Is there empirical evidence that static types reduce bugs?

I think a better way to phrase the question is: "Is there empirical evidence that static types reduce software defects that make it into production?"

Or alternatively if that's not a concern "Is there evidence that static typing increases developer velocity by reducing debugging time?"

It's pretty unquestionable that some classes of bugs are eliminated at compile time. But whether it actually ends up mattering in the big scheme of things is another question.

I'm guessing the answer to the first question is a qualified yes, while the answer to the second is no.

How could it not? By definition, strong statically typed languages won't let you release code with certain classes of bugs so they must reduce bugs going live unless humans are perfect bug detectors.