Investment in knowledge at the firm level is a primary source of productivity growth. Firms invest in R&D and related activities to develop and introduce process and product innovations that enhance their productivity. To account for the fact that investment in knowledge creates long-lived assets for firms, Griliches (1979) augmented the production function with the stock of knowledge. This knowledge capital model has remained a cornerstone of the productivity literature for more than 25 years and has been applied in hundreds of empirical studies on firm-level productivity and also extended to macroeconomic growth models (see Griliches (1995) for a comprehensive survey). While useful as a practical tool, the knowledge capital model has a long list of known drawbacks as explained, for example, in Griliches (2000).
The critical (but implicit) assumptions of the basic model include the linear and certain accumulation of knowledge from period to period in proportion to R&D expenditures as well as the linear and certain depreciation.
The link between R&D and productivity, however, is much more complex. The outcome of the R&D process is likely to be subject to a high degree of uncertainty. Discovery is, by its very nature, uncertain. Once discovered an idea has to be developed and applied, and there are the technical and commercial uncertainties linked to its practical implementation. In addition, current and past investments in knowledge are likely to interact with each other in many ways. For example, there is evidence of complementarities in the accumulation of knowledge (Klette 1996). In general, there is little reason to believe that this and other features such as economies of scale can be adequately captured by simple functional forms.
The first goal of this paper is thus to relax the assumptions on the R&D process that are at the center of the knowledge capital model. In particular, we recognize the uncertainties in the R&D process in the form of shocks to productivity. We model the interactions between current and past investments in knowledge in a flexible fashion. Furthermore, we relax the assumption that the obsolescence of previously acquired knowledge can be described by a constant rate of depreciation. This allows us to better assess the impact of the investment in knowledge on the productivity of firms.
Capturing the uncertainties in the R&D process also paves the way for heterogeneity across firms. Whereas firms with the same time path of R&D expenditures have necessarily the same productivity in the knowledge capital model, in our setting this is no longer the case because we allow the shocks to productivity to accumulate over time. The second goal of this paper is thus to assess the role of R&D in determining the differences in productivity across firms and the evolution of firm-level productivity over time.
To achieve these goals we develop a dynamic model that allows for investment in knowledge, thereby endogenizing productivity change, and derive a simple estimator for production functions in this setting. We use our approach to study the relationship between R&D and productivity in Spanish manufacturing firms during the 1990s.
We start by modeling a firm that can invest in R&D in order to improve its productivity over time in addition to carrying out a series of investments in physical capital. Both investment decisions depend on the current productivity and capital stock of the firm. The evolution of productivity is subject to random shocks. We interpret these innovations to productivity as representing the resolution over time of all uncertainties. They capture the factors that have a persistent influence on productivity such as absorption of techniques, modification of processes, and gains and losses due to changes in labor composition and management abilities. R&D governs the evolution of productivity up to an unpredictable component.
Hence, for firms that engage in R&D, the productivity innovations additionally capture the uncertainties inherent in the R&D process such as chance in discovery and success in implementation. Productivity thus follows a first-order Markov process that can be shifted by R&D expenditures. Subsequently decisions on variable (or “static”) inputs such as labor and materials are taken according to the current productivity and capital stock of the firm.
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