...will an increase in the rate of interest paid for holding money be deflationary (because it increases the demand for money), or inflationary (because it increases the growth rate in the supply of money)?
This question crops up from time to time, in comments here and on other blogs, so I thought I would lay out a simple answer. Mostly as a "teaching" post, but also because it raises an interesting question about interest on reserves and central banks' communications strategy.
The answer is: an increase in the rate of interest paid for holding money will increase the equilibrium inflation rate; but it will not cause an additional one-time jump up or down in the equilibrium price level. (Yep, you gotta keep your head clear on the distinction between levels and rates of change over time.)
Here's my simple model: assume perfectly flexible prices and rational expectations. Let the demand function for money be:
1. M = P.L(R-p) where L' > 0, R is the nominal interest rate paid on holding money, P is the price level, p is the (expected) inflation rate, and so (R-p) is the real rate of return on holding money.
This is a very standard money demand function, except I have suppressed real income, and the real interest rate on other assets, which would normally appear as additional arguments in the demand function. I am holding them constant.
And let the supply function for money be:
2. m = R.M where M is the stock of money, and m is the growth rate of the stock of money.
This supply function embodies my assumption that all new money is always paid as interest on existing money. The central bank sets R.
Start with the case where R=0, so m=0. The central bank pays no interest on its monetary liabilities, and so holds the stock of money constant over time. The equilibrium (strictly speaking one equilibrium) is p=0. There is zero inflation.
Now suppose the central bank suddenly and unexpectedly announces that it will immediately start paying 1% interest on holding money, and so the stock of money will be growing at 1% per year too. The (strictly a) new equilibrium is that M/P stays the same, and the inflation rate is now 1%. There is no initial jump in the price level (either up or down), but the price level starts rising at 1% per year.
You can see that that new equilibrium satisfies both equations.
Here is the intuition:
1. Announcing an increase in interest on money, but no change in the money supply growth rate, would cause a one-time increase in the demand for money, so M/P increases, and so cause a one time decrease in the price level, but no subsequent change in the inflation rate.
2. Announcing an increase in the money supply growth rate, but no change in the interest rate paid on money, would cause an increase in expected inflation, which would cause a one-time decrease in the demand for money, so M/P decreases, and so cause a one-time increase in the price level, on top of the increased subsequent rate of inflation.
3. If you put 1 and 2 together, the two one-time jumps in the price level exactly cancel out, leaving only the increased subsequent rate of inflation.
OK. All that was very standard money/macro. The sort of keyboard exercise that bright upper year undergrads should be able to tackle.
But here's the kicker: what happens in the real world when central banks increase the rate of interest they pay on reserves? Do people interpret that as implying an increase in the growth rate of central bank money? Because if they do interpret it that way, an increase in the rate of interest they pay on reserves will increase expected and actual inflation.
There is nothing to say they must interpret it that way, because there is nothing to stop central banks using open market operations to offset any changes in the total stock of base money that arise from paying higher interest on existing base money. But there is nothing to say they mustn't interpret it that way either. What are people holding constant in their expectations? M, or OMO? What is the central bank communicating when it changes the rate of interest it pays on reserves?
God only knows. But this is a daft way to run monetary policy.
[Thanks to commenter MR, for raising this question long ago.]
[P.S. The question here is not the same as the "Neo-Fisherite" (Irving rolls in his grave) sign-wars kerfuffle, which was about the nominal rate of interest on other assets.]