We show that, independent of entry/exit a la Hopenhayn and market size expansion, trade
with firm heterogeneity always crowds out less productive firms when countries are symmetric.
When countries are asymmetric, however, trade can crowd in less productive firms and less
productive firms almost always specialize in trade. We analyze how a country’s standing in
the world determines whether and how these phenomena will arise. Our paper helps reconcile
empirical findings that are contradictory to the existing theoretical literature, and highlights
the importance of country heterogeneity in understanding trade with firm heterogeneity.