Labor market impact of immigration exec order

Legal analyses of the President's executive order on immigration are a dime a dozen; economic analyses  are much rarer (this WSJ piece is the only one I have seen).  The courts and voters will ultimately work out the legal end, so what are the economic takeaways?

1) Most illegal immigrants face skill and language barriers in the labor market and end up taking relatively unskilled jobs.  The increased supply of such labor leads to lower wages for natives who compete in the same markets.  Most economic estimates find the wage impact is modest (a 10% increase supply leads to a 2-4% cut in wages for natives), but tell that to someone who is having trouble making ends meet.  

2) Do not be surprised to see the rate of illegal immigration accelerate since the order could be reversed on Inauguration Day 2017.  But wait, those who cross borders after the order aren't covered, right?  True, but perception is everything.  Do you seriously believe that someone in a dirt poor village in Guatemala thinks the odds of being deported have gone up?  What matters is what potential immigrants believe, not what the order actually says.  

3) To the extent that employers have used fear of deportation to keep illegals from quitting to find a better job, the order should open up some mobility options.  Illegals who have learned valuable skills and who speak/write decent English will now start competing with more skilled natives.  

4) The most critical immigration issue is making it easier for highly educated STEM students to stay in the US.  The President punted on this one.