Spillovers, rivalry and R&D investment.

• Author: Goel, Rajeev K.

1. Introduction

   Spillovers of research knowledge are unavoidable. Most technologies have some public good aspects. Moreover, rival firms are able to, through industrial espionage and reverse engineering, access and copy new innovations and are thus able to eat into monopoly profits of innovators. The threat of spillovers affects R&D investments and consequently reduces innovative activity. Imitators spend resources on acquiring or copying existing innovations -- resources that would have otherwise gone into the pursuit and development of new products and processes. Industries with excessive spillovers are likely to have little private R&D investment and might have to rely on public R&D funding.

   While patents are designed to provide protection to inventors, they provide only imperfect protection against imitation. Mansfield, Schwartz, and Wagner[13] have shown that a large number of patented innovations are copied in a relatively short time. When patents do not provide adequate protection against spillovers, fewer innovations might be forthcoming and firms might choose to not patent.

   Research spillovers, however, are not without their benefits. Whereas perfect appropriability generates static efficiency by conferring a monopoly on an innovator, spillovers might be more efficient in a dynamic sense because of reduced duplication of research effort and perhaps more innovations in the long run. The presence of R&D spillovers thus creates a wedge between private and social returns to R&D.

   While most of the literature on the economics of technical change has ignored research spillovers (see Kamien and Schwartz[9] for a review), recently researchers have provided careful accounts of different aspects of R&D spillovers[1; 2; 3; 11]. In an empirical investigation of R&D spillovers, Bernstein and Nadiri[1] find that whereas spillovers are prevalent nearly everywhere, there is substantial variation across industries in the private and social returns to R&D. Some researchers have argued that firms might voluntarily choose to disclose scientific information[3]. Griliches[7] discusses the difficulties with empirically determining the extent of R&D spillovers and provides a nice review of the literature on knowledge spillovers.

   This paper's main contribution is to look at the effects of imperfect appropriability of innovation rewards in a dynamic model where innovation is uncertain. Aspects of innovation uncertainty deal with the race to innovate first and/or with R&D investment sufficient to guarantee success. There is some probability that a firm will beat all its competitors and be the first to innovate. If the firm innovates before anyone else, it receives the rewards minus the losses from exogenous spillovers. If, on the other hand, someone else succeeds in innovating first, the firm is still able to benefit from spillovers of successful inventors. Of course, it pays to be an innovator than an imitator. Therefore, the problem facing the firm is to choose that level of R&D investment which maximizes the expected rewards from innovation, plus expected benefits from spillovers in case the firm is unable to innovate first. The effects of research spillovers and R&D rivalry on R&D spending are studied. We are also able to compare our results to similar models of R&D behavior that do not include R&D spillovers and/or innovation uncertainty. Public policy implications of our results are finally discussed.

2. The Model

   We study the R&D behavior of a firm pursuing an uncertain innovation. The expected rewards to successful innovation (R) are given. However, there is an industry held estimate that the rate of revenue loss due to knowledge leakage is K per cent. In other words, due to spillovers from imitation the first firm to invent a new product is only able to capture the...