Yes it does! I think you're misreading OP's post.
What was OP's claim?
>> The most accurate predictor of a person's lifetime income is the income of their parents. Children of wealthy parents are more likely to go to college. It's like saying "People who drive expensive cars in high school make more money over their lifetime, period".
OP's assertion about "best predictor" is true but irrelevant. The interesting question is why?
OP asserts that the answer to that question is literally "for the same reason that rich kids drive BMWs".
OP is asserting that college has the same causal effect as a parent purchasing a BMW for a child. I.e., none at all, it's just a proxy for parental wealth.
That strikes me as an unlikely causal hypothesis.
Could there perhaps be a reason other than parent income that the child of an MD drives a BMW to school? Probably not.
But could there perhaps be a reason other than parent income that the child of an MD does well in their premed program? Seems likely.
And indeed, the above article establishes a causal link that's directly relevant to falsifying that assertion, that college == bmw in terms of causal effect.
Elsewhere, OP asks if the college wage premium persists across family backgrounds. I think perhaps something related to that question is what you perhaps read into their post. But that's not actually the claim they are actually making in that post.
(BTW: CWP and PEP are positive for students from low income backgrounds... these are just numbers you can look up... why am I the thread secretary for basic statistics?)
