Notes on stochastic R&D races under hazard rate uncertainty.

摘要

The economics of innovation has long relied on the stochastic R& D race model to examine R&D investment, and its link with industry structure. As Choi (1991) points out, the stochastic R&D race model of Loury (1979), Lee & Wilde (1980), and Reinganum (1981, 1982) implicitly assumes that while the timing of innovation is stochastic, the innovation is nevertheless possible. Only certain types of research activity are captured by existing models, labeled “applied research”. However there are research activities in which an innovation may be impossible, labeled “basic research”. These notes develop a model based on Malueg & Tsutsui (1997) in which the timing of the innovation is stochastic, and firms have prior beliefs that the innovation is impossible, also known as “hazard rate uncertainty”. As the race continues without success, firms become increasingly pessimistic that the innovation is impossible, which in turn generates results at variance with the existing literature. This dissertation examines (i) rivalry; (ii) research joint ventures (RJV) and (iii) socially optimal R&D in the context of hazard rate uncertainty. We manage to obtain explicit solutions for investment in each of these cases, something that Malueg & Tsutsui (1997) could not obtain. We show that investment may exhibit non monotonic behavior over time, and the link between industry concentration and R&D investment in basic research is indeterminate, which is a reversal of earlier results for applied research. We identify conditions for firms to form a RJV than compete as rivals. It is shown that unlike the existing literature, that in terms of average expected time of innovation, no ranking of rivalry over RJVs is possible. We also identify cases where the market may over/under invest in applied research relative to the social optimum, but that it is not possible to provide an answer to this issue for basic research.