We show that finance influences innovation by young private firms, an important source of long-term economic growth. We develop a simple theoretical model that predicts that a decrease (increase) in banks' bargaining power vis-a-vis entrepreneurs increases (decreases) both the volume and riskiness of innovation. Using staggered banking deregulation by U.S. states as shocks to the bargaining power of banks, we find that, consistent with our hypotheses, inter-state banking deregulation increased both the level and riskiness of innovation by young private firms while intra-state deregulation decreased them. Further, banking deregulation primarily impacted riskier explorative innovation by young private firms than the less risky exploitative innovation. In contrast, banking deregulation did not affect public firms and mature private firms that are relatively less dependent on bank financing. These results have important policy implications by demonstrating how financial development, through its impact on innovation by young private firms, can have a first order impact on economic growth.