Jeffrey Hummel has a good article about the relationship between money and interest rates. I think that there is a bit too much emphasis on the thought experiment of a permanent change in the growth rate of the quantity of money. I have become more and more focused on a situation where the quantity of money is endogenous because the monetary regime targets something else. Sometimes I focus on the growth path of nominal GDP. That is because I am very interested in the characteristics of such a regime. I also think about a target for the inflation rate, because that appears to be a key characteristic of really existing monetary regimes.
Given these other targets, what happens when there is a temporary increase (or decrease) in the quantity of money? No longer are we working out the equilibration process of a permanent change in the growth path of the quantity of money. What happens when the quantity of money rises, and those holding the money expect the increase to be reversed because it is inconsistent with the nominal anchor?
Hummel's argument is very consistent with the Market Monetarist notion that permanent changes in the quantity of money impact spending on output. Much of the argument that changes in money growth do not impact interest rates very much depends on a prompt impact on spending on output and the consequent change in inflation and real output growth. It is much less consistent with a simplistic New Keynesian approach where monetary policy is a lower interest rate, which results in higher real consumption and real output, and so an output gap that leads to higher inflation.
It is wrongheaded to combine these two views and say that an expansionary monetary policy will not lower interest rates, and because interest rates don't fall, real expenditure and real output won't rise and so inflation won't rise, and therefore the sum of real output and inflation, nominal GDP growth, will not rise. There is a contradiction there. It is the more rapid growth in real output and inflation that eventually reverses any decrease in interest rates, and in the extreme, leave interest rates unchanged despite more rapid money growth.
But if the nominal anchor is such that an increase in the quantity of money must be temporary, and so there will be little or no increase in spending on output and so little or no inflation or additional real growth, then what does the unusually high quantity of money imply for interest rates?