Executive functions help people maintain and pursue their goals in difficult, distracting situations.
In one experiment, the participants completed a Stroop task, a common psychological test designed to exercise executive functions. Participants who had earlier been randomly assigned to a low-power group made more errors in the Stroop task than those who had been assigned to a high-power group. Smith and colleagues also found that these results were not due to low-power people being less motivated or putting in less effort. Instead, those lacking in power had difficulty maintaining a focus on their current goal.
This is one smallish experiment, so I'm cautious about drawing large conclusions. I'd like to see experiments relating to executive function and real-world status, and some work on how some people have executive functioning much better or worse than their status. Still, this could be significant.
Link indirectly thanks to en_ki. They put it in an lj post, I went to post it at Steve Barnes' forum, and found someone else had posted about (roughly?) the same article from a page which had a prettier format.