I have always been skeptical regarding "necessary" relationships between monetary policy and fiscal policy. Most recently, these relationships supposedly play a key role distinguishing the neo-Fisherite and neo-Wicksellian approach to interest rate targeting.
The neo-Wicksellian approach to lowering the inflation rate is to raise the target for the interest rate. Of course, this is only a tentative adjustment that might soon require a reduction in the interest rate to keep the inflation rate from falling too low.
The neo-Fisherite view is that the way to lower the inflation rate is to lower the target for the interest rate.
Which is correct supposedly depends on assumptions about fiscal policy in the long run.
In my view, if the "target" for the nominal interest rate is something close to a target for the growth rate for the quantity of money, then a lower target for the nominal interest rate will result in in a lower growth rate for the quantity of money This will result in lower inflation. If this is expected, then the lower inflation will lower the equilibrium nominal interest rate. This approach doesn't necessarily involve the central bank hitting the target for the nominal interest rate consistently.
There is an alternative neo-Fisherite process that I find problematic. If the expected future price level is tied down, then a fixed target for the nominal interest rate can be self-stabilizing. In that situation, if the real interest rate is too high to clear markets, the price level falls. If the expected future price level is given, then the expected inflation rate rises. This lowers the real interest rate. The price level level falls enough so that the expected inflation rate rises enough for the real interest rate to fall enough to clear markets.
If the price level falls too far, given the expected future price level, expected inflation will rise too much and the real interest rates will fall too low, which causes prices to rise. The price level should gradually rise to the expected level. The actual inflation rate should equal the expected inflation rate.
The neo-Fisherite result follows because if the nominal interest rate is increased, then it immediately would raise the real interest rate. The price level would fall. And then when it is low enough that higher expected inflation lowers the real interest rate back to the level needed to clear markets again, we now have higher inflation for the price level to return to the expected level.
Unfortunately, it is not at all obvious what ties down the future price level under this system. And that is where we get these fiscal theories. As for using it to explain actual performance? Really? People supposedly have an expectation of the future price level?
Anyway, I reject the assumption that excessively high budget deficits must lead to inflationary default. I realize that it is a possibility, but I consider it inferior to explicit default on the national debt. The monetary constitution should not allow for inflationary default. It is default either way, and inflationary default of government debt just creates a massive externality, causing the simultaneous inflationary default of private debt.
As for the notion that deficits must be sufficiently large to generate sufficient government debt for the central bank to purchase, this is simply based upon the assumption that the central bank must purchase government debt. Perhaps the most extreme version of this framing is the "bills only" doctrine. That is the view that the central bank should solely purchase short term government debt.
That might be a nice policy if there is sufficient short term government debt, but when the demand for base money outstrips the amount of short term government debt, then the obvious answer is for the central bank to expand its horizon and purchase something else. After five years of the Fed purchasing mortgage backed securities, it is hard to understand why anyone would consider the amount of short term government debt outstanding to be a constraint on monetary policy.
If government were sufficiently frugal that the national debt falls, perhaps even to zero, does that require that the nominal anchor be changed? Must there now be a deflationary policy, down to zero?
How about having the central bank purchase private debt? Isn't there a long history of insisting that central banks should solely purchase private debt? Real bills?
Don't like the central bank picking and choosing between borrowers? Privatize the issue of hand-to-hand currency and end reserve requirements.
Demand for reserves still too high? Make the sole asset of the central bank overdrafts to banks with adverse clearings. Charge high interest rates on those overdrafts and pay low, maybe negative, interest on reserve deposits. In other words, use the corridor system. (Woodford's neo-Wicksellian world.)
Suppose we lived in a world with no government debt and an evolved gold standard. Banks issue hand-to-hand currency and deposits. The banks deposit gold at the clearinghouse to settle net clearing balances. Want to stabilize the price level, inflation, or better yet, a growth path of nominal GDP? Vary the price of gold--somewhat like Fisher's compensated dollar.
Or better yet, let the price of gold be determined by the market and make the monetary liabilities redeemable with index futures contracts on the nominal anchor.
Of course, the current monetary order does include a key role for government-issued hand-to-hand currency. Reserve balances are huge and are at least quasi-government debt.
However, models that determine the current price level based upon rational expectations about what must happen to the quantity of base money in the distant (infinite?) future, is making an assumption about what systems will exist in the future. I am not sure that it is really rational to assume that monetary institutions will remain the same in the distant future.
Of course, as a long-time money reformer, perhaps that is wishful thinking.