That's very interesting. In labor economics, we know shockingly little about how companies actually manage all this stuff internally. (It turns out no one wants to open themselves up to the liability that would come with letting researchers comb through all their records.

My advisor had done some work on the effect you're talking about. We say that the minimum wage compresses the wage distribution. I think there are still measurable effects pretty far above minimum wage, since you have to keep everyone's relative position stable.