA−a−(Ψρ+Θ)2κ (6) and   LFB=B−(B−L)FB. The corresponding payoff is   VFB=aB+[prA−a−(Ψρ+Θ)]24κ; (7) the ratio with the quadratic term represents the value added by risky investment.23 I now introduce the agency problem. Recalling that only (gross) payoff K is contractible, the manager’s problem is   MaxB−L,Lβ1[prA(B−L)+aL]+β0−κ(B−L)2 (8)  ⇔MaxB−Lβ1[(prA−a)(B−L)+aB]+β0−κ(B−L)2; (9) it has solutions   B−L=β1(prA−a)2κ (10) and L the balance. Assuming owners have all bargaining power in their negotiations with the manager, and normalizing the manager’s reservation utility to zero, I have   β0=κ(B−L)2−β1[(prA−a)(B−L)+aB]. (11) Initially consider the case of shareholders ownership. As noted in Section 2, shareholders do not take the noncontractible externality −Θ(B−L) into account in maximizing their objective function (2); this is in contrast to the cost of the capital they provide. Shareholders solve   Maxβ1prA(B−L)+aL−β1[prA(B−L)+aL]−β0−Ψρ(B−L) (12)  ⇔Maxβ1(prA−a)(B−L)−Ψρ(B−L)−κ(B−L)2, (13) where I have substituted β0 from (11) and again removed the constant term aB. Using (10), I can solve for24 24 Specifically, I substitute (10) into (13) and solve for   β1SH=arg⁡max⁡β1β1(prA−a)22κ−Ψρβ1(prA−a)2κ−κ[β1(prA−a)2κ]2.  β1SH=1−ΨρprA−a, (14) with corresponding risky investment25  (B−L)SH=prA−a−Ψρ2κ. (15) The comparison of (15) with (6) reveals that shareholders incentivize the manager to make too large a risky investment. This is not without cost to shareholders, for stakeholders may not transact with the firm unless compensated for the negative externality −Θ(B−L)SH=−Θ(prA−a−Ψρ)/(2κ). Firm value under (specialized) shareholders’ ownership is   VSH=aB+[prA−a−Ψρ]24κ−Θ(prA−a−Ψρ2κ), (16) which can easily be shown to be lower than VFB in (7).26 26 Use (7) and (16) to write   VFB=[prA−a−(Ψρ+Θ)]24κ=[prA−a−Ψρ]24κ+Θ24κ−2Θ(prA−a−Ψρ)4κ>[prA−a−Ψρ]24κ−Θ(prA−a−Ψρ2κ)=VSH. Shareholders, who as owners are endowed with all bargaining power and thus receive all value created, are made worse off by their inability to commit to taking stakeholders’ externality into account. Investment is not contractible, and the compensation contract cannot be used as a commitment device toward stakeholders because shareholders in their capacity as owners are the only party able to negotiate with the manager over the terms of the compensation contract. Thus, a commitment, on the shareholders’ part, to incentivize the manager to make the first-best investment (B−L)FB in (6) by setting pay-for-performance parameter (PPP) β1FB=1−[(Ψρ+Θ)/(prA−a)] is not credible, because shareholders as owners can renegotiate the terms of the compensation contract (β0,β1) with the manager at all times, subject to satisfying the manager’s participation constraint. An initial setting of β1FB is increased to (14) by shareholders for whom the externality becomes a fixed cost following agreement with stakeholders on the payment of compensation Θ(B−L)FB for the externality. Three observations are in order at this point. First, including the compensation for the externality in the manager’s problem (8)—having him or her maximize β1[prA(B−L)+aL−Θ(B−L)SH]+β0−κ(B−L)2 instead of the objective function in (8)—fails to alter the manager’s choice of risky investment for the same reason as such inclusion fails to alter the owners’ choice of PPP β1: the externality is a fixed cost to both the manager and the owners. Second, whereas firm value is higher than the first-best under shareholder ownership if no compensation is paid to stakeholders for the externality, combined shareholder and stakeholder payoff is nonetheless lower.27 27 Formally,   aB+[prA−a−Ψρ]24κ>aB+[prA−a−(Ψρ+Θ)]24κ>aB+[prA−a−Ψρ]24κ−Θ(prA−a−Ψρ2κ). Optimal organizational ownership therefore does not depend on whether compensation is paid for the externality. Third, first-best could be achieved if payoff K were contractible to stakeholders too: a contract that sees shareholders compensate stakeholders for the externality through the payment of a payoff-dependent amount Θ(K−aB)/(prA−a) is equivalent to a contract on the externality.28 28 To see this, note that   E[Θ(K−aB)prA−a]=Θ{pr[A(B−L)+aL−aBprA−a]+(1−pr)[aL−aBprA−a]}=Θ{prA(B−L)+aL−aBprA−a}=Θ{(prA−a)(B−L)+aB−aBprA−a}=Θ(B−L). This, along with the earlier discussion in Section 2, motivates the assumption that payoff is contractible only to the owners and the manager. Stakeholder ownership naturally results in stakeholders taking the externality into account, which in fact no longer is “external” in this case, but payoff is decreased by stakeholders’ generally higher cost of capital Φ⩾Ψ in the case in which stakeholders also provide the capital. Firm value in such case is   VST=aB+[prA−a−(Φρ+Θ)]24κ: (17) analogous to (7) but with Φ replacing Ψ. The same holds true of risky investment (B−L)ST and PPP β1ST, which are29  (B−L)ST=prA−a−(Φρ+Θ)2κ (18) and   β1ST=1−Φρ+ΘprA−a. (19) This last case is that where stakeholders are owners but capital is provided by shareholders in the form of nonvoting preferred stock. The analysis is to some extent the mirror image of that of shareholder ownership: stakeholders’ externality is internalized, and shareholder capital provision becomes the externality, for stakeholders cannot commit to taking the use of capital into account in maximizing their objective function (4). I therefore have   β1ST,NV=1−ΘprA−a, (20)  (B−L)ST,NV=prA−a−Θ2κ, (21) and   VST,NV=aB+[prA−a−Θ]24κ−Ψρ(prA−a−Θ2κ). (22) The analogy with (14), (15), and (16), respectively, is immediate; the last term in (22) constitutes the dividend Ψρ(B−L)ST,NV paid to preferred shareholders, the analogue to Θ(prA−a−Ψρ)/(2κ)=Θ(B−L)SH in (16). I now wish to compare VSH, VST, and VST,NV. It is clear that all are smaller than VFB, with equality VST=VFB at Φ=Ψ.30 While VST is clearly larger than resources B, I assume this is also the case for VSH and VST,NV: a form of ownership that decreases firm value below initial resources B clearly is not considered. I first show31 Lemma 1. VSH>VST,NVif and only if Ψρ>Θ. The intuition for the result in Lemma 1 is simple. Both shareholder ownership and stakeholder ownership combined with nonvoting preferred stock introduce a distortion, due to the failure to account for stakeholder externality in the first case and for nonvoting shareholder capital in the second.32 When Ψρ>Θ, the second distortion is larger, and shareholder ownership dominates; when in contrast Ψρ<Θ, the first distortion is larger and stakeholder ownership combined with nonvoting preferred stock dominates. Lemma 1 implies that I need only compare stakeholder ownership to shareholder ownership when Ψρ>Θ, to stakeholder ownership combined with nonvoting preferred stock when Ψρ<Θ. I define the maximum cost of stakeholder capital consistent with positive risky investment by33 33 If Φ>Φmax⁡, then   (B−L)ST=prA−a−(Φρ+Θ)2κ<prA−a−(prA−a−Θρρ+Θ)2κ=0.  Φmax⁡≡prA−a−Θρ. I show Proposition 1. When Ψρ>Θ, there exists a Φ∗,SH, Ψ<Φ∗,SH<Φmax⁡, such that VSH≶VSTfor Φ≶Φ∗,SHif and only if Θ<Φmax⁡ρ−Ψρ; VSH<VST ∀Φ∈[Ψ,Φmax⁡]otherwise. When Ψρ<Θ, there exists a Φ∗,ST,NV, Ψ<Φ∗,ST,NV<Φmax⁡, such that VST,NV≶VSTfor Φ≶Φ∗,ST,NVif and only if Ψρ<Φmax⁡ρ−Ψρ; VST,NV<VST ∀Φ∈[Ψ,Φmax⁡]otherwise. The threshold costs of stakeholder capital Φ∗,SHand Φ∗,ST,NVboth increase in Θ. The intuition for the result in Proposition 1 is as follows. Firm value under stakeholder ownership VST is largest for Φ=Ψ, but decreases as the cost of stakeholder capital Φ increases toward Φmax⁡; whether VST eventually decreases below its value under alternative forms of ownership, shareholder ownership if Ψρ>Θ and stakeholder ownership combined with nonvoting preferred stock otherwise, depends on the importance of the distortion each of these two forms introduces relative to stakeholder ownership’s higher cost of capital. If Θ<Φmax⁡ρ−Ψρ, the distortion under shareholder ownership—the failure to account for stakeholder externality—is not overly high and there is a threshold cost of capital Φ∗,SH above which shareholder ownership dominates. If Ψρ<Φmax⁡ρ−Ψρ, the distortion under stakeholder ownership combined with nonvoting preferred stock—the failure to account for nonvoting shareholder capital—is not overly high and there is a threshold cost of capital Φ∗,ST,NV above which stakeholder ownership combined with nonvoting preferred stock dominates. Both Φ∗,SH and Φ∗,ST,NV increase in stakeholder externality Θ, reflecting stakeholder ownership’s better accounting for stakeholder externality: VST, VSH, and VST,NV all decrease in Θ, but VST decreases more slowly than do VSH and VST,NV. I now turn to the case of a positive externality, which I represent by Θ<0 as opposed to Θ>0 as has thus far been assumed; this makes the externality −Θ(B−L) positive as desired. An example of a positive externality provided by risky investment is the knowledge created by investment in research and development (R&D), which often profits not only the firm having conducted the R&D, but also other firms such as its customers and its suppliers. An important difference with the case of negative externality is that, whereas stakeholders previously required compensation for the (negative) externality in order to transact with the firm in the case of shareholder ownership, they are now willing to pay for the (positive) externality obtained from such transaction, −Θ(B−L)SH>0. From (20), I have β1ST,NV>1 for Θ<0. Despite such high-powered incentives being unrealistic, I allow the PPP β1ST,NV to be larger than one because I wish to maintain as much symmetry as possible between the analyses of the two cases of negative and positive externality. I thereby isolate the impact of the change from negative to positive externality to the sign of the term Θ in firm values VST, VSH, and VST,NV. Proposition 2. VSH>VST,NVif and only if Ψρ>−Θ. When Ψρ>−Θ, there exists a Φ∗,SH, Ψ<Φ∗,SH<Φmax⁡, such that VSH≶VSTfor Φ≶Φ∗,SH. When Ψρ<−Θ, there exists a Φ∗,ST,NV, Ψ<Φ∗,ST,NV<Φmax⁡, such that VST,NV≶VSTfor Φ≶Φ∗,ST,NVif and only if Ψρ<Φmax⁡ρ−Ψρ; VST,NV<VST ∀Φ∈[Ψ,Φmax⁡]otherwise. The threshold cost of stakeholder capital Φ∗,SHincreases in Θif and only if −Θ<Φ∗,SHρ−Ψρ; the threshold cost Φ∗,ST,NVincreases in Θ. The intuition for the results in Proposition 2 is similar, but not identical, to those in Lemma 1 and Proposition 1. The distortions introduced by shareholder ownership and stakeholder ownership combined with nonvoting preferred stock are still to be compared, but the former now involves a positive ( −Θ>0) rather than a negative ( −Θ<0) externality; this explains the transformation of the condition Ψρ>Θ in Lemma 1 into Ψρ>−Θ. That the externality is positive implies that stakeholders are willing to pay the firm in order to benefit from the positive externality transactions with the firm entail. This explains the unconditional existence of Φ∗,SH, where Proposition 1 required Θ<Φmax⁡ρ−Ψρ for Φ∗,SH to exist: there is no longer a payment to stakeholders to be compared to a differential in capital costs, but a payment from stakeholders to be added to the capital cost advantage of shareholder ownership.34 It also explains why the threshold cost of stakeholder capital Φ∗,SH is no longer monotone in the externality Θ. Although the intuition used in the case of negative externality applies when −Θ>Φ∗,SHρ−Ψρ, that is, when the externality is large, this is no longer the case when the externality is small, −Θ<Φ∗,SHρ−Ψρ. The lesser importance of accounting for a smaller externality increases the relative importance of the payment |Θ|(B−L)SH received for that externality under shareholder ownership; an increase in |Θ| increases that payment; it therefore increases the range [Φ∗,SH,Φmax⁡] over which shareholder ownership dominates; ∂Φ∗,SH/∂(−Θ)<0, that is, ∂Φ∗,SH/∂Θ>0, as a result. I conclude the present section by noting that the results are unchanged when the externality is associated with safe rather than risky investment; only the interpretation of the externality changes, in that a negative externality of risky investment becomes a positive externality of safe investment, and a positive externality negative.35 35 To see this, use (5) to write   arg⁡max⁡B−L(prA−a)(B−L)−Ψρ(B−L)−κ(B−L)2−Θ(B−L)=arg⁡max⁡B−L(prA−a)(B−L)−Ψρ(B−L)−κ(B−L)2−ΘB+ΘL=arg⁡max⁡B−L(prA−a)(B−L)−Ψρ(B−L)−κ(B−L)2+ΘL, where I have removed the constant term −ΘB. Contrast the minus sign preceding the externality of risky investment Θ(B−L) with the plus sign preceding that of safe investment ΘL. I associate externalities with risky rather than safe investment because this better describes the various settings I consider in Section 4. 4. Ownership Forms I now apply the results of Section 3 to provide a possible, unified explanation for a wide variety of ownership forms that are observed in practice. To a large extent, these correspond to various forms of the externality −Θ≶0 and its relation to stakeholder and shareholder costs of capital Φ and Ψ, respectively. Before doing so, I briefly recall the results of Section 3. Stakeholder ownership dominates for stakeholder cost of capital close to shareholder cost capital, Φ close to Ψ. As stakeholder cost of capital increases, stakeholder ownership may be replaced by shareholder ownership if the externality, positive or negative, is less important than is the shareholder cost of capital, |Θ|<Ψρ; stakeholder ownership is retained, possibly to be supplemented by outside equity in the form of nonvoting preferred stock, if the externality is more important than the shareholder cost of capital, |Θ|>Ψρ. 4.1 Founder, family, and dispersed ownership It is generally the case that founders, and their descendants to a perhaps lesser extent, derive valuable private benefits ( −Θ>0) from their control of the firms they or their forebears have founded.36 In countries where the possibly limited development of equity markets fails to decrease the cost of outside, public equity ( Ψ) markedly below that of private equity ( Φ), there may be little incentive to abandon private ownership for a public listing (Proposition 2). This may explain the prevalence of private ownership even among large firms across much of the world. Where the greatly increased size or riskiness of a firm makes recourse to outside, public equity unavoidable, founders and families that enjoy large private benefits ( −Θ>Ψρ) attempt to retain these by restricting outside shareholders’ voting rights (dual-class shares), or denying them altogether (nonvoting shares); these take the form of preferred shares in my model of noncontractible payoff K. Only where the cost of outside equity is of paramount importance ( −Θ<Ψρ) does a firm choose outside, dispersed shareholder ownership, with previously controlling shareholders relinquishing control, that of setting the properties of the manager’s compensation contract (β0,β1) in particular. Where control is relinquished through the unification of what were previously different classes of shares, the compensation often received by previously controlling shareholders in such case may be expected to be related to the decline in private benefits, from −Θ(B−L)ST,NV to −Θ(B−L)SH.37 37 That 0<−Θ<Ψρ implies that   (B−L)ST,NV=prA−a−Θ2κ>prA−a−Ψρ2κ=(B−L)SH, where I have used (15) and (21). 4.2 Partnerships Where tacit, noncodifiable knowledge makes important to a firm’s success the employees in whom such knowledge is embedded, like in some aspects of investment banking, for example (Morrison and Wilhelm 2007, p. 88), then disagreements may arise between the firm and the employees as to the use of the employees’ human capital.38 For example, when deciding which initial public offerings to underwrite and which to turn down, a decision that can have important reputational consequences (Morrison and Wilhelm 2007, p. 83), an investment bank will not necessarily arrive at the same conclusion as the investment bankers involved in the issue: the bankers’ reputation, however closely tied to that of the investment bank, is nonetheless distinct and will generally not be affected in the exact same way as that of the bank regardless of whether the issue succeeds or fails.39 There is therefore an externality −Θ≶0 pertaining to individual bankers’ reputation and affected by the bank’s decision of which issues to underwrite. Propositions 1 ( −Θ<0) and 2 ( −Θ>0) suggest ownership by investment bankers in such case if the cost of banker capital is markedly above that of specialized shareholder; this is the investment banking partnership. Where increased needs for capital raise its cost to investment bankers well above that to specialized shareholders, then the investment bank may abandon the partnership form for dispersed shareholder ownership or investment banker ownership combined with nonvoting preferred stock, depending on the relative importance of the externality and the cost of capital, |Θ|≶Ψρ (Lemma 1 and Proposition 2). Shareholder ownership involves compensation |Θ|(B−L)SH, to be paid to bankers in case of negative externality, by bankers in case of positive.40 Investment banker ownership with nonvoting preferred stock involves the payment of preferred dividend Ψρ(B−L)ST,NV. Much the same can be said of legal partnerships, with senior lawyers in place of senior investment bankers, and decisions about which court cases to take on or to turn down instead of decisions about new issues. That fewer legal partnerships have abandoned the partnership form than have investment banking partnerships attests to the lesser importance of (financial) capital to the former.41 4.3 Mutual banks and insurance companies By their very nature, banks are highly leveraged institutions; this gives rise to a risk-shifting problem, in which shareholders protected by limited liability may wish to engage in highly risky investment: the gains are mainly theirs because the interest on deposits is fixed, the losses are mainly depositors’ because of limited liability. Risky investment thus imposes a negative externality −Θ(B−L)SH, Θ>0, on depositors, for which they will of course require compensation for them to be willing to entrust their deposits to a bank. If the cost of capital Φ to depositors—the rate of return they require for providing the bank’s equity in addition to its deposits—is not markedly above that to shareholders Ψ, then Proposition 1 suggests that it is optimal for depositors to own the bank, that is, for the bank to be a mutual. Hansmann (1996, pp. 246–51) argues that this explains the ubiquity of mutually owned banks in the nineteenth century United States.42 He further notes (pp. 254–8) that improvements in bank regulation, which decreased the extent of the risk-shifting problem, account for much of the abandonment of the mutual form.43 A very similar argument can be made for savings and loans associations, building societies in Britain, and insurance companies (see O’Hara 1981; Valnek 1999; Mayers and Smith 1981, respectively), recalling that insurance policyholders’ claims are not unlike bank depositors’.44 4.4 Government and customer ownership The nineteen-eighties and nineties saw a wave of privatizations, not least in the United Kingdom, whose government under Prime Minister Margaret Thatcher can fairly be said to have both initiated and sustained that movement. Yet, by the first decade of the present century, many privatized utilities in the United Kingdom had reverted to some form of public ownership, either by a utility’s customers or by the government, the latter “essentially a form of consumer cooperative” (Hansmann 2013, p. 897). That reversal was in no small part the result of consumer dissatisfaction with the quality of the services provided by the privatized utilities, culminating with public anger over a number of fatal accidents that involved Railtrack, the then shareholder-owned, now defunct rail infrastructure (track, signaling, tunnels, bridges, railroad crossings, …) provider in the United Kingdom. Kay (2003, 2010) attributes the decline in service quality that followed privatization to a decrease in maintenance expenses. He argues that a judgment call is involved in determining the funds that a utility should allocate to maintenance and that a shareholder-owned utility will choose a different, lower level of maintenance expenses than would a utility owned by its customers or the government. This is because not all benefits of high maintenance, or costs of low maintenance, can be contracted by the utility and its customers; there is a negative externality −Θ<0 associated with the allocation of funds away from maintenance toward other uses. Unlike the externalities thus far considered, utilities’ negative externalities need not involve compensation to (captive) customers, because utilities generally are (local) monopolies. Using the notation of this model, maintenance expenses can be identified with safe investment L and funds allocated to other uses with risky investment B – L—it is allocation away from maintenance that gives rise to the risk of accidents. Further identifying customer and government ownership with ownership by stakeholders, (15) and (18) imply that (B−L)SH>(B−L)ST: more is allocated to other uses under shareholder ownership; maintenance expenses are consequently lower, LSH<LST.45 Where the cost of externalities is deemed excessive, Θ>Ψρ, Proposition 1 suggests that shareholder ownership is eschewed in favor of stakeholder ownership—customer or government ownership—when the cost of stakeholder capital is low, Φ<Φ∗,ST,NV, in favor of stakeholder ownership combined with nonvoting preferred stock when the cost of stakeholder capital is high, Φ>Φ∗,ST,NV. That the latter form rarely is observed suggests that, even at its maximum, the spread between stakeholder and shareholder cost of capital remains moderate, Φmax⁡ρ−Ψρ<Ψρ.46 46 Recall from Proposition 1 that a necessary condition for Φ∗,ST,NV to exist is that Φmax⁡ρ−Ψρ>Ψρ.,47 Summarizing, it is perhaps fair to say that the predictions of my model are consistent with the British experience of utilities privatization, regarding both decreased maintenance during and eventual abandonment of shareholder ownership. Further support for my model can be found in the controversy surrounding the compensation of privatized utilities’ managers, the so-called “fat cats.” As utilities’ profits soared in the wake of privatization, so did their managers’ compensation, a reflection both of these higher profits and of dramatically increased PPP. That privatization increased PPP is immediate from (14) and (19), recalling that I represent a negative externality by −Θ<0, Θ>0 in this model. That privatization increased profits requires comparing profits gross of the cost of the negative externalities—captive customers have no choice but to accept these—under both shareholder and stakeholder ownership. I therefore compare VSH+Θ(B−L)SH with VST+Θ(B−L)ST.48 The terms Θ(B−L)SH and Θ(B−L)ST represent the cost of the externalities in the two cases of shareholder and stakeholder ownership, respectively; they are added back because they are not in fact paid. It is easy to show that VSH+Θ(B−L)SH>VST+Θ(B−L)ST: profits are higher under shareholder ownership, an increase in part made possible by decreased maintenance expenses, LSH<LST.49 49 Formally, use (15), (16), (17), and (18) to write   VST+Θ(B−L)ST=aB+[prA−a−(Φρ+Θ)]24κ+Θ[prA−a−(Φρ+Θ)2κ]=aB+[prA−a−Φρ]24κ+Θ24κ−Θ[prA−a−Φρ2κ]+Θ[prA−a−(Φρ+Θ)2κ]=aB+[prA−a−Φρ]24κ−Θ24κ<aB+[prA−a−Ψρ]24κ=VSH+Θ(B−L)SH.,50 4.5 Worker cooperatives A situation of involuntary unemployment introduces a difference between the prevailing wage and the shadow cost of labor, with the former higher than the latter (Salanié 2000, p. 44). That difference introduces an externality to firms’ employment decisions: a firm’s decision to hire an involuntarily unemployed worker has a positive externality equal to the difference between the wage and the shadow cost, a firm’s decision to fire a worker in a situation of prevailing involuntary unemployment has a negative externality of the same magnitude. A shareholder-owned firm will not take such externalities into account, except in the unlikely case in which it can pay new hires a lower wage than paid to existing workers doing identical work, or make continued employment conditional on the lowering of existing wages only for those workers who would otherwise be fired. In contrast, a worker-owned firm is willing to accept the lower profits associated with higher employment because it recognizes the benefit from such policy accruing to workers, the externality that equals the difference between the wage and the shadow cost of labor. Where that externality is important, |Θ|>Ψρ, in regions with widespread un- or underemployment, one can expect workers to form cooperatives that will account for the externality. Whether these cooperatives’ capital will be provided by the workers themselves or by outside investors in the form of nonvoting preferred stock in such case depends on whether the cost of capital to workers Φ is below or above the threshold cost of capital Φ∗,ST,NV (Propositions 1 and 2). The relative paucity of worker cooperatives, even in times of difficult employment conditions, is not easy to reconcile with this model. It may be attributable to the heterogeneity of workers’ interests (Hansmann 1996, chapter 6): there is not one but many Θ’s, corresponding to different categories of workers, whose possibly diverging interests may compromise the optimality of worker ownership.51,52 4.6 Farm marketing, processing, and supply cooperatives Many agricultural products are sold to highly concentrated middlemen and processors, whose monopsony power, if exercised, keeps prices and production well short of welfare-maximizing levels (Hansmann 1996, pp. 122–3). This difference constitutes a positive externality ( −Θ>0) to raising prices and inducing production above their monopsony levels. Where that externality is important, −Θ>Ψρ, and in the absence of too large a cost of capital disadvantage to farmers, Ψ⩽Φ<Φ∗,ST,NV, Proposition 2 suggests that farmer ownership, in the form of farm marketing and processing cooperatives, dominates shareholder ownership. A very similar rationale can be provided for the existence of farm supply cooperatives, with monopsonistic purchase replaced by monopolistic supply (Hansmann 1996, pp. 150–1). 4.7 Vertical and horizontal control I have considered various forms of ownership, corresponding to different kinds of stakeholders, but have thus far neglected ownership of one firm by another firm, that other firm being the stakeholder of interest. It is to such ownership that I now turn, that is, to vertical and horizontal control. My starting point is Barzel’s (2002, 2013) observation that vertical integration serves to ensure product quality through the lowering of the power of supplier managerial incentives to a level consistent with the provision of that quality. More concretely, consider a supplier who can provide high-quality products that function in all circumstances, or lower quality products that function only with some probability. Such products may nonetheless be desired by the buyer if produced at lower prices or in higher quantities. Suppose there is a cost to determining the optimal level of quality and that, if the product fails to function as intended or at all, the cost of malfunction will in the first instance be borne by the buyer. Using the notation of this model, resources invested in providing the high quality alternative may be identified with L, those invested in developing the lower quality alternative with B – L, the probability that the lower quality products nonetheless function satisfactorily with pr, the cost of evaluating the trade-off between price/quantity and quality with κ(B−L)2, and the cost of product malfunction to the buyer with Θ(B−L), Θ>0. From (14), (15), (18), and (19), I know that an independent, shareholder-owned supplier sets managerial incentives β1SH=1−[(Ψρ)/(prA−a)] for resources invested in the high-quality alternative LSH=B−[(prA−a−Ψρ)/(2κ)], whereas the buyer having acquired control of the supplier with its own capital sets lower-powered incentives β1ST=1−[(Φρ+Θ)/(prA−a)]<β1SH, for higher resources invested in the high-quality alternative LST=B−[(prA−a−Φρ−Θ)/(2κ)]>LSH. If the buyer instead acquires control of the supplier with outside equity, raised in the form of nonvoting preferred stock, I know from (20) and (21) that the buyer sets incentives β1ST,NV=1−[Θ/(prA−a)] for resources invested in the high-quality alternative LST,NV=B−[(prA−a−Θ)/(2κ)].53 Whether vertical control is in fact desirable depends on the relative importance of quality and buyer and shareholder cost of capital. Lemma 1 and Proposition 1 together suggest that vertical control is chosen if either (1) Θ>Ψρ or (2) Θ<Ψρ and Φ<Φ∗,SH; vertical control is financed with nonvoting preferred stock if Θ>Ψρ and Φ>Φ∗,ST,NV, with buyer own capital otherwise.54 Condition (1) describes a situation in which quality is paramount and condition (2) one in which it is not, but the buyer’s cost of capital is sufficiently close to shareholders’ that buyer control and financing nonetheless dominate; this is because of buyer ownership’s better accounting for the externality, however modest that externality may be.55 I have assumed that the buyer is not itself shareholder-owned, Φ⩾Ψ. If it is, and has cost of capital Φ=Ψ, then it is clear from Proposition 1 that buyer control financed with own capital dominates, indeed attains first-best.56 Given the prevalence of shareholder ownership, at least among large firms, that vertical control attains first-best suggests widespread such control: the slightest externality in the relation between any two firms implies ownership of these firms by the same shareholders. Recognizing that competition generates what is perhaps the most widespread externality, competitors are owned by the same shareholders; this is horizontal control. Thus, if taken to the limit, this analysis suggests that all interacting firms are owned by the same shareholders who set the power of managerial incentives so as to minimize negative externalities, not least competition, among these firms.57 Before I deem such conclusion nonsensical, it is worth noting that both implications are partially borne out by the empirical evidence: many of the world’s large corporations are owned by a relatively small number of financial institutions (Vitali, Glattfelder, and Battiston 2011); at least some of these are believed to have directed their portfolio firms to settle lawsuits that pitted one firm against another (Hansen and Lott, 1996, p. 47) and to have incentivized portfolio firm managers in such manner as to soften competition among these firms (Azar, Raina, and Schmalz 2016; Azar, Schmalz, and Tecu 2016; Antón et al. 2016). I discuss this and related evidence in Section 7. Still, the world this model predicts in the case Φ=Ψ is not the one we observe. Why not? One possibility is that the coordination the preceding argument requires cannot be achieved simply through the setting of managerial incentives: it may be the case that accounting for externalities requires a level of coordination between firms that is so detailed as to require integration of these firms, vertical or horizontal.58 Section 5 thus turns to integration. 5. Integration Consider two projects that can be undertaken either separately by two independent firms or jointly by a single integrated firm. Integration has two benefits and one cost: (1) externalities can be accounted for, an option that may not be available to two independent firms and, in the case of competitive externalities in particular, may be illegal under antitrust law; (2) equity capital can be combined; this provides an opportunity to economize on costly capital as compared to the case of two independent firms; and (3) managerial incentives, for top management at least, must be provided at the level of the single integrated firm; this precludes the tailoring of incentives to the specific characteristics of each of the two projects, an option available to each of the two independent firms. I show in what follows that the desirability of integration depends on the net effect of these benefits and this cost. Index each project by i, i∈{1,2}, to write: Ai, ai, pr,i, pu,i, Bi, Li, κi, Θi, and ρi; denote ϱ the correlation between the two projects. When the two projects are undertaken jointly within the integrated firm, that firm’s payoff has variance   var[K1+K2]=ρ12(B1−L1)2+ρ22(B2−L2)2+2ϱρ1ρ2(B1−L1)(B2−L2), with capital required sd[K1+K2]. The variance of the payoff of project i undertaken separately by independent firm i is   var[Ki]=ρi2(Bi−Li)2. The total capital required for the purpose of undertaking the two projects in two independent firms is therefore   sd[K1]+sd[K2]=ρ1(B1−L1)+ρ2(B2−L2)=ρ12(B1−L1)2+ρ22(B2−L2)2+2ρ1ρ2(B1−L1)(B2−L2)⩾ρ12(B1−L1)2+ρ22(B2−L2)2+2ϱρ1ρ2(B1−L1)(B2−L2)=sd[K1+K2], with equality at ϱ=1: diversification across projects within a single firm decreases costly capital requirements; this is a first benefit of integration (Barzel and Suen, 1997). The parameter Θi, i = 1, 2, indexes the externality that project i imposes on project j, j = 1, 2, j≠i. The externality imposed by i on j is therefore Θi(Bi−Li). The two externalities Θ1(B1−L1) and Θ2(B2−L2) are accounted for by the single integrated firm, whose owners surely are mindful of the impact the risky investment made into one project has on the other, but they are not accounted for by the two independent firms: I assume coordination requires integration. This accounting for externalities is a second benefit of integration. The cost of integration is the inability to tailor the integrated firm’s incentives to the characteristics of each project. Formally, while each independent firm i sets PPP β1,i=1−Ψρi/(pr,iAi−ai) from (14), the integrated firm sets PPP β1,I to solve   Maxβ1,I∑i=1,2{(pr,iAi−ai−Θi)(Bi−Li)+aiBi−κi(Bi−Li)2}−Ψρ12(B1−L1)2+ρ22(B2−L2)2+2ϱρ1ρ2(B1−L1)(B2−L2), (23) subject to   Bi−Li=β1,I(pr,iAi−ai)2κi. (24) Note that the same PPP β1,I is used to induce the two risky investments B1−L1 and B2−L2. Substituting (24) into (23), the latter becomes   Maxβ1,Iβ1,I[(pr,1A1−a1)22κ1+(pr,2A2−a2)22κ2−Θ1(pr,1A1−a1)2κ1−Θ2(pr,2A2−a2)2κ2]−β1,I2[(pr,1A1−a1)24κ1+(pr,2A2−a2)24κ2]−Ψβ1,I2ρ12(pr,1A1−a1)2κ12+ρ22(pr,2A2−a2)2κ22+2ϱρ1ρ2(pr,1A1−a1)κ1(pr,2A2−a2)κ2. (25) Differentiating and solving for β1,I, I obtain   β1,I=1−Θ1(pr,1A1−a1)κ1+Θ2(pr,2A2−a2)κ2(pr,1A1−a1)2κ1+(pr,2A2−a2)2κ2−Ψ(pr,1A1−a1)2κ1+(pr,2A2−a2)2κ2ρ12(pr,1A1−a1)2κ12+ρ22(pr,2A2−a2)2κ22+2ϱρ1ρ2(pr,1A1−a1)κ1(pr,2A2−a2)κ2. (26) I introduce the need for tailored incentives by assuming   Ψρ2+Θ2pr,2A2−a2=γΨρ1+Θ1pr,1A1−a1, (27) 1⩽γ⩽γmax⁡≡(pr,1A1−a1)/(Ψρ1+Θ1).59 There is no need for project-specific incentives at γ = 1, for the two projects in such case involve an identical trade-off between excess return pr,iAi−ai on the one hand and cost of capital and externality Ψρi+Θi on the other; γ can be no larger than γmax⁡, for (B2−L2)FB=[pr,2A2−a2−(Ψρ2+Θ2)]/(2κ2)<0 if that were the case. The combined value of the two independent firms is, from (16) and (27),60 60 The derivation of (28), (29), and (30) uses the equalities   pr,2A2−a2=(Ψρ2+Θ2Ψρ1+Θ1)pr,1A1−a1γ and   (pr,2A1−a2−Ψρ2−Θ2)2=(Ψρ2+Θ2Ψρ1+Θ1)2(pr,1A1−a1γ−Ψρ1−Θ1)2.  Π12(γ)≡a1B1+(pr,1A1−a1−Ψρ1)24κ1−Θ2(pr,2A2−a2−Ψρ2)2κ2+a2B2+(pr,2A2−a2−Ψρ2)24κ2−Θ1(pr,1A1−a1−Ψρ1)2κ1=a1B1+(pr,1A1−a1−Ψρ1−Θ1)24κ1−Θ124κ1+a2B2+(Ψρ2+Θ2Ψρ1+Θ1)2(pr,1A1−a1γ−Ψρ1−Θ1)24κ2−Θ224κ2. (28) The value of the integrated firm is, from (25) and (27),   ΠI(γ,ϱ)=a1B1+a2B2+β1,I2(1−β1,I2)(pr,1A1−a1)2[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]−β1,I2(pr,1A1−a1)[Θ1κ1+Θ2γκ2(Ψρ2+Θ2Ψρ1+Θ1)+Ψρ12κ12+ρ22γ2κ22(Ψρ2+Θ2Ψρ1+Θ1)2+2ϱρ1ρ2γκ1κ2(Ψρ2+Θ2Ψρ1+Θ1)], (29) with   β1,I=1−1pr,1A1−a111κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2×[Θ1κ1+Θ2γκ2(Ψρ2+Θ2Ψρ1+Θ1)+Ψρ12κ12+ρ22γ2κ22(Ψρ2+Θ2Ψρ1+Θ1)2+2ϱρ1ρ2γκ1κ2(Ψρ2+Θ2Ψρ1+Θ1)]. (30) Remark 1. ∂ΠI(γ,ϱ)/∂ϱ<0from (29) and using the envelope theorem. Substituting (30) into (29), I obtain   ΠI(γ,ϱ)=a1B1+a2B2+(pr,1A1−a1)24[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]+[Θ1κ1+Θ2γκ2(Ψρ2+Θ2Ψρ1+Θ1)+Ψρ12κ12+ρ22γ2κ22(Ψρ2+Θ2Ψρ1+Θ1)2+2ϱρ1ρ2γκ1κ2(Ψρ2+Θ2Ψρ1+Θ1)]24[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]−(pr,1A1−a1)2[Θ1κ1+Θ2γκ2(Ψρ2+Θ2Ψρ1+Θ1)+Ψρ12κ12+ρ22γ2κ22(Ψρ2+Θ2Ψρ1+Θ1)2+2ϱρ1ρ2γκ1κ2(Ψρ2+Θ2Ψρ1+Θ1)]. (31) I show Lemma 2. Consider the case ϱ=1. If  −[κ1κ2(Ψρ2+Θ2pr,1A1−a1)21+κ1κ2(Ψρ2+Θ2pr,1A1−a1)2](pr,1A1−a1−Ψρ1−Θ1)2κ1+Θ12κ1+Θ22κ2<0, (32) then ∃γ∗, 1<γ∗<γmax⁡ such that ΠI(γ,1)⩽Π12(γ) if and only if γ∗⩽γ⩽γmax⁡. Proposition 3. If  −[κ1κ2(Ψρ2+Θ2pr,1A1−a1)21+κ1κ2(Ψρ2+Θ2pr,1A1−a1)2](pr,1A1−a1−Ψρ1−Θ1)2κ1+κ1κ2Ψρ2+Θ2pr,1A1−a11+κ1κ2(Ψρ2+Θ2pr,1A1−a1)2[Ψρ2κ2(Ψρ2+Θ2pr,1A1−a1)+pr,1A1−a1−Ψρ1−Θ1κ1](4Ψρ2)+Θ12κ1+Θ22κ2<0, (33) then ∃ Sγ,ϱ≡{γ|ΠI(γ,ϱ)⩽Π12(γ)}≠∅. Absent the need for tailored incentives (γ = 1), integration dominates separation because the former but not the latter accounts for externalities and, in the case ϱ<1, because it reduces costly capital requirements. However, as γ increases above 1 eventually to reach γmax⁡, the inability to provide tailored incentives constitutes so large a cost as possibly to offset the benefits of integration and reduced capital. This will be the case if (32) (when ϱ=1) or (33) (when ϱ<1) is true. It is worth interpreting the two LHS terms in (32) and (33). The two terms Θ12/κ1+Θ22/κ2 represent the benefit of integration in accounting for the externalities. The term   −FL(pr,1A1−a1−Ψρ1−Θ1)2/κ1, with   FL≡κ1κ2(Ψρ2+Θ2pr,1A1−a1)21+κ1κ2(Ψρ2+Θ2pr,1A1−a1)2, (34) represents the value lost due to the inability to tailor incentives to the characteristics of each project when γ=γmax⁡. It is expressed as a fraction of the value created by risky investment in project 1 alone, because risky investment in project 2 creates no value at γ=γmax⁡: it is easy to see from (27) that pr,2A2−a2=Ψρ2+Θ2 in such case. If the integrated firm could tailor the incentives it provides to the characteristics of each project, it would set the PPP at zero for project 2. Since the firm is unable to do so, it will distort the single PPP β1,I toward zero. The term FL represents the fraction of the value of project 1 that is lost because of that distortion. Observe that ∂FL/∂(κ1/κ2)>0: as the cost of project 1 increases relative to that of project 2, the latter project’s importance in the setting of incentives increases; this increases the distortion and the fraction of the value of project 1 that is lost FL. The same interpretation can be given of ∂FL/∂[(Ψρ2+Θ2)/(pr,1A1−a1)]>0, with (Ψρ2+Θ2)/(pr,1A1−a1) measuring relative returns rather than costs: (Ψρ2+Θ2)/(pr,1A1−a1) equals (pr,2A2−a2)/(pr,1A1−a1) at γ=γmax⁡ as pr,2A2−a2=Ψρ2+Θ2 in such case. As the return to project 1 decreases relative to that to project 2, the latter project’s importance in the setting of incentives increases. Finally consider the term that appears in (33) but not in (32): this is the value of diversification at ϱ=−1. Rewriting   1κ2Ψρ2+Θ2pr,1A1−a11κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2[Ψρ2κ2(Ψρ2+Θ2pr,1A1−a1)+pr,1A1−a1−Ψρ1−Θ1κ1](4Ψρ2)=11+κ1κ2(Ψρ2+Θ2pr,1A1−a1)2{[pr,1A1−a1−Ψρ1−Θ1+κ1κ2(Ψρ2+Θ2pr,1A1−a1)(2Ψρ2)]κ12−(pr,1A1−a1−Ψρ1−Θ1)2κ1}, I express the value of diversification as a fraction of the value gained by project 1 through reduced capital requirements. The first term of the product on the RHS equals 1−FL, with FL defined in (34); as FL is the fraction of value lost because of the distortion that is due to the inability to tailor incentives to the characteristics of each project, 1−FL is the fraction of value retained. The second term of the product is the increase in the value of project 1 made possible by reduced capital requirements; it is reflected in the term (κ1/κ2)[(Ψρ2+Θ2)/(pr,1A1−a1)](2Ψρ2). The fraction 1−FL decreases in (κ1/κ2) and in (Ψρ2+Θ2)/(pr,1A1−a1): increases in the relative importance of project 2 increase the distortion, thereby decreasing the fraction of value retained. That value, in contrast, increases in (κ1/κ2) and in (Ψρ2+Θ2)/(pr,1A1−a1): the greater is the relative importance of project 2, the more capital is allocated to that project relative to that allocated to project 1, the greater is the diversification benefit thereby provided to project 1. The same is true of project 2’s cost of capital Ψρ2: the higher is that cost, the more capital is allocated to project 2 relative to project 1, the greater is the diversification benefit thereby provided to project 1. Remark 1, Lemma 2, and Proposition 3 show that projects that should be integrated within a single firm are those that (1) share similar characteristics ( 1⩽γ≪γmax⁡), (2) are related by strong externalities ( |Θi| large), and (3) have weakly correlated payoffs ( −1⩽ϱ≪1).61 6. Contractibility I have thus far precluded contracting on the externality, the use of capital, and risky investment. While full contractibility is unlikely, except in the simplest of circumstances, the complete absence of contractibility is equally unlikely, except perhaps in the most complex of circumstances.62 I therefore consider the case where it is possible partially to contract, initially on the externality or the use of capital, then on risky investment. I examine the implications of contractibility for the optimal form of ownership. 6.1 Contractibility of the externality and of capital Suppose it is possible for the shareholder-owned firm to contract with stakeholders to an extent qΘ, 0⩽qΘ⩽1, on the externality Θ(B−L): the firm can commit to providing stakeholders with compensation qΘΘ(B−L). The now partially contractible externality naturally affects the objective functions of both the manager and the firm, the former becoming   MaxB−Lβ1[(prA−a)(B−L)−qΘΘ(B−L)]+β0−κ(B−L)2 (35) with solution   B−L=β1(prA−a−qΘΘ)2κ, (36) and the latter becoming   Maxβ1(prA−a)(B−L)−Ψρ(B−L)−qΘΘ(B−L)−κ(B−L)2 with solution   β1SH,qΘ=1−ΨρprA−a−qΘΘ (37) and corresponding risky investment   (B−L)SH,qΘ=prA−a−(Ψρ+qΘΘ)2κ. (38) The resulting firm value, from which the compensation (1−qΘ)Θ(B−L)SH,qΘ for that fraction of the externality not contracted must be subtracted, is   VSH,qΘ=aB+(prA−a−Ψρ−qΘΘ)(B−L)SH,qΘ−κ[(B−L)SH,qΘ]2−(1−qΘ)Θ(B−L)SH,qΘ=aB+[prA−a−(Ψρ+Θ)]24κ−[(1−qΘ)Θ]24κ. (39) Note that ∂VSH,qΘ/∂qΘ>0, with VSH,qΘ|qΘ=1=VFB. Contractibility increases payoff, and makes possible the attainment of first-best when it is possible fully to contract on the externality. This is intuitive as shareholder ownership’s departure from first-best was due to failure to commit to accounting for the externality, a failure partially or fully remedied by contractibility. I have Proposition 4. The threshold cost of stakeholder capital Φ∗,SH,qΘdecreases in qΘ. Contractibility increases the range of stakeholder capital cost [Φ∗,SH,qΘ,Φmax⁡] over which shareholder ownership dominates: the more contractible is the externality, the lesser is the disadvantage of shareholder ownership in accounting for the externality, the wider is the range over which shareholder ownership dominates. Remark 2. Contractibility decreases the power of incentives under shareholder ownership β1SH,qΘif and only if the externality is negative ( −Θ<0, Θ>0). Where the externality is negative and the power of incentives decreases, these nonetheless remain higher than under stakeholder ownership: β1SH,qΘ>β1STif −Θ<0. Shareholders can use contractibility partially or fully to commit to imposing a lower negative externality on stakeholders, or to providing a higher positive externality. They incentivize the manager to make the lower or higher risky investment that causes the now committed for externality by providing lower- or higher-powered incentives, respectively. As noted above, it is this ability to commit to accounting for the externality that makes the increases in firm value possible. Despite the lowering of the PPP provided by shareholders induced by contractibility in case of negative externality, the PPP remains higher than that provided under stakeholder ownership. This is true even if there is no differential cost of capital ( Φ=Ψ) and if full contractibility is possible ( qΘ=1). By making it possible to incorporate the externality into the manager’s objective function (35), contractibility lessens the need to rely on the lowering of the PPP to achieve that same effect; this is in contrast to stakeholder ownership.63 The case of positive externality is not entirely symmetrical, in the sense that the PPP under shareholder ownership with contractibility will not necessarily be lower than under stakeholder ownership, because the difference in the cost of capital, Φ>Ψ, may be so large as to keep the PPP under stakeholder ownership lower than under shareholder ownership.64 The analysis in the case of stakeholder ownership with nonvoting preferred stock proceeds along nearly identical lines. Suppose it is possible for the stakeholder-owned firm to contract with preferred shareholders to an extent qΨ, 0⩽qΨ⩽1, on the use of capital Ψρ(B−L).65 In a manner analogous to that used in the case of partially contractible externality, I can write   VST,NV,qΨ=aB+[prA−a−(Ψρ+Θ)]24κ−[(1−qΨ)Ψρ]24κ. (40) Comparing (39) and (40), I conclude that VSH,qΘ>VST,NV,qΨ if and only if (1−qΘ)|Θ|<(1−qΨ)Ψρ, that is, if the noncontractible fraction of the externality, whether positive of negative, imposes a lower cost than the noncontractible fraction of capital use. If one assumes that contracting on the externality is more feasible than contracting on the use of capital, because of the numerous influences on the latter, then qΘ>qΨ and, absent too large a differential between |Θ| and Ψρ, |Θ|/Ψρ<(1−qΨ)/(1−qΘ), shareholder ownership can be expected to dominate stakeholder ownership with nonvoting preferred stock financing. This result may explain the relative paucity of stakeholder ownership with nonvoting preferred stock observed in Section 4. 6.2 Contractibility of risky investment I introduce the contractibility of risky investment by assuming that the owner(s) of the firm can contract with stakeholders (whether the firm is shareholder owned) or with preferred shareholders (whether it is stakeholder owned but preferred shareholder financed) on a level of risky investment (B−L)C. Departure from that level is possible, (B−L)≠(B−L)C, but it imposes a cost δ[(B−L)−(B−L)C]2, δ>0, on the owner. I show in what follows that the contractibility of risky investment increases firm value under both shareholder ownership and stakeholder ownership with nonvoting preferred stock. I consider the former case first. The manager’s problem becomes   MaxB−Lβ1[(prA−a)(B−L)−δ[(B−L)−(B−L)C]2]+β0−κ(B−L)2. It has solution   B−L=β1[prA−a+2δ(B−L)C]2(κ+δβ1). (41) Shareholders’ problem is   Maxβ1(prA−a)(B−L)−Ψρ(B−L)−δ[(B−L)−(B−L)C]2−κ(B−L)2. I proceed in two steps to solve that problem: I first solve for the risky investment B – L that maximizes the objective function; I then determine the PPP that incentivizes the manager to make that investment by equating the obtained risky investment to (41). The solution to the first step is   (B−L)SH,δ=prA−a−Ψρ+2δ(B−L)C2(κ+δ); (42) equating with (41) and solving for β1, I obtain   β1SH,δ=prA−a−Ψρ+2δ(B−L)CprA−a+(δκ)Ψρ+2δ(B−L)C. (43) The corresponding firm value, with the compensation to be paid for the externality subtracted, is   VSH,δ=aB+[prA−a−Ψρ−Θ+2δ(B−L)C](B−L)SH,δ−(κ+δ)[(B−L)SH,δ]2−δ[(B−L)C]2=aB+[prA−a−Ψρ+2δ(B−L)C]24(κ+δ)−Θ[prA−a−Ψρ+2δ(B−L)C]2(κ+δ)−δ[(B−L)C]2. (44) Differentiating with respect to (B−L)C to obtain the value of risky investment to be contracted, I have   (B−L)C=prA−a−(Ψρ+Θ)2κ=(B−L)FB, (45) from (6). The parties find it optimal to contract on the first-best value of risky investment; this is despite the fact that this level will not be attained, risky investment being instead, substituting (45) into (42),   (B−L)SH,δ=(κ+δ)(prA−a−Ψρ)−δΘ2(κ+δ)κ=prA−a−Ψρ−(δκ+δ)Θ2κ>(B−L)C, if and only if Θ>0, with lim⁡δ→∞(B−L)SH,δ=(B−L)FB: when departure from the contracted value is infinitely costly, there is no such departure; risky investment equals its contracted value, which has been set to equal its first-best value. For δ finite, however, risky investment is above its first-best value if the externality is negative ( −Θ<0), below if it is positive ( −Θ>0): there is too much risky investment when such investment creates a negative externality, too little when the externality is positive. Substituting (45) into (44), I obtain   VSH,δ=aB+[(κ+δ)(prA−a−Ψρ)−δΘ]24(κ+δ)κ2−Θ2κ[prA−a−Ψρ−δΘκ+δ]−δ[prA−a−Ψρ−Θ]24κ2. (46) I show Proposition 5. Firm value VSH,δincreases in δ; the threshold cost of stakeholder capital Φ∗,SH,δdecreases in δ. The partial contractibility of risky investment imposes a cost δ[(B−L)−(B−L)C]2 to departures from contracted risky investment, which equals first-best investment. The higher is the cost δ per squared deviation, the higher is firm value under shareholder ownership. This naturally increases the range of stakeholder capital cost [Φ∗,SH,δ,Φmax⁡] over which shareholder ownership dominates. The analysis in the case of stakeholder ownership with nonvoting, preferred stock is very similar: Θ replaces Ψρ and vice versa in the various expressions. I therefore obtain   VST,NV,δ=aB+[(κ+δ)(prA−a−Θ)−δΨρ]24(κ+δ)κ2−Ψρ2κ[prA−a−Θ−δΨρκ+δ]−δ[prA−a−Ψρ−Θ]24κ2. (47) Comparing (46) and (47), I can write   VST,NV,δ−VSH,δ=[(κ+δ)(prA−a−Θ)−δΨρ]24(κ+δ)κ2−Ψρ2κ[prA−a−Θ−δΨρκ+δ]−[(κ+δ)(prA−a−Ψρ)−δΘ]24(κ+δ)κ2+Θ2κ[prA−a−Ψρ−δΘκ+δ]=(Ψρ−Θ)[2(κ+δ)(prA−a)−(κ+2δ)(Ψρ+Θ)]4(κ+δ)κ−12κ[(Ψρ−Θ)(prA−a)−δ[(Ψρ)2−Θ2]κ+δ]=Θ2−(Ψρ)24(κ+δ). (48) Thus, like in the case of noncontractibility of risky investment, δ = 0, whether stakeholder ownership with nonvoting preferred stock or shareholder ownership dominates depends on the relative sizes of Ψρ and |Θ| (Lemma 1 and Proposition 2): when the cost of equity looms larger in importance, Ψρ>|Θ|, then shareholder ownership dominates, for it is such ownership that better accounts for the use of capital; when in contrast it is the externality that is more important, then stakeholder ownership with nonvoting preferred stock dominates. 7. Empirical Evidence Vitali, Glattfelder, and Battiston (2011) consider 43,060 transnational corporations (TNCs) in an attempt to trace ownership and control links among these.66 They find that “nearly 4/10 of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of 147 TNCs” (Vitali, Glattfelder, and Battiston, 2011, p. 4); they report the top 50 control holders: all but 5 are classified as financial intermediaries. Azar, Raina, and Schmalz (2016, table 1) similarly report that the 6 largest US banks by deposits to a large extent share the same top 5 shareholders: Blackrock owns between 4.7% and 7.4% of each of J.P. Morgan Chase, Bank of America, Citigroup, Wells Fargo, U.S. Bank, and PNC Bank; Vanguard between 4.4% and 4.7%. Azar, Raina, and Schmalz (2016) find that the larger is the extent of common ownership, the higher are spreads, fees, and fee thresholds; Azar, Schmalz, and Tecu (2016) find a similar result in the airline industry, where common ownership increases ticket prices. In a somewhat different setting, Hansen and Lott (1996, p. 47) report that common ownership encourages the settlement of lawsuits. In the context of this model, if I identify (1) vigorous competition or aggressive litigation with risky investment, (2) the costs these strategies impose on competitors or defendants with a negative externality, (3) common ownership with stakeholder ownership, and (4) independent ownership with shareholder ownership, in that common ownership accounts for the externality but independent ownership does not, then the result from (15) and (18) that (B−L)ST<(B−L)SH if −Θ<0 even if Φ=Ψ can be viewed as being in agreement with the results reported in the preceding paragraph. That managers are incentivized to make lower risky investment by being provided with lower-powered incentives, β1ST<β1SH if −Θ<0 even if Φ=Ψ from (14) and (19), is consistent with the findings of Antón et al. (2016), who document a negative relation between managerial compensation and the product of common ownership and market value change: the rewards to increasing firm value are lower for the managers of those firms that are owned in common with their competitors. Proposition 4 has shown that there is an inverse relation between the ability to contract an externality and the desirability of stakeholder ownership. This result is consistent with corporate developments in the wake of the rise of mass production. Mass production made possible a dramatic decline in variable costs, but necessitated enormous investments which led to a very large increase in fixed costs.67 The substitution of fixed for variable costs introduced the need for demand and supply coordination (Piore and Sabel 1984, chapter 3): demand in excess of capacity could not easily be accommodated, demand below resulted in idle capacity. Initial attempts at coordination took the form of pools, “agreements among producers to fix prices or to limit output” (Piore and Sabel 1984, p. 55). Despite progressively increased sophistication, including “provisions for the exchange of production and sales data […] and fines for violations of the agreement ” as well as “provisions for the stronger producers to compensate the weaker ones for reducing production” (Piore and Sabel 1984, p. 55), pools, a form of contract, ultimately failed to achieve the desired coordination. That firms turned to integration through horizontal mergers rather than control through ownership is in accordance with the argument referred to at the end of Section 4 that coordination requires integration. Azoulay (2004) examines the decision by pharmaceutical companies to contract out clinical trials to Contract Research Organizations (CRO) or to conduct these “in-house.” Azoulay (2004, p. 1592) finds that “[t]he choice is […] between the hierarchy of the firm—in which subjective performance evaluations are combined with flat incentives—and the hierarchy of its subcontractor—whose virtue precisely stems from the ability to provide high-powered incentives on a narrow set of monitorable tasks.” Azoulay (2004, p. 1592) further finds that “knowledge-intensive projects are more likely to be assigned to internal teams,” with such knowledge arising from “[t]he unexpected and anomalous results of clinical experience[, which] pose new questions for basic biomedical research and enrich its ultimate payoff” (Gelijns, Rosenberg, and Moskowitz 1998, p. 693). In the context of this model, if I identify (1) clinical trials that allow for the careful investigation of unexpected results with safe investment, (2) the knowledge such investigation gives rise to with a positive externality, (3) in-house trials with stakeholder ownership in that the knowledge such trials produce is generally of much greater importance to a pharmaceutical firm than it is to a CRO, for it is the former that can make by far the most of it, (4) contracting with shareholder ownership, and (5) the ability to evaluate performance objectively and to monitor a task with contractibility, then the predictions of this analysis can be viewed as being in general agreement with Azoulay’s (2004) findings. Externalities favor stakeholder ownership (Proposition 1), whereas contractibility favors shareholder ownership (Propositions 4 and 5).68 Recalling that a positive externality of safe investment is a negative externality of risky investment (Footnote 35), the power of in-house incentives is lower than that of CRO incentives (Remark 2). Morrison and Wilhelm (2007, chapters 8 and 9) argue that the fundamental advances in financial economics that were made during the sixties and the seventies made possible the codification of much knowledge that had previously been only tacit: “[s]kills that previously could be acquired only though a long apprenticeship within a financial institution can now be learned in the classroom” (Morrison and Wilhelm 2007, p. 245). They further argue that codification caused “a drop in the relative importance of investment banker reputation in the markets where practice was most codified” (Morrison and Wilhelm 2007, p. 225), a development to which they attribute the gradual abandonment of the partnership form once quasi universal among investment banks. If I identify codification with the contractibility of risky investment, as some tasks which previously could be prescribed only with difficulty and monitored only imperfectly ceased being so, and if I associate the decline in the importance of reputation with a decrease in the (absolute) value of the externality, as reputation no longer was affected to the same extent by risky investment that could be at least partially contracted, then the predictions of this analysis can be viewed as being in agreement with Morrison and Wilhelm’s (2007) argument: the contractibility of risky investment diminishes the desirability of stakeholder ownership and capital provision (Proposition 5); the decline in the value of the externality favors the replacement of stakeholder by shareholder ownership rather than the combination of stakeholder ownership with non voting preferred shareholder capital provision (Equation (48) and the discussion that follows). 8. Conclusion I conclude by briefly discussing possible extensions to the model. The analysis here has assumed that total resources are fixed; the manager’s task has been limited to allocating resources between risky and safe investment. Yet resources are unlikely to be fixed, and an important task of the manager surely is to gather the resources necessary for investment. Put somewhat more formally, total resources B are unlikely to be exogenous but are instead endogenous. Endogeneity imparts a double role to the pay-for-performance parameter β1, which now induces resource gathering in addition to guiding resource allocation. Although this extension is not expected to affect optimal ownership, it may enrich the conclusions regarding the effects of contractibility, which now can encompass the contractibility of total resources in addition to that of risky investment. Preliminary analysis suggests that changes in contractibility may provide a combined explanation for the seemingly contradictory developments that have been the nineteenth and twentieth century rise in salaried employment (low β1) and the more recent rise in outsourcing (high β1). I leave this line of inquiry for future work. I am deeply grateful to Yoram Barzel, Josef Falkinger, Uday Rajan (the Editor), and an anonymous referee. I additionally thank, Øyvind Bøhren, Jos van Bommel, Dawei Fang, Peter Gruber, Ulf von Lilienfeld-Toal, Salvatore Miglietta, Bogdan Stacescu, and Alexander Wagner and seminar participants at the University of Gothenburg, the University of Lugano, the Luxembourg School of Finance, the CEPR First Annual Spring Symposium, the 15th Workshop on Corporate Governance and Investment at BI Oslo, and the IFABS 2015 Corporate Finance Conference at Oxford University for helpful comments and suggestions. Footnotes 1 Hansmann (1996, 2013) develops a formal theory of ownership, but he provides no model. I discuss the relation of my work to Hansmann’s in Section 1. 2 In Section 1, I place my work within the larger context of the theory of ownership. 3 Traders are generally acutely aware of their “trader’s option,” that is, the asymmetry in their gains and losses from taking large, risky positions. Profitable positions result in large bonuses, and unprofitable positions mean, at worse, job loss. 4 See Section 4.7 for a formal analysis. 5 See, for example, Gibbons (2005), Gibbons and Roberts (2013), Holmstrom (1999), and Holmstrom and Milgrom (1991, 1994). 6 I provide further justification in Section 2. I nonetheless acknowledge a limitation of the model in the failure to account for the issuance of dual-class, common shares to noncontrolling shareholders, as opposed to that of nonvoting, preferred shares. 7 See Barzel, Habib, and Johnsen (2006), Cornelli and Goldreich (2001), Gondat-Larralde and James (2008), and Jenkinson and Jones (2009). 8 For an extended discussion of firm boundaries and vertical integration, see Bresnahan and Levin (2013) and Hart (1995) and the references therein. 9 For a superb comparative analysis of various theories of the firm and the role of ownership therein, see Gibbons (2005). 10 Specifically, the manager evaluates a risky investment opportunity and decides how much to invest; see the formal analysis. 11 The present model is a much simplified version of Falkinger (2014). 12 Section 3 analyzes the case of a positive externality. 13 The prototypical example is probably bank capital, which serves to bond the value of bank deposits against possible declines in the value of bank assets. 14 I set the proportion between capital and standard deviation to one for simplicity. I use the standard deviation, rather than the variance, to keep the analysis tractable. 15 The next paragraph, as well as Section 3 present the reasons for this qualification. 16 I allow for partial contractibility of investment, the use of capital, and the externality in Section 6. 17 Limiting owners’ discretion to alter (β0,β1) or K is not realistic: changes in circumstances that are entirely unrelated to any attempt on the part of owners to exploit firm stakeholders may require a change in the parameters of the compensation contract; changes in circumstances may alter firm payoff, regardless of any attempt at stakeholder exploitation. I do not model these changes. 18 Conditioning on the compensation contract, if feasible, amounts to making investment contractible, thereby making the original problem moot. I thank the anonymous referee for alerting me to this result. 19 In Sections 4.7 and 5, I consider the case in which the other stakeholders are themselves shareholder owned. 20 Section 3 provides the exact derivations. 21 See Section 3 for details. 22 I assume prA−a⩾Ψρ+Θ for (B−L)FB⩾0. 23 Substitute (6) into (1) rewritten as (prA−a)(B−L)+aB−Ψρ(B−L)−κ(B−L)2−Θ(B−L) to obtain (7). 25 Substitute (14) into (10) to obtain (15). 29 I assume prA−a⩾Φρ+Θ for (B−L)ST⩾0. 30 I have shown in Footnote 26 that VSH<VFB; a very similar argument shows that VST,NV<VFB. That VST⩽VFB with equality at Φ=Ψ is immediate from (7) and (17). 31 The appendix provides all proofs. 32 Failure is apparent from (2) and (4). 34 There is still a distortion, however; this is why stakeholder ownership dominates for low cost of stakeholder capital Φ<Φ∗,SH. 36 That Google has “a world-class research team working on all sorts of moonshot projects, from self-driving cars to healthcare” (Bort 2015), for example, may at least in part reflect the eclectic interests of its founding and controlling shareholders. The description of research projects as “moonshots” accords well with the identification of risky investment as giving rise to positive externalities. 38 As an example of the importance of such employees, consider the following description of Michael Milken’s role at Drexel, Burnham, Lambert (Bruck 1989, p. 57): “He [Milken] had the issuers. He had the buyers. He had the most trading capital of any firm. He had the knowhow. He had the best incentive system for his people. He had the history of data—he knew the companies, he knew their trading prices, probably their daily trading prices going back to at least 1971. He had boxed the compass.” 39 As for Google’s “moonshot” projects discussed in Footnote 36, it is risky investment—those issues for which success or failure is most uncertain—that creates the externality. 40 Payment to the bank generally takes the form of lower salaries: firms that are viewed as increasing an employee’s human capital often pay lower wages, ceteris paribus, than do firms that provide no such positive externality. 41 It may also attest to the perhaps greater codifiability of at least of parts of investment banking knowledge (Morrison and Wilhelm 2007, pp. 244–6); codifiability is an issue I return to in Section 7. 42 Somewhat misleadingly, though, mutual savings banks in the United States are actually nonprofit organizations as opposed to despositor-owned banks (Hansmann 1996, pp. 246–7). I do not consider nonprofits in this paper but note that nonprofits share with mutuals the characteristic of controlling the risk-shifting problem: there are no shareholders to benefit fron risky investment at the expense of depositors. 43 This is an instance of the contractibility of investment, an issue I analyze in Section 6.2. 44 Building societies are the British equivalent to savings and loans associations. 45 Recall that safe and risky investment must add up to total resources B, a constant. 47 Section 6.1 provides a further explanation for the relative paucity of stakeholder ownership combined with nonvoting preferred stock. 48 I proxy profits by firm value. 50 Total payoff is not, however; this explains the reversal to government ownership in some cases, the adoption of customer ownership in others. 51 For an example of the difficulties posed by heterogeneous worker interests in a context of difficult employment conditions, consider the turbulent relations between United Airlines’ pilots and machinists in the run-up to the 1994 employee buyout (Hansmann 1996, pp. 117–8) and prior to the 2003 bankruptcy (Gordon 2003, p. 4). 52 In the investment banking and legal partnerships considered in Section 4.2, and the farmer cooperatives considered in Section 4.6, a single category of workers appears to be paramount, at least as concerns the externality. 53 I show below that β1ST,NV<β1SH and LST,NV>LSH under the conditions in which the buyer finances its acquisition with nonvoting preferred shares. 54 That Θ>Ψρ establishes β1ST,NV<β1SH and LST,NV>LSH. 55 Recall the discussion that follows Proposition 1. 56 Recall from Section 3 that VST=VFB at Φ=Ψ. 57 Hansen and Lott (1996, p. 43) put it very nicely: “[a]ny kind of externality, pecuniary or nonpecuniary, vertical or horizontal, suffices.” Hansen and Lott’s (1996) focus is on the incentive for portfolio value maximization induced by common ownership, mine is on the incentive for choosing common ownership in the first place. 58 Besanko, Dranove, and Shanley (1996, pp. 89–90) and Milgrom and Roberts (1992, pp. 556–8) argue that one purpose of vertical integration is to make possible the coordination a product’s multiple “design attributes” (Milgrom and Roberts 1992, p. 91) require. 59 I interchange the indices 1 and 2 if γ⩽1. 61 That (33) is more restrictive than (32) is consistent with a positive role for low or negative correlation in favoring integration: the condition is less likely to hold, and integration therefore more likely to dominate, when ϱ=−1 (condition (33)) than when ϱ=1 (condition (32)). 62 See Bolton and Dewatripont (2005, Chapter 12) and the references therein for a detailed analysis of contractibility. 63 Note that there is no need for contractibility under stakeholder ownership, for the externality is fully accounted for by stakeholders in setting the power of incentives. 64 Formally, β1SH,qΘ>β1ST if (and only if) (Φ−Ψ)ρ(prA−a)>−Θ(prA−a−qΘΦρ−qΘΘ), with −Θ>0. 65 For comparability with my previous analysis, I continue to assume that the manager cannot contract with the owner on the use of capital. 66 Distinguishing between ownership and control links changes their findings only little. 67 To illustrate the tremendously increased scale of manufacturing, consider Chandler’s (2002, p. 249) observation that a mere fifteen cigarette-making machines “could fill the total demand for cigarettes in the United States in 1880.” 68 I appeal to the analysis of Section 5 to explain why the phamaceutical firm might wish to contract out some clinical trials, despite itsef likely being shareholder-owned. 70 Failure to establish the monotonicity of 4[ΠI(γ,−1)−Π12(γ)] in γ precludes establishing the result that Sγ,−1 consists of a single interval. 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CrossRef Search ADS PubMed  Appendix Proof of Lemma 1: Use (16) and (22) to write   sign{VSH−VST,NV}=sign{[prA−a−Ψρ]24κ−Θ(prA−a−Ψρ2κ)−[prA−a−Θ]24κ+Ψρ(prA−a−Θ2κ)}=sign{[prA−a−Ψρ]2−[prA−a−Θ]2−2Θ(prA−a−Ψρ)+2Ψρ(prA−a−Θ)}=sign{[prA−a−Ψρ+prA−a−Θ](Θ−Ψρ)−2(Θ−Ψρ)(prA−a)}=−sign{(Ψρ+Θ)(Θ−Ψρ)}=+1, if and only if Ψρ>Θ. Proof of Proposition 1: Initially consider the case Ψρ>Θ and define   F(Φ)≡VST−VSH=[prA−a−(Φρ+Θ)]24κ−[prA−a−Ψρ]24κ+Θ(prA−a−Ψρ2κ); it is clear that F′(Φ)<0 for Φ<Φmax⁡ and, from Footnote 30, that F(Ψ)>0. In contrast   F(Φmax⁡)=−[prA−a−Ψρ]24κ+Θ(prA−a−Ψρ2κ); it has sign   sign{F(Φmax⁡)}=sign{−(prA−a−Ψρ)+2Θ}=sign{−Φmax⁡ρ+Ψρ+Θ}=−1, if and only if Θ<Φmax⁡ρ−Ψρ. By the intermediate value theorem, there exists a Φ∗,SH, Ψ<Φ∗,SH<Φmax⁡, such that F(Φ∗,SH)=0; F(Φ)=VST−VSH>0 for Φ<Φ∗,SH and F(Φ)=VST−VSH<0 for Φ>Φ∗,SH. To establish ∂Φ∗,SH/∂Θ>0, define F∗,SH≡F(Φ∗,SH)=0, note that ∂F∗,SH/∂Φ∗,SH<0 from F′(Φ)<0 and   ∂F∗,SH∂Θ=−prA−a−(Φ∗,SHρ+Θ)2κ+prA−a−Ψρ2κ=Φ∗,SHρ+Θ−Ψρ2κ>0, where the inequality is true by Φ∗,SH>Ψ, and use the implicit function theorem to write   ∂Φ∗,SH∂Θ=−∂F∗,SH∂Θ∂F∗,SH∂Φ∗,SH>0. The results for the case Ψρ<Θ can be obtained in a very similar manner. Define   G(Φ)≡VST−VST,NV=[prA−a−(Φρ+Θ)]24κ−[prA−a−Θ]24κ+Ψρ(prA−a−Θ2κ) and note that   G(Φmax⁡)=−[prA−a−Θ]24κ+Ψρ(prA−a−Θ2κ) has sign   sign{G(Φmax⁡)}=sign{−(prA−a−Θ)+2Ψρ}=sign{−Φmax⁡ρ+2Ψρ}=−1, if and only if Ψρ<Φmax⁡ρ−Ψρ. Further note that   ∂G(Φ∗,ST,NV)∂Θ=−prA−a−(Φ∗,ST,NVρ+Θ)2κ+prA−a−Θ2κ−Ψρ2κ=Φ∗,ST,NVρ−Ψρ2κ>0. Proof of Proposition 2: I have   sign{VSH−VST,NV}=−sign{(Ψρ+Θ)(Θ−Ψρ)}=sign{Ψρ+Θ}=+1, if and only if −Θ<Ψρ; the first equality uses the derivation in the proof of Lemma 1, the second uses Θ<0. Following the reasoning used in the proof of Proposition 1, I write   sign{F(Φmax⁡)}=sign{−(prA−a−Ψρ)+2Θ}=sign{−Φmax⁡ρ+Ψρ+Θ}=−1, where I have used Φmax⁡>Ψ and Θ<0; the existence of Φ∗,SH, Ψ<Φ∗,SH<Φmax⁡, is now unconditional. Again following the reasoning used in the proof of Proposition 1, I write   ∂F∗,SH∂Θ=−prA−a−(Φ∗,SHρ+Θ)2κ+prA−a−Ψρ2κ=Φ∗,SHρ+Θ−Ψρ2κ>0, if and only if −Θ<Φ∗,SHρ−Ψρ; ∂Φ∗,SH/∂Θ>0 in such case. The results for Φ∗,ST,NV are similar to those in the case Θ>0. Proof of Lemma 2: Substituting ϱ=1 into (31), I obtain   ΠI(γ,1)=a1B1+a2B2+14(pr,1A1−a1)2[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]+14(Ψρ1+Θ1)2([1κ1+1γκ2(Ψρ2+Θ2Ψρ1+Θ1)2]21κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2)−12(Ψρ1+Θ1)(pr,1A1−a1)[1κ1+1γκ2(Ψρ2+Θ2Ψρ1+Θ1)2]. To compare the values of the single integrated and the two independent firms, I compute   4[ΠI(γ,1)−Π12(γ)]=(pr,1A1−a1)2[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]+(Ψρ1+Θ1)2([1κ1+1γκ2(Ψρ2+Θ2Ψρ1+Θ1)2]21κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2)−2(Ψρ1+Θ1)(pr,1A1−a1)[1κ1+1γκ2(Ψρ2+Θ2Ψρ1+Θ1)2]−(pr,1A1−a1−Ψρ1−Θ1)2κ1+Θ12κ1−(Ψρ2+Θ2Ψρ1+Θ1)2(pr,1A1−a1γ−Ψρ1−Θ1)2κ2+Θ22κ2=(Ψρ1+Θ1)2([1κ1+1γκ2(Ψρ2+Θ2Ψρ1+Θ1)2]21κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2)−(Ψρ1+Θ1)2κ1+Θ12κ1−(Ψρ2+Θ2)2κ2+Θ22κ2=−(Ψρ2+Θ2)2κ1κ21κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2(1−1γ)2+(Θ12κ1+Θ22κ2). This is positive at γ = 1; it decreases in γ for γ>1; it equals the LHS of (32) at γ=γmax⁡. Thus, if (32) holds, then ∃ γ∗, 1<γ∗<γmax⁡, such that ΠI(γ,1)⩽Π12(γ) if and only if γ∗⩽γ⩽γmax⁡. Proof of Proposition 3: Set ϱ=−1; if I can establish Sγ,−1≡{γ|ΠI(γ,−1)⩽Π12(γ)}≠∅, then I will have established Sγ,ϱ≡{γ|ΠI(γ,ϱ)⩽Π12(γ)}≠∅ because ΠI(γ,ϱ)<ΠI(γ,−1) for −1<ϱ⩽1 from ∂ΠI(γ,ϱ)/∂ϱ<0 in Remark 1. Consider the two limits γ = 1 and γ=γmax⁡ in turn. At γ = 1, use Remark 1 and Lemma 2 to write 4[ΠI(1,−1)−Π12(1)]>4[ΠI(1,1)−Π12(1)]>0. At γ=γmax⁡, substitute ϱ=−1 and γmax⁡=(pr,1A1−a1)/(Ψρ1+Θ1) into (28) and (31) to obtain69 69 Rewrite ΠI(γ,ϱ) in (31) as   ΠI(γ,ϱ)=a1B1+a2B2+1411κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2×{(pr,1A1−a1)[1κ1+1γ2κ2(Ψρ2+Θ2Ψρ1+Θ1)2]−[Θ1κ1+Θ2γκ2(Ψρ2+Θ2Ψρ1+Θ1)+Ψρ12κ12+ρ22γ2κ22(Ψρ2+Θ2Ψρ1+Θ1)2+2ϱρ1ρ2γκ1κ2(Ψρ2+Θ2Ψρ1+Θ1)]}2 for the calculation that follows.  4[ΠI(γmax⁡,−1)−Π12(γmax⁡)]=11κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2×{(pr,1A1−a1)[1κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2]−[Θ1κ1+Θ2κ2(Ψρ2+Θ2pr,1A1−a1)+Ψρ12κ12+ρ22κ22(Ψρ2+Θ2pr,1A1−a1)2−2ρ1ρ2κ1κ2(Ψρ2+Θ2pr,1A1−a1)]}2−(pr,1A1−a1−Ψρ1−Θ1)2κ1+Θ12κ1+Θ22κ2=11κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2×{(pr,1A1−a1)[1κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2]−[Ψρ1+Θ1κ1+Θ2−Ψρ2κ2(Ψρ2+Θ2pr,1A1−a1)]}2−(pr,1A1−a1−Ψρ1−Θ1)2κ1+Θ12κ1+Θ22κ2=11κ1+1κ2(Ψρ2+Θ2pr,1A1−a1)2{pr,1A1−a1−Ψρ1−Θ1κ1+2Ψρ2κ2(Ψρ2+Θ2pr,1A1−a1)}2−(pr,1A1−a1−Ψρ1−Θ1)2κ1+Θ12κ1+Θ22κ2, which is the LHS of (33). If it is negative, then the intermediate value theorem and continuity together imply the existence of a nonempty set Sγ,−1={γ|ΠI(γ,−1)⩽Π12(γ)}.70 Proof of Proposition 4: Define   F(Φ)≡VST−VSH,qΘ=[prA−a−(Φρ+Θ)]24κ−[prA−a−(Ψρ+Θ)]24κ+[(1−qΘ)Θ]24κ, and F∗,SH,qΘ≡F(Φ∗,SH,qΘ)=0. Using F′(Φ)<0 for Φ<Φmax⁡ to obtain ∂F∗,SH,qΘ/∂Φ∗,SH,qΘ<0 and   ∂F∗,SH,qΘ∂qΘ=−(1−qΘ)Θ22κ<0, I conclude using the implicit function theorem that   ∂Φ∗,SH,qΘ∂qΘ=−∂F∗,SH,qΘ/∂qΘ∂F∗,SH,qΘ/∂Φ∗,SH,qΘ<0. Proof of Remark 2: The first part of the remark is immediate from (37). The second part is proved by contradiction. Assume   β1SH,qΘ<β1P⇔ΨρprA−a−qΘΘ>Φρ+ΘprA−a⇔Ψρ(prA−a)>(Φρ+Θ)(prA−a−qΘΘ)⇔0>(Φ−Ψ)ρ(prA−a)+Θ(prA−a−qΘΦρ−qΘΘ), (49) which is false if −Θ<0. Proof of Proposition 5: Differentiate (46) with respect to δ to obtain   ∂VSH,δ∂δ=−[(κ+δ)(prA−a−Ψρ)−δΘ]24(κ+δ)2κ2+2[(κ+δ)(prA−a−Ψρ)−δΘ][prA−a−Ψρ−Θ]4(κ+δ)κ2+Θ22(κ+δ)2−[prA−a−Ψρ−Θ]24κ2. The first, second, and fourth term equal   14(κ+δ)2κ2{−[(κ+δ)(prA−a−Ψρ)−δΘ]2+2(κ+δ)[(κ+δ)(prA−a−Ψρ)−δΘ][prA−a−Ψρ−Θ]−(prA−a−Ψρ−Θ)2(κ+δ)2}=14(κ+δ)2κ2{−(κ+δ)2(prA−a−Ψρ)2−(δΘ)2+2(κ+δ)(prA−a−Ψρ)δΘ+2(κ+δ)2(prA−a−Ψρ)2−2(κ+δ)2(prA−a−Ψρ)Θ−2(κ+δ)(prA−a−Ψρ)δΘ+2(κ+δ)δΘ2−(κ+δ)2(prA−a−Ψρ)2−(κ+δ)2Θ2+2(κ+δ)2(prA−a−Ψρ)Θ}=14(κ+δ)2κ2{−(δΘ)2+2(κ+δ)δΘ2−(κ+δ)2Θ2}=−Θ24(κ+δ)2. Combining with the third term, I obtain   ∂VSH,δ∂δ=Θ24(κ+δ)2>0. (50) Define   F(Φ)≡VST−VSH,δ and F∗,SH,δ≡F(Φ∗,SH,δ)=0. Using F′(Φ)<0 for Φ<Φmax⁡ to obtain ∂F∗,SH,δ/∂Φ∗,SH,δ<0 and   ∂F∗,SH,qΘ∂δ=−∂VSH,δ∂δ<0, from (50), I conclude using the implicit function theorem that   ∂Φ∗,SH,δ∂δ=−∂F∗,SH,δ/∂δ∂F∗,SH,δ/∂Φ∗,SH,δ<0. © The Author 2017. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Journal

Review of Corporate Finance StudiesOxford University Press

Published: Mar 1, 2018

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