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The independence of the European Central Bank (ECB), seemingly guaranteed by its statutes, is presently under attack. The ECB has been led to acquire large amounts of government debt of the weaker euro zone members, both to help contain their interest costs and to help protect the solvency of banks throughout the zone that hold their debt. This paper presents a model of a dependent central bank that internalizes the government’s budget constraint. Using a Barro-Gordon framework, the model embodies both the desire to stimulate output and to provide monetary financing to governments. As a result of the inability to pre-commit to first-best policies, the central bank produces excess inflation — a tendency partially reduced in a monetary union. The model implies that not only shock asymmetries, but also fiscal asymmetries, are important in the membership calculus of desirable monetary unions. On the basis of this framework, calibrated to euro zone data, the current membership is shown not to be optimal: other members would benefit from the expulsion of several countries, notably Greece, Italy and France. A narrow monetary union centred around Germany is sometimes mooted as a preferable alternative, especially if it could guarantee central bank independence. However, simulation results suggest that such a narrow monetary union would not be in Germany’s interest: though better than the euro zone with a dependent central bank, it would not internalize enough trade to make it more attractive than the resumption of monetary autonomy by Germany.