R&D and Productivity: Estimating Production Functions when Productivity is Endogenous

We develop a simple estimator for production functions in the presence of endogenous productivity change that allows us to retrieve productivity and its relationship with R\&D at the firm level. By endogenizing the productivity process we build on the recent literature on structural estimation of production functions. Our dynamic investment model can be viewed as a generalization of the knowledge capital model (Griliches 1979) that has remained a cornerstone of the productivity literature for more than 25 years. We relax the assumptions on the R\&D process and examine the impact of the investment in knowledge on the productivity of firms. We illustrate our approach on an unbalanced panel of more than 1800 Spanish manufacturing firms in nine industries during the 1990s. Our findings indicate that the link between R&D and productivity is subject to a high degree of uncertainty, nonlinearity, and heterogeneity across firms. By accounting for uncertainty and nonlinearity, we extend the knowledge capital model. Moreover, capturing heterogeneity gives us the ability to assess the role of R&D in determining the differences in productivity across firms and the evolution of firm-level productivity over time.