Standard new trade models depict producers as heterogeneous in total factor productivity. In this paper, I adapt the Eaton and Kortum (2002) model of international trade to incorporate tradable intermediate goods and producer heterogeneity in value-added productivity. In equilibrium, this yields a positive relationship between the international trade elasticity and the share of intermediate goods in production. This relationship is absent from the standard model and is driven by the extensive margin of trade. I then use cross-country sectoral data from 1995 to 2010 and estimate the trade elasticity, finding empirical support for this relationship and for the importance of the extensive margin. This model yields results that are similar to those of the standard model with respect to the overall magnitude of gains from trade. Importantly, however, whereas the standard model suggests that gains from trade are higher in sectors that use intermediate goods, I find that this is no longer true under the value-added heterogeneity model.