Suppose you live in a Neo-Wicksellian economy, where the central bank sets a nominal rate of interest. Black holes are a theoretical possibility. Nominal demand for goods can spiral down to zero, if people expect it to. And white explosions are a theoretical possibility too. Nominal demand for goods can spiral up to infinity, if people expect it to. And Neo-Wicksellian theory says that the only thing that can prevent those things happening is a wise central bank that adjusts the nominal interest rate in the right way to prevent people expecting those things to happen.
But what is happening to the nominal stock of base money if the economy sprials down into a black hole? And what is happening to the nominal stock of base money if the economy spirals up into a white explosion? Neo-Wicksellian models are silent on that question. Because they think that the stock of money is unimportant. Which is very strange, because Neo-Wicksellian models are models of monetary exchange economies, where people buy and sell all other goods for money. If they were models of barter economies, the unemployed workers who cannot sell their labour, and the firms who cannot sell their goods, would all get together and barter their way back to full employment. Black holes would be impossible if barter were easy. I would swap my unsold apples for your unsold bananas.
So money must be in the Neo-Wicksellian model implicitly, even if it's not there explicitly.
And according to Neo-Wicksellian models, the danger of a black hole is greatest when the central bank hits the Zero Lower Bound on nominal interest rates. And that ZLB exists because it is hard in practice for central banks to set a negative nominal interest rate on currency. So any Neo-Wicksellian model with a ZLB must have currency in the model implicitly, even if it's not there explicitly.
Suppose a Neo-Wicksellian central bank hits the ZLB. If it lets the stock of base money spiral down to zero too, then of course the economy would spiral down into a black hole. But central banks don't have to do this. And central banks did not in fact do this, when they hit the ZLB. They did the opposite. Which is why their economies did not spiral down into a black hole.
If the economy did spiral into a black hole, I would buy the whole world with the $20 note in my pocket. Why wait? Except that you and another guy would see this coming, and would jump in before me, and each buy half the world with the $20 notes in your pockets. Except that I and three other guys would see this coming, and would jump in before you, and each buy a quarter of the world. And so on. The black hole theory comes apart backwards, as long as we still have some currency in our pockets.
Nominal demand can fall, but it can't fall to zero, unless the stock of base money falls to zero too. And central banks can stop it falling to zero, ZLB or not.
Neo-Wicksellian models include money implicitly. But we need to introduce money explicitly if we want to understand what happens at the ZLB. But then why not go the whole hog and include money explicitly, whether or not we are at the ZLB?
Take a related question -- the Neo-Fisherite question. If the central bank permanently raises the nominal interest rate, will this result in higher or lower inflation? If you tell me what permanently raising the nominal interest rate does to the base money supply growth rate, I can answer your question. If it causes the base money growth rate to increase permanently, like in John Cochrane's model, then inflation will increase. If it causes base money growth to decrease, then inflation will decrease. Tell me how the central bank raises interest rates, and what it is doing with base money growth when it does this.
So why not just change the question? Ask what happens to inflation and nominal interest rates if the central bank permanently increases the money growth rate? Inflation and nominal interest rates will eventually increase too. What happens to inflation and nominal interest rates immediately is a little more complicated. It depends on whether prices and inflation are sticky, and on how quickly expectations adjust and people learn that the increase is permanent.
If a question is too hard to answer clearly, that probably means you are asking the wrong question.
The Neo-Wicksellian perspective, in which central banks are seen as setting a nominal interest rate, is what leads us to ask those badly-posed questions. And since central banks' communications strategy is central to the success of monetary policy, central banks should stop doing things that cause people to ask badly-posed questions about what central banks are doing and what the results will be.
That is the real world policy implication of all this angels-on-pins talk about black holes and the Fisher relation.
[I'm just riffing off, or ripping off, Scott Sumner's very good post. Which in turn was a response, like this is, to John Cochrane's very good post. But I really must stop blogging about this stuff. Time to get out and do some last yard work, before the snow.]