Responding to the recent recovery in Latvia, Paul Krugman tries to dismiss it by saying the recent drop in unemployment is due to emigration, and while he writes that labor mobility isn't bad, it's not a model for all of Europe, because "somehow having all of Europe move to someplace else in Europe doesn’t quite seem like a sustainable proposition".
Well, if you phrase it in the stupid way Krugman did, then it makes no sense. But no one is suggesting that all of Europe should move somewhere else in Europe. What does make sense however is if unemployed workers in for example Greece, Spain or Latvia move to countries where their skills are wanted by employers. This will (except perhaps in the construction sector which is a special case for reasons I explained here) reduce unemployment in the countries of origin of these workers And large parts of Europe, most notably the German-speaking countries Germany, Austria, Liechtenstein, Switzerland and Luxembourg but also Norway and Åland, have low unemployment and are likely having labor shortages in some sectors.
This doesn't mean that increased labor mobility, even outside of the construction sector, will alone come even close of solving all problems in Europe, but while the effect wouldn't be very big it would still be positive.
Finally, it should be noted that Krugman is wrong to assert that the drop in unemployment in Latvia is entirely or even mainly due to emigration. The main cause is an increase in the employment rate by about 7% (4 percentage points) since the low in early 2010, and the drop in population reflects to a large extent the effects of the dramatic drop in Latvia's birth rate in the early 1990s something that for obvious reasons means that there will be a lot fewer youngsters in their late teens by now.