Yes. A couple of weeks back on either hacker news or reddit (I just searched, and could not find it quickly), there was a seemingly well conducted experiment, with a large number of students randomized to static and dynamic languages, that found no statistically significant difference.
Actually, the study found that static languages were worse. They tested students on two problems. In one there was no significant difference, and in the other the static language performed worse.
Here is that study: "An Experiment About Static and Dynamic Type Systems", by Stefan Hanenberg, University of Duisberg-Essen, 2010.
However, they didn't use existing languages; they created a brand new language and IDE that had a typed and untyped variant. Whether this confounds or strengthens the case is unclear to me.
In any case, I think any survey of static type systems that doesn't include a language with type inference is very flawed. Java's type system is an annoyance in the small, and is a mixed bag in the large. Haskell's type system is a totally different story.
If you look at the HN thread where that paper was discussed, people on both sides were shooting holes in it. That's partly why I'm asking, is there anything solid on this out there at all? People are just repeating the same beliefs over and over. We've all heard them a zillion times and we all divide them into two categories: "shit I agree with" and "bullshit".
What experiments could be done to test these beliefs?
I think one would need to start by testing a different question first : "With everything else being equal, should your language choice be affected by the level of competence of the developers?".
It seems discussions on topics like this all boil down to clash between the idealist and the pragmatist. Idealist: "I want to use language X because it is powerful and lets me to Y". Pragmatist: "but that feature will be abused by the average developer and your project will suffer". So you can't win. Either you have to work in a mediocre language that the mediocre developer knows how to use, or you will work in a great language that the mediocre developer will use to shoot you in the foot.
If the answer to the above question is no, then we can put this discussion to rest - otherwise we will need to probe further and understand how developer competence should guide your language choice.