Edit: and are you sure that your higher-wages claim (source?) is not just evidence that STEM majors act as an effective filter for the smart and driven.
Quote: "People in STEM jobs benefit from being in such high demand. Study[1] after study[2] confirms that STEM professionals get paid more than non-STEM professionals -- often much more -- even when you control for their education and other factors. Contrary to Charette's claim that STEM wages have stagnated, reports from Georgetown, the Commerce Department[3], and the Information Technology Innovation Foundation[4] show that they have risen faster than non-STEM wages, even in recent years. That is a sign that employers are feeling the pinch."
The Studies linked: [1] http://www.esa.doc.gov/Reports/stem-good-jobs-now-and-future
[2] https://cew.georgetown.edu/report/stem/
[3]http://www.esa.doc.gov/Reports/stem-good-jobs-now-and-future
[4] http://www.itif.org/publications/real-story-guestworkers-hig...