and human capital. In this specification, previous knowledge is used as one of the main inputs for new knowledge. A key feature of this specification is that previous knowledge can be accessed at no additional cost, as if it were a pure public good, for producing new designs of intermediate capital goods. This approach has been taken by many others in the development of endogenous growth models. Although this could be a reasonable assumption as a first approximation to the knowledge function within a closed economy, it might be inappropriate in a global context. Importantly, the first attempt to analyze the predictions of endogenous growth models in the context of an open economy were also made implicitly under the closed-economy assumption. Indeed, in their seminal paper Rivera-Batiz and Romer (1991) (RBR henceforth) developed two approaches for the knowledge function of an economy. In particular, in addition to the stock of (domestic) knowledge, the authors included R&D expenditures as an independent explanatory variable that is unaffected (theoretically) by the stock of previous knowledge. When using the cumulative-knowledge production function, RBR assume that knowledge coming from the domestic and the foreign economy are complements and that both generate positive spillovers of equal magnitude.

This paper generalizes the RBR cumulative-knowledge production function by investigating the impact of several sources of existing knowledge on the generation of new knowledge. That is, we split the sources of the stock of knowledge into domestic, regional or income group, and rest of the world. This approach allow us to test if geographical distance or income per capita gaps are relevant notions of distance for the diffusion of knowledge spillovers across countries. The analysis of product innovation by firms adds another dimension of distance, namely the technological distance between firms, which cannot be assessed using the cross-country patent data.

Thus, the paper is related to the literature on innovation, productivity, and knowledge spillovers. Some contributions, including Bernstein and Nadiri (1989), Jaffe et al. (1993), Audrestsch and Feldman (1996), and Branstetter (2001), highlight that knowledge spillovers are partly localized because the ability to receive knowledge is influenced by the distance from the knowledge source. Others, such as Coe and Helpman (1995), Eaton and Kortum (1996), Xu and Wang (1999), VanPottelsberghe-De-La-Potterie and Lichtenberg (2001), Keller (2004), Javorcik (2004) and MacGarvie (2006) suggest instead that knowledge flows across countries embodied in international trade flows, either in intermediate input or equipment imports or in final goods.

The analysis of patents seems similar to research by Bottazzi and Peri (2007), who used cointegration techniques to test for a long-run relationship between a country’s R&D, its stock of ideas, and the stock of ideas from the rest of the world. They use as sample of fifteen OECD countries for the period 1973-1999. We depart from their analysis by testing directly the validity of the assumptions behind endogenous growth theories rather than its expected consequences. We also test for spillovers from patents stocks and R&D impact on new knowledge. Finally, we estimate panel-count-data models that allow us to deal with the integer nature of patent counts, and the 2