Although central banks have recently taken unconventional policy actions to try to shore up macroeconomic and financial stability, little theory is available to assess the consequences of such measures. This paper offers a theoretical model with which such policies can be analyzed. In particular, the paper shows that in the absence of the fiscal authorities' full backing of the central bank's balance sheet, strange things can happen. For instance, an exit from quantitative easing could be inflationary and central banks cannot successfully unwind inflated balance sheets. Therefore, the fiscal authorities' full backing of the monetary authorities' quasi-fiscal operations is a pre-condition for effective monetary policy.