Many of the facts about the extensive margin of trade—which firms export, and how many products are sent to how many destinations— are consistent with a surprisingly large class of trade models because of the sparse nature of trade data. We propose a statistical model to account for sparsity, formalizing the assignment of trade shipments to country, product, and firm categories as balls falling into bins. The balls-and-bins model quantitatively reproduces the pattern of zero product- and firm-level trade flows across export destinations, and the frequency of multiproduct, multidestination exporters. In contrast, balls-and-bins overpredicts the fraction of exporting firms.

We estimate a model of importers in Hungarian microdata and conduct counterfactual analysis to investigate the effect of imported inputs on productivity. We find that importing all input varieties would increase a firm’s revenue productivity by 22 percent, about one-half of which is due to imperfect substitution between foreign and domestic inputs. Foreign firms use imports more effectively and pay lower fixed import costs. We attribute one-quarter of Hungarian productivity growth during the 1993–2002 period to imported inputs. Simulations show that the productivity gain from a tariff cut is larger when the economy has many importers and many foreign firms.

Using detailed U.S. and Spanish export data, we document that trade costs of a per-shipment nature are associated with less frequent and larger shipments (i.e., more lumpiness) in international trade. This finding is pervasive across broad product categories, but most apparent for industrial supplies, parts and accessories, and food products.