Customs data reveal the heterogeneity and granularity of relationships among buyers and sellers, showing how more exports to a destination break down into more firms selling there and more buyers per exporter. We develop a quantitative general equilibrium model of firm‐to‐firm matching that builds on this insight to separate the roles of iceberg costs and matching frictions in gravity. In the cross section, we find matching frictions as important as iceberg costs in impeding trade, and more sensitive to distance. Because domestic and imported intermediates compete directly with labor in performing production tasks, our model also fits the heterogeneity of labor shares across French producers. Applying the framework to the 2004 expansion of the European Union, reduced iceberg costs and reduced matching frictions contributed equally to the increase in French exports to the new members. While workers benefited overall, those competing most directly with imports gained less, even losing in some countries entering the EU.
We develop an aggregative games approach to study oligopolistic price competition with multiproduct firms. We introduce a new class of IIA demand systems, derived from discrete/continuous choice, and nesting CES and logit demands. The associated pricing game with multiproduct firms is aggregative and a firm's optimal price vector can be summarized by a uni-dimensional sufficient statistic, the ι-markup. We prove existence of equilibrium using a nested fixed-point argument, and provide conditions for equilibrium uniqueness. In equilibrium, firms may choose not to offer some products. We analyze the pricing distortions and provide monotone comparative statics. Under (nested) CES and logit demands, another aggregation property obtains: All relevant information for determining a firm's performance and competitive impact is contained in that firm's uni-dimensional type. We extend the model to nonlinear pricing, quantity competition, general equilibrium, and demand systems with a nest structure. Finally, we discuss applications to merger analysis and international trade.