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We introduce imperfect creditor protection in a multi-country version of Schumpeterian growth theory with technology transfer. The theory predicts that the growth rate of any country with more than some critical level of financial development will converge to the growth rate of the world technology frontier, and that all other countries will have a strictly lower long-run growth rate. The theory also predicts that in a country that converges to the frontier growth rate, financial development has a positive but eventually vanishing effect on steady-state per-capita GDP relative to the frontier. We present cross-country evidence supporting these two implications. In particular, we find a significant and sizeable effect of an interaction term between initial per-capita GDP (relative to the United States) and a financial intermediation measure in an otherwise standard growth regression, implying that the likelihood of converging to the U.S. growth rate increases with financial development. We also find that, as predicted by the theory, the direct effect of financial intermediation in this regression is not significantly different from zero. These findings are robust to alternative conditioning sets, estimation procedures and measures of financial development.