A quick search turned up:
Questions about software engineering practices are, in general, very difficult to study objectively, because how often do you run the same project from the same requirements with the same tech tools and two teams of precisely identical knowledge and talent, but with different processes? Still, studies do get run, usually comparing large projects in similar fields, and using measures like defect rates and various code metrics as proxies for fuzzier things like "productivity".
There's more out there, but those should get you started.
Edit: I'd like to expand on a good point ArneRie made in another answer: Refactoring working code that you don't plan to change costs effort rather than saving it. A large part of the value of refactoring is that it lowers the cost of change (by encouraging modularity & single responsibilities, eliminating logic duplication, &c). It follows, though, that you lose this value if you have no intent to change the code. Refactoring efforts should be focused on code being modified.