Suppose a real shock hits the economy. It affects relative prices. The prices of the green firms must rise relative to the prices of the red firms. The prices of the red firms must fall relative to the prices of the green firms. Same thing. But which happens? Do the green prices rise, or do the red prices fall, or is it a bit of both?
It might depend on the central bank's target. Is it targeting the green price level, or the red price level, or a bit of both?
Here's another thing it might depend on: which firms hear about the shock first? If the green firms hear about it first, they will raise their prices. If the red firms hear about it first, they will lower their prices. The firms who hear the news first will respond to the news, because they know the other firms won't. It's a mixture of a Hayek/Lucas local knowledge problem, and a Keynes coordination who-moves-first problem.
Even if both green and red firms hear about it at the same time, but the green firms don't know the red firms hear it, and the red firms know the green firms don't know that the red firms hear it, we get the same results: the green firms will raise their prices and the red firms won't cut theirs.
We only get indeterminacy when it is common knowledge that all firms hear about the real shock at the same time. That is unlikely to happen. Real shocks may have general equilibrium effects on all relative prices, but the shocks themselves are nearly always local in origin, and some firms will hear about them first.
If the shock hits the green firms, they will know about it first, and it will be a positive shock to the price level. The SRAS curve shifts up.
If the shock hits the red firms, they will know about it first, and it will be a negative shock to the price level. The SRAS curve shifts down.
If the central bank accommodates these price shocks, it will help all firms coordinate on the new set of relative prices. It lets firms set their prices using local knowledge and partial equilibrium analysis, which most people understand, rather than economy-wide knowledge and monetary general equilibrium analysis, which hardly anybody understands.
Strict NGDP targeting will do a better job of accommodating price shocks than strict price level or strict inflation targeting. Flexible NGDP targeting might do better than strict NGDP targeting, if the central bank has enough information to distinguish between: Aggregate Demand shocks; SRAS shocks; and LRAS shocks. But we don't want to rely too much on central banks' being able to solve the monetary general equilibrium model in real time.
I see this as maybe an interpretation of what Bill Woolsey has been saying?
It's an update on my old post on Sticky prices vs sticky coordination.