Theoretical Background

Theoretical Background

Discussions of the hold-up problem and its implications for firm boundaries typically list a standard string of references—including Williamson (1975, 1985), Klein et al. (1978), Grossman and Hart (1986), and Hart and Moore (1990)—as if they were the building blocks in a single coherent theory of ownership. This is not the case. There are certainly points of similarity, particularly that contractual incompleteness necessitates ex post bargaining, causing potential problems for efficiency. But the detailed logic of the stories differs, resulting in quite different empirical predictions.[3] Our brief review of the transactions cost and property rights theories aims at highlighting these distinctions.

Modern transactions cost economics originated with Williamson. His views have evolved somewhat over the years. His early work (Williamson 1975) tended to emphasize ex post inefficiencies that arise in bilateral relationships—for example, when bargaining occurs under asymmetric information—rather than relationshipspecific investments and hold-ups, while his later work has paid more attention to initial, specific investments (Williamson 1979, 1985). But this shift in emphasis has not significantly affected the operational content of his theory, which remains premised on the idea that one can identify key dimensions of individual transactions such that, when described in terms of these dimensions, every transaction can be mapped into a most efficient institutional arrangement.

Williamson (1985) suggests that three transaction characteristics are critical: frequency, uncertainty, and most especially, asset specificity (as measured by the foregone economic benefits of discontinuing a relationship). Each characteristic is claimed to be positively related to the adoption of internal governance. The basic logic is that higher levels of uncertainty and higher degrees of asset specificity, particularly when they occur in combination, result in a more complex contracting environment and a greater need for adjustments to be made after the relationship has begun and commitments have been made. A hierarchical relationship, in which one party has formal control over both sides of the transaction, is presumed to have an easier time resolving potential disputes than does a market relationship. The frequency of a transaction matters because the more often it takes place, the more widely spread are the fixed costs of establishing a non-market governance system.

For the purpose of later comparison, we want to single out a few distinguishing features of Williamson's three-factor paradigm. First, it makes no reference to the direct costs of up-front, ex ante investments. For example, there is no differentiation between a case where a specialized asset costs $10 million and one in which the asset costs $100 million, provided that the assets in both cases are worth the same amount more inside the relationship than outside it. There need not even be any up-front expenditures at all: The original, ex ante "investment" could just be an initially costless choice of partner or standard or something similar that limits a party's later options. Williamson (1985) places particular weight on this last case, referring to "The Fundamental Transformation" that occurs when an exchange relationship moves from an ex ante competitive situation, with large numbers of potential trading partners, to an ex post, small-numbers one, once commitments have been made. The theory's indifference to the level of initial investments is consistent with the assumption that the carrying out of such investments is fully contractible (as might well be the case with the investment in automobile dies) and hence poses no incentive problems.

Second, in Williamson's approach the implicit measure of asset specificity is the aggregate level of quasi-rents created by the investment. With two parties, say a buyer B and a seller S, asset specificity and aggregate quasi-rents are measured as V VB VS, where V is the capitalized value of the jointly controlled assets in a continued relationship and VB and VS are the go-alone values of the individually controlled assets in case B and S separate. In this expression, only the sum VB + VS, rather than the individual values VB and VS, matters. On this account, an asymmetric relationship with one party in a dominant position is no different from a symmetric one with the same level of aggregate asset specificity.

Third, taking the transaction as the unit of analysis runs into problems when one starts to consider the costs of bureaucracy and hierarchy more generally, because these costs quite clearly relate not to one single transaction, but to the whole collection of transactions that the hierarchy covers (Milgrom and Roberts 1992, pp. 32–33).

Finally, Williamson treats market trade as a default that is assumed superior to within-organization trade unless levels of uncertainty, frequency, and asset specificity are high enough to pull the transaction out of the market. Because the market is the default, its benefits are not spelled out as clearly as its costs. In transactions cost economics, the functioning market is as much a black box as is the firm in neoclassical microeconomic theory. An assortment of conditions has been adduced by Williamson and others to limit firm size—costs of bureaucracy, the weakening of individual incentives, the hazards of internal politicking, and so on—but none of these costs is easy to measure, and (perhaps for this reason) they have not played much of an empirical role.[4]

A major strength of the modern property rights approach, pioneered by Grossman and Hart (1986),[5] is that it spells out the costs and benefits of integration in a manner that does not rely on the presence of an impersonal market. The theory takes ownership of non-human assets as the defining characteristic of firms. A firm is exactly a set of assets under common ownership. If two different assets have the same owner, then we have a single, integrated firm; if they have different owners, then there are two firms and dealings between them are market transactions. Decisions about asset ownership—and hence firm boundaries—are important because control over assets gives the owner bargaining power when unforeseen or uncovered contingencies force parties to negotiate how their relationship should be continued. The owner of an asset can decide how it should be used and by whom, subject only to the constraints of the law and the obligations implied by specific contracts. Assets become bargaining levers that influence the terms of new agreements and hence the future payoffs from investing in the relationship. In contrast to transactions cost economics, the standard property rights models assume that all bargaining, including any that occurs after investments are made, is efficient. Thus, everything turns on how ownership affects initial investments, but unlike Klein et al. (1978), it is essential that these investments are non-contractible.[6]

To illustrate, in Hart and Moore (1990) each agent makes (non-contractible) investments in human capital that are complementary with a set of non-human assets. Each agent necessarily owns his or her own human capital. The ownership of the non-human assets, however, affects the incentives to invest in human capital. Once the investment is made, ex post bargaining determines the allocation of the returns from the investments. This bargaining is assumed to give each party—that is, the buyer B or the seller S—what it could have obtained on its own, VB or VS, plus a share of the surplus created by cooperation.

Specifically, payoffs take the form Pi = Vi +½(V Vi Vj), i, j = B, S, where as before V is the capitalized value of cooperation. Ownership influences the separation payoffs VB and VS, since the owner of a particular asset gets to deny the other party the use of it if cooperation is not achieved. Ownership does not influence V, since all assets are in use when the parties cooperate. Neither party's investment affects the other's separation payoff, because if they do not cooperate then neither has access to the other's human capital and the investment in it.

Individual incentives to invest are driven by the derivatives of the payoff functions PB and PS. If V VB + VS for all levels of investment, then individual returns to investments coincide exactly with the social returns, as measured by the derivatives of V. This case corresponds to a competitive market, because no extra value is created by the particular relationship between B and S; both parties would be equally well off if they traded with outsiders. In general, however, the social returns and the individual returns differ, resulting in inefficient investments. In particular, if the payoff functions are supermodular,[7] so that the payoff to incremental investment by one party is increasing in both the volume of non-human assets available to that party and the amount of the other party's investment, then there is underinvestment. One can strengthen the incentives of one party by giving that party control over more assets, but only at the expense of weakening the incentives of the other party. There is a trade-off, because ownership shares cannot add up to more than 100 percent. This trade-off determines the efficient allocation of ownership.

Several conclusions follow from this model. For instance, as investment by the buyer B becomes more important (for generating surplus V) relative to investments by the seller S, B should be given more assets. B should be given those assets that make VB most sensitive to B's investment. If an asset has no influence on B's investment it should be owned by S. For this reason, no outsider should ever own an asset—that would waste bargaining chips that are precious for incentive provision. For the same reason, joint ownership—meaning that both parties have the right to veto the use of the asset—is never optimal. As a consequence, assets that are worthless unless used together should never be separately owned.

While these implications regarding joint ownership, outside ownership, and coownership of perfectly complementary assets are often stressed, it is important to keep in mind that they are easy to overturn by slight changes in assumptions. For instance, joint ownership may be desirable when investments improve non-human assets. Third-party control can be desirable if, otherwise, parties would invest too much in improving their outside opportunities to strengthen their bargaining positions (Holmström and Tirole 1991, Holmström 1996, Rajan and Zingales 1998).And most conclusions are sensitive to the particular bargaining solution being used (de Meza and Lockwood 1998). What does survive all variations of the model is the central idea that asset ownership provides levers that influence bargaining outcomes and hence incentives.

In contrast to Williamson's three-factor framework, there is no uncertainty in this model. Frequency plays no role either (although it can be introduced with interesting results, as in Baker, Gibbons, and Murphy 1997, or Halonen 1994). Most strikingly, the level of asset specificity has no influence on the allocation of ownership. The predictions of the model remain unchanged if one increases the total surplus V by adding an arbitrarily large constant to it, because investments are driven by marginal, not total, returns. This is problematic for empirical work, partly because margins are hard to observe when there are no prices and partly because some of the key margins relate to returns from hypothetical investments that in equilibrium are never made. Indeed, as Whinston (1997) has noted, the extensive empirical research geared to testing Williamson's three-factor framework casts no light on the modern property rights models.

As noted earlier, a virtue of the property rights approach is that it simultaneously addresses the benefits and the costs of ownership. Markets are identified with the right to bargain and, when necessary, to exit with the assets owned. This greatly clarifies the market's institutional role as well as its value in providing entrepreneurial incentives. On the other hand, firms are poorly defined in property rights models and it is not clear how one actually should interpret the identities of B and S. In an entrepreneurial interpretation, B and S are just single individuals, but this seems of little empirical relevance. If, on the other hand, firms consist of more than one individual, then one has to ask how one should interpret the unobserved investments (in human capital) that cannot be transferred. An even more fundamental question is why firms, as opposed to individuals, should own any assets. At present, the property rights models are so stylized that they cannot answer these questions.[8]

[3]Whinston (1997) takes a close look at the empirical distinctions of transactions cost theory and property rights theory.

[4]This is changing. Recently, for example, influence cost ideas (Milgrom and Roberts 1988, 1990, Meyer, Milgrom, and Roberts 1992) have been used to explain observed inefficiencies in internal capital markets (Scharfstein 1998, Shin and Stulz 1998).

[5]Hart and Moore (1990) and many others have developed the property rights approach further. See Hart (1995). Recent additions include DeMeza and Lockwood (1998) and Rajan and Zingales (1998). Holmström (1996) offers a critical commentary.

[6]If the parties can contract on the investments, the assumption of efficient bargaining means that they will be made at the efficient levels, irrespective of ownership patterns.

[7]Supermodularity of a function means that an increase in one argument increases the incremental return from all the other arguments. With differentiable functions, the cross-partials are all non-negative. In the Hart-Moore model, supermodularity refers both to human capital and to assets, so that having more assets implies a higher marginal return to all investments. See Milgrom and Roberts (1994).

[8]Holmström and Milgrom (1994) and Holmström (1996) argue that the function of firms cannot be properly understood without considering additional incentive instruments that can serve as substitutes for outright ownership. Employees, for instance, typically own no assets, yet they often do work quite effectively. In these theories asset ownership gives access to many incentive instruments and the role of the firm is to coordinate the use of all of them. That may also explain why non-investing parties, including the firm itself, own assets.