Thank you for detailed analysis in response to my question - much appreciated.
One charge leveled at the D&K study is that they had a pretty expansive definition of “most selective colleges”. I believe it included HYPSM down to the CWRU tier. So it’s possible that there is a benefit to Ivies/equivalents (or HYPSM) for all that is swamped out. Though given the opportunity cost of compounded money/money for grad school (as well as major/skills driving earnings differentials to a greater extent than school attended in most cases), it’s still hard to justify a multiple 6-figure cost differential for undergrad (unless you have decently multiple millions so just don’t care that much).
I believe you are describing Barron’s selectivity index. The D&K study compared results with 2 proxies for selectivity – one was average SAT score of students attending the college, and the other was Barron’s selectivity index. Average SAT score would distinguish between HYPSM and CWRU. Barron’s selectivity index would not. Both metrics showed the same result, which was a slight negative coefficient after self-revelation controls (negative = lower earnings) that was not statistically different from zero.
My experience is that first year students get more financial aid by far than transfer students at most schools. And tranferring almost always delays your progress on graduation, socializing unless you already know people or are very extroverted and in many cases it also extends the time to decide what you want to do.
So unless one really can’t afford it I would send someone to the four year school and save money by applying for more scholarships within the dept once you are there and then taking comm college classes during summer or even in last year and transfer them back to the,4 year college to graduate from there.
I write this as my humble opinion but with 20 years working at schools as academic advisor and having three kids in private schools.