Knowledge accumulation means either new knowledge (an increase in its quality), greater access to existing knowledge (an increase in its quantity), or both. The authors examine the relative contribution of these two components of knowledge to total factor productivity (TFP) for North-North and North-South trade-related knowledge diffusion, with quantity, proxied by openness, and quality by the research and development (R&D) content of trade. The measure of foreign R&D used in the literature on trade-related knowledge diffusion, imposes equal contributions to TFP of openness, and of R&D content of trade. The authors' analysis show that R&D has a greater impact on TFP, than openness for North-North trade and, conversely, openness has a greater impact on TFP, than R&D for North-South trade. These results imply that the impact of openness on TFP in developing (industrial) countries is larger (smaller) than previously obtained in this literature, and that developing countries can obtain larger productivity gains from trade liberalization than previously thought.