Linear and Non-Linear Models of Innovation

Making use of Schumpeter’s trilogy, and based on the neoclassical approach, linear models of innovation were developed in the mid-twentieth century. A characteristic feature of linear models is that the innovation process is formalized into sequential stages.

Arrow (1962a, 1962b) contributed to linear models by focusing on the supply side and introducing knowledge and learning as two essential ingredients of the innovation process. Since the production of knowledge is risky and not (perfectly) predictable, future payoffs of R&D are uncertain. This together with the fact that private benefits are smaller than social benefits (especially with respect to basic research) may result in underinvestment, creating the necessity of government intervention. Arrow also argued that competition propels innovation: a monopolist innovates less since he has less to gain from innovation than firms under competitive pressure.

Arrow (1962b) introduced increasing returns to investment in physical capital in a Solow-type growth model. In this context, uncertainty exists only with regard to innova­tions, but not the diffusion process, where learning effects prevail. Once knowledge is created, it is irreversible, that is, if workers change jobs they take with them their expe­rience, which renders them more productive irrespective of where they work. In other words, knowledge once created is directly incorporated in the firm’s workers and costless to move between firms.

Applied to international specialization, Arrow’s argument implies that there are “first mover advantages”: late movers have difficulties making up for the experience first movers have already acquired. The involved aspect of path dependency played an important role in the contributions of Paul A. David, Douglass C. North and Brian Arthur.

Linear models suffer from a lack of feedback effects in the innovation chain. In crit­icizing Arrow for concentrating solely on the role of the innovator, Rosenberg (2000: 62) emphasized the role of imitators for technological change: imitators are “the essential carriers of an improvement process”. Moreover, Rosenberg (1982) stressed that R&D is a complex learning process involving many actors which is clouded by uncertainties. In this process both forward and backward linkages as well as the insti­tutional structure of research systems matter (Mowery and Rosenberg 1989). In early non-linear models, the utilization of innovations and their commercial applicability during the diffusion phase are the focus of attention. Uncertainty turns out to be not only present at the innovation stage, but also during diffusion. Rosenberg (1982) also introduced the concept of “learning by using”: users report their experience with a new machine back to the engineers, who constructed it and who then improve it; a case in point is the aviation industry. As a result, the firm cannot be treated as a “black box” whose internal organization and structure are irrelevant to technological change.