Numerous countries have implemented financial reforms in the past three decades, but how these reforms affect economic growth has not been established. I develop a novel dynamic equilibrium model with heterogeneous firms and endogenous leverage to isolate the effects of changing financial frictions on economic growth. Changes in financial frictions affect aggregate productivity by shifting the allocation of resources across firms. However, common shocks to productivity unrelated to finance also change the allocation of resources across firms, because more-productive firms respond to shocks by changing leverage. I show using plant-level microdata from India that although difference in difference regressions and aggregate productivity decompositions suggest that financial reforms have led to economic growth in India since 1990, I can generate the same patterns in my calibrated model with only common shocks to productivity. In addition, when I calibrate a model to match the dynamic evolution of the size-productivity distribution in India, I find that financial factors explain 71% of Indian labor productivity growth from 1990 to 1995, but only 2%--8% from 1995 to 2011. My work suggests that factors that affect productivity within firms are more important determinants of aggregate productivity growth than financial development, and might explain why developing economies lag behind the United States in growth and productivity.