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, those French firms skew their export sales towards their best performing products; and also extend the range of products sold to that market. We develop a theoretical model of multiproduct firms and derive the specific demand and cost conditions needed to generate these product-mix reallocations. Our theoretical model highlights how the increased competition from demand shocks in export markets - and the induced product mix reallocations - induce productivity changes within the firm. We then empirically test for this connection between the demand shocks and the productivity of multi-product firms exporting to those destinations. We find that the effect of those demand shocks on productivity are substantial - and explain an important share of aggregate productivity fluctuations for French manufacturing.