What Studies Show that Elite Colleges Are Worth the Cost?

Question: Can you direct me to any studies that support what I will call the "reputational difference" of attending an "elite" school. My son is applying to UPenn, Princeton, Stanford, WashU, Northwestern as well as a few smaller private institutions. The cost to attend these "elite" schools is $25K - $30K higher than these smaller schools. We are planning on helping him pay for his school, but not as much as the government or these schools expect us to. So he needs to make a decision to go to an "elite" school and graduate with over $100,000 in student loans, or go to a smaller private institution and graduate with $10,000 - $15,000 in loans. He is convinced it is worth the extra cost, I am not. I know these "elite" schools have no incentive to do such a study as there is no shortage of students and parents that seem to just accept it is worth the cost. Just hoping someone somewhere has done a study that can help him make his decision.

The Dale and Krueger study cited here is the most famous one:

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