Can a country grow faster by saving more? We address this question both theoretically and empirically. In our theoretical model, growth results from innovations that allow local sectors to catch up with frontier technology. In poor countries, catching up re- quires the cooperation of a foreign investor who is familiar with the frontier technology and a domestic entrepreneur who is familiar with local conditions. In such a country, domestic saving matters for innovation, and therefore growth, because it enables the local entrepreneur to put equity into this cooperative venture, which mitigates an agency problem that would otherwise deter the foreign investor from participating. In rich countries, domestic entrepreneurs are already familiar with frontier technology and therefore do not need to attract foreign investment to innovate, so domestic saving does not matter for growth. A cross-country regression shows that lagged savings is positively associated with productivity growth in poor countries but not in rich countries. The same result is found when the regression is run on data generated by a calibrated version of our theoretical model.