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.