We use an appropriate nonparametric two-step approach on conditional efficiencies to investigate how foreign direct investment (FDI) and time affect the process of catching up. By using a dataset of 44 countries over 1970–2007, we explore the channels under which FDI fosters productivity by disentangling the impact of this factor on the production process and its components: impact on the attainable production set (input–output space) and the impact on the distribution of efficiencies. We extend existing methodological tools—conditional nonparametric efficiency measures—to examine these interrelationships. We emphasize the usefulness of smoothing over time to better analyze the potential dynamic influence of FDI on efficiency. We find that both FDI and time play an important role as influencing efficiency distribution and affecting, to a smaller extend, the production set. This effect of FDI does not seem to vary much over time. By the second-stage nonparametric regression of the conditional efficiencies over FDI and time we identify clearly the effect of time and FDI on conditional efficiency and we determine idiosyncratic efficiency, which represents the‘Solow residual’, measured by looking to the unexplained part of the conditional efficiencies. Copyright © 2014 John Wiley & Sons, Ltd.