Empirical studies at the individual firm level often find a positive impact of external R&D on innovation. However, external R&D sourcing might produce an impoverishment of the local knowledge base and thus damage innovation production at the regional level. To address this possible fallacy of composition, we first review the various forms of ‘external’ R&D. We then use the French R&D survey to assess the impact of four different ways of transacting or collaborating on R&D: onshore affiliate external R&D, offshore affiliate external R&D, onshore non-affiliate and offshore non-affiliate external R&D. We then estimate knowledge production functions on the 94 metropolitan French NUTS3 regions observed between 1997 and 2008, differentiating internal R&D and these categories of external R&D. We obtain that the impact of onshore non-affiliate external R&D is significantly negative. The other external R&D categories are non-significant and we do not detect any complementarity between internal and external R&D.