Thats normal for me and I think in general its true. Heart rate is really a measure of effort though limited and dependent on many internal and external factors. Note that HR shouldnt necessarily be constant throughout and some coaches (Greg McMillian) say that its normal for it to increase over the total distance and for older runners like myself its even normal to be at a higher %maxHR. See Greg McMillian's book "YOU (Only Faster)", Chapter 13: The Endurance Zone, under "Nerdy Note: The Science of Endurance Zone Training" first paragraph.
For long runs at an easy effort I let myself run a little fast mainly just to establish a good easy effort. After 2-3 miles or about 20 minutes my heart rate stablizes and pace slows/stablizes but as the distance gets longer my pace will still drop slightly at the same HR & effort. Lately I have been trying to keep the same rhythm and pace near the end of a long easy run and even though it feels like Im pushing harder and harder to keep the same pace my heart rate only goes up slightly. Its kind of shocking because near the end I'll feel like Im running a faster run or a tempo pace.
If you look at race prediction times (which tend to follow the curve of world records scaled to your most recent race time) then you'll see there is a large change in pace for shorter distance than longer ones. I think effort over distance is kind of proportional to this curve, and can be used to understand how effort changes over distance in a single run.