This is what I think he was saying. This is my attempt to say it more clearly.

Paul Krugman is a very good communicator. I try to emulate him. But I think he blew it on this post . Everybody has an off-day. No big deal. And it wasn't a simple thing to talk about anyway.

Here's my version of his two diagrams, rolled into one:







(I couldn't get the curves exactly the same as he drew them, because I'm not that good at "Paint". But it doesn't really matter.)

Update: Kevin Donoghue emails me this diagram, which is much closer to what Paul drew:



And, I managed to download it and put it in the post! Thanks Kevin!

The blue curve is a regular Phillips Curve. It shows how the unemployment rate determines the inflation rate. Paul assumes it eventually goes vertical, higher up (as it probably should, but I couldn't draw it right). And he assumes it flattens out lower down, reflecting some sort of longer-run downward wage-rigidity or price-rigidity. It's fairly standard.

The red curve is an IS curve. (Paul draws it with a kink at high inflation, and I'll come back to that later).

We normally draw an IS curve with the real interest rate on the vertical axis, and output on the horizontal axis. So this one looks weird. But if we assume there's a negative relation between unemployment and output (high unemployment means low output) that explains the horizontal axis. And if we assume the nominal rate of interest is stuck at 0%, then there's a negative relation between inflation and the real interest rate, that explains the vertical axis. The higher the inflation rate, the lower the real interest rate, the higher is output demanded, the higher is output, and the lower is unemployment. So the IS curve slopes down in this space too.

Paul puts a kink in his IS curve so it goes vertical at higher inflation rates. That's because when the inflation rate gets high enough, the real interest rate gets low enough, that the Fed can raise nominal interest rates above zero if it wants, and it will want to, to prevent the real interest rate falling any further. I've ignored the kink in my IS curve.

You get an equilibrium where the two curves cross. It's rather like supply and demand curves. Only in this case the curves cross twice, so you get two equilibria. Right now we're at the bad equilibrium, with high unemployment. We want to go to the good equilibrium.

The good equilibrium requires higher inflation than we have now. Paul thinks it's around 4% inflation. So if the Fed promises 4% inflation, and people believe the Fed, the economy moves to the good equilibrium. (Or the Fed could promise 5% inflation, raise the nominal interest rate to 1%, so we get the same real interest rate, and get to the good equilibrium that way.)

But suppose the Fed promises 2% inflation. More than the bad equilibrium, but less than the good equilibrium. That promise can't be fulfilled. If people expect 2% inflation, the economy would go to the point on the IS curve at 2% inflation, but the Phillips Curve is below the IS curve at that point, so actual inflation would be less than 2%. If people figure this out in advance, they know the Fed's promise of 2% inflation is not credible. Even if they don't figure it out in advance, and believe the Fed's promise, they will soon discover inflation is less than the 2% they expected, so will stop believing the promise, and the economy will collapse back to the bad equilibrium.

The bad equilibrium is stable (unfortunately). Suppose inflation at the bad equilibrium is 0%. If people expect 1% inflation, we climb up along the IS curve, but actual inflation, as determined by the Phillips Curve, will be above 0% but less than 1%. So expected inflation adjusts downwards and the economy reverts to the bad equilibrium.

The good equilibrium is unstable. But if the inflation rate is high enough the Fed can raise the nominal interest rate above 0% (that's where Paul's kink comes in), and still get the real interest rate that's needed for the good equilibrium. And if the Fed can adjust the nominal interest rate up and down more quickly than expectations adjust to changes in actual inflation, the Fed can make the good equilibrium stable.

That's what I think Paul is saying.

There is nothing logically wrong with what he's saying. It makes sense. But that doesn't mean he's right. I think he's wrong. I think the IS curve is flatter than the Phillips curve at the current bad equilibrium, so the bad equilibrium is unstable. But that's not the point of this post.