This new set of rankings shows which colleges pay off the most

If you want a high salary after college, you should probably major in engineering.

This isn't a new lesson, but it's reinforced by a new set of college rankings that try to determine the best college based on its students' earnings and their ability to repay their student loans. The rankings, from the Brookings Institution, determine whether a college's graduates earn more than you'd expect, given their test scores and demographics.

The rankings try to take gender, race, and household income out of the equation to figure out the economic value of higher education. These are the best colleges (all tied for first place) based on how much they boost their graduates' earnings:

• California Institute of Technology
• Colgate University
• Massachusetts Institute of Technology
• Rose-Hulman Institute of Technology
• Carleton College
• Washington and Lee University
• SUNY Maritime College
• Clarkson University

The new rankings have three big lessons: first, that majoring in engineering or the sciences is generally a good way to make a good salary. Second, that even a lot of student debt can sometimes end up being worth it. And third, that pinpointing what works in higher education is much harder than creating a fancy regression.

Lesson 1: It's your major, not your college, that matters (within limits)

(Shutterstock)

Whether you major in engineering or in English makes a much bigger difference, broadly speaking, than where you do it. That's why well-known, prestigious colleges like CalTech and lesser-known places like Clarkson, which also focuses on the sciences, are neck-and-neck on this list.

A college's curriculum, and the skills it teaches its graduates, made the most difference in its place on the Brookings rankings. At CalTech, where graduates make almost 50 percent more at mid-career than would be predicted given the students' test scores and demographics, the focus on the sciences, curriculum, and skills explains nearly all of the difference.

Beyond the very top of the list, the best-ranked colleges are mostly a mix of well-known and prestigious universities (the Ivy League, Stanford, the University of California Berkeley) and smaller colleges, including many with a focus on STEM.

Lesson 2: Not all student debt is bad student debt

Rose-Hulman Institute of Technology, which does exceptionally well in the Brookings rankings, is also known for graduating students who are deeply in debt. It's been highlighted multiple times by the Institute for College Access and Success as a university whose graduates have a particularly heavy debt load. About 70 percent of its students borrow, and on average they take out more than $42,000 in loans.

But they also pay back those loans: the college has an even lower default rate, which measures the percentage of former students who quit repaying their loans in the first years of repayment, than would be expected given its demographics. For their graduates, the degree, however expensive, is probably a good investment.

Lesson 3: We don't know why liberal arts colleges work

(Stephanie Gross / The Washington Post via Getty Images)

Brookings didn't just look at the earnings gap between graduates at various colleges; it tried to explain why. Very quickly, it becomes clear that some colleges have far better outcomes than others, and it's extremely difficult to explain why.

Take Washington and Lee, an outlier on the list of the colleges that add the most value. It's not entirely clear what makes Washington and Lee different from other liberal arts colleges — and the formula Brookings used can't explain it. It attributes half of the difference Washington and Lee makes to an "X-factor."

This pops up over and over with liberal arts colleges. Macalester College, Grinnell College, and Carleton College are all similar liberal arts colleges in Iowa and Minnesota. Brookings predicted that their graduates would all earn about the same amount at mid-career, around $73,000.

But Carleton graduates earn 43 percent more than that, while Macalester graduates earn 22 percent more, and Grinnell graduates earn just 6 percent more. And at Carleton, most of the difference is attributed to an X-factor. It's clearly outperforming its peers — but no one knows why.

If you're trying to decide between those three colleges, the fact that Carleton's graduates make much more than would be expected is useful information. But if Macalester and Grinnell are trying to catch up, this study tells them nothing. The Brookings calculations are clearly missing something big and important. We just don't know what it is.

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