Potential limitations to applying strategic complementarity

The following discussion of limits to the applications of supermodularity and strategic complementarity in practice specifically focuses on Porter’s “What is Strategy” paper (Porter, 1996). The emphasis on that paper reflects two issues. First, as with Porter’s paper, this investigation has a specific focus on descriptive theory and implications for practice, rather than the development of econometric models.

Second, Porter’s paper provides one of the most recognized treatments of the strategic complementarity framework. The limitations identified heredo not detract from the relevance, importance, or rigor of Porter’s publication. The goal is to identify potential extensions of theory that help explain observations in an entrepreneurial context and point towards normative theory.

To begin, the translation from the mathematical specificity of supermodular functions operating on a lattice to complementarity or synergy of organisational elements may be somewhat greater than characterized in the literature. It is important to distinguish between the two, both to characterize application to practice as well as present limitations to descriptive and predictive theory. Supermodularity is the characteristic of a function or system in which elements are mutually reinforcing at every quantity and change effect. Supermodularity is not necessarily a good mathematical interpretation of complementarity, because complementarities may incorporate complex functional features whereas supermodular functions may be represented with strictly monotonically increasing relationships (Chambers &

Echenique, 2006). In other words, it isn’t necessarily appropriate to extend results of econometric and mathematical exercises based on supermodularity to the application of strategic complementarity or synergy in real world contexts without clearly specifying the relaxation of assumptions and resulting effects.

Even considering this restriction, a theory of strategic complementarity as driver of organisational performance has certain limitations. First, models of complementarity rely on objectively assessable characteristics of resources or activities and the mathematically specified potential benefits, or costs, associated with their interactions. In reality, of course, the interaction of resources, activities, and higher-level organisational functions are mediated via human agents, creating

two potential sources of uncertainty. Interaction between otherwise complementary elements may be imperfect because of human error; similarly the interpretation of outcome may be flawed either ex ante or ex post, inhibiting the effects or misinterpreting the source of complementarity. Milgrom and Roberts (1995) argue that centralization may mitigate the risk of failing to implement systematic changes required to achieve complementarity. Regardless, it is difficult to objectively determine whether unachieved benefits are due to incomplete complementarity or flawed implementation or interpretation.

Additionally, complementarity relies on the assumption of objectively identifiable measurements of “fitness:”

While operational effectiveness is about achieving excellence in individual activities, or functions, strategy is about combining activities…. Fit locks out imitators by creating a chain that is as strong as its strongest link. (Porter, 1996) 70

This is a form of structural contingency theory (Woodward, 1965) that presumes an “ideal” configuration must exist for a given set of internal elements for a given exogenous context. Even if real, such a configuration would be ephemeral and specific to constantly changing circumstances. The presumption that ideal configurations either do not change or change slowly and smoothly may be reasonable for some industries, but certainly not universally so. Recent research on Lincoln Electric, in fact, has suggested that the very activities and resources that serve as the basis of complementarity in one context may not function synergistically in another (Siegel & Larson, 2009).

Another limitation lies in the selection of set elements intended to demonstrate complementarity. On the one hand, limiting the set to homogeneous elements, such as similar resources or activities, but not both, improves the probability of effectively

assessing the complementarity of the output function. At the same time, such restrictions reduce the accuracy of measuring performative effects at the firm level, because few firms operate on homogenous resource sets. Kim and Finkelstein (2009) mitigate these limitations by assessing potential rather than actualized value associated with complementarities in acquisition processes, but this has the effect of transferring the uncertainty of assessment from the independent to the dependent variable. Related research ties achieving complementarity to the combination of resource fit and alliance status in an institutional framework (Lin et al., 2009). A study on knowledge complementarity suggests that benefits accrue only in the presence of relatedness across heterogeneous product, customer, and managerial knowledge types (Tanriverdi & Venkatraman, 2005).

In part, these limits stem from cognitive effects. In the case of objectively-identified, absolute, and uniform resources, as described for example, by Wernerfelt (Wernerfelt, 1984), the utility of complementarity may also be objectively specified.

Few, however, if any organisations can realistically be reduced to bounded portfolios of such resources. The addition of intangible resources and dynamic capabilities seems to render an objective complementarity-derived utility function impossible.

From an institutional perspective, a critical component in the operationalization of complementarity outcomes may be the norms and structures both within and without the organisation (Siegel & Larson, 2009). Both the application and perceived value of these resources and elements are mediated through cognitive processes. agents within an organisation utilising cognitive models of observed information to enact decisions, events, and outcomes within that model as part of the decision and action process (Child, 1997; Daft & Weick, 1984). In addition, managerial action is heavily driven by attention (Ocasio, 1997) as managers only develop models via

attention-based observations. Cognition, then, is inextricably intertwined within the complementarity of the resource or activity-based system. Organisations are not simple machines; the processes of black-box cognition within organisations remains an important determinant of behavioral and organisational outcomes. In most, if not all organisations, then, cognition plays a role in the potential and obtained complementarity of elements, especially non-objectively defined elements such as vision and leadership or intangible talents and dynamic capabilities.

Another potential problem with strategic complementarity is the lack of testability. Organisational systems specified as supermodular or quasi-supermodular functions may have no testable implications (Chambers & Echenique, 2006). In other words, it may not be possible to prove or disprove whether systems of mutually-reinforcing elements result in competitive advantage. Although the mathematical derivation is specific to supermodular systems (Chambers & Echenique, 2009), it is uncertain whether the relaxation of assumptions associated with quasisupermodularity and strategic complementarity are sufficient to enable testing of inherent competitiveness.

Finally, the strategic complementarity treatment incorporates a potential tautology. First, strategic complementarity of elements leads to competitively advantage positions via optimal, hard-to-imitate fitness:

Strategy is creating fit among a company's activities. The success of a strategy depends on doing many things well- not just a few- and integrating among them. If there is no fit among activities, there is no distinctive strategy and little sustainability… (Porter, 1996: 75)

While fitness is valuable because it improves configurations of uniquely complementary elements:

Although some fit among activities is generic and applies to many

companies, the most valuable fit is strategy-specific because it enhances a position's uniqueness…(Porter, 1996: 71)

In other words, strategic advantage comes from unique sets of well-fitted activities, because unique sets of well-fitted activities generate strategically advantageous positions. Strategic complementarity qua supermodularity was presented as a mathematically sound interpretation of “fitness” (Milgrom & Roberts, 1995) that extended prior research on the relevance of fit to organisational behavior and outcomes (Drazin & Van de Ven, 1986). The strict mathematical treatment explains the virtuous cycle of economies of scale, for example, but the inherent competitive value of a unique and difficult-to-imitate set of activities has not been demonstrated. It seems unlikely that the fundamental, necessary and sufficient attributes of strategic success are strangeness and inimitability. The tremendous success of generic pharmaceutical firms like Teva would seem to present counterexamples.