A hard arrow rest will move the point of impact up, and a soft arrow rest will drop the point of impact. I was reminded of this when I started hitting high a few months ago, so moved my nock point up 1/8 to compensate. A few days ago, I noticed that my arrow rest was getting worn out, so I replaced it with a new Martin rug rest, which is a soft arrow rest. My point of impact dropped and I was hitting low, even though the arrow was a sitting a little higher on the new rest than it was on the old worn-out rest. I moved my nock point back down where it had been when I first started shooting the bow, and my arrows were on target again.
I didn't realize it at the time, but the reason I had been hitting high is that my arrow rest was wearing out, and getting harder in the process. Since that happened over time, it wasn't something I noticed, but it sure was evident when I put on the new rest and the point of impact dropped a good 6" at 20 yards.