Recent studies have concluded that R&D grants can induce firms to export and that exporting and innovating can be complementary activities at the firm level. Yet the trade literature has paid little attention to the scope of innovation policy as a stimulus to both trade and innovation. To investigate this question we rely on a general work-horse model of trade and firm heterogeneity with firm investments in R&D activities. The multiplicity of equilibria together with the interplay of innovation and trade policies uncover novel results. In particular, we show that the effects of either policy depend on the degree of protectionism in a country. Therefore, countries can respond differently to the same policy, and similarly to different policies. In such a context, different governments may face different degrees of freedom regarding how to achieve a given target. This finding leads us to discuss the issue of policy coordination.JEL: F12, F13, F15, F61, O32. Keywords: innovation, innovation policy, heterogenous firms, technology adoption, trade policy. * This article is an enhanced and modified version of EUI Working Paper ECO 2007/58 titled "Technology Adoption and the Selection Effect of Trade". We are grateful to numerous seminar participants for their discussions and to some anonymous referees for their comments. All remaining mistakes are ours.