It's a beautiful Saturday here in Seattle, so I'll make this quick (and somewhat out of order). Nick Rowe has new post up where he puts a few ideas very clearly:
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.
This is basically what happens in the information transfer model -- the existence of money means that the economy can't deviate too far from the NGDP-M0 path without some randomly irrationally exuberant people stepping in and cleaning up.
So any Neo-Wicksellian model with a ZLB must have currency in the model implicitly, even if it's not there explicitly.
Something of a side note on this one: I think that ZLB comes from the existence of money -- an asset that pays a 0% nominal interest rate; that's how it enters implicitly. If you think the ZLB is important, you're implicitly assuming currency. (I think that is the traditional economics answer.)
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.
This is what I tackled in these two posts:
And yes, the result is complicated, but it doesn't have to do with expectations or the ZLB (I have explicit money in this model, not implicit, so the ZLB is not relevant), but rather the relative size of the monetary base and the size of the economy. There is a way to translate expectations into this measure if you like expectations more.