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 multi-product 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.