1. What happens if the central bank instead suddenly raises the nominal interest rate to 4%, and is expected to keep it there? The answer is that the 2014 price level instantly halves to 50, and there is a steady 1% inflation rate until 2084. So the real interest rate stays at 3%.

If the central bank sets a nominal interest rate of 3%, and is expected to keep it at 3%, the equilibrium price level in 2014 will be 100, and there will be 0% inflation until 2084. The real interest rate is 3%, just like the natural rate.

Also suppose, but just for simplicity, that the natural rate of interest is 3%, and everybody knows it will stay at exactly 3% until 2084.

Suppose, just suppose, that everyone knows that the price level will be exactly 100 in 2084. ( That's 70 years from now, to keep the math simple ). Because in 2084 the central bank will redeem all the outstanding notes, in exchange for real goods, at a price of 100 notes per real good. And will then start afresh with a new money.

2. And if the central bank instead suddenly cuts the nominal interest rate to 2%, and is expected to keep it there, the 2014 price level instantly doubles to 200, and there is steady 1% deflation until 2084. So the real interest rate stays at 3%.

Changes in nominal interest rates have the "right" sign in their effect on the price level, but the "wrong" sign in their effect on the inflation rate.

But we can easily eliminate that "right" sign on the price level, by changing the questions slightly.

1a. What happens if the central bank instead suddenly raises the nominal interest rate to 4%, and is expected to keep it there? And at the same time announces that the price level will be 200 in 2084, because it will redeem the outstanding notes at a price of 200? The answer is that the 2014 price level does not jump, and there is a steady 1% inflation rate until 2084. So the real interest rate stays at 3%.

2a. And if the central bank instead suddenly cuts the nominal interest rate to 2%, and is expected to keep it there, and at the same time halves the 2084 price level to 50, the 2014 price level does not jump, and there is steady 1% deflation until 2084. So the real interest rate stays at 3%.

It is very easy to get the "wrong" sign for the effect of nominal interest rates on inflation, without getting the "right" sign for the effect on the price level. But it is the change in the 2084 price level target, that accompanies that change in nominal interest rates, that is doing all the work.

(And the equilibrium path is a stable path, given standard assumptions. A lower than equilibrium price level today means higher expected inflation from now on, to get back to a price level of 100 in 2084. And higher expected inflation means a lower real interest rate for any given nominal interest rate. And a lower real interest rate means higher demand for goods. Which causes the price level to jump back up to the equilibrium path.)

If prices are sticky, it won't be quite as simple as in my answers above, because the price level won't jump up or down instantly when the central bank does something silly with the nominal interest rate. It will take time for the price level to adjust to the new equilibrium path. Raising the nominal interest rate, with no change in the 2084 price level, will cause inflation to decrease initially, and increase eventually. Cutting the nominal interest rate, with no change in the 2084 price level, will cause inflation to increase initially, then decrease eventually. You get the "right" sign initially, and the "wrong" sign eventually.

Pinning down the expected future price level provides a wonderful nominal anchor. It lets the central bank fall asleep at the nominal interest rate wheel, or do any stupid thing it wants with nominal interest rates, without causing the economy to explode into hyperinflation or implode into hyperdeflation. We don't need the central bank to follow the Howitt/Taylor Principle (raise nominal interest rates more than one-for-one with inflation) to do that job.



Price level path targeting, or NGDP level path targeting, amounts to much the same thing as pinning down the 2084 price level at 100. As long as everybody expects the central bank to wake up eventually, and do what it had promised to do in the past, we avoid nominal indeterminacy. We avoid the Wicksell Problem. The economy is self-stabilising.

Unfortunately, we don't live in a world like that. Nothing pins down the price level in 2084, or in any future year. There is no long run nominal anchor that could help the economy self-equilibrate despite central banks falling asleep at the nominal interest rate wheel, or doing silly things with it.

But we could live in a world like that, if we adopted price level path targeting, or NGDP level path targeting.

[For JP Koning. And for John Cochrane. And with thanks to Lorenzo from Oz, who told me the Bank of England once fell asleep at the nominal interest rate wheel for nearly a century. That was when the gold standard provided a long run nominal anchor.]