Product mix and firm productivity responses to trade competition

We document how demand shocks in export markets lead French multi-product exporters to re-allocate the mix of products sold in those destinations. In response to positive demand shocks, French firms skew their export sales towards their best performing products. We develop a theoretical model of multi-product firms and derive the specific demand conditions (with endogenous price elasticities) needed to generate these product-mix reallocations. Under those demand conditions, the increased competition from demand shocks in export markets also induce productivity changes within the firm. We empirically test for this connection between demand shocks and the productivity of multi-product firms. We find that this connection is economically substantial.