For some reason a fairly extensive part of the literature on monetary economics is dedicated on the “interaction between monetary and fiscal policy”. I am not sure what this means, nor why it matters at all. As a core idea, and again resorting to Friedman’s notion that “Inflation is always and everywhere a monetary phenomenon in the sense that it is and can be produced only by a more rapid increase in the quantity of money than in output”, the level of inflation is 100% under the control of and thus determined by the central bank. The only additional assumptions required to make this hold is central bank independence, the importance of which has been long established, and at least some degree of central bank competence, without which we can essentially stop talking about monetary policy in general.
Let’s start from a point where a central bank is achieving its target, however defined. Now let’s bring in fiscal policy, and let’s say it tries to increase spending. Clearly this increase in spending would, momentarily, move the economy away from what the central bank is targeting, which would require central bank intervention to bring it back on track. In the end, for the macroeconomic indicators that are generally included in the objective function of central banks, the fiscal policy does not do much after the initial short-lived shock. The whole concept is essentially summarized by the concept of “monetary offset”, basically explained in this paper by Scott Sumner (.pdf). This inability of fiscal policy to do much on a macroeconomic level in a world where the central bank actually does its job is a feature, not a bug. Fiscal policy should concentrate on achieving democratically determined goals, and as such it can legitimate alter e.g. the income and wealth distribution in an economy in order to bring them in line with this consensus view on what it should be, as well as give the central bank a different target if it so desires. The optimal target a central bank should be given very much depends on what is possible on a fiscal level, particularly in terms of the ability of governments to tax different things. Yet once that is determined, the central banks job is to make sure that whatever the fiscal authorities do does not move the economy away from the target it’s job it is to achieve. Apart from the target setting itself this is essentially a strictly objective task.
In other words the central bank will always dominate the fiscal authorities given the two basic assumptions I made. It should not be the job of fiscal policy to achieve these targets in the first place. If a situation arises where someone has to give in, it is always the fiscal authority that will unless at least one of the two assumption is violated. In terms of final macroeconomic variables targeted by the central bank (once its target is set) like the level of inflation or the level of NGDP, what fiscal policy does, or even its very existence, is irrelevant.