The cooler temperature of the air above implies that, for a given pressure, it's density will be greater.
For a given power setting, 65% for example, the fuel flow should be the same at all levels, for a given RPM. However, as we climb, the temperature drops, so, for a given manifold pressure, the air density increases. The consequence is that, to mantain the same percent power with the same RPM as we climb, the MP should be reduced.
I like the line of thought, but I don't think it quite explains the numbers. Try these:
18" 2400 at sea level (ISA temp 288 K) produces 75 BHP
18" 2400 at 12,000 (ISA temp 264 K) produces 97 BHP
97 BHP has an "equivalent sea level MP" of 21" (i.e. 21"/2400 produces 97 BHP at sl).
If it were purely a density effect, I'd expect to see an equivalent of 288/264 * 18" = 19.6". So it explains about half of the effect. Is it possible that the rest is pumping loss?