Firms do not always patent their innovations. Instead, they often rely on secrecy to appropriate the returns of innovations. This paper endogenizes firms’ patent propensity, and shows that when the equilibrium patent propensity is small, strengthening patent protection can decrease firms’ incentive to innovate. Paradoxically, this result holds precisely when a stronger patent policy induces more patent applications. Also, these results can arise even in the simplest patent race model with independent innovations as well as with complementary innovations.