Matt Yglesias says that "Inflation doesn't create jobs, jobs create inflation".
Well, yes and no. Both. Neither. It's simultaneous causation. It's a non-linear story, in the Artsie sense of "non-linear". And don't forget expectations. When we add in expectations, the story becomes very non-linear.
Here's a simple plot summary. (OK, it's not at all simple, but it's as simple as I can make it. Sorry.)
An increase in expected inflation, and/or an increase in expected real growth [Scott Sumner interjects: "Hell Heck Nick, why not just add the two together, and say 'an increase in expected NGDP growth'?"] causes an increase in (the) Aggregate Demand (curve).
An "increase in (the) Aggregate Demand (curve)" means a change in the whole relationship between prices and output demanded, so that more output will be demanded at the same price and/or the same output will be demanded at a higher price.
An increase in Aggregate Demand causes an increase in inflation and/or an increase in real growth. [Scott again interjects: "Heck Nick, why not just add the two together, and say 'an increase in NGDP growth'?".] It will be some mix of the two. (The exact mix is determined by the shape of the Short Run Aggregate Supply curve.)
The more inflation in the mix, the less real growth in the mix. The more real growth in the mix, the less inflation in the mix. When we start talking about this mix, inflation and real growth move in opposite directions, not the same direction. But we still can't really talk about higher inflation causing lower real growth, or higher real growth causing lower inflation. It's all non-linear. It's the shape of the Short Run Aggregate Supply curve that causes (determines) the particular mix we get.
If real growth increases, job growth increases too. (No, once again, you can't really say that one causes the other, or the other causes the one, because it's not like that.)
And here comes a flashback (or is it a flashforward?). Remember where this story started, with an increase in expected inflation and/or an increase in expected real growth? And where it seems to end, with an increase in actual inflation and/or an increase in actual real growth? Well, guess what, what actually happens validates, at least in part, the very expectations that caused it to happen. So if the characters in the story see where the story is heading, you could say that their expectations, at least in part, cause themselves. Those expectations are, at least partly, self-fulfilling.
When I say "at least in part", how big a part might that be? I'm not going to answer that question here, except to say "it depends". And it depends in part on what the central bank does, and is expected to do, or even threatens to do, if the actors in the story don't follow the script. It might be 50%, it might be 100%, or it might even be 150%. The central bank wants it to be exactly 100%, if they follow the script the central bank has written. The director is also a character in the story.
Everything I've said has been absolutely standard macro, just said in words, without diagrams or equations. Man, but isn't macro incredibly non-linear?