Studies which are based on Coe and Helpman (1995) and use weighted foreign R&D variables to estimate channel-specific R&D spillovers disregard the interaction between international R&D spillovers and other unobserved common spillovers and shocks. Using a panel of 50 economies from 1970-2011, we find that disregarding this interaction leads to inconsistent estimates whenever knowledge spillovers and other unobserved effects are correlated with foreign and domestic R&D. When this interaction is modeled, estimates are consistent; however, they confound foreign and domestic R&D effects with unobserved effects. Thus, the coefficient of a weighted foreign R&D variable cannot capture genuine channel-specific R&D spillovers