Central banks are usually owned by governments, and transfer their seigniorage profits to those governments. This creates a link between monetary and fiscal policy. But the presence of that link says nothing about the direction of causation.

John Cochrane (pdf) says that central banks' paying interest on reserves allows them to conduct monetary policy independently of fiscal policy. It breaks the link. He sees it as a game-changer.

John's approach to this question is based on the Fiscal Theory of the Price level. I want to approach this same question from a totally different perspective. I will use a very standard Quantity Theory perspective and replicate his results. It's quite simple really. If the central bank increases the growth rate of the money supply, but issues new money as interest on old money, there will be the standard increase in the equilibrium inflation rate, but without the standard once-and-for-all jump in the price level due to lower equilibrium real money balances. And there will be no effect on the central bank's seigniorage profits, and so there is no link to fiscal policy. I think that's what's going on in his model.

Since increases in the money growth rate and increases in interest rates on reserves would always move together under that sort of monetary regime, it would look like increases in interest rates on reserves cause increases in inflation rates. But they don't, of course. If we increased interest on reserves, but held the money growth rate constant, the equilibrium price level would fall.

The Bank of Canada has been paying interest on reserves for 20 years. And when it wants to increase the inflation rate, because it fears inflation will fall below the 2% target if it does nothing, the Bank of Canada lowers the interest rate on reserves. And the Bank of Canada seems to have gotten the sign right, because it has hit the 2% inflation target on average, which would be an amazing fluke it if had been turning the steering wheel the wrong way for the last 20 years without going off in totally the wrong direction. Interest on reserves is old stuff in lots of other countries, outside the US. It's not a game changer for us.

Take a simple version of the Quantity Theory. The central bank sets the money supply Ms. There is a money demand function: Md is proportional to the price level P, a positive function of real income Y, and a negative function of the opportunity cost of holding money. That opportunity cost is the difference between the market nominal interest rate Rb and the nominal rate of interest paid for holding central bank money Rm. Ms=Md=P.L(Y,Rb-Rm). The price level P equilibrates the supply and demand for money. Market nominal interest rates adjust to expected inflation.

Suppose the central bank unexpectedly permanently doubles the supply of money. The price level would double. If the central bank buys assets with the new money, the central bank's real seigniorage profits will increase, at the expense of the one-time inflation tax on individuals who held money when the price level doubled.

Suppose the central bank unexpectedly permanently doubles the money supply by using a helicopter drop. The price level would double, but there would be no change to the central bank's real seigniorage profits. Lucky individuals would gain more from the helicopter than they lost in the inflation tax, and unlucky individuals would gain less.

Suppose the central bank unexpectedly permanently doubles the money supply by doubling each individual's stock of money. We can think of this as like a one-shot payment of new money as interest on old money. The price level would double, but there would be no change to the central bank's real seigniorage profits. Each individual would gain in interest exactly what he lost from the inflation tax.

Suppose the central bank unexpectedly announced that one year from today it would permanently double the money supply by doubling each individual's stock of money. (Again, there will be a one-shot payment of new money as interest on old money). The announcement would have no effect on the price level today. But the doubling of the money supply one year from today would cause the price level to double on that day. (No individual has an incentive to get rid of money the day before the doubling, because what he loses from the inflation tax he gains from interest on money, so it's a wash.) Again, there is no effect on the central bank's real seigniorage profits. It's like an announced currency reform, where two new dollars replace one old dollar.

Suppose the central bank announces that it will increase the money supply growth rate by 10% per year, and will do so by paying daily interest on money at the rate of 10% per year. The announcement would have no immediate effect on the price level, but it would have an immediate effect on the rate of inflation, which would increase by 10% per year. There would be no effect on the central bank's real seigniorage profits, or on the real stock of money. The reason is that the interest rate differential between money and other assets is unchanged, so the opportunity cost of holding money is unchanged. All nominal interest rates will rise by the same 10% from the Fisher relationship. It's like an announced ongoing currency reform.

An increase in the growth rate of the money supply will cause an equal increase in the rate of inflation. One way to issue new money is to use it to pay interest on existing money, which increases the demand for money. An increase in the growth rate of the money supply by itself will cause an increase in the inflation rate and a once-and-for-all jump in the price level and (unless we are on the wrong side of the Laffer curve) an increase in real seigniorage profits. An increase in the growth rate of the money supply plus a pari passu increase in the interest rate paid on money will cause an increase in the inflation rate but no jump in the price level, and no effect on real seigniorage profits.

What these examples show is that by issuing new money in the form of interest on existing money, and so adjusting the money growth rate and interest rate on money pari passu, the central bank can control the inflation rate without having any effect on its real seigniorage profits.

If we further assume that the central bank is owned by the government, and that the central bank's seigniorage profits are (sooner or later) transferred to the government, and so affect the government's fiscal policy, we get a further implication. If the central bank adjusts the money supply growth rate and interest paid on money pari passu, it can control inflation with zero implications for the government's fiscal policy. Monetary and fiscal policy can be independent of each other.

But then we could say exactly the same thing if the central bank dropped the new money out of a helicopter, or gave it away to its favourite charity. Unless we define that as "fiscal policy". But then we could define paying interest on money as "fiscal policy" too.

John Cochrane says (page 10): "In sum, then, in this frictionless model, the government can set a nominal interest rate target; it can set that target without any adjustments to fiscal policy {E(t)S(t+j)} [expected future primary fiscal surpluses NR], and by setting nominal interest rates, the government can control expected inflation. This is the central result, which we need to digest and interpret."

This is my interpretation: If interest on old money is always paid with new money, and an increase in the rate of interest always means an equal increase in the expected growth rate of the money supply, it will cause an equal increase in the expected inflation rate (but will have no effect on the current equilibrium price level).

A little later (page 11) he says: "Even a completely fixed interest rate target does not lead to inflation instability or indeterminacy."

Yes, if a fixed interest rate target meant a fixed money growth rate target, because new money is always issued as interest on existing money, monetarists would not say this leads to explosive time paths for inflation or price level indeterminacy.

This result has nothing to do with the Fiscal Theory of the Price Level. It follows equally well from standard Quantity-Theoretic reasoning. This result has nothing to do with the presence or absence of monetary frictions that motivate monetary exchange and a demand for money when money pays less interest than other assets like government bonds. (It does depend in part on assuming perfectly flexible prices, but only because it would take longer for monetary policy to affect prices and inflation if prices were sticky.) And setting a higher nominal interest rate on money will cause a higher inflation rate only because it means the central bank has increased the growth rate of the money supply by the same amount.

John Cochrane's paper is a long one, as well as an interesting one. I may come back to it later, but that's enough for now.