We hypothesise that North–South trade is associated with knowledge spillovers that create labour productivity gains depending on various aspects of Southern absorptive capacity. We use the novel World Input–Output Database (WIOD) that provides bilateral and bisectoral panel data for 39 countries and 35 sectors for 1995–2009. We examine growth in relative South–North labour intensities (South–North convergence) for 31 industrialised source and eight emerging recipient countries. We find strong evidence that various components and individual indicators of absorptive capacity interact with imports of investment goods in such a way that the relative labour intensity is reduced. GMM and GLS estimations corroborate the results. Policies that improve various of the identified aspects of absorptive capacity are more promising than policies that select only one. Elevating the absorptive capacity of emerging economies to the maximum level in the world would halve the South–North gap in labour intensities within a couple of decades if it were solely achieved through the trade channel.