The availability of rich …rm-level data sets has recently led researchers to uncover new evidence on the eects of trade liberalization. First, trade openness forces the least produc- tive …rms to exit the market. Secondly, it induces surviving …rms to increase their innovation eorts and thirdly, it increases the degree of product market competition. In this paper we propose a model aimed at providing a coherent interpretation of these …ndings. We intro- ducing …rm heterogeneity into an innovation-driven growth model, where incumbent …rms operating in oligopolistic industries perform cost-reducing innovations. In this framework, trade liberalization leads to higher product market competition, lower markups and higher quantity produced. These changes in markups and quantities, in turn, promote innovation and productivity growth through a direct competition eect, based on the increase in the size of the market, and a selection eect, produced by the reallocation of resources towards more productive …rms. Calibrated to match US aggregate and …rm-level statistics, the model predicts that a 10 percent reduction in variable trade costs reduces markups by 1:15 percent, …rm surviving probabilities by 1 percent, and induces an increase in productivity growth of about 13 percent. More than 90 percent of the trade-induced growth increase can be attributed to the selection eect.