Do all those using New Keynesian models have to believe everything in those models? To answer this question, you have to know the
history of macroeconomic thought. I think the answer is also relevant to
another frequently asked question, which is what the difference is between a
‘New Keynesian’ and an ‘Old Keynesian’?
You cannot understand macro today without going back to the New
Classical revolution of the 1970s/80s. I often say that the war between
traditional macro (Keynesian or Monetarist) and New Classical macro was won and
lost on the battlefield of rational expectations. This was not just because
rational expectations was such an innovative and refreshing idea, but also
because the main weapon in the traditionalists armoury was so vulnerable to it.
Take Friedman’s version of the Phillips curve, and replace adaptive
expectations by rational expectations, and the traditional mainstream Keynesian
story just fell apart. It really was no contest. (See Roger Farmer here,
I believe that revolution, and the microfoundations programme
that lay behind it, brought huge improvements to macro. But it also led to a
near death experience for Keynesian economics. I think it is fairly clear that
this was one of the objectives of the revolution, and the winners of wars get
to rewrite the rules. So getting Keynesian ideas back into macro was a slow
process of attrition. The New Classical view was not overthrown but amended.
New Keynesian models were RBC models plus sticky prices (and occasionally
sticky wages), where stickiness was now microfounded (sort of). Yet from the New Classical point of
view, New Keynesian analysis was not a fundamental threat to the revolution. It
built upon their analysis, and could be easily dismissed with an assertion
about price flexibility. Specifically NK models retained the labour leisure choice, which was at the heart of RBC analysis. Monetary policymakers were doing the Keynesian thing
anyway, so little was being conceded in terms of policy. 
So labour supply choice and labour market clearing became part of the core New Keynesian
model. Is this because all those who use New Keynesian models believe it is a
good approximation to what happens in business cycles? I doubt it very much.
However for many purposes allowing perfect labour markets does not matter too
much. Sticky prices give you a distortion that monetary policy can attempt to
negate by stabilising the business cycle. The position you are trying to
stabilise towards is the outcome of an RBC model (natural levels), but in many
cases that involves the same sort of stabilisation that would be familiar to
more traditional Keynesians.
This is not to suggest that New Keynesians are closet
traditionalists. Speaking for myself, I am much happier using rational expectations than
anything adaptive, and I find it very difficult to think about consumption
decisions without starting with an
intertemporally optimising consumer. I also think Old Keynesians could be very
confused about the relationship between aggregate supply and demand, whereas I find the New Keynesian approach both coherent
and intuitive. However, the idea that labour markets clear in a recession is
another matter. It is so obviously wrong (again, see Roger Farmer). So
why did New Keynesian analysis not quickly abandon the labour market clearing
Part of the answer is the standard one: it is a useful
simplifying assumption which does not give us misleading answers for some questions. However the reason for
my initial excursion into macro history is because I think there was, and still
is, another answer. If you want to stay within the mainstream, the less you
raise the hackles of those who won the great macro war, the more chance you have
of getting your paper published.
There are of course a number of standard ways of complicating
the labour market in the baseline New Keynesian model. We can make the labour
market imperfectly competitive, which allows involuntary unemployment to exist.
We can assume wages are sticky, of course. We can add matching. But I would
argue that none of these on its own
gets close to realistically modelling unemployment in business cycles. In a
recession, I doubt very much if unemployment would disappear if the unemployed
spent an infinite amount of time searching. (I have always seen programmes
designed to give job search assistance to the unemployed as trying to reduce
the scaring effects of long term unemployment, rather
than as a way of reducing aggregate unemployment in a recession.) To
capture unemployment in the business cycle, we need rationing, as Pascal
Michaillat argues here (AER article here). This is not an alternative to these other
imperfections: to ‘support’ rationing we need some real wage rigidity, and
Michaillat’s model incorporates matching. 
I think a rationing model of this type is what many ‘Old Keynesians’ had
in mind when thinking about unemployment during a business cycle. If this is
true, then in this particular sense I am much more of an Old Keynesian than a
New Keynesian. The interesting question then becomes when this matters. When
does a rationed labour market make a significant difference? I have two
suggestions, one tentative and one less so. I am sure there are others.
The tentative suggestion concerns asymmetries. In the baseline
NK model, booms are just the opposite of downturns - there is no fundamental
asymmetry. Yet traditional measurement of business cycles, with talk of
‘productive potential’ and ‘capacity’, are implicitly based on a rather
different conception of the cycle. A recent paper (Vox) by Antonio Fatás and Ilian Mihov takes a
similar approach. (See also Paul Krugman here.) Now there is in fact an asymmetry
implicit in the NK model: although imperfect competition means that firms may
find it profitable to raise production and keep prices unchanged following
‘small’ increases in demand, at some point additional production is likely to
become unprofitable. There is no equivalent point with falling demand. However
that potential asymmetry is normally ignored. I suspect that a model of unemployment based on rationing will produce asymmetries
which cannot be ignored.
The other area where modelling unemployment matters concerns
welfare. As I have noted before,
Woodford type derivations of social welfare give a low weight to the output gap
relative to inflation. This is because the costs of working a bit less than the
efficient level are small: what we lose in output we almost gain back in additional leisure. If we
have unemployment because of rationing, those costs will rise just because of
However I think there is a more subtle reason why models that
treat cyclical unemployment as rationing should be more prevalent. It will
allow New Keynesian economists to say that this is what they would ideally
model, even when for reasons of tractability they can get away with simpler models
where the labour market clears. Once you recognise that periods of rationing in
the labour market are fairly common because economic downturns are common, and
that to be on the wrong end of that rationing is very costly, you can see more
clearly why the labour contract between a worker and a firm itself involves
important asymmetries - asymmetries that firms would be tempted to exploit during a recession.
Yet you have to ask, if I am right that this way of modelling
unemployment is both more realistic and implicit in quite traditional ways of
thinking, why is it so rare in the literature? Are we still in a situation
where departures from the RBC paradigm have to be limited and non-threatening
to the victors of the New Classical revolution?
 When, in a liquidity trap, macroeconomists started using
these very same models to show that fiscal policy might be effective as a
replacement for monetary policy, the response was very different.
Countercyclical fiscal policy was something that New Classical economists had
thought they had killed off for good.
 Some technical remarks.
(a) Indivisibility of labour, reflecting the observation (e.g.
Shimer, 2010) that hours per worker are
quite acyclical, has been used in RBC models: early examples include Hansen
(1985) and Hansen and Wright (1992). Michaillat also assumes constant labour
force participation, so the labour supply curve is vertical, and critically
some real wage rigidity and diminishing returns.
(b) Consider a deterioration in technology. With flexible
wages, we would get no rationing, because real wages would fall until all
labour was employed. What if real wages were fixed? If we have constant returns
to labour, then if anyone is employed, everyone would be employed, because
hiring more workers is always profitable (mpl>w always). What Michaillat
does is to allow diminishing returns (and a degree of wage flexibility): some
workers will be employed, but after a point hiring becomes unprofitable, so
rationing can occur.
(c) Michaillat adds matching frictions to the model, so as
productivity improves, rationing unemployment declines but frictional unemployment
increases (as matches become more difficult). Michaillat’s model is not New
Keynesian, as there is no price rigidity, but there is no reason why price
rigidity could not be added. Blanchard and Gali (2010) is a
NK model with matching frictions, but constant returns rules out rationing.
 I do not think they will rise enough, because in the
standard formulation the unemployed are still ‘enjoying’ their additional
leisure. One day macroeconomists will feel able to note that in reality most view the cost of being unemployed as far greater than its pecuniary
cost less any benefit they get from their additional leisure time. This may be a
result of a rational anticipation of future personal costs (e.g. here
or a more ‘behavioural’ status issue, but the evidence that it is there is undeniable. And please do not tell me that
microfounding this unhappiness is hard - why should macro be the only place
where behavioural economics is not allowed to enter!? (There is a literature on using
wellbeing data to make valuations.) Once we have got this bit of reality (back?) into
macro, it should be much more difficult for policymakers to give up on the unemployed.
References (some with links in the main text)
Olivier Blanchard & Jordi Galí (2010), Labor Markets and Monetary Policy: A New Keynesian Model with Unemployment, American Economic Journal: Macroeconomics, vol. 2(2), pages 1-30
Hansen, Gary D (1985) “Indivisible Labour and the Business
Cycle” Journal of Monetary Economics 16, 309-327
Hansen, Gary D and Wright, Randall (1992) “The Labour Market in
Real Business Cycle Theory” Federal Reserve Bank of Minneapolis Quarterly
Review 16, 2-12.
Pascal Michaillat (2012), Do Matching Frictions Explain
Unemployment? Not in Bad Times, American Economic Review, vol. 102(4), pages
Shimer, R. ‘Labor Markets and Business Cycles’, Princeton, NJ:
Princeton University Press, 2010.