I'm currently doing a research paper for Jan Libich, one of my supervisors, on Fiscal-Monetary interaction.
A key area of research in the field is determining the game theoretic relationships between fiscal players---who are overly viewed as pouring fiscal `gravy' onto the electorate at any given chance---and monetary players, who are inflation hawks, and so take away Greenspan's punch as the party gets going. Jan knows about as much as there is to know with this game theoretic relationship (though he is more modest of himself than I am of him), and so his papers are worth reading. The essential insight from this strand of research is that independent central banks have the capacity to punish overly expansionary monetary policy if a few conditions are satisfied.
In layman's terms, the conditions boil down to the assumption monetary policy tightening hurts the same people who enjoy licking up the government's gravy. So in countries with no political business cycle (dictatorships), and in monetary unions, like the EU, the model requires modification, which is partly what my paper-in-progress is about.
What hasn't been researched in this literature so far (to my knowledge) is how central banks, which are mandated by law to target price stability, output gaps, or both, may have had their hands tied in punishing governments for reckless deficit spending. This view would say that Greenspan kept interest rates low well into the 00s because the Fed's implicit price target was not breached, due to the huge disinflationary pressure of Chinese imported goods.
If this holds, then blame for the explosion in house prices in the US can not only be pinned to China and the GCC for running huge surpluses---the so-called `global imbalances thesis'---but establish a degree of causality between Chinese currency policy (which kept export prices low in UD dollar terms) and US monetary/fiscal policy during the period.