The theory of optimal currency areas initiated by Robert Mundell states that a monetary union should be beneficial between regions that have labor and capital mobility, fiscal transfer mechanisms and synchronized business cycles, or at least something approaching these conditions. In the case of Europe, this is clearly not met, but I guess the hope was that these conditions would eventually be met. The literature has been been rather superficial on what it means to not quite meet these criteria and what the consequences are. Yet, we have now techniques to model this better and test policies that could improve outcomes.
Philipp Engler and Simon Voigts do this with a DSGE model where they explicit the market structure, following the situation in the current European Monetary Union: no labor mobility, imperfect goods market integration, incomplete financial markets, no fiscal transfers at business cycle frequency, and asymmetric shocks. They find that adding a monetary union to the mix increases the volatility of consumption and employment significantly, essentially because country-specific monetary policy cannot be enacted. What can be done then? Engler and Voigts show that area-wide fiscal policy can do a lot of good, and much more than isolated fiscal policy would. And this is exactly what is missing in Europe. Absent this, one could imagine increasing labor mobility, but the trend in Europe right now seems to go the other way, with several countries thinking about restricting immigration from member countries. European integration is hard.