Of course we don't have evidence. Neither side wants good evidence. It's a battle of ideology, not facts.

The gun banners don't want it because most criminals don't have legal guns in the first place. Nothing you can do short of disarming society will have much effect on the criminals and most of them don't want to admit that's their actual objective.

The gun nuts don't want it, either, because it will show some benefits of gun regulations (for example, locking up guns around kids helps.)