International Trade with Heterogeneous Firms: Theory and Evidence

International trade is dominated by a small number of very large firms. Models of trade with heterogeneous firms have been developed to study the causes and consequences of this observation. The canonical model of trade with heterogeneous firms shows that trade leads to between-firm reallocations and selection: it shifts employment towards firms with the best attributes and forces marginal firms to exit. The model also illustrates the role of heterogeneity, and its various sources, in explaining the volume of trade and the firm-level margins of adjustment. Consistent with the model, earlier empirical studies have documented that exporting is a rare activity, that exporting firms are larger and more productive than other firms, and that trade liberalization reallocates market shares towards the best-performing firms in various countries. More recent studies using transaction-level data have unveiled additional salient features of trade flows. First, sales by foreign firms are very heterogeneous and highly concentrated. Second, both the extensive margin (number of exporting firms) and the intensive margin (average export per firm) are important in explaining the level of exports and its changes over time. More heterogeneity in sales across firms is associated with a higher volume of trade along both margins. Third, increased foreign competition reallocates market shares towards top firms and hence can increase concentration from any country of origin. Numerous extensions of the benchmark model have been proposed to study other important aspects, such as the relevance of multi-product and multinational firms and the extent to which heterogeneity is endogenous to firms' choices, but some open challenges still remain.