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You do. (For a particular sense of "above average" that's appropriate here.) The people who choose to leave country A to seek their fortune in country B are going to be (on average) atypical in a bunch of ways.
They will tend to be more optimistic about their prospects in country B and maybe less optimistic about their prospects in country A. It's not immediately clear what we should expect this to say about them overall, but let's "change basis" as follows: they will tend to have a higher opinion of how much better they'd do in B than in A, and this seems like it should correlate with actual prospects in B if it's a healthier country than A.
They will tend to be more proactive, more go-getting. This seems like it should also correlate with productive work.
They will tend to be actually able to get themselves from country A to country B without starving, getting arrested by overzealous police in country A or B or in between, failing to get past border controls, etc. This all seems like it would correlated with effectiveness in getting stuff done. (Both directly, and because their ability to do this will be affected by the resources they have in country A, which for multiple reasons will correlate with their ability to get things done.)
There will probably be differences in their relationships with other people in country A, but I'm not sure which direction the overall effect goes. (Maybe they have looser ties, and that correlates with being less good with people, and that correlates with doing badly; maybe they have good friends and family making them feel well supported and confident, and that correlates with doing well.)
Having got from A to B, they are then going to be strongly motivated to make the trouble and expense worth while, which probably means that whatever their underlying competence they will work harder and more resourcefully in country B than they would have in country A.
So there are lots of reasons to expect people who have emigrated from dysfunctional country A to more-functional country B to be more effective workers in country B than the population average in country A.
(Note: I don't think this is by any means the dominant reason to agree with Nancy and disagree with Azathoth on this point.)
Something like that was formerly more true. Now I suspect part of the problem is that improvements in transportation have made it "too easy" to immigrate.