How can you tell whether a worker is "low-skilled" or "high-skilled"? Most economists' knee-jerk reaction is to see how many years of education the worker has. But a far better measure is simply labor income. If you've got a Ph.D. but you earn $10,000/year, you're probably a low-skilled worker, whatever your diploma says. And if you've got an 8th-grade education but you pull in 500k/year, you're probably a high-skilled worker, even if you don't know how to diagram sentences.
This is an important insight, because a basic fact about public opinion is that education has a lot more predictive power than income. Highly-educated people with low earnings basically agree with highly-educated people with high earnings; less-educated people with low earnings basically agree with less-educated people with high earnings. The straightforward interpretation is that belief differences are primarily about understanding and/or socialization, not self-interest.
Application: Mayda and Rodrik's well-known working paper presents a rational self-interest explanation of the fact that the less-educated are more protectionist than the more-educated. Low-skilled labor - which M&R equate with less-educated labor - is very abundant on the world market. Therefore, low-skilled workers benefit less, and in fact may lose, from greater openness. No wonder they're more protectionist, right?
Not so fast. Jens Hainmueller and Michael Hiscox have an excellent critique of M&R which points out that people do not change their minds about trade policy when they retire. Even after they exit the labor force - and cease to be in competition with the world's low-skilled billions - less-educated workers remain about as protectionist as they were before. (H&H also test and dismiss the theory that retirees are trying to protect the interests of their families). H&H conclude that the effect of education on beliefs about trade probably reflects the fact that the well-educated know more about trade and/or are socialized to be more tolerant of foreigners.
If you buy my story about measuring skill, of course, this is the hypothesis that Mayda and Rodrik should have started with. If you want to show that the conflicting interests of high- and low-skilled workers drive disagreements about trade, then you should show that income, not education, is in the driver's seat. Of course, it would be amazing if they were able to show this, because on issue after issue - including economic issues - public opinion researchers have found exactly the opposite.
P.S. For a lot more details, check about the Social Science Statistics blog here, here, and especially here.