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We discuss how standard computable equilibrium models of trade policy can be enriched with selection effects. This is achieved by estimating and simulating a partial equilibrium model that accounts for a number of real world effects of trade liberalisation: richer availability of product varieties; tougher competition and weaker market power of firms; better exploitation of economies of scale; and, of course, efficiency gains via firms selection. The model is estimated on EU data and then simulated in counterfactual scenarios. Gains from trade are much larger in the presence of selection effects with substantial variability across countries and sectors.