I study the implications of endogenous productivity choices ("innovation") on the effects of trade liberalization. I find that a model with innovation generates an elasticity of trade volumes to tariff reductions that is fifty percent larger than models without innovation, and consistent in magnitude to empirical estimates. To show this, I develop a new model of international trade with innovation, and calibrate it to data on Canada and the United States before the Free Trade Agreement. Feeding into the calibrated model the tariff drop that resulted from the agreement, the increase in the trade volumes is similar to that observed in the data. Without innovation, the change in trade volumes is considerably lower, and similar in magnitude to what existing models without innovation have found.