Do New Keynesians assume full employment?

I’ve tried to write this as jargon free as I can, but it is mainly for economists

Nick Rowe claims that the New Keynesian model assumes full employment. I think he is onto something, but while he treats it as a problem with the model, I think it is a problem with the real world.

Nick sets up a simple consumption only economy with infinitely lived self employed workers, where we are at the steady state (=long run) level of consumption C(t)= output Y(t)=100. Then something bad happens (what macroeconomists call a shock):

“every agent has a bad case of animal spirits. There's a sunspot. Or someone forgets to sacrifice a goat. So each agent expects every other agent to consume at C(t)=50 from now on. ... So each agent expects his income to be 50 per period from now on. So each agent realises that he must cut his consumption to 50 per period from now on too, otherwise he will have to borrow to finance his negative saving and will go deeper and deeper into debt, till he hits his borrowing limit and is forced to cut his consumption below 50 so he can pay at least the interest on his debt.”

To put it more formally: each agent believes the steady state level of output has fallen. That in turn has to imply that everyone makes a mistake about the desired labour supply of everyone else. I assume this is a mistaken belief. If the belief was correct, then there is no problem: the steady state level of output should fall, because people want more leisure and less work.

Nick says that there is nothing a monetary authority that controls the real interest rate can do about this mistaken belief about the steady state, because changing real rates only changes the profile of consumption (shifting consumption from the future to the present) and not its overall level. That is correct. Furthermore if each individual simply assumes what they think is true, and does not even bother to offer his pre-shock level of labour to others, then this is indeed a new equilibrium which the monetary authority can do nothing about.

But people and economies are not like that. Each agent wants to work at the pre-shock level, and will signal that in some way. They will see that the economy had widespread underemployment, and as a result they will revise their expectations about the steady state. I think Nick knows that, because he writes that the NK model needs “to just assume the economy always approaches full employment in the limit as time goes to infinity, otherwise our Phiilips Curve tells us we will eventually get hyperinflation or hyperdeflation, and we can't have our model predicting that, can we.”

He treats that as if it were a problem, but I do not see that it is. After all, we have no problem with the idea that consumers will revise down their expectations of their future income if they unexpectedly find they are always in debt. Equally I have no problem with the idea that in Nick’s economy with widespread and visible involuntary underemployment consumers might think they had made a mistake about others desired labour supply.

Let me put it another way. In a single person economy we never get underemployment. The problem arises because in a real economy we need to form expectations about what others will do. But if there exist signals which help us get our expectations right, that should shift us out of a mistaken belief equilibrium.

Which gets us to why I think Nick is on to something about the real world. Suppose there is a shock like a financial crisis, which for the sake of argument just temporarily reduces demand by a lot and creates unemployment. Central banks cannot cut real interest rates enough to get rid of the unemployment because of the zero lower bound. Inflation falls, but because everyone initially thinks this is all temporary, and maybe also because of an aversion to nominal wage cuts, we get a modest fall in inflation.

Now suppose people erroneously revise down their beliefs about steady state output, to be more like current output. Suppose also that visible unemployment goes away, because firms substitute labour for capital (UK) or workers get discouraged (US). We get to what looks like Nick’s bad equilibrium. Even inflation moves back to target, because the current output gap appears to disappear. We no longer have any signals that there is an alternative, better for everyone, inflation at target equilibrium with higher output.

Now we could get out of this bad equilibrium, if some positive shock or monetary/fiscal policy raised demand ‘temporarily’ and people saw that, because firms substituted capital for labour, or discouraged workers came back into the labour force, inflation did not rise well above target. But suppose policymakers also start to hold these erroneous beliefs, and so do not try and get us out of the bad equilibrium. Could that describe the secular stagnation we are in?