This paper develops a multi-industry growth model in which firms require external funds to conduct productivity-enhancing R&D. The cost of research is industry-specific. The tightness of financing constraints depends on the level of financial development and on industry characteristics. Over time, a financially constrained economy may converge to the growth path of a frictionless economy, so long as an industry with the fastest expanding technological frontier does not permanently fall behind due to low R&D. The model's industry dynamics map into a differences-in-differences regression, in which industry growth depends on the interaction between financial development and industry level R&D intensity.