That is always true, everywhere, just as it is always true that some will handle money wisely and some will not. The wise can become ignorant or have bad fortune and the ignorant can learn but generally speaking the wise remain wise and the ignorant remain ignorant.
"Generally speaking" is pretty vague. If I correctly recall Thomas Sowell's discussion of this point, the shift out of the lowest-20% income group and the shift out of the highest-20% income group over a 10-year period is pretty significant, in the 25% range. These aren't all the same people trading places, of course.
The less ossified a society's economic opportunities are, the more likely it is that a person's income will reflect his most recent displays of wisdom or foolishness.