Game theorists know that a change in the "strategy space" can change the equilibrium of a game. The classic example, now over a century old, is the difference between the Cournot-Nash equilibrium and the Bertrand-Nash equilibrium in oligopoly theory.

For a monopolist, it makes no difference whether the firm chooses output to maximise profit or chooses price to maximise profit; we get exactly the same equilibrium either way. In oligopoly it does make a difference. In Cournot-Nash, each firm chooses output taking other firms' outputs as given. In Bertrand-Nash, each firm chooses price taking other firms' prices as given. The Cournot-Nash equilibrium has a higher price and lower output than the Bertrand-Nash equilibrium, even when everything else is the same.

Oligopolists that play Cournot-Nash will earn higher equilibrium profits than oligopolists that play Bertrand-Nash. If you were an oligopolist, you would want to shut up about your price, and the other firms prices. You would want to talk about your output, and the other firms' outputs, instead. You would want to change the game you are playing from a Bertrand-Nash game into a Cournot-Nash game. And maybe you can change the strategy space by shutting up about one strategy space and talking a lot about the other strategy space.

I think that central banks should shut up about interest rates too, and talk about something else instead. That way they might change the strategy space into a different strategy space that leads to a better equilibrium.

It makes no sense to argue about whether an oligopolist, taking the other firms' decisions as given, is really choosing price or output. By picking a point on his demand curve, by choosing price he is ipso facto choosing output, and vice versa. What matters is not whether he is in fact choosing price or output (a distinction that makes no sense anyway), but whether other firms think of him as choosing price or output (and whether he thinks of them as choosing price or output). And the oligopolist wants the other firms to think of him as choosing output, not price. Which is why he should shut up about price, and talk about output instead.

It also makes no sense to argue about whether central banks choose an interest rate or something else. Since interest rates are linked to a lot of other things, by choosing an interest rate the central bank is ipso facto choosing a lot of other things, and vice versa. What matters is not whether a central bank in fact chooses an interest rate or something else, but whether other people think of the central bank as choosing an interest rate or something else. Which is why central banks should shut up about interest rates, and talk about something else instead.

To think of central banks as choosing a rate of interest is a social construction of reality. What is so very unfortunate is that this is a social construction of reality that is not merely maintained but created by central banks themselves in how they talk about what they are doing. It is like oligopolists spending all their time talking about prices, and discouraging any talk about quantities.

Why is it so bad if people think of central banks as choosing an interest rate? What's wrong with that strategy space? Right now the most important reason is this: if people think of central banks as setting an interest rate, then they think the central bank must be powerless to increase demand for goods if the interest rate is at the lower bound. And most of the power of a central bank comes from its ability to influence people's expectations of the future. Like governments, police, armies, and referees, most of central banks' power comes from belief in their power.

The strategy space matters when others' expectations of your choices matter. Those expectations are defined over the strategy space. Expectations of monetary policy matter. That means the strategy space matters.

So, central banks: stop talking about choosing an interest rate; stop talking about the time-path of future interest rates; just shut up about interest rates altogether. Start talking about something else instead.

Like what? Something that moves in the right direction, for starters. Nominal interest rates move in the wrong direction. If you think about monetary policy in terms of interest rates, then if the bank chooses to loosen monetary policy you think of that as the bank choosing a lower interest rate. But if the bank is successful, and monetary policy is in fact loosened, so expected inflation rises, and expected future income rises, then nominal interest rates will rise. So you have no idea what success means. Does it mean falling or rising nominal interest rates? So success cannot be self-promoting. Central banks' power, and belief in their power, move nominal interest rates in opposite directions.

Instead, talk about something that moves in the same direction when you choose to loosen monetary policy and when you succeed in loosening monetary policy. Share prices maybe, commodity prices, or whatever. Anything but interest rates.