In studies of firm's innovation performance, regression analysis can involve a significant level of model uncertainty because the ‘true’ model, and therefore the appropriate set of explanatory variables are unknown. Drawing on innovation survey data for France, Germany, and the United Kingdom, we assess the robustness of the literature on inbound open innovation to variable selection choices, using Bayesian model averaging (BMA). We investigate a wide range of innovation determinants proposed in the literature and establish a robust set of findings for the variables related to the introduction of new-to-the-firm and new-to-the-world innovation with the aim of gauging the overall healthiness of the literature. Overall, we find greater robustness for explanations for new-to-the-firm rather than new-to-the-world innovation. We explore how this approach might help to improve our understanding of innovation.