"In any event, Song and Richards's measurements take advantage of this offset. The simplest (but not only) explanation of their observed movement of the inner core is that the inner core's rate of spin is slightly faster than the earth's crust and mantle. The evidence presented so far, however, is not a direct measurement of the inner core's rate of rotation, nor does this evidence require that the inner core's spin axis be different from the earth's spin axis (it is probably the same).
"The reasons for this inferred differential spin are not yet known; they may or may not be caused by the earth's magnetic field. Purely physical factors, such as the slowing of the outer part of the earth resulting from tidal friction between the earth's oceans and the moon, might suffice. I suspect that if you ask 100 geophysicists this question you will get 99 different answers, and at least one of them will turn out to be right! A lot of folks are right now sitting down to rework the torque balances for an inner sphere rotating inside a fluid nearly frictionless rotating frame of reference."
[We note that Glatzmaier's answer would seem to rule out this lunar explanation--but as Froelich observes, there is still much uncertainty in our understanding of the earth's inner core.