As I have argued before: "Does the macroeconomy self-equilibrate?" is a stupid question, because the answer depends on the monetary policy being followed. Your answer also depends on your model of the economy. And that's what I want to look at here.
"Compare and contrast Old Keynesian and New Keynesian views on whether the economy self-equilibrates to full employment" is my exam question. (The definition of "full employment"/"potential output"/"the natural rate of unemployment" may be problematic, but that doesn't matter for this question, as long as our definition isn't completely vacuous.)
What Paul Krugman says isn't wrong. But it's not quite right either. It's easy to explain the Old Keynesian models' answers to this question; but the New Keynesian model's answer is a bit of a mess, even ignoring the ZLB.
Here's my answer to the exam question:
1. Old Keynesian Income-Expenditure model. This is the first macro model I learned in school in the 1970's. It's still taught as the macro model in many first year university texts. It's the one with desired real Aggregate Expenditure AE on the vertical axis, real income Y on the horizontal, an upward-sloping AE curve (because AE depends on Y), a 45 degree line where AE=Y for the "equilibrium condition" (which says only that output=output demanded, and says nothing about the supply-side), and "equilibrium" where the AE curve cuts the 45 degree line.
This model has zero tendency to self-equilibrate at full employment. There is a unique equilibrium level of AE and Y, but there is nothing in the model that says that this equilibrium has any relation whatsoever with anything we might (non-vacuously) call full-employment. That's because the supply-side of the economy doesn't affect that equilibrium at all. If people save too much, or invest too little, equilibrium Y will be below full-employment Y, and will stay there forever. Unless the economy gets lucky, or fiscal policy gets the economy to full employment, it simply won't ever get there by itself. (In this model, monetary policy doesn't even appear.)
2. Old Keynesian ISLM model. If you start with the Old Keynesian Income Expenditure model, assume that investment (and maybe savings too) depends on the rate of interest, and add in the assumption that money supply = money demand, and that money demand depends on Y and the rate of interest, you get the Old Keynesian ISLM model. This model is the main model in most second year university texts, and has been for decades.
This model may or may not have a tendency towards full employment "in the long run". It depends. It depends on the monetary policy being followed. (With a really stupid monetary policy, like where the central bank cuts the money supply in the same proportion as any fall in the price level, there will be zero tendency towards long run full employment.) But it depends on other things too. It depends on the shapes of the IS and LM curves, because it may be that no fall in the price level or increase in the money supply can get the rate of interest low enough to get the economy to full employment. It also depends on the interaction between expected inflation/deflation and actual inflation/deflation. It may be that a fall in the price level causes people to expect further falls in the price level, which increases the wedge between real and nominal interest rates (makes real interest rates higher for any given nominal rate), which reduces demand still further.
The basic mechanism is that if Y is less than full employment the price level will eventually fall, which will increase the real money supply M/P, which will shift the LM curve right, and increase output demanded, and increase output.
The ISLM model answers the question. It's not a simple answer, but it is a clear answer. The answer is "it depends", but the model tells you what it depends on.
3. The New Keynesian model. There are lots of "New Keynesian" models, going all the way back to the late 1970's. They have changed quite a bit over the years. And different New Keynesian models would have answered this question differently. What I am talking about here is the simplest version of the "canonical" New Keynesian model, as taught for the last decade or so to upper-year undergrads or graduate students. This model has replaced ISLM as the new "workhorse" model.
It has three equations. The new "IS curve" is an equation in which the ratio of current demand to expected future demand is a negative function of the real rate of interest. There is an equation for the expectations-augmented Phillips Curve, which both defines "full-employment" and tells you the relationship between deviations of output from full employment and deviations of actual from expected inflation. And there is an equation for the monetary policy reaction function, which tells you how the central bank sets the nominal interest rate, typically as a function of output and inflation. (You can call the assumption of rational expectations a fourth equation, if you wish.)
What I will say next may be a little controversial.
This model has zero tendency towards full employment, even if you assume a sensible monetary policy. New Keynesian modellers just assume a tendency towards "long run" full employment, even though it's not there in the model.
I explained why in my old post. Here's the short version: even if monetary policy is perfect, so the central banks always sets an interest rate that's exactly right, all that tells you is that the ratio of today's demand to tomorrow's demand will be exactly right. But we will only be at full employment today if people expect full employment tomorrow; and they will only expect full employment tomorrow if they expect full employment the day after tomorrow, and so on. A cut in real interest rates does not increase today's demand; it only increases the ratio of today's demand to expected tomorrow's demand. And there are two ways a ratio can increase: a rise in the numerator; or a fall in the denominator. New Keynesian modellers just assume that the people in their model expect a long run tendency towards full employment.
Think back to the ISLM model. In that model, if monetary policy wasn't really stupid, there was normally a force that tended to push the economy eventually towards full employment. (It might be offset by forces pushing the other way, but no matter.) At less than full employment, prices would fall, so the real money supply M/P would rise, shifting the LM curve right, and increasing demand for output.
That equilibrating mechanism in the Old Keynesian ISLM model is simply not there in the canonical New Keynesian model. Because M isn't there in the model. (And P isn't really there in the model either; only the rate of change in P -- the inflation rate -- is there in the model. And changes in the inflation rate, as opposed to the price level, are normally a disequilibrating force, because expected deflation increases real interest rates for given nominal rates, which in the ISLM model reduces demand.)
4. My reflections on all this:
As a teenager I looked at the Old Keynesian Income-Expenditure model, and thought: "Hmmm. Something's not quite right with this model. Because for most of history, we haven't had fiscal policy being done by sensible governments that understood this model. So how come we ever spend as much time as we do anywhere near full employment?"
I was like a pre-Darwinian biologist being taught The Argument From Design, and that God had only existed since the 1940's. It didn't make sense.
Nowadays, looking at the canonical New Keynesian model, I have a similar sort of question to the one I had as a teenager. We've only had a Designer who understood the model for the last decade or so, and according to this model even a perfect Designer can't get it right, unless we all have Faith. It doesn't make sense.