There's some data out there but it's also hard to compare reliably since you need to account for differences in skill level when comparing salaries.

My point was that the large companies which have the best data, and whole teams of people doing the math on this issue, have consistently fought to preserve the old ways of doing it and since they're for-profit corporations it seems unlikely that they're doing this for any reason other than the econ 101 explanation that they profit from workers who can't negotiate as well.