This post is not a critique of Paul Krugman's critique of Scott Sumner (though that's what got me thinking along these lines). It's a critique of all of us, especially all of who use New Keynesian models (which includes me). Framing matters. Tinkerbell is real and all-pervasive. She flies in New Keynesian models all the time.

A. In the IS curve in old Keynesian models, a fall in the real rate of interest causes an increase in demand.

B. In the IS curve in New Keynesian models, a fall in the real rate of interest causes an increase in current demand, relative to planned future demand.

C. In the IS curve in New Keynesian models, a fall in the real rate of interest causes a decrease in planned future demand, relative to current demand.

A and B sound very similar. It's just that B adds an extra variable (planned future demand) that can shift the IS curve. An increase in planned future demand will shift the IS curve to the right. That sounds quite plausible from an Old Keynesian perspective anyway. If planned future demand increases, expected future incomes should increase too, and so people will want to consume more today, and firms will want to invest more today. So B makes the New Keynesian IS curve sound very similar to the Old Keynesian IS curve. It isn't. They are very different.

C sounds totally different from B. But it's not. C and B are logically equivalent. They are just different ways of describing the same Euler equation that underlies the New Keynesian IS curve. C is a way of describing the New Keynesian IS curve that forces you to realise that it is very different from the Old Keynesian IS curve.

Suppose the central bank cuts the real interest rate one morning. What happens?

B leads you to think that current demand will increase.

C leads you to think that planned future demand will decrease.

It's all in the framing. Framing matters. And don't think it doesn't matter in the real world economy too.

Take the simplest possible New Keynesian model. Consumption is the only source of demand (ignore investment, government, and net exports). So income = output = desired consumption in equilibrium. The consumption-Euler equation determines the ratio of current desired consumption to planned future desired consumption as a negative function of the real rate of interest. The central bank sets the real rate of interest.

Suppose that, due to past monetary mismanagement, the economy is currently in recession, and is expected to be in recession next period as well. What should the central bank do?

In an Old Keynesian model, the answer is simple. Cut the real interest rate, so consumption demand increases, and the economy moves down along the IS curve till it gets to "full employment" (or whatever the central banker thinks is full employment, the natural rate, the NAIRU, or whatever).

In a New Keynesian model, the answer is not simple. In fact, there isn't a well-defined answer to this question. A cut in the real interest rate might cause an increased level of consumption today, and no change in planned future consumption. That will help the economy escape the recession. But it might also cause a cut in planned future consumption, with no change in consumption today. That will not help the economy escape the recession.

It doesn't help to assume the cut in the real interest rate is expected to be permanent. A permanent 1% cut in the interest rate might just cause people to decrease planned future consumption by (say) 2% every year from the year before, so that planned consumption asymptotically approaches zero. That will simply cause people to expect the economy to slide progressively deeper into recession.

There is only one time-path of real interest rates that is compatible with a 100% full employment time-path in a new Keynesian model. But that exact same time-path of real interest rates is also compatible with a time-path where output is only 90% of full employment, or 80%, or 70%, or any time-path of output whatsoever, as long as the ratios between one year's output and the next year's output are the same as in the 100% path.

How do New Keynesian macroeconomists avoid the problems posed by this question? They avoid asking the question. They simply assume that at some time in the future the economy will be at full employment, where output is determined by the supply-side, and that people's currently planned future consumption for that date equals full employment output. With current plans for future consumption pinned down exogenously at some future time, they can solve the model backwards to find the path of real interest rates that will keep the economy at full employment up till that time.

What would an Old Keynesian have said, if he had heard of such a model back in the 1950's, 60's, or even early 70's? "You are assuming (future) full employment!" is what he would have said: exactly the same accusation (except for the added word "future") that demolished many a classical economist's model in the Keynesian heyday.

My imaginary Old Keynesian critic would be right to make this accusation. At least the Old Keynesians, and the Classical economists, had a mechanism whereby price flexibility, and the real balance effects - M/P rising and the LM moving right along the IS curve - might get the economy to full employment. New Keynesians have no such mechanism. They just assume people expect future full employment, with no justification whatsoever for that assumption.

How can we possibly assume that people's 2010 plans for consumption in 2020 (or whenever) are based on their knowledge that the economy will be at full employment in 2020? When the model itself has no mechanism for ensuring that the economy will tend towards full employment, even with a good central banker?

What would it take to get to full employment in a New Keynesian model? A good central banker, setting the right real interest rate. Plus Tinkerbell.

Tinkerbell makes sure that when the central banker cuts the real interest rate, people don't cut their planned future consumption; instead they increase their planned current consumption. Tinkerbell tells each of us that the cut in the real interest rate will cause everyone else to increase their planned current consumption, so that our current income will increase, so that we will be able to afford to consume more now, without having to cut planned future consumption.

If Tinkerbell were mischievous, she would instead tell each of us that the cut in interest rates would cause everyone else to keep their current consumption constant, and reduce their planned future consumption, so our future income will fall. The fall in our expected future income, plus the cut in the real interest rate, means that we will choose to do exactly what a mischievous Tinkerbell tells us that everyone else will do.

In other words, monetary policy will work if Tinkerbell tells us it will work, and we believe her; and won't work if Tinkerbell tells us it won't work, and we believe her. And this has nothing to do with nominal interest rates being at the zero lower bound, because I have assumed that the central bank can cut real interest rates. Monetary policy, in a New Keynesian model is always a Tinkerbell effect.

It all depends on the framing. Does the cut in the real interest rate increase current demand (relative of course to planned future demand)? Or does the cut in the real interest rate decrease planned future demand (relative of course to current demand)? Tinkerbell just knows how to frame it the right way to get the desired result.

Fiscal policy is also a Tinkerbell effect in New Keynesian models.

D. In the IS curve of an Old Keynesian model, a temporary increase in government spending causes an increase in demand, for a given real rate of interest.

E. In the IS curve of a New Keynesian model, a temporary increase in government spending causes an increase in current demand relative to planned future demand, for a given real rate of interest.

F. In the IS curve of a New Keynesian model, a temporary increase in government spending causes a decrease in planned future demand relative to current demand, for a given real interest rate.

E and F are logically equivalent, but framed differently. There's presumably no need for me to repeat the rest of the argument.

(Tinkerbell and framing aside, this reveals another critique of our thinking about monetary policy as setting interest rates. Why did we ever think that cutting real interest rates would increase demand permanently, as Old Keynesian models suggest? Cutting real interest rates merely shifts demand towards the present, and away from the future. That won't work if both present and future demand are too low. Maybe monetary policy is about the supply and demand for money?)