We build a theoretical model of multi-product firms that highlights how competition across market destinations affects both a firm’s exported product range and product mix. We show how tougher competition in an export market induces a firm to skew its export sales toward its best performing products. We find very strong confirmation of this competitive effect for French exporters across export market destinations. Theoretically, this within-firm change in product mix driven by the trading environment has important repercussions on firm productivity. A calibrated fit to our theoretical model reveals that these productivity effects are potentially quite large.

Quantifications of gains from trade in heterogeneous firm models assume that productivity is Pareto distributed. Replacing this assumption with log-normal heterogeneity retains some useful Pareto features, while providing a substantially better fit to sales distributions-especially in the left tail. The cost of log-normal is that gains from trade depend on the method of calibrating the fixed cost and productivity distribution parameters. When set to match the size distribution of firm sales in a given market, the log-normal assumption delivers gains from trade in a symmetric two-country model that can be twice as large as under the Pareto assumption.