There are many problems with economic research on the costs and benefits of intellectual property protections. For one, the most common measure of research output is the rate of patenting; but changing the strength of patents both changes the incentives over doing research and the incentives over patenting that research, introducing a huge bias.
For another, a lot of what you want to measure is pure counterfactual: what would have happened under a different (i.e. stronger or weaker) intellectual property system—but how can we track research that might have happened but didn't actually? There is little info kept on, for example, promising drug compounds that pharmaceutical firms never followed up on.
A third is that patent laws are fairly uniform within countries. Where they vary in practice across areas the industries are often too variegated to accurately compare. There are some variations across the developed world, but aside from the fact that countries systematically vary in relevant ways, small changes in individual countries' policies are rarely big enough to matter. If Denmark changes its standard term length from 17 to 20 years this has very little impact on the incentives international firms face.
Canny researchers have tried to get around some of these problems. For example Lerner (2009) looks at the impact tighter patent protection in Austria has on patenting by Austrians who live in the UK. Though stricter patent provisions did lead to more patenting within a country, it was not associated with extra patenting by nationals abroad.
Other research has attempted to measure total Research & Development spending, total scientific papers published, total citations to scientific papers, or even clinical trials and drug approvals, in order to get a better grip on the actual pace of innovation.
A highly interesting new NBER paper by Heidi L. Williams at MIT, entitled "Intellectual Property Rights and Innovation: Evidence from Healthcare Markets" (pdf) lucidly explains these problems and the standard framework for economic research on intellectual property. Viz: does the free market under-provide research without IP? Do the benefits IP rights generate in terms of extra innovation outweigh the costs of restricting an idea's use for 20 years or more?
Williams manages to identify a variation between the delay in commercialising early-stage and late-stage cancer treatments, and hence the effective length of the patent (even though the statutory length is the same). Firms patent when they discover things, not when they commercialise them, and this means that the length of Federal Drug Agency trials and other hold-ups influence how long they actually get a monopoly on a drug's sale. In this context, late-stage cancer drugs are often rushed to market, whereas early-stage cancer drugs take longer to approve (and hence firms get a shorter effective patent).
Williams finds that shorter commercialisation lags lead to more investment in innovation in that area.
Taking advantage of our surrogate endpoint variation, we estimate counterfactual R&D allocations and induced improvements in cancer survival rates that would have been observed if commercialization lags were reduced. Our back-of-the-envelope calculation suggests that the distortion of private research dollars away from long-term projects has quantitatively important implications for the survival outcomes of US cancer patients: we estimate that among one cohort of patients - US cancer patients diagnosed in 2003 - longer commercialization lags generated around 890,000 lost life-years. Valued at $100,000 per life-year lost (Cutler, 2004), the estimated value of these lost life-years is on the order of $89 billion for this single cohort of patients.