In seeking a shift to high-skilled immigration, Trump is moving with the grain. Net migration to the U.S. from Mexico, which the Pew Research Center says has produced the lowest-skilled immigrants on average, fell to zero between 2007 and 2014 and has not bounced back to anywhere close to previous levels.

Meanwhile, immigration from Asia has been increasing. China and India together have accounted for more immigrants than Mexico since at least 2012. Asian immigrants are not all high-skilled. But their education and skill levels are, on average, significantly higher than those from south of the border.

So America is already moving toward an inflow of high-skilled immigrants, and Trump enforcement policies may be discouraging low-skilled people to immigrate or stay here illegally.

Requiring E-Verify for job applicants and establishing a visa-tracking system — which might require legislation but might be partly accomplished by regulation — would move us further toward a higher-skilled and legally sanctioned immigrant population.