A number of stylized facts have been documented about the extensive margin of trade---which firms export, and how many products they send to how many destinations. We argue that the sparse nature of trade data is crucial to understanding these stylized facts. Trade data are collected through customs forms, one for each export shipment, specifying the country of destination and the product code. Typically the number of observations---that is, total shipments---is low relative to the number of possible classifications---e.g., countries and product codes. Given the sparse data, we note that some of the reported facts would be expected to arise even if exports shipments were randomly allocated across classifications. These facts are, thus, not informative of the underlying economic decisions. We propose a statistical model to account for the sparsity of trade data. We formalize the assignment of shipments to categories as balls falling into bins. The balls-and-bins model quantitatively reproduces the prevalence of zero product-level trade flows across export destinations. The model also accounts for firm-level facts: as in the data, most firms export a single product to a single country but these firms represent a tiny fraction of total exports. In contrast, the balls-and-bins cannot reproduce the small fraction of exporters among U.S. firms and overpredicts their size premium relative to non-exporters. We argue that the balls-and-bins model is a useful statistical tool to discern the interesting facts in disaggregated trade data from patterns arising mechanically through chance.
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