Look: the standard New Keynesian model is a version of the Prescott RBC model, minimally tweaked to deliver Old Keynesian qualitative behavior. Its purpose is to show that the methodological straitjacket demanded by Prescott has no implications other than making it much harder to fit the data.

It has no other proper purpose.

Nick Rowe's criticisms are correct:

Nick Rowe: New Keynesians Just Assume Full Employment: "Anyone with even an ounce of Old Keynesian blood... if they understood what the New Keynesians are doing, would be screaming blue murder that we are teaching this New Keynesian model to our students as the main macro model, and that central banks are using this model to set monetary policy...

I'm now going to make this point so simply and clearly that any New Keynesian macroeconomist will be able to understand it.... Only consumption.... Self-employed hairdressers, cutting each other's hair.... All goods are services... labour the only input... counsumption, output, and employment... all the same thing. And... prices and wages... the same thing too.... No exogenous shocks.... No growth.... A constant population of very many, very small, identical, infinitely-lived agents, with logarithmic utility of consumption, and a rate of time-preference proper of n.

The individual agent's consumption-Euler equation, with r(t) as the one-period real interest rate, is therefore:

C(t)/C(t+1) = (1+n)/(1+r(t))....

Assume the central bank sets a real interest rate r(t). Suppose the "full employment"... equilibrium is... 100 haircuts per agent per year consumption, income, and employment. Forever and ever. The central bank's job is to set r(t) such that C(t)=100, for all t. Inspecting the consumption-Euler equation, we see that this requires the central bank to set r(t)=n for all t. Assume the central bank does this.... [But] setting r(t)=n for all t only pins down the expected growth rate of consumption... to zero.... It does not pin down the level....

Suppose initially we are at full employment. C(t)=100. Then 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.... His optimal response... if he expects the central bank to continue to set r(t)=n, is to cut his own consumption immediately to 50 and keep it there. C(t)=50... is also an equilibrium with r(t)=n. So is any rate of unemployment between 0% and 100%.

What can the central bank do to counter the bad animal spirits? If it cuts r(t) below n, even temporarily, we know there exists no rational expectations equilibrium in which there is always full employment. All we know is that we must have negative equilibrium growth in consumption for as long as r(t) remains below n. It is not obvious to me how making people expect negative growth in their incomes from now on should cause everyone to expect a higher level of income right now from a higher level of everyone else's consumption right now. Sacrificing a goat sounds more promising as a method of restoring full employment. Did every other New Keynesian macroeconomist already know about this, and just swept it under the mathematical rug? Didn't I get the memo?

Here's Gali:

Under the assumption that the effects of nominal rigidities vanish asymptotically [lim as T goes to infinity of the output gap at time T goes to zero]. In that case one can solve the [consumption-Euler equation] forward to yield..."

Bull----. It's got nothing to do with the effects of nominal rigidities. What he really means is "We need to just assume the economy always approaches full employment... otherwise... we will eventually get hyperinflation or hyperdeflation, and we can't have our model predicting that, can we?" That Neo-Wicksellian/New Keynesian nonsense is what the best schools have been teaching their best students for the last decade or so...

The way out I prefer to take is to say: Look: the central bank doesn't set r(t) = n for all t--it follows some reasonable feedback rule to stabilize the economy. Want to know what are reasonable feedback rules? They are the ones that stabilize the economy. Unhappy with that? Go back to Lloyd Metzler's version of IS-LM, and recognize that the New Keynesian model is a jerry-rigged minimally-tweaked RBC model...