both market and hierarchy: an incentive-system theory ... - SSRN papers

姝 Academy of Management Review 2009, Vol. 34, No. 2, 297–319.

BOTH MARKET AND HIERARCHY: AN INCENTIVE-SYSTEM THEORY OF HYBRID GOVERNANCE FORMS RICHARD MAKADOK RUSSELL COFF Emory University We create a taxonomy of hybrid governance forms and develop a formal theory that predicts when a given hybrid form will be efficient. Our model is unique in that we consider cross-task synergies in a multitask principal-agent model, where hybrid forms result as principals try to motivate cooperation among agents indirectly through incentives, ownership, and formal authority. We conclude with a discussion of other mechanisms that might also help us understand and predict hybrid governance forms.

Academics, consultants, and practitioners have long advocated bringing the market inside the firm. . . . wave after wave of organizational restructuring has advocated radical decentralization, empowerment, “intrapreneurship,” and the like—in short, making employees feel like owners (Baker, Gibbons, & Murphy, 2001: 212).

thority, ownership, and incentives distinguish markets from hierarchies (Holmstrom & Milgrom, 1994), and true hybrid governance forms are market-like in some of these dimensions while being hierarchy-like in others. Although empirical research has generally kept pace with the spread of such hybrid governance forms (see David & Han, 2003; Macher & Richman, 2006), formal theory explaining true hybrids has lagged behind. One limitation of existing theories is that they treat the menu of governance options as a unidimensional continuum, from pure market to pure hierarchy, with intermediate forms between these extremes (e.g., Hennart, 1993; Holmstrom & Milgrom, 1994; Williamson, 1991a). This approach cannot address the growing popularity of true hybrids, since the resulting intermediate forms cannot be both market-like on some dimensions and hierarchy-like on others. We develop a formal model that predicts when a given hybrid governance form might be observed. Our approach focuses on the dilemma that arises when some tasks, such as cooperation among agents (e.g., teamwork), cannot be motivated directly through incentives or through any other motivational instruments (like authority or ownership). Such cooperation can be critical for complex transactions that require substantial interaction (Alchian & Demsetz, 1972), or it can be irrelevant (or even costly) when transactions are modular (Ethiraj & Levinthal, 2004; Galunic & Eisenhardt, 2001; Sanchez & Mahoney, 1996). Holmstrom and Milgrom (1994) argued that, in order to avoid distracting agents

Today, firms increasingly use hybrid governance forms that fuse elements of market transactions into hierarchies or integrate elements of hierarchies into market transactions (Zenger & Hesterly, 1997). The quotation above refers to firms that create more market-like hierarchies by giving workers more powerful incentives or greater autonomy (Pfeffer, 1995; Seibert, Silver, & Randolph, 2004). Conversely, some market relationships have gained a more hierarchical character by making incentives less tied to short-term performance or by imposing quasihierarchical authority (Dyer & Singh, 1998; Oxley & Sampson, 2004). The dimensions of au-

We thank guest editor Mike Ryall for his guidance, patience, and encouragement, and the anonymous reviewers for their detailed, helpful, and constructive comments. In addition, numerous other people offered us helpful comments along the way, including Gary Dushnitsky, Nicolai Foss, Witold Henisz, Peter Klein, Glenn MacDonald, Joe Mahoney, Kyle Mayer, Steve Michael, Jackson Nickerson, Anne Parmigiani, Evan Rawley, Anand Swaminathan, Govert Vroom, Gordon Walker, and Todd Zenger. We also received valuable insights from seminar participants at Emory, INSEAD, Washington University, and Wharton, along with those at the 2007 Academy of Management annual meeting in Philadelphia, the Atlanta Competitive Advantage Conference, and the Copenhagen Conference on Strategic Management. Of course, any remaining errors are our own. 297

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away from a difficult-to-motivate task like cooperation with other agents, principals may adopt hierarchical governance because of its inherently weak motivators for other tasks. In contrast, we offer a mechanism for actively inducing effort on hard-to-motivate tasks—not just passively avoiding distractions. If there are synergies among an agent’s tasks (as job design principles mandate; e.g., Wong & Campion, 1991), the principal may indirectly induce effort on a task by motivating other tasks that it is synergistic with. For example, if an agent’s output is boosted by cooperation with others, then strong productivity incentives may indirectly spur cooperation. Or if teamwork helps agents pursue personal goals, then granting autonomy may nurture cooperation. Unlike prior models that can only explain pure or intermediate governance forms, our indirect-inducement mechanism can explain a variety of true hybrid forms since strong motivators are used for selected tasks to indirectly induce effort on other tasks that cannot be motivated directly. Accordingly, this paper contributes in two ways. First, we create a theory-grounded taxonomy of hybrid forms. Second, we develop a formal theory to predict when different hybrid forms might be optimal. Although our model predicts hybrid governance forms from the need to resolve challenging cross-task motivational problems, we conclude with a discussion of other possible causal mechanisms that might also be used to understand and predict hybrids.

TAXONOMY OF HYBRID GOVERNANCE FORMS We begin by developing an understanding of what hybrid governance forms are. The notion that governance can be market-like in some dimensions and hierarchy-like in others begs the question, “What dimensions differentiate markets from hierarchies?” While ownership may be the one that is most often considered (since it defines the legal boundaries of a firm), there are also other dimensions that distinguish markets from hierarchies. We use these to develop a taxonomy of hybrid governance forms, and we then develop a theory to predict when each hybrid might be efficient.

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Dimensions of Governance Researchers from several disciplines (e.g., Bradach & Eccles, 1989; Holmstrom & Milgrom, 1994; Williamson, 1991a) have observed that markets and hierarchies differ from each other along three key dimensions: authority, ownership, and incentives. In a prototypical market the party performing the work (i.e., supplier or contractor) (1) has authority to determine how to do the work and what other activities to engage in, (2) owns the key assets used for the work, and (3) is compensated according to the output produced, thereby bearing both the risk in case of poor performance and the rewards in case of strong performance. In contrast, in a prototypical hierarchy the party performing the work (i.e., employee or organizational subunit) (1) submits to superiors’ authority to decide how the work will be done and what other activities can be performed (e.g., personal activities or moonlighting on other jobs), (2) does not own the key productive assets, and (3) is compensated according to the inputs provided (e.g., time worked, skills, or experience), thereby bearing neither risk from poor performance nor reward for strong performance. For conceptual clarity, we distinguish intermediate governance forms from true hybrids by defining an intermediate form as being between a market and a hierarchy in all of the dimensions that distinguish markets from hierarchies, and defining a true hybrid form as being market-like in some dimensions while simultaneously hierarchy-like in others. This distinction is consistent with the common usage of these words, since the American Heritage Dictionary defines hybrid as “of mixed origin or composition” and intermediate as “in a middle position or state.” Because prior theories have tended to view alternative governance as intermediate forms arrayed on a single continuum, between the extremes of market and hierarchy, they have focused on mechanisms that cause all three of these dimensions—authority, ownership, and incentives—to move together simultaneously toward either market or hierarchy (e.g., Holmstrom & Milgrom, 1994; Williamson, 1991a). We do not deny either the existence or the importance of intermediate forms, such as a joint venture in which authority, ownership, risks, and rewards are all shared jointly by two partners.

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Still, researchers increasingly recognize that organizational design elements can combine in many more ways than the intermediate forms described above (Grandori, 2001; Grandori & Soda, 2006). Even a casual scan of realworld transactions reveals many that rely on a variety of true hybrid governance forms. Some hybrids, such as the highly fluid employment practices of investment banks, bring marketlike elements inside organizational hierarchies. Others bring hierarchical attributes to market transactions. For example, while franchising is a market contract between legally distinct entities, it features an almost hierarchy-like authority structure. We generate a taxonomy of hybrid governance forms by permutating all possible combinations of high and low values on the three dimensions that delineate markets from hierarchies, as shown

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graphically in the three-dimensional “governance space” of Figure 1. Pure hierarchy governance (top left corner of the cube) involves asset ownership by the principal, low-powered productivity incentives, and strong authority for the principal to determine the type, methods, and timing of the agent’s work and other activities. In contrast, at the opposite corner of the cube, pure market governance involves asset ownership by the agent, job autonomy, and high-powered rewards tied to output. These pure forms of markets and hierarchies may not be as common as is often assumed. For example, even the seemingly atomistic financial markets are socially embedded (Baker, 1984). Yet, as Holmstrom and Milgrom (1994: 989) have pointed out, these three dimensions are sufficiently practical that the U.S. Internal Revenue Service uses them to determine whether income is taxable as employee wages (i.e., hier-

FIGURE 1 Taxonomy of Pure and Hybrid Governance Forms

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archy) or as the profit of an independent contractor (i.e., market). From Dimensions to Prototypical Hybrid Forms Figure 1 shows a central continuum between pure markets and pure hierarchies in which all three dimensions move in concert. A governance form on this continuum, with moderate levels of ownership, incentives, and authority, would be an intermediate form in that it lies directly between a market and a hierarchy. Yet most of the governance space in Figure 1 lies off of that central continuum, representing hybrid forms that are market-like in some ways and hierarchylike in others. This does not imply that every part of governance space is populated with viable forms. Indeed, some parts of the space might be sparsely populated— or even empty, when the particular combination of governance elements is impractical, infeasible, or unstable. However, it is possible to identify some stable real-world hybrids that are highly popular. We now turn to six prototypical hybrids, each mapped in Figure 1 to illustrate approximately where it fits along the dimensions. They are shown as cloud-like regions rather than points, because these terms are used loosely enough that a variety of similar arrangements may fall under the same label. Empowerment (hierarchy with autonomy). While retaining hierarchy’s weak incentives and principal-owned assets, an empowered organization lets employees engage in selfgovernance rather than relying on formal authority. Advocating greater empowerment, Pfeffer noted that autonomy is one of the most important dimensions of jobs . . . moving from a system of hierarchical control and coordination of activity to one in which lower-level employees, who may have more or better information, are permitted to do things to enhance performance (1995: 61).

This increased autonomy may never reach the pure market extreme (e.g., moonlighting may still be prohibited), but nevertheless is substantially more autonomy than in pure hierarchy.1 1

We would not categorize worker cooperatives as empowerment since they involve an ownership stake. Rather, cooperatives would be somewhere between the empowerment region and the consortium region (low authority but moderate to high ownership).

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Empowerment is common in human-capital– intensive firms and is the norm for faculties of research universities. Piece-rate employment (hierarchy with strong incentives). Another variation on hierarchy has strong authority and principal-owned assets, but, unlike prototypical hierarchies, includes powerful productivity incentives. Again, Pfeffer argued, “If people are responsible for enhanced levels of performance and profitability, they will want to share in the benefits” (1995: 59). We see this in many sales jobs, where commissions are the norm, and in firms like Lincoln Electric (Berg & Fast, 1975; Handlin, 1992) and Nordstrom (Simons & Weston, 1990), which are famous for offering powerful incentives but are hierarchy-like in other ways. The piece-rate label may be somewhat misleading, since the productivity incentives could be quantity based and/or quality based. Autonomus profit center (hierarchy with strong incentives and autonomy). In some cases, when the principal owns the key assets, a transaction may be governed within the legal boundaries of a firm, even though all other governance dimensions are market-like (i.e., weak authority and strong productivity incentives). For example, Walker and Poppo (1991: 67) observed that, in some firms, “in-house units may be governed like market suppliers,” where each division maximizes its own profit and is free to develop both internal and external business opportunities. A similar governance structure can be found in many professional service firms like major investment banks (Eccles & Crane, 1988) and corporate venture capital units, where the main productive assets (intellectual property, reputation, client relationships, etc.) are owned by the firm, yet each senior professional is treated as a profit center, with compensation that is closely tied to his or her productivity (typically in business development) and with a high degree of autonomy. Consortium (market with weak incentives). Some transactions are market-like in all ways except for having relatively weak productivity incentives. For example, a consortium is a mechanism that firms and/or individuals use to collaborate on projects (Evan & Olk, 1990), such as developing shared technical standards or platforms that can be used as part of other products. Open-source consortia in software and online “wikis” are recent popular examples (Kogut & Metiu, 2001). As in markets, consortium members are legally separate entities with their own

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assets, and no member has the authority to dictate operational methods over others. Yet, compared to a market contract, productivity incentives are very weak: consortium members often contribute time and effort on a volunteer basis, with no direct compensation. Rather, their motivation may be the opportunity to influence the project outcome or to gain knowledge (Olk & Young, 1997)—indirect incentives at best. Franchising (market with strong authority). Over 13 percent of U.S. GDP and over 33 percent of retail sales (LaFontaine & Shaw, 1998) take place through franchised businesses—a governance form that provides, in effect, an external market for authority. Franchising resembles a market transaction except for its relatively strong authority relationship: the franchisor (principal) provides the business model—skills, knowledge, routines, procedures, rules, and policies—and, in return, the franchisee (agent) agrees to faithfully apply the model under the franchisor’s direction. Holmstrom and Milgrom identified franchising as a governance form that did not fit their model: Many companies, including McDonald’s, for instance, use in-house managers to operate some units and franchisees to operate others. . . . Franchisees typically receive very strong incentives; in McDonald’s case they pay 5–10 percent royalties on sales, implying an effective commission rate of more than 90 percent. . . . They also get to keep the value added from selling the unit. By contrast, inhouse managers typically receive little or no incentive pay and of course, they receive no portion of the increase in value of the franchise outlet. . . . However, other parts of the franchising evidence do not match our predictions. . . . Franchisees remain on a tight leash: they cannot sell the products of other firms, and many of their operating rules are determined by the franchisor (one could not tell from visiting a McDonald’s whether it is franchised or company-owned) (1994: 988).

Although franchising may not always achieve fully hierarchy-like authority (Michael, 2000, 2002), it nevertheless entails substantially stronger authority than a prototypical market relationship would. Quasi-integration (market with weak incentives and strong authority). Some transactions may take the legal form of a market (the agent owns the assets), even though other governance dimensions are hierarchy-like. Walker and Poppo (1991: 67) noted that “market suppliers may be governed like organizational units,” with long-term contracts as substitutes for vertical integration. Blois

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(1972) observed that such quasi-integration usually occurs when a supplier depends heavily on a single large customer. This grants the customer bargaining power to exercise considerable (though not complete) authority over the supplier. Blois recounted cases where customers used this authority to dictate not only the supplier’s product attributes and production methods but also what other customers it could serve, who its own suppliers were, and even the makeup of its management team. On the incentive side, two common contractual provisions weaken the supplier’s productivity incentives. First, since the customer is often relatively large, it offers a large guaranteed minimum purchase quantity—in effect, a “take-or-pay” provision (MacLeod & Malcomson, 1993) that limits the supplier’s downside risk. Second, the supplier will often give the buyer very significant volume discounts (Blois, 1972: 262), thereby limiting the supplier’s potential upside reward. Taken together, these two provisions can give the supplier lower-powered incentives—that is, more like a flat salary than one might expect from a prototypical market transaction. Although an agent’s incentives and autonomy in quasi-integration may be stronger than those in a prototypical hierarchy, they are still significantly weaker than in a prototypical market. We can see both the strong authority and weak incentive features of quasi-integration in Japanese keiretsu. One analyst captured the strong authority by noting that “Toyota knows its suppliers’ cost structure better than its suppliers do” and captured the weak incentives by noting that “you may never get rich being a supplier to Toyota, but you will never ever go out of business” (WGBH, 1992). Quasi-integration is also common in construction and health care (Eccles, 1981; Luke, Begun, & Pointer, 1989). Theoretical Feasibility of Hybrid Forms Williamson’s (1988, 1991b) “selective intervention” argument contends that hierarchies can never fully achieve all of the incentive intensity or all of the autonomy that one finds in markets (e.g., Foss, 2003), nor can markets ever fully achieve all of the authority that one finds in hierarchies (e.g., Michael, 2000, 2002). We do not disagree with this argument, but we do not believe that it precludes the existence of true hybrid forms. Rather, we simply interpret it to mean that extreme hybrid forms

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that are very close to or exactly at the corners of the cube in Figure 1 may be infeasible. This is why we represent the six hybrid forms in Figure 1 as cloud-like shapes that are somewhere in the general vicinity of their respective corners, but not too close to those corners. This interpretation is consistent with other recent research on this topic. For example, based on a detailed longitudinal case study, Foss argued that hybrids, “in their radical forms, are inherently hard to successfully design and implement” (2003: 331; emphasis added). It is these “radical forms” that would be exactly at or very close to the corners of the cube in Figure 1. Less radical forms, in the cloud-shaped areas of Figure 1, would not be precluded, even though they would still deviate substantially from the pure forms of markets and hierarchies, and from intermediate forms. Furthermore, hybrids pass the “reality check” test of feasibility. As shown above, at least six commonly observed categories of stable hybrids exist in reality. So they must actually be feasible in practice, regardless of whether any conceptual paradigm might view them as infeasible in theory. Nonetheless, there may also be other infeasible areas in governance space that are not near the corners—an empirical question that deserves further exploration. A FORMAL MODEL OF HYBRID GOVERNANCE FORMS Having articulated a taxonomy to describe hybrid forms, we now ask, “When will each hybrid form be optimal?” Many factors may help answer this. Gibbons (2005) has outlined four causal mechanisms—rent seeking, property rights, incentive systems, and adaptation—that play a role in the adoption of hierarchical governance. We do not deny that these (or any other) mechanisms may also help explain hybrid forms—indeed, we discuss a range of such possibilities in our conclusion. Nevertheless, our model draws only on what Gibbons calls “incentive systems,” since this offers a particularly plausible explanation for why some governance elements might become hierarchy-like while others might become market-like. That is, hybrid forms arise as principals exploit synergies across tasks to indirectly induce effort on tasks that cannot be motivated directly. We focus on one causal mechanism to keep the model tractable, manageable, and

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clear. After all, since this is the first formal model of hybrid governance, it is important to avoid overcomplicating the analysis. Governance Dimensions As Motivational Levers for Different Tasks We begin by recognizing that each of the dimensions distinguishing markets from hierarchies also acts as a motivational lever for a category of tasks that an agent2 may perform: (1) Incentives for output completed (sales commissions, piece rates) motivate an agent to increase current production. (2) By allowing the agent to appropriate the value of long-lived productive assets, asset ownership motivates an agent to maintain (or even improve) these assets. (3) Giving a principal authority to enforce rules about what personal activities his or her agent may not perform for the agent’s own benefit, or for other principals (e.g., moonlighting), demotivates the agent from performing those activities.3 Conversely, granting autonomy encourages an agent to pursue such personal activities. Therefore, the three governance dimensions correspond to three activities for which they serve as motivational levers: production, asset maintenance, and personal activities.4

2 For generality, we allow for the possibility that the agent may be either an individual or a firm and that the transaction may be internal or external to the legal entity known as a firm. So, here, an agent may be an employee (individual agent, internal transaction), a contractor (individual agent, external transaction), an organizational subunit (organizational agent, internal transaction), or a supplier firm (organizational agent, external transaction). 3 This includes rules specifying how, when, and where work will be done. Such rules prohibit the agent from mingling work duties with personal activities that he or she might want to do for his or her own benefit, or for other principals. 4 The three governance dimensions motivate the three tasks by allocating three residuals: residual claimancy on the value of output produced, residual rights of control over use of assets (including residual claimancy on their terminal value), and residual rights of control over actions. When the agent’s residual claimancy on the value of output increases, his or her productivity incentives strengthen, encouraging effort on current production. When the agent gains more residual control over assets, he or she achieves added control over their sale, and thereby greater residual claimancy on their sale value, encouraging the agent to maintain the assets more aggressively. When the principal gains more residual rights of control over actions, the principal’s authority increases and the agent’s autonomy declines, thereby discouraging the agent’s pursuit of personal activities.

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“Leverless” Tasks Yet, in addition to these three activities, there may be other potentially important tasks that the agent performs but for which there is no effective motivational lever. For example, jobs requiring cooperation between agents may yield free-rider problems in which some agents shirk rather than exert their full effort (Jacob & Page, 1980; Jones, 1984). Here, cooperation between agents is especially difficult to motivate since it is so hard to monitor (Alchian & Demsetz, 1972; Sewell, 1998; Zenger & Marshall, 2000). When a failure of cooperation occurs, it may be impossible for a principal to identify which of the agents were responsible for the breakdown. As Kerr observed: Goals in areas where quantification is difficult often go unspecified. The organization therefore often is in a position where it hopes for employee effort in the areas of team building, interpersonal relations, creativity, etc., but it formally rewards none of these (1975: 775).

When there are no levers to motivate a task directly, we refer to this as a leverless task. Although cooperation and creativity are classic examples of tasks that can be leverless, other tasks may also be leverless. For the purposes of our model, any leverless task will suffice.5 However, we draw on examples where the leverless task is cooperation among agents. Such cooperation is important in some situations, but not all. Some tasks are modular and require little cooperation (Ethiraj & Levinthal, 2004; Galunic & Eisenhardt, 2001; Sanchez & Mahoney, 1996). In such situations cooperation might even impose costs by encouraging customization and cospecialization, thereby threatening the flexibility that underlies the value of modularity. The fact that the importance of cooperation varies across settings is central to our analysis because our model focuses on how changing the importance of cooperation, or any other leverless task, affects the optimal governance form.

Cross-Task Synergies and the Impact of Leverless Tasks on Governance In situations where leverless tasks are critical, principals may face the classic dilemma of rewarding one behavior while hoping for another (Kerr, 1975), since incentivizing leverable tasks may distract agents’ effort away from leverless tasks (Holmstrom & Milgrom, 1991). Holmstrom and Milgrom (1994) argued that this dilemma can provide a distractionavoidance rationale for using pure hierarchy: by giving agents weak productivity incentives, little asset ownership, and low autonomy, pure hierarchy offers poor motivation for agents to pursue the three leverable tasks, but it also provides little distraction from leverless tasks.6 However, this reduced distraction comes at the severe cost of reducing an agent’s total effort across all tasks. So, distraction-avoidance will only lead to adoption of hierarchy in extreme cases where leverless tasks are absolutely essential. Limitations of the distraction-avoidance mechanism. There are two key problems with the distraction-avoidance mechanism. First, it is passive insofar as it depends critically on the agent’s intrinsic motivation to spur effort on the leverless task. Distraction-avoidance cannot stimulate effort on the leverless task beyond the agent’s own intrinsic motivation. So, for example, if agents are not naturally cooperative (a leverless task), then merely avoiding motivators for other tasks that might distract them from cooperating cannot guarantee that any cooperation will actually occur. A second limitation is that distractionavoidance relies heavily on an assumption that there are no positive synergies across an agent’s tasks. Holmstrom and Milgrom (1994) concluded that as the importance of leverless tasks increases, all three governance dimensions shift together toward hierarchy. But, as we will see, this depends on their assumption

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5 Holmstrom and Milgrom (1994) call these types of tasks “nonselling activities,” since they focus on a scenario where the agent is a salesperson. We use the term leverless instead to emphasize that the model can be applied to many types of agents beyond salespeople and that the central feature of these tasks is the lack of an effective motivational lever.

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As Holmstrom and Milgrom explain, “The only way to provide incentives for nonselling activities [see previous footnote], is by not providing as strong incentives for the other activities” (1994: 984–985). Yet this phrasing is somewhat misleading, since doing so does not “provide incentives” for anything; rather, it merely removes distractions from an activity for which the agent already has some intrinsic motivation. It does not work without some intrinsic motivation.

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that the tasks are not synergistic. In fact, they assumed the opposite—that tasks are countersynergistic (i.e., exerting effort on one task hinders the pursuit of other tasks). While this assumption may hold in certain special cases, it seems unlikely that it will hold in general. Indeed, decades of job design research demonstrates substantial benefits from grouping synergistic tasks into a single job to boost efficiency and motivation (Wong & Campion, 1991). Thus, it would be inefficient to design jobs containing countersynergistic tasks as Holmstrom and Milgrom assumed. Indeed, even Holmstrom and Milgrom acknowledged this by noting that “complementarities in the agent’s private cost of attention can have an important effect both on how jobs should be designed and how agents should be compensated” (1991: 50). The indirect-inducement alternative to distraction-avoidance. As we will show, relaxing this exclusion of cross-task synergies affects the theory in two novel ways. First, it offers a new way to stimulate effort on leverless tasks that is less passive than distraction-avoidance since it does not rely on the agent’s intrinsic motivation. If there are synergies between a leverable task (e.g., production) and a leverless task (e.g., cooperation), then using motivational levers to encourage the leverable task can indirectly induce the agent to increase effort on the leverless task. Holmstrom and Milgrom acknowledged this possibility in writing that a sales agent’s leverless tasks “are undertaken only to the extent that the agent’s marginal cost is negative, which can occur if these activities make selling easier [i.e., a cross-task synergy, which they then explicitly assume away] or if the agent simply values customer appreciation [i.e., intrinsic motivation]” (1994: 982). The second effect of allowing synergies is that it offers a rationale to explain true hybrids. If all task pairs are countersynergistic, as Holmstrom and Milgrom assumed, then increasing the importance of a leverless task will diminish the value of motivating any leverable task, since that would distract the agent away from the leverless task. Thus, all three motivational levers would then be reduced (weaker productivity incentives, lower asset ownership, and less autonomy), so the optimal governance form would shift toward pure hierarchy on all dimensions. However, if

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some tasks are synergistic, the principal might be able to actively, albeit indirectly, induce effort on the leverless task by increasing the motivational levers on leverable tasks that are synergistic with it. Then, depending on the pattern of cross-task synergies, changes in the importance of a leverless task can push the motivational levers in opposite directions (raising some while lowering others) and can thereby shift the optimal governance form closer to any one of the hybrid forms discussed earlier. Concrete Examples of Task Pair Synergies and Countersynergies As mentioned earlier, we consider four types of tasks an agent can perform: current production, asset maintenance, personal activities, and leverless tasks like cooperating with other agents. Examining synergies among these four tasks requires that we look at them not just individually but, rather, in pairs. Among four tasks, there are six possible pairs, which we consider below. Current production and asset maintenance. Countersynergies among these tasks occur for physical assets that deteriorate through use and must be taken “off-line” (i.e., out of production) in order to be maintained. For example, an airplane cannot have maintenance done while it is flying passengers. However, a synergistic interaction can occur for intangible assets—for example, individual skills or organizational routines— that are improved, rather than deteriorated, through use. Such a synergy can occur for any agent whose work consistently requires ongoing “learning-by-doing.” Similarly, a reputational asset may be boosted by meeting or exceeding the current output expectations of the principal (or, if applicable, of the principal’s customers) and may be diminished by output shortfalls. Current production and leverless tasks (cooperation). In many cases an agent’s productivity can be harmed by helping other agents. This is especially true where helping requires transferring or expending a scarce resource like time, money, or physical strength. But sometimes a synergistic effect can occur where cooperation makes the agent more productive. For example, two salespeople might cooperate to sell to a large client that neither could win if working alone. Similarly, an agent may be more effective

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at performing a task when he or she is setting an example for another agent. Current production and personal activities. An agent’s personal activities can lower output by passively diverting scarce resources (e.g., time, money) or by actively impairing the agent’s ability—for instance, sleepiness after a night of partying or from moonlighting on another job. However, synergy can occur when the agent’s personal activities are work related, as when a wine enthusiast works in a wine shop. Productivity may also be enhanced as professional service providers (e.g., lawyers) leverage personal networks to attract clients. If personal activities include work done for other principals, synergies can arise from the production of byproducts (e.g., a slaughterhouse producing beef and leather for different buyers) or nonrival goods (e.g., a consulting report prepared for a client in one industry that can also be used by clients in other industries). Asset maintenance and leverless tasks (cooperation). Helping other agents can reduce an agent’s ability to perform asset maintenance tasks, especially if helping requires transferring or expending a scarce resource like time, money, or physical strength. But a synergistic interaction may be possible for intangible assets like knowledge, skills, or routines when, for example, helping another agent involves transferring that knowledge or skill. As the Roman philosopher Seneca wrote, people learn best by teaching—for example, responding to probing questions from an apprentice may force a craftsman to rethink and improve his or her methods. Similarly, in organizations, knowledge must often be transferred between agents to enhance its value (Kogut & Zander, 1992; Osterloh & Frey, 2000). Synergy may also occur when the key asset in question is reputational, since cooperating with other agents can build social networks that boost and transmit this reputation widely. Asset maintenance and personal activities. The pursuit of personal activities may reduce an agent’s ability to perform asset maintenance tasks, particularly when such activities divert scarce resources (e.g., time, attention) away from asset maintenance. But when the assets used in work for a principal are also used in an agent’s personal activity or in working for other principals, there can be a synergistic interaction. For example, the knowledge

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of vineyards and vintages that the wine enthusiast gathers to inform personal consumption choices can also be a valuable asset for the wine shop where he works. Conversely, any wine knowledge learned via on-the-job training may inform the wine enthusiast’s personal consumption choices. When the personal activity is work done for other principals and the asset is a reputation for performance, synergy is virtually automatic: the more principals whose performance expectations are met, the stronger the reputational asset. Leverless tasks (cooperation) and personal activities. There can be a countersynergistic interaction effect between these tasks when personal activities divert resources (e.g., time, attention, or money) that would otherwise be applied to help other agents. However, a synergistic interaction may occur if the agent’s personal activities are work related and other agents do similar work. For example, knowledge that the wine enthusiast gains from personal consumption may be useful to teach other salespeople at the wine shop where he works. Likewise, an individual may exchange personal contacts with coworkers and thereby enhance both private social networks and team cooperation. Basic Model Assumptions Shared with Holmstrom and Milgrom (1994) Wherever possible, we maintain consistency with Holmstrom and Milgrom’s (1994) notation. We define t1, t2, t3, and t4 as the amount of effort the agent devotes, respectively, to the four tasks discussed above: current production, asset maintenance, leverless activities (e.g., cooperating with other agents), and personal activities. Assume that the ti effort allocations cannot be directly observed by the principal (or by any third party) and are noncontractible. These effort variables represent inputs into the four tasks, not the actual completed performance output from these tasks. For each task, actual performance is determined not only by the effort allocated to it but also by exogenous factors that can either assist or impede the agent in performing that task. Since these exogenous factors are numerous and varied, their aggregate impact on task performance, following the central limit theorem, is a normally distributed random noise term, de-

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noted as ␧i for task i. These noise terms are unobservable and independent, with means of zero and variances of 1/␩i. Thus, we define the performance level on each of the four tasks as follows. Let the dollar value (to the principal) of current output produced over the duration of the contract be X ⫽ t1 ⫹ ␧1, let the assets’ terminal dollar value after the completion of the contract be Y ⫽ t2 ⫹ ␧2, let the performance on the leverless task (e.g., cooperation achieved) be W ⫽ t3 ⫹ ␧3, and let the dollar value (to the agent) of personal activities performed be Z ⫽ t4 ⫹ ␧4. Let the strictly positive parameters pi represent the value created, in dollars, by a unit of performance on the performance metric for task i. However, we have already standardized the performance metrics X, Y, and Z (current production, asset maintenance, and personal tasks, respectively) by defining them in terms of their dollar values to the principal and/or agent. We therefore have p1 ⫽ p2 ⫽ p4 ⫽ 1, leaving only p3 (i.e., the importance of the leverless task relative to other tasks) as a freely adjustable model parameter.7 Following Holmstrom and Milgrom (1994: 975–976), we assume the following. (1) The value of current output, X, is a nontransferable private benefit accruing only to the principal, but it is contractible, and the optimal incentive scheme follows the linear form of s ⫽ a1X ⫹ ␤, where ␤ is the base compensation and a1 is the commission rate or piece rate.8 (2) The terminal asset value, Y, is noncontractible (perhaps because it is permanently unverifiable to any

7 Fixing p1, p2, and p4 in this way simplifies the mathematics but does not qualitatively affect either of the main results we derive from the model—neither the synergyrotation theorem nor the asset-centric synergy proposition. These results are about how governance forms change when p3 changes, which is unaffected by the values of p1, p2, and p4. 8 In a dynamic, multitask, principal-agent model, Holmstrom and Milgrom (1987) showed that if the environment is statistically stationary in the way they defined it, and if the agent can monitor his or her performance continuously, then the optimal dynamic incentive contract is the same as the optimal contract in a reduced-form static model where the principal is constrained to pay the agent a static linear function of the available time-aggregated performance metrics, and where the agent is constrained to choose a static vector of effort allocations. We follow Holmstrom and Milgrom (1994) in using this earlier result to focus exclusively on the static reduced-form model with linear compensation.

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third party, or perhaps because it cannot be observed until so late that ex post “settling up” is no longer viable) but is nevertheless transferable by reassigning asset ownership, in whole or in part, where a2 僆 [0,1] represents the share of asset ownership taken by the agent (with the remainder retained by the principal). (3) The value of personal activities performed, Z, is a nontransferable private benefit accruing only to the agent that cannot be contracted through compensation (i.e., not by the agent paying the principal for the privilege of enjoying these private benefits) but, rather, can only be contracted through exclusions (i.e., rules excluding the agent from engaging in these activities), and where a4 僆 [0,1] represents the percentage of these private personal activity benefits that the agent is permitted to enjoy—that is, the degree of autonomy retained by the agent. (4) The value generated by the leverless task (e.g., cooperation with other agents) is a private benefit accruing only to the principal that is neither contractible nor transferable. While each of the other tasks has an adjustable motivational lever through which it can be manipulated directly (a1, a2, and a4, respectively), there is no corresponding lever for the leverless task. We therefore assume the fixed value of a3 ⫽ 0. Let t be the column vector of effort allocations t1, t2, t3, and t4; let p be the column vector of performance valuations p1, p2, p3, and p4; let ␩ be the column vector of performance measure precisions ␩1, ␩2, ␩3, and ␩4; and let a be the column vector of motivational levers a1, a2, a3, and a4. Let C(t) be the agent’s private cost-ofeffort function, which translates the effort allocation vector t into a dollar value cost in a nonrandom way. Our assumptions about the specific form of C(t), which diverge from those of Holmstrom and Milgrom, will be discussed in the next section. Under governance form a, financial payoffs to the principal and agent, respectively, are then

P ⫽ X ⫹ ( 1 ⫺ a 2 ) Y ⫹ p 3 W ⫺ s ⫽ ( 1 ⫺ a 1 )( t 1 ⫹ ␧ 1 ) ⫹ ( 1 ⫺ a 2 )( t 2 ⫹ ␧ 2 ) ⫹ p 3 ( t 3 ⫹ ␧ 3 ) ⫺ ␤

and (1)

A ⫽ s ⫹ a 2 Y ⫹ a 4 Z ⫺ C ( t) ⫽ ␤ ⫹ a1(t1 ⫹ ␧1) ⫹ a2(t2 ⫹ ␧2) ⫹ a4(t4 ⫹ ␧4) ⫺ C(t). (2)

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Since t, C(t), a, ␤, and p are all nonrandom, it follows that both P and A are linear functions of normally distributed random variables (␧i) and so are also normally distributed themselves. We assume that the principal is risk neutral and, thus, cares only about the expected value:

allow for the possibility of synergies among the tasks, as the principles of job design mandate (e.g., Wong & Campion, 1991), as opposed to assuming that they are always countersynergistic. To accomplish this, we assume a quadratic cost-of-effort function9:

E ( P ) ⫽ ( 1 ⫺ a 1) t 1 ⫹ ( 1 ⫺ a 2) t 2 ⫹ p 3t 3 ⫺ ␤ .

C ( t) ⫽ c0 ⫹ (t ⫺ ␮)⬘⌫d(t ⫺ ␮). (3)

In contrast, we assume the agent has constant absolute risk aversion, as expressed in the exponential utility function U(A) ⫽ ⫺exp(⫺rA). So, under governance form a, the agent bears a risk premium of

R ( a,␩) ⫽ (r/2)关(a21/␩1) ⫹ (a22/␩2) ⫹ (a24/␩4)兴.

(4)

Consequently, the agent’s utility measure can be written in certainty equivalent form as

ACE ⫽ E ( A ) ⫺ R ( a, ␩) ⫽ ␤ ⫹ t⬘a ⫺ C(t) ⫺ R(a, ␩) ⫽ ␤ ⫹ a1t1 ⫹ a2t2 ⫹ a4t4 ⫺ C(t) ⫺ (r/2)关(a21/␩1) ⫹ (a22/␩2) ⫹ (a24/␩4)兴. (5) By merely adjusting the base compensation ␤, a dollar’s worth of certainty equivalent can always be transferred between principal and agent without affecting the agent’s motivational levers or incentives—and, hence, without affecting the agent’s behavior. Therefore, any efficient solution for the principal’s choice of governance form a and the agent’s choice of effort allocation t must maximize their joint surplus—that is, the total certainty equivalent of both the principal and the agent,

TCE ⫽ PCE ⫹ ACE ⫽ E ( P ) ⫹ 关 E ( A ) ⫺ R ( a,␩)兴 ⫽ t1 ⫹ t2 ⫹ p3t3 ⫹ a4t4 ⫺ C(t) ⫺ (r/2)关(a21/␩1) ⫹ (a22/␩2) ⫹ (a24/␩4)兴, (6) subject to the agent’s optimal choice of t to maximize ACE given a. We cannot specify this efficient outcome for (a, t) without first specifying C(t), so we turn to that question next. Our Differentiating Assumption: Cross-Task Synergies in the Cost-of-Effort Function Our sole substantive deviation from the assumptions of Holmstrom and Milgrom (1994) is to

(7)

Each of the elements on the main diagonal of the 4 ⫻ 4 symmetric positive-definite cost structure matrix ⌫d captures the main effect of one task’s effort level on the agent’s private cost of effort, while each of the off-diagonal elements captures a two-way interaction effect between two of the tasks—that is, the extent to which those two tasks may be synergistic or countersynergistic.10 Thus, the elements on the main diagonal of ⌫d must be positive, while the offdiagonal elements are negative if the relationship between the two corresponding tasks is synergistic (since the negative sign indicates that the combined cost of doing the two tasks together is less than the sum of the separate costs of doing the two tasks individually) or are positive if the relationship among the two corresponding tasks is countersynergistic (since the positive sign indicates that the combined cost of doing the tasks together is greater than the sum of the separate costs of doing them individually). The elements ␮1, ␮2, ␮3, ␮4 of the column vector ␮ represent the cost-minimizing values of t1, t2, t3, and t4, respectively. If there were no extrinsic motivational levers whatsoever, the agent would simply minimize C(t) by setting t ⫽ ␮. Therefore, any positive element of ␮ would indicate that the agent has some intrinsic motivation for the corresponding task—the agent would exert some effort on that task even with-

9 This quadratic form for the agent’s private cost-of-effort function simplifies the analysis by limiting synergies to two-way interactions (three- and four-way interactions are set to zero). This preserves the model’s tractability and the intuitive comprehensibility of its results. However, excluding complex higher-order interactions also creates a boundary condition. This compromise is warranted to avoid overcomplicating this initial foray into modeling hybrid governance forms. Future research may generate additional (albeit more complicated) insights by exploring higher-order synergies. 10 The subscript d on ⌫d will be used later to index different possible scenarios about cross-task synergy patterns.

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out extrinsic motivators. Again, Holmstrom and Milgrom’s (1994) model relied on such intrinsic motivation, especially ␮3 ⬎ 0, to ensure that the agent would exert positive effort on a leverless task. However, intrinsic motivation is far less relevant for our model since cross-task synergies allow principals to boost effort on the leverless task indirectly by manipulating the motivational levers for other tasks with which it is synergistic (for further elaboration on this point, see Holmstrom & Milgrom, 1991: 32–33, and footnote 9). Derivation of Efficient Governance Form After substituting the cost-of-effort function from Equation 7 into the agent’s certainty equivalent function from Equation 5, differentiating the resulting ACE with respect to t yields the first-order conditions for the agent’s optimization problem. Assuming an interior solution to the agent’s optimization problem, solving these first-order conditions for the effort vector t would then yield the agent’s optimum effortsupply function, which is linear in the governance form a:

t(a) ⫽ ␮ ⫹ (2⌫d)⫺1a.

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Recalling that p1 ⫽ p2 ⫽ p4 ⫽ 1 and substituting Equations 8 and 9 into Equation 6, we can rewrite the joint surplus, subject to the agent’s effort-supply constraint, as

TCE ⫽ G(a1, a2, a4, p3) ⫹ H(a1, a2, a4, p3), where G(a1, a2, a4, p3) ⫽ 关p ⫺ e ⫺ (a/2)兴⬘(2⌫d)⫺1a

and

H ( a 1 , a 2 , a 4 , p 3 ) ⫽ ( p ⫺ e)⬘␮ ⫺ R(a, ␩) ⫺ c0. (10) We define a1*(p3), a2*(p3), and a4*(p3) as the specific values of the three motivational levers a1, a2, and a4, respectively, that maximize the joint surplus in Equation 10 (recalling that these levers appear in both a and e). We also define the efficient governance form g*(p3) as the vector containing the optimal values of the three levers, a1*(p3), a2*(p3), and a4*(p3), as its elements. Next, we need a way of expressing the directions that these three optimal motivational levers move in response to a change in the importance of the leverless task. So we define the derivative signs

h i ⫽ Sgn(⭸ai*( p3)/⭸p3)

(8)

⫽ (⭸ai*( p3)/⭸p3)/兩⭸ai*( p3)/⭸p3兩 僆 兵1, ⫺1其 (11)

In order to solve for the efficient governance form, the agent’s effort-supply function in Equation 8 then becomes a constraint on the optimization of the two parties’ joint surplus—that is, their total certainty equivalent from Equation 6. First, we substitute Equation 8 into Equation 7 to generate the equilibrium cost of effort as a function of the governance form a under this effortsupply constraint:

and the derivative sign vector h containing elements h1, h2, and h4. Since these sign elements can only take two possible values11 (i.e., 1 or ⫺1), there are 23 ⫽ 8 possible values for h. We therefore define the set D that contains all eight of these possible values—all three-dimensional vectors whose elements are either 1 or ⫺1: D ⬅ {(i, j, k)兩i, j, k 僆 {1, ⫺1}}. Any d 僆 D is called a direction vector.

C ( t(a)) ⫽ c0 ⫹ a⬘(4⌫d)⫺1a.

(9)

Unlike the other tasks, the full benefit of personal activities will not be realized by either party if such activities have been excluded, in part or in whole, under the principal’s authority. The agent’s degree of autonomy, a4, captures the portion of personal activity benefits realized by the agent, and its complement, the principal’s degree of authority, 1 ⫺ a4, captures the excluded portion that neither party can realize. Since this exclusion is unique to the personal activity task, we define e to be the column vector of exclusions, containing 1 ⫺ a4 as its fourth element and zeros as its other three elements.

Synergy-Rotation Theorem The central result from Holmstrom and Milgrom’s (1994) model is illustrated graphically by the central continuum of intermediate forms 11

We intentionally omit cases where one or more of these hi signs is zero, since, for the present paper, we are only interested in cases where changing the importance of the leverless task (p3) moves the efficient governance form closer to one of the eight corners of the governance space in Figure 1. If one or two of the hi signs is zero, then changing the importance of the leverless task alters the efficient governance form but does not move it closer to a corner of the cube.

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shown as the double-ended arrow in our Figure 1. In their model, if the agent’s tasks are all countersynergistic with one another, then increasing the importance of a leverless task, p3, will shift the efficient governance form toward the pure hierarchy end of this continuum in Figure 1. Conversely, in their model, decreasing p3 will shift the efficient governance form toward the pure market end of this continuum. For a graphic visualization of our central result, imagine taking this same continuum from Figure 1 and rotating it so that it points toward any pair of opposite corners of governance space. Rather than having the end of the continuum point toward the pure forms of market and hierarchy, we might have it point toward any hybrid form. We show that for any of the eight corners of the cube in Figure 1, there is some synergy pattern (i.e., some ⌫d) under which increasing the importance of a leverless task (i.e., increasing p3) will move the efficient governance form closer to that particular corner (and farther from the opposite corner). We call this the synergy-rotation theorem. Synergy-rotation theorem: For any direction vector d 僆 D, there exists some cost structure matrix ⌫d such that the corresponding derivative sign vector h ⫽ d. In other words, for any given corner of the governance space, there is some synergy pattern for which the efficient governance form will move closer to that corner when the importance of the leverless task is exogenously increased. We provide formal proof of this theorem in the Appendix. As part of the proof of the theorem, we examine eight specific synergy patterns that generate movement toward each of the eight corners of governance space as the importance of the leverless task increases. This theorem thus offers one mechanism by which hybrid governance forms might arise: Corollary: In the presence of cross-task synergies, hybrid governance forms may arise as a way to indirectly induce effort on a leverless task by motivating some other task or tasks with which the leverless task is synergistic. The following section provides a concrete example of how this theorem and its corollary

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apply to a particular empirical context that can be described by a specific plausible synergy pattern.

EMPIRICAL EXAMPLE: SHIFT TO INTANGIBLE AND REPUTATIONAL ASSETS A recurring theme from our earlier section on concrete examples of task pair synergies was that asset maintenance is more likely to be synergistic with other tasks if the key asset is intangible or reputational than if it is physical. This occurs because maintaining physical assets usually makes them unavailable for use in other tasks, whereas many intangible and reputational assets can actually be maintained more easily when they are being actively used. For example, meeting output expectations, helping other agents, and serving other principals all may help build a reputation for reliable performance. Hence, reliance on intangible and reputational assets tends to create what we call an “asset-centric” synergy pattern, where asset maintenance is synergistic with each of the other three tasks. Such an asset-centric synergy pattern can be seen in the cost structure matrix ⌫d3, from Equation 12 of the appendix. As shown in Case 3 of the Appendix, this asset-centric synergy pattern rotates the continuum of efficient governance forms so that it moves closer to quasi-integration when the leverless task becomes more important, and closer to an autonomous profit center when the leverless task becomes less important. Thus, our model predicts the following (see Case 3 of the Appendix for the proof): Asset-centric synergy proposition: Under the cost structure matrix ⌫d3 (as defined in the Appendix, Equation 12), the derivative sign vector h ⫽ d3 ⫽ (⫺1, 1, ⫺1). In other words, under an asset-centric synergy pattern (i.e., asset maintenance is synergistic with each of the other tasks), increases in the importance of the leverless task (cooperation with other agents) move the efficient governance form closer to quasi-integration, whereas decreases move it closer to autonomous profit centers.

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Lean Manufacturing Creates an Asset-Centric Synergy Pattern Walker and Poppo (1991) offered a ready-made empirical illustration of this phenomenon in their examination of a U.S. automobile manufacturer’s adoption of hybrid supply relationships. In the 1980s, U.S. automobile manufacturers began the process of adopting the “lean manufacturing” techniques that their Japanese rivals, notably Toyota, had pioneered since the 1950s. Essential to the lean manufacturing approach was the concept of “design for manufacturability” (DFM), whereby the product design was radically simplified and streamlined to make the product easier to assemble, thereby resulting in both lower costs and higher quality. This simplified assembly process, in turn, allowed for further efficiency gains by adopting a just-intime (JIT) inventory management system for parts (Abegglen & Stalk, 1985). Shift to intangible assets. The adoption of a lean manufacturing system has two major implications for the relationship between an assembler and its parts suppliers, regardless of whether those suppliers are internal (i.e., other divisions within the same company) or external (i.e., other companies). First, DFM requires that suppliers have much greater involvement in product design at an early stage in the process (Swink, 1999). Indeed, in their study of Japanese and U.S. automobile parts suppliers, Liker, Kamath, and Wasti confirmed that “involving suppliers early and giving them influence over design is associated with greater contributions of suppliers to cost reduction, quality improvement and design for manufacturability” (1998: 214). Noting that this “early sourcing” approach “has long been a practice in Japanese manufacturing firms . . . and is becoming widely adopted” in the United States, Walker and Poppo (1991: 83) observed that the major goal is “to utilize the supplier’s technological expertise.” Thus, suppliers must build and maintain a much higher level of product design skills—a fundamental shift toward intangible assets that improve with experience and use. Shift to reputational assets. A second effect of lean manufacturing on the parts supply relationship is that it makes the assembler much more dependent on a single supplier for each part—a dependence further heightened through the JIT inventory management system—thereby reducing supplier market competition and in-

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creasing the assembler’s switching costs. In the face of this increased vulnerability, assemblers place a much higher premium on a supplier’s reputation for reliable performance. For example, Walker and Poppo observed a dramatically increased preference for single-source suppliers that “consistently performed better than their competitors,” because this performance “represented an investment in reputation that would be damaged if they began to take advantage of their new close relationship” (1991: 71). In sum, a transition to lean manufacturing means that an assembler is no longer simply buying physical parts from its suppliers. Instead, it is now buying a bundled combination of physical parts, design services, and a guarantee of reliable on-time delivery. This change in the product being supplied also provides a convenient “natural experiment” by changing which assets are most critical to the supplier. Previously, the supplier’s critical assets were the physical equipment used to produce the parts, but under lean manufacturing the critical assets now shift to product design skills and reputation for reliable on-time delivery—the very kind of intangible assets whose maintenance is synergistic with the supplier’s other tasks. So, when an assembler shifts to lean manufacturing, one should expect its suppliers to experience a shift to an assetcentric synergy pattern. Need for hybrid governance forms. The assetcentric synergy proposition predicts that when such a shift in assets occurs, the assembler will no longer use the two pure forms of market and hierarchy in its sourcing. Instead, it will begin using the two hybrid alternatives of quasi-integration and autonomous profit centers. Walker and Poppo observed that this is exactly what happened. For internal suppliers, the corporation “released the assembly division from its mandated relationships with the component divisions and allowed it to force them to compete with potential outside suppliers” (1991: 70). In addition, relationships with external suppliers shifted toward quasiintegration. The degree of risk in suppliers’ compensation was significantly reduced, as Walker and Poppo observed: “Before the new policies were implemented, suppliers were contractually obligated to absorb changes in material costs. The new policies replaced this obligation with negotiated adjustments based on an evaluation of supplier costs” (1991: 71). Likewise, the assembler’s authority over suppliers, particularly regarding

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their process improvements and disclosure of their private cost data, was significantly increased: “Suppliers . . . were expected to improve their productivity and quality continuously. These changes increased the level of information exchange with suppliers, especially regarding costs” (Walker & Poppo, 1991: 71). Impact of cooperation between suppliers. In this situation, according to the asset-centric synergy proposition, the importance of cooperation with other parts suppliers should predict whether quasi-integration or autonomous profit centers are used. Adopting DFM means that an assembler cannot delegate the design of different subsystems to separate engineering groups that act independently. Instead, DFM requires that the assembler’s engineers adopt a more holistic team approach to avoid conflicts between subsystems that might impede manufacturability (e.g., avoiding using different fasteners, which require different tools, on different parts of the same car). Dyer and Hatch (2004) have discussed how Toyota created a supplier association (kyohokai) to encourage supplier interaction. In addition, they have described how, when multiple suppliers’ parts interacted in critical ways (e.g., tight tolerances or major consequences from failing to work together), Toyota created more focused cross-supplier teams (jishuken) to address interdependencies in specific subsystems. Both of these structures have been replicated in Toyota’s U.S. supplier networks. Of course, some suppliers’ parts do not interact in critical ways with those of other suppliers, and therefore require little cooperation. Some parts are standard or modular and would be more expensive if they were cospecialized unnecessarily. In this case, cooperation would be unimportant or even undesirable, and the assembler might actually prefer to discourage it. If there are asset-centric synergies, the principal can encourage cooperation between suppliers indirectly through asset ownership. Accordingly, for parts where cooperation with other suppliers is important, our model predicts that the supplier should own the critical intangible and reputational assets, which means using an external supplier. In contrast, for parts where such cooperation is not needed, the assembler should own the assets, which means using an internal supplier.

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In cases where an external supplier is used, asset ownership indirectly motivates cooperation, but it also indirectly motivates effort on current productivity and personal activities. But because these activities are motivated indirectly through asset ownership, it would be wasteful to also motivate them directly through their respective motivational levers (incentives and autonomy). After all, it would be costly to provide strong productivity incentives because of the need to compensate suppliers for bearing the additional risk that is inherent in stronger incentives. From the assembler’s perspective, adding this extra cost would be unnecessary, because the synergy between asset maintenance and production ensures that the supplier’s asset ownership already indirectly motivates production. Likewise, granting autonomy would also inflate costs by allowing the supplier to indulge in “personal” perks, distractions, or other inefficiencies. As a single-source supplier, it might then be able to pass these inflated costs on to the assembler through higher prices. So, to avoid this potentially costly effect of autonomy, the assembler demands authority to ensure that the supplier keeps its costs under control. The resulting combination of agent-owned assets with weak productivity incentives and strong authority generates quasi-integration, as the proposition predicts. The same story runs in reverse for the case of an internal supplier division. In that case the internal supplier’s lack of asset ownership indirectly demotivates current productivity and “personal” activities like selling to other outside assemblers. Using the direct motivational levers of incentives and autonomy counteracts this demotivation, restoring current production to a level that satisfies the assembler and personal activities to a level that satisfies the supply division. The resulting combination of principal-owned assets with strong productivity incentives and weak authority generates an autonomous profit center, as the proposition predicts. A Substantial Departure from Transaction Cost Economics From the perspective of transaction cost economics, these predictions seem counterintuitive. After all, we are suggesting that, under certain circumstances, greater need for cospecialization can cause firms to use external suppliers (albeit quasi-integrated ones) and reduced need for co-

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specialization can cause firms to use internal supplier divisions (albeit divisions of a highly autonomous kind). Interestingly, Walker and Poppo found that conventional transaction cost measures of asset specificity were not very useful in distinguishing between these two hybrid forms, as they had been in earlier studies distinguishing between the pure forms of market and hierarchy: The hybrid characteristics of these supply relationships challenge both the [transaction cost] theory’s basic assumptions and its predictive power. Corporate decentralization and relational contracting [i.e., quasi-integration] in the market diminish the role of asset specificity as a necessary condition for low transaction costs in-house and as a sufficient condition for high transaction costs in the market (Walker & Poppo, 1991: 66).

Of course, our model predicts that the key distinguishing variable should be the importance of cooperation among the parts suppliers, not asset specificity. A replication of the Walker and Poppo study that measures both asset specificity and the importance of cooperation between suppliers would be useful in determining whether our model does a better job at predicting hybrid forms than conventional transaction cost economics. In addition to the asset-centric case discussed here and the fully countersynergistic case that Holmstrom and Milgrom (1994) examined, the Appendix offers six other synergy patterns that can generate movement toward the other six corners of governance space when the importance of the leverless task increases. We do not have enough space in this article to describe real-world cases of these other six synergy patterns, but we are confident that concrete empirical examples for some of these other synergy patterns exist. A researcher interested in finding them might simply start with the examples of task pair synergies that we provided earlier and then look for situations where the right combination of these pairwise synergies would apply. For example, just as the asset-centric synergy pattern was evident for types of assets whose maintenance is broadly synergistic with other tasks, so, too, might a production-centric synergy pattern be evident for types of production processes whose completion is broadly synergistic with other tasks.

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DISCUSSION Although there has been no prior formal theory predicting true hybrid (as opposed to intermediate) governance forms, empirical work shows that hybrids are increasingly important in the organization of economic activity. The examples of stable real-world governance forms in our taxonomy also underscore the need for a more nuanced theory to reflect the complex realities of how economic activities are organized today. Hybrids are now common in large sectors of the economy: (1) in the United States, franchising accounts for over 13 percent of GDP and 33 percent of retail sales (LaFontaine & Shaw, 1998); (2) autonomous profit centers are far more common than most theories would predict (Ramanujam & Varadarajan, 1989) and are the norm for managing senior professionals in many professional service firms; (3) opensource collaborations, standard-setting consortia, and wikis are common in the technology sector; (4) piece-rate-like commissions are the norm for sales employees; and (5) empowerment is the norm in many professions, including academia. At the same time, it is also questionable just how “pure” a pure form can be. Even the purest of market forms, such as financial markets, often have strong relational components (Baker, 1984). So, if we look closer, we may ultimately find that hybrids are the norm and pure forms are the exceptions. We have contributed to the theory of alternative governance forms in three ways. First, we have offered a clear distinction between hybrid forms and intermediate forms that was previously blurred in the literature. Second, we have devised a taxonomy of true hybrid forms that can arise when the three dimensions of incentives, ownership, and authority vary independently. Third, we have developed the first formal model predicting when one might expect to observe a wide variety of hybrid governance forms. Our model is based on the classic problem of how to influence behaviors that lack motivational levers. It addresses why a rational principal might counterintuitively choose a hybrid governance form that rewards one behavior in hopes of achieving another. While the classic article views this as “folly” (Kerr, 1975), our model highlights how incentive patterns that appear superficially to be dysfunctional can nevertheless be quite effective when the right pattern of cross-task synergies is present. This seemingly small change in assumptions about synergies

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generates profoundly different predictions about the viability of hybrid forms than prior governance theories. Implications for Future Research These contributions have a variety of implications for future research that range from testing the relationships implied by the model to extending the model in a variety of ways. An empirical agenda. In terms of empirical research, each of the eight cases considered in the Appendix offers a testable prediction about how cross-task synergy patterns and the importance of leverless tasks can interact to move the optimal governance form toward different corners of the governance space— often generating hybrids. The challenge is to determine when a given synergy pattern will apply to a given empirical context. We offer one example of how this can be done in our discussion of how the shift to lean manufacturing changed the critical assets and thereby created an asset-centric synergy pattern. Another approach within organizations would be to use information that is collected as part of routine job analysis. Many firms gather information on job dimensions and composition to organize tasks effectively and to manage internal and external pay equity (Baron, Davis, & Bielby, 1986; DiPrete, 1987). In the course of these analyses, some tasks are identified as measurable and motivatable while others are recognizable as leverless tasks that may vary considerably in their importance. Of course, not all of these job tasks would correspond to the four task categories that we have modeled here, but it should be possible to identify some that do. In this way, within a firm, it may be possible to examine how and when elements of market governance are applied to motivate leverless tasks. Extending the model. There are also important opportunities to extend our model to develop a more comprehensive formal theory of hybrid governance forms. For example, our model relies only on a single causal mechanism—incentive systems—to explain governance structure. As Gibbons (2005) has pointed out, there are three other causal mechanisms that have been theorized as drivers of hierarchy, and each of these might offer explanations (or insights) for hybrid forms as well. Hierarchical governance, Gibbons argues, may arise (1) as a way to prevent costly ex post “rent seeking” (Williamson, 1975), (2) as a way to moti-

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vate ex ante investments by using property rights to ensure a given distribution of investment returns (Grossman & Hart, 1986; Hart & Moore, 1990), and (3) as a way to facilitate ex post adaptation of the transacting parties’ relationship under externalities (Simon, 1951). It may be worthwhile to extend our model so that it incorporates more of these other mechanisms, in case they, too, might help to explain hybrid forms, and not just pure hierarchy. Yet another possible mechanism for generating hybrid forms would be through the legal and institutional structures in which the transaction is embedded. There may be regulatory reasons to locate a transaction within a firm or as a separate entity that are quite independent of the economic logics that Gibbons enumerates. For example, locating a transaction in a consortium or in a franchise system might avoid some regulations or taxes that apply to firms or markets. Also, different legal regimes that strengthen or weaken property rights— especially the more contestable property rights over intellectual property and other intangible assets— can have a significant impact on which party in a transaction gets assigned ownership of key assets. Some forms of productivity incentives or authority may be illegal in a given jurisdiction (e.g., minimum wage laws or California’s prohibition on noncompete clauses). And some forms of asset ownership may be illegal under securities laws (e.g., insider trading or corporate governance regulations). These legal requirements may place binding constraints on the set of feasible governance forms and might thereby force some transactions into a hybrid form. Our theoretical model abstracts away from all of these legal issues, but they would have to be considered in any relevant empirical context. A final opportunity to make the theory more complete would be to incorporate additional motivational levers beyond just productivity incentives, asset ownership, and job autonomy. Socialization would be one likely candidate. Ouchi (1980) argued that, especially in a “clan” form of organization, socialization and culture can provide a control mechanism that remains effective even when performance ambiguity causes both markets and bureaucracies to fail. He argued that even when tasks are leverless, socialization and culture may substitute for other motivational levers by altering the agents’ underlying preferences to make them more congruent with the principal’s interests: “It is not necessary for these

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organizations to measure performance to control or direct their employees, since the employees’ natural (socialized) inclination is to do what is best for the firm” (Ouchi, 1980: 132). Likewise, Bradach and Eccles argued that “trust” can serve as a control mechanism since it “alleviates the fear that one’s exchange partner will act opportunistically” (1989: 104). In order to be consistent with the standard principal-agent framework, our model has taken the agent’s underlying motivations (i.e., risk preferences and cost-of-effort function) as exogenous and not susceptible to manipulation. Future models might allow for such manipulation by assuming that the principal can, at some cost, use socialization to influence the agent’s motivations—for example, reducing risk aversion or the perceived cost of effort. Implications for Practice Finally, our model may also have implications for practice. It can offer practitioners prescriptive guidelines about when they might change governance structures. In particular, our theory highlights the importance of considering crosstask synergies as a factor in choosing governance forms—a factor that has previously been largely omitted. While our formal model may seem abstract, the underlying motivational problem of leverless tasks is fundamental. Managers are aware of when tasks cannot be directly motivated, and the notion of designing governance structures to motivate them indirectly is not hard to convey. Managers would simply identify how tasks must be grouped, which ones can be directly motivated, and which ones can only be encouraged indirectly. In this way our theory may prove relatively easy to apply in an actual organizational context. APPENDIX: PROOF OF SYNERGY-ROTATION THEOREM This Appendix offers a formal proof of our theorem (below) that, for any direction in governance space, there is a cross-task synergy pattern that will move the efficient governance form in that direction. To accomplish this, we present eight specific task synergy patterns that would generate movement toward each of the eight corners of governance space. Two of these eight patterns have already been discussed at length—the fully

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countersynergistic pattern that Holmstrom and Milgrom (1994) discussed (Case 1 below) and the asset-centric pattern that we discussed (Case 3 below). While a full exposition of concrete examples for each of the remaining six patterns would be too long to include in this article, we are confident that at least some of them correspond to viable real-world settings. Theorem: For any direction vector d 僆 D, there exists some cost structure matrix ⌫d such that the corresponding derivative sign vector h ⫽ d. There are only eight possible direction vectors d 僆 D. We define these as follows: d1 ⫽ (⫺1, ⫺1, ⫺1), d2 ⫽ (⫺1, ⫺1, 1), d3 ⫽ (⫺1, 1, ⫺1), d4 ⫽ (⫺1, 1, 1), d5 ⫽ (1, ⫺1, ⫺1), d6 ⫽ (1, ⫺1, 1), d7 ⫽ (1, 1, ⫺1), and d8 ⫽ (1, 1, 1). Corresponding to each of these direction vectors, we define a cost structure matrix as

⌫ d1 ⫽

⌫ d3 ⫽

⌫ d5 ⫽

⌫ d7 ⫽

冤 冤 冤 冤

␪ ␾ ␾ ␾

␾ ␪ ␾ ␾

␾ ␾ ␪ ␾

␾ ␾ ␾ ␪

␪ ␥ ␾ ␾

␥ ␪ ␥ ␥

␾ ␥ ␪ ␾

␾ ␥ ␾ ␪

␪ ␥ ␥ ␥

␥ ␪ ␾ ␾

␥ ␾ ␪ ␾

␥ ␾ ␾ ␪

␪ ␾ ␥ ␥

␾ ␪ ␥ ␥

␥ ␥ ␪ ␾

␥ ␥ ␾ ␪

冥 冥 冥 冥

冤 冤 冤 冤

␪ ␾ ⌫ d 2⫽ ␾ ␥

␾ ␪ ␾ ␥

␾ ␾ ␪ ␥

␥ ␥ ␥ ␪

␪ ␥ ␾ ␥

␥ ␪ ␥ ␾

␾ ␥ ␪ ␥

␥ ␾ ␥ ␪

␪ ␥ ␥ ␾

␥ ␪ ␾ ␥

␥ ␾ ␪ ␥

␾ ␥ ␥ ␪

␪ ␾ ␥ ␾

␾ ␪ ␥ ␾

␥ ␥ ␪ ␥

␾ ␾ ␥ ␪

⌫d4 ⫽

⌫d6 ⫽

⌫ d8 ⫽

冥 冥 冥 冥 (12)

where parameters ␪ ⬎ 0, ␾ 僆 [0, ␪), and ␥ 僆 (⫺␾, 0], or, equivalently, ⫺␾ ⬍ ␥ ⱕ 0 ⱕ ␾ ⬍ ␪. The limits on ␾ and ␥ jointly guarantee the positivedefiniteness of ⌫di for all i 僆 {1, 2, . . . , 8}, thereby ensuring that C(t) is convex. Each off-diagonal element of the cost structure matrix ⌫di represents the interaction effect on the agent’s cost of effort from combining two different tasks. When an off-diagonal element of the cost structure matrix ⌫di assumes the negative value ␥, this negative sign indicates that the cost of doing the

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two corresponding tasks together is less than the sum of the costs of doing those two tasks separately—that is, that the two tasks are synergistic. Conversely, when an off-diagonal element assumes a positive value, this positive sign indicates that the cost of doing the two corresponding tasks together is more than the sum of the costs of doing those two tasks separately—that is, that the two tasks are countersynergistic. The efficient governance form g*(p3) maximizes the joint surplus TCE from Equation 10. The derivative sign vector h contains the directions that elements of g*(p3) move (1 for up or ⫺1 for down) when the importance of the leverless task, p3, increases. So, for each i 僆 {1, 2, . . . , 8}, we must prove that these derivative signs match the specific pattern contained in di when the particular cost structure matrix ⌫di is substituted into the joint surplus TCE function. To show this, following Holmstrom and Milgrom (1994), we apply the monotone comparative statics theorem for optimization of supermodular functions (Topkis, 1998). Thus, for each i 僆 {1, 2, . . . , 8}, we must demonstrate that the TCE function, with the particular cost structure matrix ⌫di substituted in, is supermodular (over the set of parameters representing the governance form and the importance of the leverless task) when its governance form arguments (a1, a2, a4) are reparameterized so their signs match the pattern in di. When TCE is supermodular with respect to these re-signed parameters, then the monotone comparative statics theorem ensures that the optimum governance form will move in the direction di as p3 increases, so the derivative sign vector h will equal di. Since the joint surplus TCE function is smooth in all cases, it will be supermodular if and only if all of the mixed partial derivatives for every pair of relevant parameters are nonnegative. As Equation 10 shows, TCE is the sum of two functions, G(a1, a2, a4, p3) and H(a1, a2, a4, p3). All of the mixed partial derivatives of H(a1, a2, a4, p3), with respect to any pair of the four parameters, are zero, so H will be supermodular regardless of how one might reparameterize the signs of the three governance form arguments (a1, a2, a4). Since the sum of two supermodular functions is itself supermodular (Topkis, 1998), proving that a reparameterized TCE is supermodular then just boils down to demonstrating the supermodularity of the correspondingly reparameterized G.

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Furthermore, out of the six possible pairings among the four parameters of G, two of these pairs have mixed partial derivatives equal to zero. First, let us rewrite G as follows:

G ( a 1 , a 2 , a 4 , p 3 ) ⫽ 关( 1 ⫺ ( a 1 / 2 )) p3

( 1 ⫺ ( a 2 / 2 ))

( a 4 / 2 )兴( 2⌫ d)⫺1关a1 a2 0 a4兴⬘.

(13)

Then, it can be shown algebraically, for any symmetric ⌫d, that ⭸ 2G ⭸ 2G ⭸2G ⭸2G ⫽ ⫽ ⫽ ⫽ 0 and ⭸a 1 ⭸a 4 ⭸ ( ⫺a1)⭸a4 ⭸a1⭸(⫺a4) ⭸(⫺a1)⭸(⫺a4) 2 2 2 2 ⭸G ⭸G ⭸G ⭸G ⫽ ⫽ ⫽ ⫽ 0. ⭸a2⭸a4 ⭸(⫺a2)⭸a4 ⭸a2⭸(⫺a4) ⭸(⫺a2)⭸(⫺a4)

(14) Therefore, these two mixed partial derivatives must be nonnegative, regardless of how one might reparameterize the signs of the three governance arguments (a1, a2, a4). So, for each of the eight cases, we need only check that the four remaining mixed partial derivatives are nonnegative. Case 1

T 1 ( ⫺a1, ⫺a2, ⫺a4, p3) ⫽ TCE ⫽ G1(⫺a1, ⫺a2, ⫺a4, p3) ⫹ H1(⫺a1, ⫺a2, ⫺a4, p3)

(15)

Consistent with Holmstrom and Milgrom (1994), our model predicts that in this fully countersynergistic case increases in the importance of the leverless task (p3) move the efficient governance form closer to the pure hierarchy corner of governance space, while decreases move it closer to the pure market corner. The TCE, G, and H functions are reparameterized as T1, G1, and H1 so that the signs on their governance arguments (a1, a2, a4) match the pattern of signs in d1 (i.e., all negative). For convenience, let ␻1 ⫽ ␾/(2(␪ ⫺ ␾)(␪ ⫹ 3␾)) ⱖ 0. Once ⌫d1 is substituted into G1, as parameterized in Equation 15, it can be shown algebraically that

⭸ 2G 1 ⭸2G1 ⭸2G1 ⫽ ⫽ ⭸ ( ⫺a1)⭸(⫺a2) ⭸(⫺a1)⭸p3 ⭸(⫺a2)⭸p3 ⫽

⭸2G1 ⫽ ␻1 ⱖ 0. (16) ⭸(⫺a4)⭸p3

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Case 2

T 2 ( ⫺a1, ⫺a2, a4, p3) ⫽ TCE ⫽ G2(⫺a1, ⫺a2, a4, p3) ⫹ H2(⫺a1, ⫺a2, a4, p3) (17) In this case, where personal activities are synergistic with all other tasks, increases in p3 move the efficient governance form closer to empowerment, while decreases move it closer to franchising. T2, G2, and H2 are parameterized so that the signs on (a1, a2, a4) match the pattern in d2. Let ␻2 ⫽ ⫺␥/(2␪(␪ ⫹ 2␾) ⫺ 6␥2) ⱖ 0 and ␻3 ⫽ (␪␾ ⫺ ␥2)/((␪ ⫺ ␾)(2␪(␪ ⫹ 2␾) ⫺ 6␥2)) ⱖ 0. Once ⌫d2 is substituted into G2, it follows that

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a2, a4) in the reparameterized T4, G4, and H4 match the signs in d 4 . Let ␻ 4 ⫽ ⫺ ␥ / (2(␪⫹␾)2⫺8␥2) ⱖ 0 and ␻5 ⫽ (␾(␪ ⫹ ␾) ⫺ 2␥2)/[(␪ ⫺ ␾)(2(␪ ⫹ ␾)2 ⫺ 8␥2)] ⱖ 0. Substituting ⌫d4 in G4, it then follows that

⭸ 2G 4 ⭸2G4 ⭸2G4 ⫽ ⫽ ⫽ ␻4 ⱖ 0 ⭸ ( ⫺a1)⭸a2 ⭸a2⭸p3 ⭸a4⭸p3 and Case 5

T 5 ( a 1 , ⫺a2, ⫺a4, p3) ⫽ TCE ⫽ G5(a1, ⫺a2, ⫺a4, p3)

⭸ G2 ⭸ G2 ⭸ G2 ⫽ ⫽ ⫽ ␻3 ⱖ 0 ⭸ ( ⫺a1)⭸(⫺a2) ⭸(⫺a1)⭸p3 ⭸(⫺a2)⭸p3 2

2

2

⭸2G2 ⫽ ␻2 ⱖ 0. (18) and ⭸a4⭸p3 Case 3

T 3 ( ⫺a1, a2, ⫺a4, p3) ⫽ TCE ⫽ G3(⫺a1, a2, ⫺a4, p3) ⫹ H3(⫺a1, a2, ⫺a4, p3) (19) This is the asset-centric case from our empirical example, where asset maintenance is synergistic with all other tasks. Our model predicts that increases in p3 move the efficient governance form closer to quasi-integration, while decreases move it closer to autonomous profit centers. T3, G3, and H3 are parameterized so that the signs on their governance arguments (a1, a2, a4) match the pattern of signs in d3. Once ⌫d3 is substituted into G3, it can be shown algebraically that

⭸ 2G 3 ⭸2G3 ⫽ ⫽ ␻2 ⱖ 0 ⭸ ( ⫺a1)⭸a2 ⭸a2⭸p3 and

⭸2G3 ⭸2G3 ⫽ ⫽ ␻3 ⱖ 0. (20) ⭸(⫺a1)⭸p3 ⭸(⫺a4)⭸p3

Case 4

T 4 ( ⫺a1, a2, a4, p3) ⫽ TCE ⫽ G4(⫺a1, a2, a4, p3) ⫹ H4(⫺a1, a2, a4, p3) (21) In this case our model predicts that increases in p3 move the efficient governance form closer to a consortium, while decreases move it closer to piece-rate employment. Again, the signs on (a1,

⭸ 2G 4 ⫽ ␻5 ⱖ 0. (22) ⭸(⫺a1)⭸p3

⫹ H5(a1, ⫺a2, ⫺a4, p3) (23) In this case, where current production is synergistic with all other tasks, our model predicts that increases in p3 move the efficient governance form closer to piece-rate employment, while decreases move it closer to a consortium. Again, the signs on (a1, a2, a4) in the reparameterized T5, G5, and H5 match the signs in d5. Once ⌫d5 is substituted into G5, it then follows that

⭸ 2G 5 ⭸2G5 ⫽ ⫽ ␻3 ⱖ 0 ⭸ ( ⫺a2)⭸p3 ⭸(⫺a4)⭸p3 and

⭸2G5 ⭸2G5 ⫽ ⫽ ␻2 ⱖ 0. (24) ⭸a1⭸(⫺a2) ⭸a1⭸p3

Case 6

T 6 ( a 1 , ⫺a2, a4, p3) ⫽ TCE ⫽ G6(a1, ⫺a2, a4, p3) ⫹ H6(a1, ⫺a2, a4, p3) (25) In this case our model predicts that increases in p3 move the efficient governance from closer to autonomous profit centers, while decreases move it closer to quasi-integration. Again, the signs on (a1, a2, a4) in the reparameterized T6, G6, and H6 match the signs in d6. Substituting ⌫d6 into the reparameterized G6, it can be shown algebraically that

⭸ 2G 6 ⭸2G6 ⭸2G6 ⫽ ⫽ ⫽ ␻4 ⱖ 0 ⭸a 1 ⭸ ( ⫺a2) ⭸a1⭸p3 ⭸a4⭸p3 and

⭸2G6 ⫽ ␻5 ⱖ 0. (26) ⭸( ⫺ a2)⭸p3

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Case 7

T 7 ( a 1 , a 2 , ⫺a4, p3) ⫽ TCE ⫽ G7(a1, a2, ⫺a4, p3) ⫹ H7(a1, a2, ⫺a4, p3) (27) In this case our model predicts that increases in p3 move the efficient governance form closer to franchising, while decreases move it closer to empowerment. Again, the signs on (a1, a2, a4) in the reparameterized T7, G7, and H7 match the signs in d7. Substituting ⌫d7 into G7, it follows that

⭸ 2G 7 ⭸ 2G 7 ⫽ ⫽ ␻4 ⱖ 0 ⭸a 1 ⭸p 3 ⭸a 2 ⭸p 3 and

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cases. Since Ti is parameterized so that the signs of its governance arguments (a1, a2, a4) match the signs of the elements of di, the monotone comparative statics theorem ensures that the efficient governance form will move in the direction described by di as p3 increases, so the resulting derivative sign vector h will equal di.

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Case 8

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(29)

In this case, where the leverless task is synergistic with all other tasks, our model predicts that increases in p3 move the efficient governance form closer to pure market, while decreases move it closer to pure hierarchy— exactly opposite Holmstrom and Milgrom’s (1994) prediction. Again, the signs on (a1, a2, a4) in T8, G8, and H8 match the signs in d8 (all positive). Once ⌫d8 is substituted into the reparameterized G8, it can be shown algebraically that

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and

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Conclusion Each of the eight possible direction vectors d 僆 D corresponds to one of the eight cases indexed by i 僆 {1, 2, . . . , 8}. In each of these eight cases, the particular cost structure matrix ⌫di shown in Equation 12 makes all of the mixed partial derivatives of G i nonnegative, and thereby makes Gi supermodular in all eight cases. Since Hi is also supermodular in all eight cases, it follows that the joint surplus total certainty equivalent function Ti, being the sum of Gi and Hi, must also be supermodular in all eight

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Richard Makadok ([email protected]) is an associate professor of organization and management at Emory University’s Goizueta Business School, Atlanta, Georgia. He is also founder and chairperson of the Atlanta Competitive Advantage Conference. He received his Ph.D. from the Wharton School of the University of Pennsylvania. His current research focuses on applying economic modeling techniques to the central theoretical problems and research questions of strategic management. Russell Coff ([email protected]) is an associate professor of organization and management at Emory University’s Goizueta Business School, Atlanta, Georgia. He received his Ph.D. from the University of California Los Angeles. His current research focuses mainly on the role of knowledge-based assets in creating and sustaining a competitive advantage.