This paper devises an endogenous growth model with physical capital, human capital and product variety.
Differently to previous works, innovation is subject to externalities associated to the duplication of research
effort, as well as to R&D spillovers. We provide conditions for the existence of a unique feasible steady-state
equilibrium with positive long-run growth. For appropriate parameter values, the transitional dynamics of the
model is represented by a two-dimensional stable manifold. Numerical simulations show that the
incorporation of duplication externalities significantly increases the ability of the model to fit the observed
data.
Physical capital accumulation, knowledge formation, and R&D-based technological progress are considered the three main sources of growth. Although the bulk of the theoretical literature has treated them as alternative rather than complementary explanations, Arnold, 2000 and Funke and Strulik, 2000 (AFS henceforth) have combined them into an endogenous growth model with physical capital, human capital and R&D, whose equilibrium dynamics has been correctly analyzed by Gómez (2005). In the AFS model, invention of new ideas depends solely and linearly on effective time devoted to these activities. Based upon empirical evidence (e.g., del Barrio-Castro et al., 2002), Sequeira (forthcoming) incorporates R&D spillovers in innovation – a “standing on shoulders” effect (e.g., Jones, 1995a) – to the AFS model. However, the simulation results reported by Gómez (2005) – for the AFS model – and Sequeira (forthcoming) exhibit counterfactual highly oscillatory dynamics for variables as, e.g., education and innovation time for which history has shown a monotonic evolution (see, e.g. Jones, 2002).
This paper shows that adding an externality in R&D associated to the duplication and overlap of research effort – a “stepping on toes” effect (e.g., Jones, 1995a and Stokey, 1995) – to the Sequeira (forthcoming) model with R&D spillovers significantly increases its fit to data. Such duplication externality can be justified intuitively because the larger the number of people searching for ideas, the more likely it is that duplication of research would occur. In that case, doubling the number of researchers will less than double the number of unique ideas or discoveries. Empirical evidence of diminishing returns caused by duplicative research has been reported, e.g., by Kortum (1993). Lambson and Phillips (2007) found that the probability of duplication is not low for most industries. Griliches (1990) reported some evidence of diminishing returns found in the patent literature. Therefore, this duplication externality is also entirely plausible.
The purpose of this paper is twofold. First, we analyze the equilibrium dynamics of the model. Whereas the system that describes the dynamics of the AFS model has order three, Sequeira (forthcoming) shows that the introduction of R&D spillovers increases its order to four. We show that adding also duplication externalities further increases the order of the dynamic system to five. We provide conditions for the existence of a unique feasible steady-state equilibrium with positive long-run growth. We then analyze its (local) stability. The transition dynamics is represented by a two-dimensional stable manifold and, despite the complexity of the dynamic system, we provide a sufficient condition for stability. However, the instability outcome cannot be ruled out. Second, we present some numerical results showing that the introduction of duplication externalities significantly increases the ability of the model to generate realistic transition dynamics.
The rest of this paper is organized as follows. Section 2 presents the model. Section 3 analyzes the balanced growth equilibrium. Section 4 presents some simulation results. Section 5 concludes.
This paper devised an integrated endogenous growth model with physical capital, human capital and R&D. The main novelty with respect to previous literature is that innovation is subject to externalities associated to the duplication of research effort, as well as to R&D spillovers. First, we provide conditions for the existence of a unique feasible steady-state equilibrium with positive long-run growth. Then, we analyze its (local) stability. The transitional dynamics of the economy is represented by a two-dimensional stable manifold, and a simple sufficient condition for stability is provided. However, equilibrium instability cannot be ruled out. Our simulation results show that the introduction of a duplication externality significantly increases the ability of the model to fit the observed data.
