Tinkerbell in New Keynesian models

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?)

Comments

[Kevin Donoghue]

"Why did we ever think that cutting real interest rates would increase demand permanently, as Old Keynesian models suggest?"

OK models only suggest that where there is involunary unemployment, obviously. In those circumstances there is no presumption that cutting real interest rates merely shifts demand from future to present.

I think I agree with most of what you say about NK models, but my endorsement isn't worth much since I haven't studied tham in any depth. However I do wonder why you have to ask what an OK economist would have said about NK models. Tobin defended OK models to his dying day. Anyway Krugman is an OK economist roughly three days a week. He only shifts to NK models when he wants to smack down the likes of Fama and Cochrane, since he knows they just snigger at IS-LM.

[Luis H Arroyo]

Nice; I don´t know what I am really.
Answer me, please: The markets are falling in the World; The reason? mismanagement of the euro -basically- and the contagion to US and Asia. The risk of a deflation, or at least a severe double dip contraction, is quite high. So, what damn model must be try? OK? NK? NNK? that of Krugman´s in Tuesday? Or Austrian model Perhaps?
I suppose that the fiscal stimulus is exhausted, in spite What Krugman says in his post today. At least in many countries, where any increase in deficit means an increase in interest rate. Only a monetized fiscal stimulus could work, I think.
So, I only am capable of thinking on a general rise in inflation objective by the central banks, to 4% 5% until near NAIRU is reached. Is this OK, NK, NNK, OOK? I don´t know. I´m sure it is no Austrian.

[Alex]

Sorry, I'm just a layman, so forgive me if this is a stupid question.

The central bank cuts the interest rate. I can see why that might cut planned future demand, but why would it simultaneously not affect present demand? Surely saving is just deferred consumption, so if because of what the central bank does you choose to demand less at a point in future, then surely you either demand more now or demand more at a different future date instead (or a bit of both)?

I am though a physics student, so perhaps a mathematical equation might be useful to me as well. Thanks.

[Alex]

At least in many countries, where any increase in deficit means an increase in interest rate.

It surely depends how much interest rates increase. If you borrow, say, 5% of GDP, and the interest rate on 10-year government debt goes from 3.00% to 3.05% then there's no need to worry.

[Joe D.]

Austrian Economics = Currency(token) issued against another token(gold) = Ponzi Scheme. To manipulate the system all one needs to do is buy and store food grains for few years till food shortage comes along.

Keynesian Economics = Paper Currency issued against future tax obligation but fractional nature of the system ie banks can issue more loans than the currency in circulation makes it unstable and inflationary. Keynesian system works only if there is unlimited supply of food/fuel. The system is "Total Scam" - for the banksters by the banksters. The problem with today's economics / banking is reserve banks don't have food/fuel reserves to redeem the currency they issue and the fractional banking system makes it rich get richer system = Oligarchy.

Real Economics = Issue currency against food/fuel with redemption obligation by reserve banks. Reserve banks should have food/fuel reserves to be called reserve banks. Banks should only loan long term share holder capital, depositor money can only be lend short term(90 days). The money supply will increase as food/fuel supply increases and will decrease as the food fuel supply decreases. Prosperity for all and obscene wealth for none = ideal system.

Think a bit and ye will understand.....

[Nick Rowe]

Kevin: In this post I only concentrated on one difference between OK and NK macro: the re-interpretation of the IS curve as an Euler equation. There's a lot more to NK than that (and some of it I like a lot). I just Googled, and found that James Tobin died in 2002. I'm trying to think if the Euler equation approach to the IS (even though it pre-dated 2002, I think) was really in common usage at the time James Tobin would have been able to comment on it?

I thought that I understood NK macro (except for all the math) until I came to write this post. Then I realised I didn't understand it. My guess is that a lot of people were like me. We hadn't realised how big a difference this makes. Probably Paul Krugman too. We have an OK model at the back of our minds, when we write in prose, then only bring out the NK model, when we write in math, and only when we need to. And we think it says the same thing, just with greater rigour. It doesn't. A cut in r in OK models increases demand. A cut in r in NK models shifts relative present vs future demand. Nothing gets you to full employment, even with a good central bank.

Luis. I don't know either. I'm trying to re-orient my thoughts. I've always been 1/3 monetarist, 1/3 OK, 1/3 NK, and 1/3 someone who thinks wild thoughts and can't do arithmetic. I thought I had the relationship between the various models roughly clear in my head. Now I realise I didn't.

Alex: Take a 2-period model for simplicity. The individual consumer maximises U(C1) + BU(C2) subject to the budget constraint Y1-C1 + (Y2-C2)/(1+r) = 0

Where C1 is consumption in period 1, Y1 is income in period 1, B is a psychological constant, just less than 1 (time preference), and r is the real interest rate.

Assume U(C) is log(C) for simplicity, so dU/dC=1/C.

The First order condition is (something like, because I always get muddled) C1/C2 = 1/B(1+r)

For the individual, *who takes Y1 and Y2 as exogenous*, this problem has a well-defined solution. And it's exactly as you describe it. If r goes down, C1 will go up, and C2 will go down. A bit of both.

Here's what (I think) you missed. It's the *macro* kicker. One person's spending is another person's income. So Y1 and Y2 are exogenous to the individual, but not in aggregate. In equilibrium, Y1=C1 and Y2=C2. (Closed economy, no government, no investment).

So even though the individual's (micro) problem is well-defined, the aggregate (macro) problem isn't.

All we get is Y1/Y2 = 1/B(1+r). We can't know Y1 unless we assume that Y2 is pinned down at full-employment.

Joe: but if there are unemployed resources, due to deficient aggregate demand, what you say about "Keynesians" isn't correct.

[Kevin Donoghue]

Nick,

In the simple NK models I’ve seen, (e.g., what Jordi Gali calls the Basic NK Model in his book, Monetary Policy, Inflation and the Business Cycle), there’s an assumption which is doing an awful lot of the work. In Gali’s own words (page 49): “the effects of nominal rigidities vanish asymptotically.” I love the way economists pluck assumptions like that from their sleeves while the attention of the audience is distracted.

NK models are (as Joan Robinson would say) the bastard children of New Classical models and their Neo Keynesian whores. They resemble their New Classical fathers in assuming (future) full employment. Since the Old Keynesians castigated the New Classical economists on that score they could hardly pretend to love their NK progeny.

You say that “the [NK] model itself has no mechanism for ensuring that the economy will tend towards full employment, even with a good central banker” which is true in the sense that the NK school simply assumes that price flexibility is all you need to ensure that full employment will eventually be reached. Tobin and other Old Keynesians objected to that assumption. Krugman is a bit more accommodating, but my impression is that that’s just a strategic concession on his part. He has enough enemies without taking on Woodward & Co.

I don’t think I disagree with anything you’ve said, I just wanted to note that we really don’t need to speculate about what the OK school might think of NK. They’ve told us. People like Tobin, Solow and Hahn didn’t drop their objections to the New Classical style of theorising when it was incorporated in NK models.

[kevin quinn]

Nick: great post, provocative as usual. As you saw from my post on econospeak, I am in exactly the position you describe, trying to graft the NK models into my default OK mindset and not doing do very successfully. One irony: as an OK sort, why does it bug me so that these NK models have no self-correcting mechanism?!!

[Luis H Arroyo]

Ok, I supopose that I am 2/3 monetarist, 1/3 keynesian (pre - General Theory). If that is possible. Well, perhaps, taken account what Friedman said about Keynes in "Keynes", I can add the 1/3 and 2/3 conponents of me and can say simply I am full monetarist. Sorry, I can not evolve much more.
Kevin has a point: I always thoughk the NK were disguised monetarists. I remember an article of Mankiw where he said not to be comfortable at all with the keynesian label.

[Luis H Arroyo]

Oh sorry, an other idea (don´t know if correct, perhaps too old): I suppose that the NK Mankiw-type don´t give possibility to fiscal activism, but some short term possibility to monetary policy, because they believe in Philips Curve... I mean that I don´t understand how the NK had could admite perfect micro adjustment prices... If ther is uncertainty. Is not that Neo classicism?

[RSJ]

Excellent post. I'm going to have to read re-read a few more times :)

But some initial comments:

The interest rate -- do you mean the consol rate? -- is set by the CB in your model because there is no investment. If there were investment, then the consol rate would be endogenous, or at least would be pushed to a rate that depended on the long run profit opportunities at each point in time. Certainly expectations of what those profit opportunities are will fluctuate, but over the long run -- very long run? -- those expectations errors would cancel out.

So wouldn't the possibility of investment -- and more importantly, of borrowing to fund investment -- tend to stabilize your model over the long run? I don't think you could remain at 70% employment forever. Of course, "long run" can be a decade out.

"tinkerbell" -- expectations, right -- influences the desire to borrow and spend, but the point is that we have a chain:

expectations (+ deficits) --> spending --> aggregate demand (+ supply) --> employment/output --> expectations (+deficits)

Just as a business that has three customers that supply revenue -- tinkerbell, the foreign sector, and the government sector. A loss of income from the first customer does not negate the effectiveness of the other two customers, but makes them more important. But the standard NK "line" is that there is just a small bit of room due to price rigidities that allow for the deficits to influence spending. This is not the case if balance sheet expansion is allowed in the model. If you allow for balance sheet expansion, then the deficits can be additive.

[Kaleberg]

I see. The new Keynesian models don't accept the possibility of economic growth! That makes sense. You can trade off demand now and demand in the future, but spending now cannot grow the economy to increase future demand. That is SOOOO much smarter than the old Keynesian analysis.

[Nick Rowe]

kevin: Thanks! I thought that I *did* understand how to graft NK models onto an OK mindset. Now I realise I didn't.

"One irony: as an OK sort, why does it bug me so that these NK models have no self-correcting mechanism?!!"

And why does it bug me too?? (Even though I'm less OK than you).

I think the answer is that the OKs did understand the question. Namely: "What, if anything, are the forces that will tend to make the economy eventually revert towards something vaguely like "full employment?". And the better Monetarists understood the question too, and thought they had the answer. I'm not sure that NK's even understand the question any more. What's even more peculiar, the OKs always said that good monetary/fiscal policy could get you to full employment, even if there were no "natural" tendencies of the economy to get there by itself. But the NKs assume (future) full employment, even though their model has no tendencies to go there, *even if monetary/fiscal policy is correct*.

Of course, to be fair to the NKs, there have been a lot of very different NK models over the years. The ones that I am talking about here are a subset. But they are the most modern and influential subset. Canonical, you could say.

I don't like models that say the economy is continuously at full employment. But models that have zero tendency towards anything that could be vaguely defined as full employment are even worse. Empirically, it just does not seem to be the case that any unemployment rate between 0% and 100% is equally likely, a priori. Most economies seem to spend most of their time fairly close to some sort of natural rate, even when policy isn't aimed at getting them there.

RSJ: Thanks! The interest rate is a one-period interest rate, not a consol. It's the one-period real rate of interest that determines the ratio between current and next period's demand. Slightly more complicated NK models add an investment-Euler equation to the consumption-Euler equation, and get the same basic result. But I don't understand investment-Euler very well.

The central bank sets the real rate of interest in this sort of NK model. But if it sets it at the wrong level, so that demand is too high or too low, the result will be accelerating inflation or deflation. I ignored inflation and the Phillips curve in this post, for simplicity. It wouldn't affect the results at all.

[Nick Rowe]

Kaleberg: that's not quite right. Long run economic growth comes from the supply side. It is quite possible to build economic growth on the supply side into a NK model. I have ignored the supply side here, since it didn't affect my point. My point is about full employment, not economic growth.

[2slugbaits]

Nick: I'm not entirely convinced as to the Euler constraint in your "consumption only" model that says increasing current consumption implies a reduction in planned consumption. Isn't there really a further hidden constraint that says consumers will not upscale their tastes? If lower interest rates increase my current consumption of a good called "housing" (or quality beer!) wouldn't we think that this is more likely to increase my future demand for even more living space (or even better quality beer)? And the model really breaks down when you expand it to include investment. Here the hidden assumption seems to be that increasing current period demand will reduce planned future demand because current period capital will be consumed. But will it? What if we include human capital, which unlike physical capital tends to augment with use rather than depreciate with use.

[RSJ]

Why wouldn't adding investment to the model result in helping to stabilize employment?

Fundamentally, if there are slack resources -- e.g. idle labor-- then there is no trade-off between investment and consumption. You can have more of both. If there is a shortage of, say, oil, but slack labor, then there is somewhat of a trade-off, but the degree of the trade-off depends on the substitutability of one for the other, and of course the speed/feasibility of the substitution. I guess this goes back to the multi-firm discussions, in which unemployment can arise out of a mismatch in the capital stock ratios.

But in any case, you will still get a surplus by using more labor.

There is a *monetary* trade-off for each *individual* household between consuming and investing. But in aggregate there is not a trade-off, because the income spent on lending becomes income available for consumption to someone else (the wages and profits of the suppliers and workers of the firm that is increasing capacity).

In aggregate, $X spent on lending to others does not reduce the aggregate consumption opportunities by $X, if your period is defined so that the firm not only borrows the money but also spends the money in the same period. That's the "loans creates deposits/Debts create Assets" view.

[Panayotis]

Nick Rowe,
As before, an enjoyable and thought provoking post.

The "knowledge" about the future, an information stream, is not only for a target period in the future but also the employment level at each period reconstructed backwards towards the present. This means knowledge of the whole path and its stochastic tree, a Markov process(?) with no arbitrage opportunities. Thus it is not only the mechanism that drives you there that is missing but also the whole knowledge structure that is required. How is this knowledge structure learned? Via the derivatives market? Implied expectations? These , hoever, are anchored on a risk free estimate for the period. Is this the CB rate? Is it possible to have such markets for such a LT? All this without bringing imperfection and complexity into play. I will show you this sometime......

[Panayotis]

Nick Rowe,

Would you please explain to me how you get changes of the "real" interest rate? For such a sort period, the inflationary expectations are also dependent on the "knowledge" of the LT path of CB policy? Am I reading you correctly? Please define.

[Nick Rowe]

Panayotis: The NK model assumes that actual inflation, and hence expected inflation, adjusts slowly, while monetary policy adjusts quickly. That means that by setting the nominal interest rate, taking account of expected inflation, the central bank can, in effect, set the short term real rate.

This assumption may or may not be a problem. I have ignored any such problems here. I wanted to make it as simple as possible, and give the NK model the benefit of the doubt, so I could explore what I think is the major problem. I just assumed the central bank can set the real rate.

RSJ: I think Adam P knows more about the investment-Euler equation in NK models than I do. But again, the main idea is that a fall in the interest rate just causes demand switching. Current investment means more demand for resources now, relative to demand for resources in the future. It's an intertemporal profit-maximisation problem. Nothing to do with the supply of bonds and stuff, in NK models.

2slugsbait: Interesting, but none of that is in the NK model. If you are exploring an internal inconsistency in a model, you don't add interesting flourishes to the model. You keep it as simple and standard as possible. No Baroque stuff.

[Jon]

Great post Nick.

But why is unemployment linked to output? Two words: "sticky-prices", which puts right back to where we were with the old classical models.

And perhaps more relishing, "B" and "C" are precisely what the Austrians claimed with their capital theory. Economics is right back where it was eighty years ago when Keynes was dueling with Hayek.

[Jon]

"The NK model assumes that actual inflation, and hence expected inflation, adjusts slowly, while monetary policy adjusts quickly. That means that by setting the nominal interest rate, taking account of expected inflation, the central bank can, in effect, set the short term real rate."

Which is also an Austrian idea.

[Panayotis]

Nick Rowe,

I am familiar with NK models. I wanted to point out the problems with the "knowledge" of the future and the problems with setting the "real" rate as the effects from the rate set upon inflation are long term and unknown and the current inflation might not be relevant for adjusting the "real" rate. Economic units with (ASSUMED)RE know this and their response is different from the behavior assumed by the current and known inflation rate. How economic units are going to access the "real value" of the rate and thefuture effect as they have different opinions? Again the "knowledge" structure becomes relevant because future ST rates set by the CB can and will change!

[Josh]

"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?"

:-D

[Adam P]

Oh dear Nick! As a user and critiquer of NK models you should really have at least some understanding of how they work. The models do not just assume we return to full employment automatically, it is a feature of the model.

So, how does it work? Well, for this you need to go beyond the euler equation and actually look at the whole model and NOT just it's reduced form (3 equation) representation. It works through the labour market.

In the canonical version of the model wages are not sticky, the labour market always clears. In this sense unemployment is always voluntary like in an RBC model. So when a shock reduces AD we get the following chain:

1) those firms that can change prices immediately do it, and wages fall immediately. This is because labour is substitutable across firms so while there are many prices there is one nominal wage. At the micro (firm) level it works because the firm that couldn't cut prices sees a drop in demand and so offers a lower wage and firms that do reduce prices can only afford a lower wage and maintaint their target mark-up.

2) Since the aggregate price level is slow to fall it is now stuck too high, thus real wages have fallen causing some labour to withdraw from the market. We now have reduced employment.

3) Over time succesively more firms reduce their prices, this means these firms can sell more output, increasing their demand for labour, while at the same time it means the aggregate price level is falling, so the real wage is rising, and so agents return to the labour market. Thus labour supply rises to meet the increased labour demand without NOMINAL needing to rise. This continues until all firms have changed their prices to the new steady state level at which time real wages are back where they started, so full employment is restored, but the price level has been reduced.

Thus, the tendency to full employment IS derived from maximizing behaviour in the model.

Finally, as a technical matter, a process like the one described above is actually ensured by specifying the demand elacticities of the goods to be such that when a firm finds its price is too high but wages have fallen (so it sells less but earns a bigger margin) it is always the profit maximizing response for the firm to reduce the price (and mark-up) and sell more.

[Adam P]

Really I should add that the technical point in my last paragraph is in some sense the real key to this.

With that specification even if we make wages sticky as well (so there is involuntary unemployment) that assumption will always make wages adjust (when/as they can) towards the full employment level.

[Adam P]

correction in step 3: "Thus labour supply rises to meet the increased labour demand without NOMINAL wages needing to rise"

the orignal left out the word "wages".

[Adam P]

I guess I'll add, just in case it's not brutally obvious, that since the economy does tend to a full employment steady state this paragraph:

"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."

IS ALL WRONG, AS IS JUST ABOUT EVERYTHING IN THIS POST.

[Stephen Gordon]

I should probably mention at this point that Nick will be traveling for the next 10 days or so, and he may not be able to respond in a timely manner.

[Nick Rowe]

Adam P. I am very glad to see you commenting, especially on this post. You know more about this sort of NK model than anyone else commenting here. I was wondering why it took you so long!

By the way, before I get into the meat of your comment, can you give me the intuition behind the investment-Euler equation? Will a simplified canonical investment-Euler equation look very similar to the consumption-Euler equation I have above? i.e. (I1/I2)=D(r) D' negative ?

Now for the meat:

You are wrong. What you are talking about is the supply-side of the model. Everything that underlies the Calvo Phillips curve equation, and in particular the determination of the natural rate/NAIRU level of output in the model. And I agree. As long as we make reasonable assumptions about the elasticity of labour supply, technology, elasticity of individual firms' demand curves, we get a well-defined natural rate/NAIRU Y* in a macro model with imperfectly competitive firms. And if Y is less than Y*, prices and wages will eventually fall without limit.

I understand that stuff very well. (Remember, I even beat Blanchard and Kiyotaki by a couple of months in 1987 on publishing a worked out model of this. http://ideas.repec.org/a/oup/ecinqu/v25y1987i1p83-102.html
Sorry for the immodesty, but when your publication record is as thin as mine, you take every opportunity!)

In other words, you get a well-defined (vertical) LRAS curve from the interaction between the labour supply curve, the production function, and imperfectly competitive firms' desired markups of prices over marginal costs.

And if you marry that supply side to an *Old Keynesian AD curve*, coming from the textbook ISLM model, for example, you get a tendency towards "full employment" (the NAIRU/Natural rate/LRAS curve). No problem.

It's when you marry it (or marry anything vaguely reasonable) to the New Keynesian AD, with an Euler equation IS, that you run into trouble.

Aggregate output is demand-determined. If Y is less than Y*, real wages will be lower than at Y* (assuming flexible W, sticky P). Each individual firm will want to cut its P relative to other firms' P, and so move down along it's demand curve. So prices fall. But unless this fall in the general price level creates an increase in aggregate demand, Y will not increase.

With an Old Keynesian AD curve, it will increase AD. The fall in P increases M/P, so LM shifts right, along the IS, r falls, and Yd increases. We get back to Y* (unless something else goes wrong).

But with a NK AD curve, we don't. Or rather, we don't necessarily. Even if the central bank cuts r in response to deflation, a fall in r has a very different effect in NK than in OK.

In OK, (assuming C is the only form of demand), the IS curve is C=D(r), so a fall in r increases C.

In NK, the IS curve is (C1/C2)=D(r). A fall in r increases the ratio of C1 to C2. It will only increase C1 if we assume C2 is constant (e.g. pinned down at full employment).

I've got another post nearly ready to go on this. It all depends, not on r, but on the reaction function for r, and in particular on what happens to expectations of C2 in out-of-equilibrium moves by the central bank. If you have static expectations of C2, for example, the CB reaction function can get you back to Y* by cutting r temporarily in the face of deflation or Y less than Y*. Under model consistent expectations, anything can happen.

[Nick Rowe]

Thanks Stephen. I'm leaving this evening. Will try to keep blogging until then.

[Nick Rowe]

I should have added: when an individual firm cuts its P relative to other firms' P, the individual firm will move down along its demand curve, and increase its output and sales y. But unless a general fall in P causes aggregate demand to increase, all that is happening is that the firm that cuts its P first, and so cuts its relative P, re-allocates demand away from other firms. And if all firms cut P together, relative prices don't change, and its the relative price that's on the axis of an individual firm's demand curve.

[Adam P]

No Nick, I'm not wrong. In this model (without capital) all income is wage income and there is a transversality condition associated with the intertemporal maximization problem that says eventually every bit of that income is spent on consumption (you may have to wait forever, but the infinitely lived agents can in fact do that). Thus your case C can't happen forever unless the labour market gets stuck at less than full employment and I just showed it doesn't.

[Adam P]

Essentially the fall in P does raise AD by raising the real wage.

[Adam P]

that said, it is still true here that output is demand determined.

[Nick Rowe]

Adam: suppose that Y*=100 for all periods. Suppose that C=Y=100 and r=5%, for all periods, is an equilibrium. This satisfies the Euler equation, (C1/C2)=D(r) by assumption. It also satisfies transversality.

Then C=Y=90 and r=5%, for all periods, is also an equilibrium. It satisfies the Euler equation, since C1/C2 is 1, just as before. It also satisfies the transversality condition. There will of course be ever-accelerating deflation, since Y is less than Y*

Same for C=Y=80 for all periods.

The canonical NK model does not have AD depend on the distribution of income between wages and profits. For given Y, an increase in a houesehold's wage income, and equivalent decrease in their share of firms' profit income, does not affect desired C.

[Nick Rowe]

And if we are initially at the C=Y=90 forever equilibrium, and Tinkerbell says "We have nothing to fear but fear itself. Let's all fly to the C=Y=100 forever equilibrium", and people believe her, they do fly there. r stays at 5%.

[Jon]

I think your point is that full employment can follow without full output? That does not seem possible in an economy with profit maximizing firms and r at the natural rate. Won't everyone try to expand at the margin?

[Kevin Donoghue]

There will of course be ever-accelerating deflation, since Y is less than Y*

Can a path of that kind really be called a steady state? On the Humpty-Dumpty principle, I suppose it can. But it's surely misleading to call such a model New Keynesian. It's more like Chapter 19 of the General Theory. Won't the real balance effect kick in somehow? Since Nick Rowe is planning another post on this topic, it may be an idea if I sketch what I thought his main point was (I'm not so sure now), so that he can see how at least one reader is misinterpreting him.

The only important difference between a simple 1970s New Classical model and the simple NK model is that the latter assumes (a) Dixit-Stiglitz-type monopolistic competition and (b) sluggish price adjustment. It follows that in all other respects the NK model is just as Panglossian as the simple New Classical model. In particular, there is a unique steady-state full-employment equilibrium to which the system tends. All agents know this and they optimize accordingly.

Is Nick merely saying that the gulf between the Old and New Keynesian schools is very wide indeed? If so, I agree. The NK model should be called the New Friedmanite model or something like that. It’s a lot closer to Friedman’s adaptive-expectations Phillips-curve model than it is to anything the OK school ever endorsed.

But I’m guessing that Nick is saying something more than that and I look forward to his next post.

[Nick Rowe]

Jon: No. employment = output, and full employment gives full employment output and vice versa. At least, that's what I'm assuming for this discussion.

Kevin: My next post isn't really ready for prime time. But since I can't get it ready for prime time before I head off to England, and since it does throw some light on this, I think i will post it anyway.

[Adam P]

No, the point is that the Euler equation is the first order condition of an intertemporal maximization problem. The solution to that problem will always have all income eventually spent. This condition is part of the transversality condition.

Nick, in your example above C=Y=90 forever is NOT an equilibrium because Y=90 MUST MEAN LESS THAN FULL EMPLOYMENT because the marginal product of labour (a REAL quantity) is unaffected by any relative prices (it's entirely determined by the level of technology). But less than full employment doesn't persist forever.

[Nick Rowe]

Adam: Yep, (if we assume constant elasticity of demand, for simplicity) the Marginal Revenue Product of labour is a real quantity, determined by technology and elasticity. And that determines Y*.

At Y=90, MRP of labour is greater than W/P. So all firms *want* to increase output and sales, *if* there were sufficient demand to buy that extra output. But there isn't sufficient demand. So they don't.

Why can't less than full employment persist forever (Y less than Y*) in this model?

[Kevin Donoghue]

Thanks Nick, I had a quick look. Maybe I'm wrong but my impression is that you are rediscovering an objection which the Old Keynesians were making to Lucas back in the 1970s, when rational expectations (RE) was a new gimmick. Much the same objection can be made to NK models.

RE implies that I can't expect to be unemployed in the future and my employer can't expect to have unsold inventory, because I know that she knows (that I know that she knows...) that I will buy her products with the wages she will pay me. This is the objectionable aspect of RE. Hardly anybody argues with the idea that expectations should be rational in the everyday sense. But RE is misnamed: it should be called Panglossian expectations. The assumption is that everyone expects the best of all possible worlds and everyone knows that everyone else expects this.

This, together with some other assumptions about tastes and technology, ensures that the intertemporal maximization problem has a unique solution. So the mathematics is fine but the economics strains credulity.

[azmyth]

"Why did we ever think that cutting real interest rates would increase demand permanently, as Old Keynesian models suggest?"

If savers confused a currency injection for an increase in savings, they would expect investment, and hence future productivity to go up. That would allow them to consume more now (because others did their savings for them) and later when GDP rose. They would be able to reap the benefits from the higher investment, even if they did not themselves invest, due to externalities and government transfers from taxes on capital. I suppose once people realized that the interest rates were temporary they would have to cut consumption, triggering the ABCT cycle. Perhaps Keynes had in mind unemployed resources that could be permanently put into production. If a cut in interest rates increased GDP with a multiplier effect, more could be both consumed and invested allowing for higher future consumption as well. It was probably just a mistake, pure and simple. No one can cut real interest rates in the long run anyway.

Joe D.: It's the non-money alternate uses of gold that are the reason why (some) Austrian economists advocate a gold standard (Hayek did not). Otherwise, it would be equivalent to a fiat standard, as you imply. Food would make a horrible money because it is a poor store of value - it rots. It's also bulky, which make is a poor medium of exchange. It is non-uniform, which makes it a poor unit of account and susceptible to Gresham's Law. Famine is an extremely unlikely event outside of totalitarian countries. Agricultural productivity has been skyrocketing for the last 150 years and doesn't seem to show any signs of slowing down.

[Adam P]

Nick, didn't I already cover this?

You say: "At Y=90, MRP of labour is greater than W/P. So all firms *want* to increase output and sales, *if* there were sufficient demand to buy that extra output. But there isn't sufficient demand. So they don't."

But, as I've already explained, at Y=90 firms will still be decreasing their prices. Why? Exactly because MRP of labour is greater than W/P and this combined with the demand elasticity that they face means that lowering price and increasing volume raises total profit. THUS P IS FALLING.

The falling P, with W not falling, means higher real incomes and so higher demand(this is the demand elasitcity again), so THERE IS SUFFICIENT DEMAND TO BUY THE EXTRA OUPUT AT THE LOWER P!

[Adam P]

Seriously Nick, you ask: "Why can't less than full employment persist forever (Y less than Y*) in this model?"

But when I explained above (@2:43am) exactly why less than full employment can't persit forever you agreed with me!

[Nick Rowe]

Adam: "But, as I've already explained, at Y=90 firms will still be decreasing their prices. Why? Exactly because MRP of labour is greater than W/P and this combined with the demand elasticity that they face means that lowering price and increasing volume raises total profit. THUS P IS FALLING."

Agreed. That's the Calvo Phillips Curve in action.

"The falling P, with W not falling, means higher real incomes and so higher demand(this is the demand elasitcity again), so THERE IS SUFFICIENT DEMAND TO BUY THE EXTRA OUPUT AT THE LOWER P!"

Disagree. That's the microeconomist's fallacy. For a given aggregate level of output and employment, a rise in real wage income means an equivalent fall in real profit income, so no change in total income, and no change in demand (unless you bring in distribution effects). Income always equals output, regardless of W/P.

[Nick Rowe]

Adam: "But when I explained above (@2:43am) exactly why less than full employment can't persit forever you agreed with me!"

What you were describing @2.43 was the supply-side of the New Keynesian model -- the derivation of Y* in the Calvo Phillips Curve, for example. I agreed with your description of the supply side. But that's not the aggregate demand side.

If Y=Y*, each firm has MR=MC. If Y less than Y*, each firm has MR greater than MC. Firm i cuts Pi, trying to slide along its demand curve to get to a higher y. But all firms do the same, so Pi/P stays the same. So each firm stays at the same point on its micro-demand curve. Unless the fall in P causes aggregate Yd to increase, which causes each firm's micro demand curve to shift to the right. That will happen in an Old Keynesian ISLM model of AD. It won't happen with a NK model, where the IS gets replaced with an Euler.

[Adam P]

No Nick, you're not understanding the structure of the model.

You say: "Firm i cuts Pi, trying to slide along its demand curve to get to a higher y. But all firms do the same, so Pi/P stays the same"

No, only some firms can change prices, others have to wait for the Calvo god to grant the chance to change prices. In the meantime the ones who could change prices have gained market share and increased employment. Later, when others finally get their chance they adjust price and increase their employment.

But the real point is, as I've already stated, the fall in P DOES cause Yd to increase, through the increase in real wages. Now we do need rational expectations here to solve a coordination problem. But the role of rational expectations is to allow firms to know thier demand curves so they understand that if they decrease price and simultaneously increase employment then the demand will turn up (wich then validates the expectations).

Now, you can try to call ratex the tinkerbell principle but that is not how you use it in the post. In the post you claim that their is no tendency to return to full employment unless agents believe it will happen, this is just plain false. Agents only need to fully understand their own market, the demand curve they face.

This economy does tend to full employment without agents believing that it will.

[Adam P]

PS: ratex also comes up in the intertemporal utility maximization problem that determines agent's consumption path.

But again, the agent only needs to understand the demand for his own labour. The agent does not need any beliefs about whether the economy as a whole will tend to full employment automatically or not. This just happens, as a result of rational agents who know the demand for their labour interacting with rational firms who know the demand curve for their output.

[Adam P]

PPS: and Nick, what I described @2:43 was NOT the determination of Y*!

Y* is determined by the level of productivity (what I called technology before).

What I described was exactly why Y < Y* forever is NOT an equilibrium.

[Lord]

But the ones that could not change prices immediately suffer reduced demand and income until they do in the same proportion as those that changed them immediately benefit. And while falling P increases real wages of those working, it doesn't necessarily increase Y due to increased unemployment. And ratex concerning future demand for his own labor is absolutely Panglossian.

[Adam P]

"And while falling P increases real wages of those working, it doesn't necessarily increase Y due to increased unemployment." Simply false, explained above.

"And ratex concerning future demand for his own labor is absolutely Panglossian. "

We're debating how the model works, not its realism.

[Bill Woolsey]

Adam P:

"We're debating how the model works, not its realism."

Who cares?

"Nick, in your example above C=Y=90 forever is NOT an equilibrium because Y=90 MUST MEAN LESS THAN FULL EMPLOYMENT because the marginal product of labour (a REAL quantity) is unaffected by any relative prices (it's entirely determined by the level of technology). But less than full employment doesn't persist forever."

What process leads to firms selling the full employment level of output?

"The falling P, with W not falling, means higher real incomes and so higher demand(this is the demand elasitcity again), so THERE IS SUFFICIENT DEMAND TO BUY THE EXTRA OUPUT AT THE LOWER P!"

You must be joking. The New Keynesian Model shows that falling prices, and fixed wages will raise demand through maintaining workers' purchasing power? So it is all based upon the Herbert Hoover theory of macroeconomics?

Perhaps this isn't in the new Keynesian model, but the usual notion is that the higher real wages results in less employment and if we assume all income is wage income, lower employment lowers output lowers income lowers real wage income.

My answer to Nick, however, is that the reaction function has future interest rates being at the level needed to keep current consumption equal to full employment output. And so the equilibrium where interest rates remain constant (5%) forever at low output is inconsistent with the reaction function. The target real interest rate must be dropping.

I suppose, of course, that the interesting point how a zero nominal bound fits into this.

[Adam P]

Bill: " "We're debating how the model works, not its realism."

Who cares? "

If you don't understand how the model works you can't judge its realism. You first have to understand the model.

[anon]

It might also encourage rich people to shove their fortunes up their noses instead of lending it out to more competent people.