I think a person's innate element is to do with their inherent character traits. In fact, a few years back, I made a little quiz based on what I'd observed in Chrono Cross!
http://quizilla.com/users/darthmongoose/quizzes/What's%20your%20Chrono%20Cross%20innate%20element%3F/If I redid the quiz of course, I'd take into account that really, Crono is more
likely to be a white innate than a yellow (not really sure, could be either).
But generally (there are some exceptions, but in general):
White/Heaven element are spiritually in tune, insightful and benevolent, but naive.
Black/Dark are intellegent and organised, but scheming and self serving.
Red/Fire are passionate and creative, but hot tempered.
Blue/Water are nurturing, level headed and brave, but hard to fathom.
Yellow/Earth are homely, stoic guardians who like the simple things.
Green/Air are lofty and adventurous and can be loners.