Definitely not a scientific study, but on a recent road trip I was "forced" to use 89 octane in my HAH. (It was cheaper than the 87!

) I went from getting 37 mpg to 35 mpg. The roads seemed the same, as well as the ambient temperature, and elevation changes. But, I have no way of knowing for sure if the higher octane is the cause of the 2 mpg drop.
Also while on this trip, I used 86 octane with no noticeable change. One station even had 85! I stayed away from that stuff. The HAH is rated at 86+.