I'm aware of the theory of optimal currency areas, and that both the Euro and the US dollar* are technically not optimal. This would tend to cause their optimal monetary policy to diverge over time.
In the case of the dollar, this is partly resolved by extremely large fiscal transfers between regions. In the case of the Euro, on the other hand, this has largely been papered over by credit-based liquidity injections from the North into the South**.
The result is that ECB interest rates that are appropriate for Germany may cause Spain to stagnate, and rates that are appropriate for Spain may cause Germany to overheat. If the rate is set at an intermediate level (as generally happens in practice), and in the absence of fiscal transfers, the net effect is that Northern countries are using a perpetually-depressed Southern Europe as a boat anchor for their exchange rate, artificially boosting their own exports.
Has any analysis been done - either theoretical or empirical - investigating the optimal rate of fiscal transfer within a currency union to prevent this kind of divergence? Haven't seen anything in the literature, but I wouldn't necessarily know where to look.
If we could place a value on the boat anchor, that would allow us to identify areas that have been "monetarily disadvantaged", and distinguish where regional poor performance arises from cultural factors vs monetary headwinds. In particular, it could provide a strong argument for larger transfers from North to South Europe, from London to the rest of the UK, or from coastal US states to flyover country, by making clear the degree to which the benefits of currency membership flow the other way.
* As used in the US; the dollar's usage as a de-facto gold standard in poorer countries is a whole other kettle of fish.
** I'm aware that I'm simplifying the situation to the point of caricature - this narrative is just to give a cute example for my general question. Please feel free to disagree with me on the history of the Euro.