I have been arguing with John Cochrane and Steve Williamson over whether central banks announcing higher nominal interest rates is inflationary or deflationary. The very fact that economists are arguing about that very basic question tells us something important about central banks' using nominal interest rates as a communications strategy: it sucks. This is a point that economists like Scott Sumner and I have been making for some time. Do low nominal interest rates mean monetary policy is loose or tight? It depends.
(And if the answer to that question is "it depends", it also means that the Zero Lower Bound on nominal interest rates does not mean that central banks cannot loosen monetary policy.)
Suppose the central bank suddenly announces a new time-path for the monetary base. Or for the money supply, or the nominal exchange rate, or the price of gold, or something else with $ in the units. The new announced time-path is different from the one people had previously expected.
[Update: just to keep it simple, I'm assuming this announcement is not a response to some shock. Or, if it is a response to some shock, people already know about that shock, so we can separate out the effects of the shock and the effect of the announcement. The contents of the announcement are news.]
Consider the set of all such possible announcements.
Let us divide that set into those that cause an immediate increase in the nominal interest rate, and those that cause an immediate decrease in the nominal interest rate. (Strictly speaking there will be some members of the set that have exactly zero effect on nominal interest rates, so you could add a third category, if you insist, but let's ignore those borderline cases, to make my life easier.)
Let us also divide that set into those that cause an immediate increase in the inflation rate, and those that cause an immediate decrease in the inflation rate. (Strictly speaking there will be some members of the set that have exactly zero effect on the inflation rate, so you could add a third category, if you insist, but let's ignore those borderline cases, to make my life easier.)
So we have partitioned the set of all announcements into four subsets.
How exactly you allocate members of the total set into those four subsets will depend on your macroeconomic model.
But ask yourself this question: can you say that two of those sets are empty sets? I don't think you can.
Let's start with an extreme macroeconomic model, in which prices are perfectly flexible, and in which money is always neutral and super-neutral. In that model, monetary policy has no effect on real interest rates, so inflation rates and nominal interest rates must always respond in the same direction. That seems to imply that the North-East and South-West sets are empty sets.
But it's not so obvious. Because some monetary policy announcements will cause a downward jump in the price level and an upward jump in the nominal interest rate. For example: "We will cut M in half immediately but will double it again 10 years from now." If by "inflation rate" we mean "percentage change in the current price level relative to just before the announcement" this is an example where the inflation rate falls and nominal interest rate rises. It is only after the announcement that the (forward-looking) inflation rate increases.
Now let's consider a different macroeconomic model, with sticky prices, where monetary policy is not neutral. It is tempting to say that, with such a model, any monetary policy announcement that caused an immediate increase in nominal interest rates would cause a recession and a fall in inflation, so the North-West and South-East sets are empty sets.
But that isn't right either. For example, suppose the announcement is: "M will stay the same today, but will double in 10 years time". Even if the price level is sticky, so cannot jump immediately on the news, people know that the price level will eventually double, so expected inflation, and hence actual inflation, can increase immediately, and this can cause the nominal interest rate to rise immediately.
Suppose you were an economist who knew that the central bank had made an announcement about monetary policy, but you did not hear that announcement, and the only thing you did know was that the announcement had caused nominal interest rates to rise.
Simply knowing that the central bank's announcement caused nominal interest rates to rise does not give you sufficient information to tell you whether inflation (or the price level) will rise or fall.
If the central bank announces a higher nominal interest rate, that does not give you sufficient information to tell you whether inflation (or the price level) will rise or fall.
Central banks' announcing targets for the nominal interest rate is a very bad communications strategy for monetary policy. We do not know what they mean.