There is a large and growing literature on the benefits and costs of moving to a single currency in Europe. Much of the literature is theoretical in nature with very little empirical evaluation of the magnitudes of effects. This paper places some quantitative magnitudes on the scale of some issues in European monetary integration. It uses the European version of the MSG2 multi-country model to evaluate the variance of a number of European variables in the face of shocks to money markets, fiscal policy and total factor productivity, under three alternative European monetary regimes: the current European monetary system; a European monetary Union with a European central bank setting monetary policy; and a system of floating exchange rates within Europe. For each type of shock we consider the adjustment to global shocks, European wide shocks, shocks in Germany and shocks in Europe excluding Germany. Within the constraints of each monetary regime we allow any unconstrained monetary instruments to be set either cooperatively between European countries or non-cooperatively where each country is allowed to set their policy instruments to maximize an objective function. We find that no monetary regime consistently dominates for all shocks and regimes are ranked differently across European economies for the same shock. Abstracting from the serious question of policy credibility, this suggests that maintaining some flexibility in the setting of monetary policy in countries could potentially be invaluable to facilitate smooth adjustment to global, regional and country specific shocks.