I am going to give what I think is the intuition behind John Cochrane's paper (pdf), that is the subject of his recent post. (Or maybe what I'm doing is reverse-engineering his model's results.) The key result of his paper is the "Neo-Fisherian" finding that an increase in the rate of interest set by the central bank results in an increase in the inflation rate. And this equilibrium is stable. And with sticky prices, if the central bank sets a higher interest rate this causes a boom.
My old brain is tired, I can't do math, so I may have misunderstood him. (There is a lot of his paper I do not understand, and it's a long paper and I haven't read it all). But my little "model" gets the same results as his and is also simpler and more general. And much easier to understand.
It's based on exactly the same "model" I presented in my old post "If new money is always paid as interest on old money".
Take a very standard monetarist model, with a very standard money demand function. Make one small change. Assume that all new money is always paid as interest on old money. [Update: Any other change in the money supply has consequences for the long run government budget constraint, so is called "fiscal policy".]
Assume perfectly flexible prices initially.
Start in a stationary equilibrium where the interest paid on money is 0%, and so the money growth rate is also 0%, and so the inflation rate is also 0%.
If the central bank now pays 1% interest on money, the money growth rate is also 1%, and the inflation rate is also 1%. But the real stock of money does not change. That's because the 1% interest earned by holding money exactly offsets the 1% inflation, so the real return on holding money is unchanged, and so the opportunity cost of holding money is unchanged.
There are no fiscal consequences from this "inflation tax", because the inflation tax is exactly offset by the interest paid on money. So it looks like the Fiscal Theory of the Price Level, with a continuous 1.01 for 1 stock-split. There is no change to the central bank's seigniorage profits delivered to the government that owns the central bank.
But notice: I do not need to assume that money pays the same rate of return as other assets (which is normally assumed in FTPL). In that sense, my "model" is more general.
Now drop the assumption of perfectly flexible prices. Assume that prices are set in advance. So it takes time for the inflation rate to increase when the central bank increases the interest rate paid on money and the money growth rate. And when the inflation rate does eventually increase, it will temporarily overshoot the money supply growth rate (so the price level can catch up to the money supply). So the real interest rate on holding money first rises above its "normal" level, then falls below its normal level, then returns to normal.
Now remember the relationship between consumption and real interest rates from the standard New Keynesian Euler equation. There is a positive relationship between the level of the real interest rate and the growth rate of consumption.
Put the two together and we get the following result: if the central bank increases the rate of interest paid on money and the money growth rate, we observe first rising consumption then falling consumption, as it returns to normal.
Old Monetarists will not find this result surprising. An increase in the growth rate of the money supply causes a temporary boom in consumption (and output), and a lagged increase in inflation. What is different is that new money is paid as interest on old money, so an increase in the money growth rate also means an equal increase in the rate of interest on holding money.
I'm still trying to figure out if John Cochrane's model is really a monetarist model, even though he doesn't think it is. Because one of the tenets of monetarism is that interest rates do not tell you the stance of monetary policy.
His papers are food for thought. And this probably won't be my last thought on this subject.
[And thanks to MR, for getting me thinking along these lines, many months ago.]