In the eyes of future generations, the ultimate test of the success of monetary union will one day consist of three questions: Has monetary union been able to safeguard lasting monetary stability? Have the participating economies coped with the conditions of monetary union? And: has the euro brought the people and peoples of Europe closer together?
The answers to those questions have a lot to do with convergence, although not only with economic convergence in the narrow sense of parallel trends in the hard data on productivity, labour costs, or whatever. It also has much to do with convergence in values, in beliefs and in aims. That is something which cannot be measured mathematically, but it is nevertheless important.