We study the cross-sector allocation of R&D resources in a multi-sector growth model with an innovation network, where one sector’s past innovations may benefit other sectors’ future innovations. Theoretically, we solve for the optimal allocation of R&D resources. We show a planner valuing long-term growth should allocate more R&D toward central sectors in the innovation network, but the incentive is muted in open economies that benefit more from foreign knowledge spillovers. We derive sufficient statistics for evaluating the welfare gains from improving R&D allocation. Empirically, we build the global innovation network based on patent citations and establish its empirical relevance for knowledge spillovers. We evaluate R&D allocative efficiency across countries using model-based sufficient statistics. Japan has the highest allocative efficiency among the advanced economies. For the U.S., improving R&D allocative efficiency could generate more than 8% welfare gains.