The economics of endogenous growth imply a non-linear relationship between intellectual property rights (IPR) and innovative activity. Very low patent protections (or other types of IPR) and no one will want to bother innovating because they will not be able to reap any benefits before someone comes along and copies their idea. Too much patent protection (or other IPR) and it will be too hard to replace existing companies, so no one will bother to innovate. This means that there is a hump-shaped relationship of patent protection and innovation, with some area of optimal patent protection that maximizes the amount of innovation that gets done - just enough to encourage new innovators, but not so much that we freeze existing companies in place.
Two recent papers have some clues about that patent/relationship curve, but not in the way I was originally expecting. Bhaven Sampat and Heidi Williams have a paper (h/t Joshua Gans) on cumulative or follow-on innovation, meaning patents that are filed that rely on existing patents. They looked specifically at patents for genes, which allows them to clearly identify subsequent patenting activity. Within the patent office. They use a nifty strategy involving the random assignment of patent officers to get variation between genes that are patented and genes that are not. Comparing those with patents to those without, they find no difference in future innovation.
This is not what Alberto Gallaso and Mark Schankerman find (h/t Free Exchange). They use invalidations of patents by US Court of Appeals as the source of variation in intellectual property rights in their study. For some fields, invalidating a patent meant a tripling of the number of citations in future patents for that invalidated patent. So removing the IPR was a boon to future innovation. But this only held in fields where products rely a host of patents, think biotechnology in general or IT. For fields that they classified as simple, there was no effect of invalidating a patent on future innovation - similar to the Sampat and Williams finding.
Perhaps what these papers are telling us is that we should be more worried about shifts in the patent/innovation relationship, rather than movement along that curve. The Sampat and Williams paper shows that cumulative innovation is the same, regardless of whether the gene is patented or not. This suggests that a patent is simply re-distributing the total gains of cumulative innovations towards the current patent holder and away from the new innovator. But, the gains are realized though the cumulative innovation - the market appears to be figuring out for itself how to ensure these innovations get made. But note that this works for a very specific sub-field of research in which the use of an innovation (a gene) is clear cut.
The Galasso and Schankerman paper shows us what happens when the cumulative innovation is more complex. When a patent is struck down in a field that relies on webs of patents, there is a burst of cumulative innovative activity. Why? The many parties involved in the web of patents will find it hard to negotiate and allocate out the rents from the cumulative innovation. Practically speaking, it may be too hard to get everyone in the same room together. The court ruling solves the bargaining problem exogenously. It eliminates the need for the meetings, the e-mails, the lawyer's fees, etc.. etc..
What Galasso and Schankerman are measuring, then, is the effect on innovation of lowering bargaining costs. This shifts the entire patent/innovation relationship up, meaning more innovation at any level of formal patent protection. In the Sampat and Williams study, the bargaining problem was already straightforward, so the difference in having a patent or not doesn't affect anything. The costs were already low.
Now I'm not sure that his means we can fundamentally change innovation rates by lowering bargaining costs. The bargaining costs seem to be driven by the nature of the field. If the innovation is complex and relies on lots of other patents, then you cannot legally just decree that it is less complex. But definitive legal rulings are probably a boon to innovation, regardless of which way they decide. From a social point of view, we want to maximize innovations, and the exact distribution of the rents to the various patent-holders is not really our concern (Quick, do you care or know how the Apple/Samsung trial turned out? As long as various versions of smartphones remain available, probably not). So based on this, our goal with the patent system should probably be focused on making it transparent, fast, and cheap to navigate, as opposed to worrying precisely about who gets protected for how long.