A Balls-and-Bins Model of Trade

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. Typically the number of observations---that is, total shipments---is low relative to the number of possible classifications---e.g., countries and product codes. 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 model cannot reproduce the small fraction of exporters among U.S. firms. We discuss the implications for identifying the relevant model of the extensive margin in trade.