Take the Fisher Equation in its full non linearised form.
r denotes the real interest rate, i denote the nominal interest rate, and π denotes the inflation rate.
Is this a good target for monetary policy?
It is not because it does not measure the full numeraire effect of the money in circulation. Its use has led to inflation consistently undershooting Central Bank targets.
A better target would be
Where g is the ratio of the deficit to the current broad money stock in circulation.
It linearise after two taylor expansions to the approximation
Its importance is because of the accounting identity that the public sector deficit is equal to the public sector surplus.
So if the deficit is expanding at less that the rate of growth then the deficit is sustainable. Note it is the first derivative that matters, and when you have a delay between the rate of money destruction – the point in time taxation takes place, and the point of time it is spent, which you always have with annual budgets, then you will get a classic accelerator effect; a mere change in the rate of change in the deficit will be sufficient to cause a change in effective demand even though the deficit may still be growing. The reduction in the rate of the deficit has led to an accelerated reduction in the numeraire effect causing deflation.