The College Scorecard of the Federal Government now provides average salary by completed major at a school. After selecting a school you click on "Fields of Study" and can then sort Top Fields of Study by largest size, highest earnings, and lowest debt. For example, for UMass Amherst, the 5 highest-earning bachelor's degrees were

Computer Science - $75,400
Computer Engineering - $75,100
Electrical, Electronics and Communications Engineering - $66,000
Nursing - $65,400
Mechanical Engineering - $63,700

For MIT, the highest-earning majors are

Mathematics - $120,300
Computer Science - $118,100
Electrical, Electronics and Communications Engineering - $116,600
Business/Commerce, General - $88,700
Aerospace, Aeronautical and Astronautical Engineering - $80,100

The site says the numbers are "the median annual earnings of former students one year after graduation. Only data from students who received federal financial aid is included in the calculation." Earnings of children are positively correlated with those of their parents, so excluding full-pay students may bias the numbers downwards.

Do students in one school earn more than students in another school with the same major because (1) they learn more and employers value that school more or (2) because of differences in student characteristics such as SAT scores upon matriculation? Maybe both.

ETA: An article about this is
Feds release data on wages, debt for specific college majors
Associated Press
November 20, 2019