(When) Do stronger patents increase continual innovation?

Under continual innovation, greater patent strength expands innovating firms' profit against imitation, but also shifts profit from current to past innovators. We show how the impact of patents on innovation, as determined by these two opposing effects, varies with industry characteristics. When the discount factor is sufficiently high, the negative profit division effect is negligible, and innovation monotonically increases in patent strength; otherwise, innovation has an inverted-U relationship with patent strength, and stronger patents are more likely to increase innovation when the discount factor or the fixed innovation cost is higher. We also show how the impact of patents on innovation may change with firms' innovation capability and with the intensity of competition from imitators.