There are certainly studies, but not published
I did a little digging with IT friends after this talk, and I discovered that at least one company had done before/after research on the effectiveness of both Agile and static analysis, using their bug database spanning 20 years. Their conclusion: 70% increase in critical bug clearance rate after implementing scrum, and double the feature clearance rate. Static analysis improved the bug counts down by 60%, while slowing the speed minimally. Only, given that this was proprietary information, they haven't published.
Now if one company did this, surely they weren't alone. Management loves numbers, remember?