Migration barriers have complex effects, among which is a cost to global economic efficiency. A recent research literature has asserted that, far from having an economic cost, migration barriers may in fact enrich the world economy. It is claimed that barriers do this by stopping the spread of impoverishing ‘culture’ or ‘institutions’ from poor to rich countries. This is the new economic case for migration restrictions. We assess the economy theory and evidence behind this claim. While it is possible in principle for such effects to arise, they would occur at orders of magnitude higher migration rates than presently observed. That is, the new efficiency case for some migration restrictions is empirically a case against the stringency of current restrictions.