In models with heterogeneous …rms trade integration has a positive impact on aggregate productivity through the selection of the best …rms as import competition drives the least productive ones out of the market. To quantify the impact of …rm selection on productivity, we calibrate and validate a multi-country multi-sector model with monopolistic competition and variable markups using …rm-level data and aggregate trade …gures on a panel of 11 EU countries. Simulating the model, we …nd that EU trade has a sizeable impact on aggregate productivity. For instance, in 2000 the introduction of prohibitive trade barriers would have caused an average productivity loss of roughly 13 per cent, whereas a reduction of intra-EU trade costs by 5 per cent would have generated a productivity gain of roughly 2 per cent. Productivity losses and gains, however, vary a lot across countries and sectors depending on market accessibility and trade costs, which maps into di¤erential responses of average markups, prices, quantities and pro…ts. We show that our results are robust to alternative distance and productivity measures.