Regions and industries are not isolated islands; so, when evaluating productivity growth, regional and sectoral growth paths should not be expected to generate independently. Moreover, accounting for spatial interactions via econometric models has become normal practice; but modelling interindustry dependencies has not. Thus, we expand labour productivity econometric convergence models by introducing interindustry spillovers in addition to spillovers that are spatial in nature. To illustrate our findings, we present an empirical application predicated upon Galicia (extreme northwest Spain), a region posing major challenges to such modelling. Our results point to the relevance of interindustry spillovers in explaining productivity growth. Furthermore, the approach allows us to better interpret covariates that explain the different growth paths across regions and industries, thus enabling more reliable policy recommendations. We find that interindustry dependencies transmit productivity shocks across regions. In addition, our results suggest that spatial and interindustry dependencies should be considered when formulating (sub)regional economic development policies. Finally, our approach corrects possible misspecification problems that arise from data scarcity. This makes it a viable alternative for multiregional econometric tests in which some sectoral detail is needed. It is particularly useful for sets of regions where data needed to populate such models is scarce.