Old and New Keynesians and self-equilibration

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.

Comments

[Min]

The answer is No, because the macro-economy is chaotic. Like most human systems.

[Nick Rowe]

Min: which would mean we would always have been dead. How could we have survived without homeostasis mechanisms? Unless somebody up there likes us.

[Nick Edmonds]

Nick,

If I understand correctly your comments in previous posts, you see the money supply as being determined in the market for bank loans (at least at one level). Even if the central bank can control the money supply very accurately, it is still having to do so via bank lending. How do see that working within the IS/LM analysis? Presumably, the position on the IS curve is saying something about what is going on with bank loans - lower interest rates, more borrowing for investment. The money supply and therefore the LM curve itself seems to depend on the solution to the model.

I'm not asking you to defend the IS/LM analysis. I don't think it stands up well to close scrutiny. I just wondered whether you had a view on this.

[Benoit Essiambre]

I too was thinking about this issue this morning but in a more abstract layman way. I always see this assumption mentioned that in the long term, real wages will adjust to the supply of money and we will get to full employment. However, since falling wages also means falling demand, unless the unemployed are very quickly put to work to offset the decrease in demand it doesn't necessarily work. What if there is a lag?

This also means that without enough monetary stimulus, the shortage of investment in the economy gets to be paid by workers, especially the not long ago unemployed workers through a wage reduction. What I mean by that is that without enough monetary easing that would push wealthy savers into making productive investment, employers rely instead on wage cuts, especially of entry level wages to finance their infrastructure and stay profitable.

But this means the burden to pay for the needed investment disproportionately falls on a population of poor or young workers. Needless to say, relying on a pool of poor and unemployed people to finance a proper level of investment and to get to full employment might not be the fastest way to get there. If the central bank would do proper easing, the financing burden would be shared more widely amongst workers and investors and it is likely that everybody would gain in the end through higher real GDP and higher stock prices.

[Frank Restly]

Nick,

Do either the Old or New Keynesian models address who is the debtor and who is the creditor? Do positive real interest rates negatively affect monopoly enterprise debtors?

[Ron Ronson]

"But we will only be at full employment today if people expect full employment tomorrow"

It does seem like this statement is likely to be true: If people make investment decision today based upon expectations about demand for the goods they are investing in tomorrow then the higher expectations are about the tomorrow the higher employment levels will be today.

The issue that NK models appear to dodge is "what determines expectations about future employment (and demand) levels?". This seems like a hard question to answer. I suppose it would be nice if the answer was "monetary policy determines expectations about future employment levels". Because then a policy (like NGDPLT) that made commitments about the future would likely have a big effect on employment levels in the present.

[Nick Rowe]

Nick Edmonds: at the moment, my views on this are still too incoherent to be worth stating. What you say sounds very roughly in line with my thinking.

Benoit: "I always see this assumption mentioned that in the long term, real wages will adjust to the supply of money and we will get to full employment."

Nope. It's *nominal wages* that need to adjust to the supply of money.

"However, since falling wages also means falling demand, unless the unemployed are very quickly put to work to offset the decrease in demand it doesn't necessarily work."

Nope: a common Vulgar Keynesian error, that comes from trying to think a general equilibrium question in partial equilibrium terms. Capitalists are people too. Wage income is not the same as income. Demand (either real or nominal) depends on *income* (either real or nominal), and not *wages*. And the Keynesian Income-Expenditure model already incorporates the feedback effect between income and demand. Which is not to say that wages might not have other effects on demand, either via distribution effects or via the profitability of investment.

Frank: come on now. Given the amount of time you spend reading and commenting on economics blogs, you really should read a first year (and second year) textbook. Or just Google it. I get *paid* to teach my students. I don't get paid to chase down every red herring you throw onto the blogosphere.

[Frank Restly]

Nick,

Most of our conversations end with "Frank please stop" so I'll stop now.

[Doug M]

The economy never finds "equilibrium." If the balance of pressures point us toward the equilibrium condition, we have the tendency to overshoot.

[Benoit Essiambre]

Ok I see what you are saying. I guess I too would need to read a textbook (any particular one you recommend for someone comfortable with relatively advanced science/engineering math?).

Although, I was indeed thinking of "profitability of investment" hence the last paragraph of my post. In a liquidity trap, when central banks are understimulating, the "capitalists" tend to hoard their income into cash or cash like instruments. The only ones who stand to gain very much from investment are the unemployed/underemployed because it makes jobs available to them. The problem is that the burden of investing in the economy falls on people with little money. Sure they can do it by accepting low wages but it might not have a large effect given what they in aggregate have to work with.

But this is all tangential to the current post which seems to be more about how NK models are derivatives that are missing some kind of convergence factor.

[Nick Rowe]

Doug M: that's not what the three models say. And if those oscillations were explosive, then my teenage self asks you the same question that I asked myself back then: how come all economies haven't exploded by now? How come most of the time we're somewhere vaguely near what might vaguely be called "full employment"? You think there's a Big Designer up there somewhere, who sorta likes us, but who throws just enough bad stuff at us to punish us for our sins?

[Martin]

"New Keynesian modellers just assume that the people in their model expect a long run tendency towards full employment."

I guess one could say that this is what makes New Keynesians more Keynesian than the Old and the Post-Keynesians :P

[notsneaky]

I'm not sure if this contradicts your point or not (I'm a bit confused by what you mean exactly by "interest rate that's just right") but this is the difference between the "traditional IS curve" and the "forward looking IS curve" no? In the latter case, you plug in for future expected output gap, and the current output gap becomes a function of the (expected) path of the interest rates. Timing of the lags/responses plays a role here. Looking it up in Carlin and Soskice (like here http://www.ucl.ac.uk/~uctpa36/3equation_2005_withtitle.pdf - this will probably end up making the comment send off into spam) in the latter case there's self-equilibratin' going on, but there might be some rabbits stuffed into some hats here.

[Tom Brown]

Nick, I wish you had an "Ask Nick" page for O/T questions. I've been discussing HPE, reflux & MOE w/ Mike Sproul over at JP's, and I'd love to ask you a question. Of course that perhaps PRECISELY the reason you don't have an "Ask Nick" page! Lol.

[Joseph]

Most NK models rely on log-linearization for tractability which implicitly turns them into equilibrium analyses with small deviations and are not very well suited to long run analysis. Is it possible that this linearization strips out the equilibrium forces? Do most NK macroeconomists just assume forces outside the standard NK model (erosion of price/wage/information stickiness dissipating,pigou effects?) are responsible for long run equilibrium and that as long as monetary policy doesn't amplify shocks that these other forces will dominate?

In most physics models, quadratic taylor series are needed to produce stable equilibrium. Do you think extending the linearization used in NK one more term to a quadratic series would have any effect on the stability or does the lack of money in these models force one to impose a full employment boundary condition at infinity?

[Philippe]

"my teenage self asks you the same question that I asked myself back then: how come all economies haven't exploded by now? How come most of the time we're somewhere vaguely near what might vaguely be called "full employment"? "

Quite a strange comment in the context of what has happened over the last few years. The financial sector was about to completely explode - probably taking the whole economy with it - and the only reason it didn't is because of actions by governments and their central banks. And we're still nowhere near 'full employment'. Look at countries where governments haven't been able to act counter-cyclically, like Greece. Total catastrophe.

[Alex Godofsky]

Echoing Philippe, with the data we have isn't the answer possibly just "I reject the premise of the question"? As I understand it, for most of history only a fraction of the economy involved monetary exchange, with the majority based on barter. We have observed really extreme cases of monetary exchange breakdown in response to central bank actions that, to the contemporary participants in the real economy, must have felt like mysterious, intangible forces. We have observed hyperinflation actually destroying currencies and forcing them to be re-made.

Finally, monetary disequilibrium could show up not as unemployment but as widespread misemployment - e.g. PhD's working as bartenders. So the data saying "most of the time we're near full employment" may be very misleading.

[W. Peden]

So perhaps we should introduce M and a Pigou Effect into the NK model? Thus, M's role is as a God of the Output Gaps...

(Sorry, it's late here, and this post is too interesting to go without a comment.)

[Tom Brown]

Nick writes: "You think there's a Big Designer up there somewhere, who sorta likes us, but who throws just enough bad stuff at us to punish us for our sins?"

Nick, I think you're onto something there! I bet that concept sells! I bet you might even be able to avoid taxes on such a venture!

[Nick Rowe]

Philippe: which is more common: 10% unemployment or 90% unemployment? Why isn't 50% unemployment modal?

Benoit: almost any standard university text will do. In Canada: Mankiw, Ragan/Lipsey, Parkin, whatever. They will be much less mathematical than you would want, but there's a big danger in only looking at the math. I want to push you outside your comfort zone!

"But this is all tangential to the current post which seems to be more about how NK models are derivatives that are missing some kind of convergence factor."

Yep.

notsneaky: "I'm not sure if this contradicts your point or not (I'm a bit confused by what you mean exactly by "interest rate that's just right").."

The natural rate of interest.

"... but this is the difference between the "traditional IS curve" and the "forward looking IS curve" no? In the latter case, you plug in for future expected output gap, and the current output gap becomes a function of the (expected) path of the interest rates."

And the terminal value of the output gap.

Here's another way of looking at it: assume U=log(C) for simplicity, and solve for the time-path of the real interest rate consistent with full employment where C(t)=Y*(t) for all t. Now halve C(t) for all t. Your new solution for C(t) satisfies the consumption-Euler equations for the same time path of r(t).

Tom Brown: try the search box top right.

Joseph: I don't think log linearisation (or any poncy math) has anything to do with it. The equilibrating force is just AWOL in NK models. Real interest rates merely affect the intertemporal *distribution* of demand.

W Peden: well, we are talking about the demand for goods *in exchange for money*. "Do you want to hold money, or goods?" This question wouldn't even arise in a barter economy. So we need to have some sort of M, and some sort of real balance effect (*some sort* of effect of M/P) whether Pigou or not.

[Frank Restly]

Nick,

Are you making a back handed reference to "Divine Coincidence" - a phrase coined by Gali and Blanchard?

[Nick Rowe]

Frank: No. "Divine coincidence" is relevant to my NGDPLT vs IT posts. Divine coincidence says IT is a perfect guard dog.
All my metaphors here are to Darwin vs creationists.

[Joseph]

Sorry if this is obtuse but what is the actual mechanism through which consumption is shifted in the NK model? There's no money balances or investment goods and output=consumption for each period or are they hidden in there implicitly. Isn't that and not just money the missing link to forcing the economy to long run full employment? Like you said consumption and output could be cut in half in each period without removing the economy from equilibrium but in reality cutting consumption in half each year would imply a large increase in investment producing a surplus of consumption and productive/falling real wages at some point in the future which combined with consumption smoothing leads to equilibrium.

[notsneaky]

"I'm a bit confused by what you mean exactly by "interest rate that's just right").."

The natural rate of interest.

But that still leaves me confused. In the NK model, the natural rate of interest is the one such that output is at full employment. But if the economy is not at full employment (i.e. it got shocked) the model doesn't say "set the interest rate equal to natural interest rate right away and keep it there". It says "choose an optimal path for the interest rate which gradually brings the economy back to full employment". But the "interest rate that's just right" is the end of the process, not a constant - along the way the CB doesn't set r=r(natural). This is because the CB cares about BOTH output gap and inflation, and setting r equal to the natural rate right away would result in too high rate of inflation.

Here's another way of looking at it: assume U=log(C) for simplicity, and solve for the time-path of the real interest rate consistent with full employment where C(t)=Y*(t) for all t.

This is sort of right and sort of wrong. True, the Euler equation only defines how consumption adjusts over time, not its level. This is the same as in, say, Ramsey model, where we got the same equation and draw all kinds of arrows in the phase diagram going in all sorts of directions. But only one of those is the stable, optimal path - tied down by initial value, the transversality condition and the second order condition. This is true of pretty much any dynamic system - to actually solve it you need a point on the solution path.

But the model doesn't say, that if the economy's not at Y* then the CB will choose r so that C(t)=Y*(t) for all t. It chooses r's so that C(t) gets back to Y* over time "at least possible cost" (in terms of inflation). Are you saying that the only reason why the CB can choose the "right" initial value is because people in the economy expect to get back to full employment?

Another way of putting it is this. Take the Philips Curve and the (forward looking) IS curves as the "primitives" of the economy and then ask "is there a path of nominal interest rates which bring the economy back to full employment". And can this path be expressed as a simple policy rule - IIRC, that's how Taylor got his rule in the first place. At the end of the day, the model is just a two variable VAR and its stability depends on the coefficients (which are actually up to the CB's discretion). And the ability of the CB to pick the initial condition for one of the variables, given the initial condition for the other.

So there's definitely equilibrating. Is there SELF-equilibrating? Like if we had a really crazy Fed that believed that nominal interest rates must always equal 13.34849% no matter what. Would it still come back to full employment? That's still about the coefficients of the VAR and the answer is maybe, maybe not. It's just another way of saying that there may exist CB monetary rules which can destabilize the economy. Or what if the Congress abolished the Fed tomorrow? How would the nominal interest rate be determined and is there any guarantee that whatever mechanism throws it up is such that we get back to full employment?

If that's the point here then I agree - the NK model does not have a non-CB model of the nominal interest rate. But you said we get to assume "sensible monetary policy". I read the other post on the stupidity of the question itself. But here you seem to be making a stronger argument - that the economy doesn't equlibriate even with a sensible monetary policy (not the worst possible one that can be imagined).

The thing about the Crazy Fed is actually sort of related to the ZLB. In the liquidity trap it's sort of AS IF the Congress abolished the Fed or AS IF we had a crazy Fed that believed interest rates must always equal 0.0000% (as opposed to negative whatever that's needed). And that's why there is no equilibratin', self or otherwise in the ZLB.

I apologize for the length and for missing the point - I think it has to do with what the "self" in "self-equilibrating" means.

[Min]

Moi: "The answer is No, because the macro-economy is chaotic. Like most human systems."

Nick Rowe: "which would mean we would always have been dead. How could we have survived without homeostasis mechanisms? Unless somebody up there likes us."

Negative feedback does not mean that a system is not chaotic (in the technical sense, OC :) ). And positive feedback does not mean that a system will fall apart. The fact that a system is relatively stable over time does not mean that it is not chaotic, and, OC, it does not mean that it tends to an equilibrium. The solar system is stable over long time periods, and planetary orbits appear to approach equilibria as circles. But the solar system is chaotic. And that's not even a human system. ;)

Consider all of the arguments that you have examined in which expectations play a part. You often invoke the god, Chuck Norris, as an explanatory device. That does not indicate a very well developed theory of expectations. Perhaps the lack of such a theory reflects the chaotic nature of macroeconomics. :) You also frequently invoke sudden, unexplained changes in mass psychology. How does that make sense unless the economy is chaotic?

[Kevin Donoghue]

Nick: New Keynesian modellers just assume a tendency towards "long run" full employment, even though it's not there in the model.

I honestly think you're just nit-picking here, so you deserve a nit-picky answer. Everything in the model rests on the assumptions made. If long-run full employment is assumed then it is there in the model, by assumption.

All you're doing is taking out an axiom, like Saccheri. You're showing that a Non-NK model, which never attains full employment, is logically possible. Yes, it is. So what?

[J.V. Dubois]

Kevin: How can you say that this post is nitpicky? The main role of monetary policy is to stabilize the economy, with unemployment being one of the most important parameters of the system. How can you say that it does not matter for stabilization of the system that we assume that the system will stabilize itself by some unknown means?

Imagine that you are to solve some different stabilization problem, like for instance you want to solve how to stabilize the heating system in a house. Does it make sense to say that no matter what we do with the thermostat the people in the house will in the future reach optimal temperature by some unknown means (opening windows? turning on the stove to heat the house?) so we may use some backwards induction and adjust some parameters that in the past data correlated with this unknown activity? What about special ocassions? What if for some reason people cannot turn on the stove (it is broken) or open windows (it very windy out there). Should we still assume that there will for sure be an optimal temperature in the future, just stick with what we know from the past? It does not make any sense to me.

[Nick Rowe]

notsneaky: assume (for simplicity) that the CB observes the shocks in real time, or can even foresee the shocks, or that there are no exogenous shocks. Setting r=rn is a necessary but not a sufficient condition for the full employment consumption path. Because C(t) = 50% of full-employment output for all t from now on is also consistent with r=rn.

"Are you saying that the only reason why the CB can choose the "right" initial value is because people in the economy expect to get back to full employment?"

yes.

The initial value of C(t) doesn't matter. There is nothing to prevent C(t) jumping. It's not like the capital stock. If people go to bed at night expecting full employment from now on, then have a dream in which everyone else chooses 50% of full employment C(t) from now on, each individual's optimal response is also to choose 50% of full employment C(t) from now on.

[J.V. Dubois]

Nick: Just a sideonote, it seems that you may have started something with your post about New vs Old Keynesians. Mike Konczal wrote a pretty good article about it with Paul Krugman responding.

I do not understand Krugman that much.

1) First, Krugman links to his paper that he named as "New Keynesian in its setup" on his blog. He used money in this model and avoided the NK vs OK dichotomy away by obligatory nod toward New Keynesianism stating that:

"We need not explicitly introduce the money supply; the results that follow will hold for a variety of approaches, including the "cashless limit" as in Woodford (2001), a cash-in-advance constraint as in Krugman (1998), and a money in the utility function approach as in Eggertsson and Wooford (2003))"

So he introduced money into his model and claimed that it is so similar with no-money New Keynesian models that is safe to say that the model "New Keynesian in setup". I am not really convinced, it is no explanation of the dichotomy - which brings us back to square one - to your question for NK economists.

2) Second, Krugman uses a lot of buzzwords to drown the question with:

"OK, even Keynes wasn’t that pessimistic: he argued that investment would eventually recover once “use, decay, and obsolescence” created a sufficient scarcity of capital. Once we take the problem of debt into account, I think you’d want to add deleveraging and default — which reduce the debt overhang — to his list. So even on a very Old Keynesian view, depressions aren’t forever."

[Nick Rowe]

Joseph: for simplicity (in my discussions here with notsneaky) we are assuming that consumption is the only form of demand. No investment, government, or foreigners.

Kevin: So, when some Old Keynesian critic says "what, if anything, would bring the economy to full-employment?" the New Keynesian answer is: "Full employment (or full employment on average, or eventual return to full employment) is just an axiom in our model!"? The level of employment is supposed to be an endogenous variable. NKs can explain fluctuations in employment around the average, but cannot explain its average value.

[Nick Rowe]

JV: I don't think Mike Konczal was responding to my post on "NKs really need the Pigou effect". I don't think he understands the (absence of) equilibrating mechanism in NK models. I don't think PK really understands it either. He seems to think there's a dichotomy between the interest rate Euler equation consumption function and any real balance effect. There isn't. r determines rates of change; M/P determines levels.

[Nick Rowe]

Simplify:
Ignore exogenous shocks. Ignore growth, ignore time preference proper. Ignore inflation. The CB sets r(t). There is a full employment level of consumption C* that never changes. The CB wants to set r(t) such that C(t)=C* for all t.

The IS equation is: C(t)/C(t+1)=1/(1+r(t))

The initial C(t) is not pinned down by history. Bygones are forever bygones. There is no "memory" in this system.

Setting r(t)=0 for all t is a necessary condition for the CB hitting its target every period. It is not a sufficient condition. The CB cannot do it.

[Nick Rowe]

All agents are identical. If everyone else halves their C(t) from now on, for all t, my income halves from now on for all t. In order to meet my personal transversality condition (to stop me going deeper and deeper into debt) I will have to halve my C(t) from now on too. So 50% permanent unemployment is also an equilibrium.

In other words, the NK model, when the CB sets the right rate of interest, is exactly like a version of the OK Income-Expenditure Keynesian Cross model, except that the APC=MPC=1 for all Y, so the AE curve coincides with the 45 degree line.

How come it takes someone (a nobody who can't do math) like me to make this point?

[JKH]

Nick,

I gather the traditional ISLM has an offspring with a (horizontal?) “LM” curve consisting of the (short term?) “target rate” set by the central bank (e.g. Romer?). I think you’ve written about this in the past. How does that sub-model fit into your sequence of models? Was it a minor development? If the money supply is absent from that model directly, how does that affect the interpretation of equilibrium possibilities? What replaces the price level/money supply effect you describe for the traditional ISLM?

Ref: http://elsa.berkeley.edu/~dromer/papers/JEP_Spring00.pdf

P.S. my impression was that the IS curve says nothing directly about bank loans or any kind of financial intermediation – that’s all incidental.

[Kevin Donoghue]

Nick: So, when some Old Keynesian critic says "what, if anything, would bring the economy to full-employment?" the New Keynesian answer is: "Full employment (or full employment on average, or eventual return to full employment) is just an axiom in our model!"?

Well Jordi Gali says the limit, as t goes to infinity, of the expectation of the output gap is zero. He doesn't derive that claim from any other assumption. So yes, it's an independent axiom AFAICT.

I can't see that this is any more objectionable than Friedman's waffling about "the level that would be ground out by the Walrasian system of general equilibrium equations, provided there is imbedded in them the actual structural characteristics of the labor and commodity markets, including market imperfections, stochastic variability in demands and supplies, the cost of gathering information about job vacancies and labor availabilities, the cost of mobility, and so on."

[Kevin Donoghue]

Hopefully this link goes to the relevant page of Gali's book.

[Martin]

I agree with Kevin here, I don't think that "it depends on expectations" is an unreasonable answer to give. What else is it going to depend on? How millions of individuals achieve coordination is not tackled in any of the models discussed above, instead it is assumed that they will.

The answer the New Keynesians give is more honest (and general) than the answer given by those of the IS-LM variety:

"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."

How grinding deflation should lead to actors being able to coordinate on any equilibrium is not explained. Yet it is assumed that expectations of the actors will be consistent with one another under these circumstances and thus that they do coordinate to an equilibrium and in particular to a full employment equilibrium. It is one thing to draw the curves and their intersection that describe the equilibria in the three markets, it is another thing to assume that these curves remain the same or can be drawn at all under all scenarios.

As far as I can tell the difference is that the New Keynesians give a more general answer: "For a coordination to a full employment equilibrium we need actors to expect that full employment will be restored. Only this will guarantee that their actions will be consistent with it and only that will guarantee a return to full employment".

[Frank Restly]

Nick,

"The IS equation is: C(t)/C(t+1)=1/(1+r(t))"

"Setting r(t)=0 for all t is a necessary condition for the CB hitting its target every period. It is not a sufficient condition. The CB cannot do it."

Hence the need for fiscal policy - fiscal policy is the only way to set C(t+1) = C(t) irrespective of the interest rate and without relying on expectations. Interest rates (real or nominal) don't affect governments (monopoly enterprises) the way they do individuals.

[Alex Godofsky]

Nick:

Philippe: which is more common: 10% unemployment or 90% unemployment? Why isn't 50% unemployment modal?

Why can't the mechanism I suggested (substitution into suboptimal job allocations) be responsible?

[Kevin Donoghue]

J.V. Dubois: How can you say that it does not matter for stabilization of the system that we assume that the system will stabilize itself by some unknown means?

NKs don't rely on unknown means. They rely on wonderfully well-informed agents with rational expectations anticipating an asymptotically optimal outcome clearly visible to them all.

[Nick Rowe]

Frank: no. Fiscal policy doesn't help, in this case. It just complicates the issue.

JKH: it's a minor development. If the central bank sets r, and holds it constant, you get a horizontal LM and vertical AD curve which means zero self-equilibrating force. If the central bank sets r exactly right, you get full employment. If it doesn't, you don't, and never will get to full employment. If the central bank adjusts r in response to unemployment and inflation, you eventually get to full employment, provided the central bank does it roughly right, and responds quickly enough.

Kevin: "Well Jordi Gali says the limit, as t goes to infinity, of the expectation of the output gap is zero. He doesn't derive that claim from any other assumption. So yes, it's an independent axiom AFAICT."

That's how it seems to me too.

(I edited your comment and removed the " " around your link, so it works, but Google still won't let me read it. I will have another try later.

I don't like that paragraph in Friedman either. He muffed it. It's not a *definition* of the natural rate; it's a statement about what sorts of things might determine the natural rate. But here's the big difference: if you presented Friedman with a real (non-monetary) model of the natural rate, he would have been able to tell you about the forces that lead a monetary exchange economy towards that natural rate. He would not have *just assumed* the economy tends to go there. The New Keynesians *just assume* it goes there.

Martin: to my mind, there's a big difference between:
1. Assuming agents somehow get to a Nash Equilibrium that's unique
2. In a model with a continuum of Nash Equilibria, agents *always* coordinate on the best of those equilibria.

Back later.

[Nick Rowe]

Thanks to Kevin who emailed me the relevant quote from Gali:

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

Bullshit. What he really means is "We need to assume the economy always approaches full employment in the limit as time goes to infinity, otherwise we will get explosive hyperinflation or hyperdeflation."

Bullshit. Total bullshit.

Why aren't the Old Keynesians screaming blue murder at this stuff? Are they all dead? Do none of them understand the model? Why is it left to some old monetarist like me to call them on it??

Does everybody else in the illuminati know the NK's are just sweeping the whole thing under the rug? Am I the only one who never got the secret memo?

Please level with me guys. This is important to me.

1. Did you understand this before?
2. Did you get taught NK macro properly and recently by someone who at least seemed to know what he was talking about, and had all the qualifications, at a good skool, etc.?

[Sjysnyc]

Simplification is good. But I think you're simplifying too much.

So I can't see the entire Gali derivation in the book, but it looks like his underlying utility function has both consumption and labor supply in it. That means instead of your simplification of

u = ln(c)

it should be

u = ln(c) - ln(n)

And that gives you a stable path. Intuitively what it means is if you halve consumption then you also drastically reduce labor supply. The marginal utility of additional consumption is then much higher than the marginal disutility of additional work. You're no longer in an equilibrium since the assumption of these models is that labor supply and labor demand match -- this is one of the much more problematic areas in my view.

So essentially what the model has is something like the phase diagrams mentioned for the Ramsey model above implicitly in it, just that somewhere in the algebra the labor part gets subsumed into the deviation of output from trend and doesn't show up in the 3 equation version. That's why the "under the assumption that the nominal rigidities vanish asymptotically" isn't really sweeping it under the rug. What it's saying is if the nominal rigidities go away there is a stable saddle path back to y=y* that he assumes the economy follows.

I think some derivations may be a bit murky that this is going on. And if you didn't have the disutility of labor in here I don't think it would work. Or I could be wrong -- it's been a couple of years since graduate school and I've fled academic economics.

[notsneaky]

I guess another way to riposte is to ask - if what you're saying is correct then how do all'dem New Keyensian model (top journals and all) articles derive them impulse response functions (of the calibrations not econometric VARs)? If the model does imply hyperfinflations or hyperdeflations then shouldn't that jump out in the simulation? What do they plug in in the matlab/mathematica program where it says "E_t(x(t+1))" exactly?

[JW Mason]

Wow, this is a great post. Just great. I don't disagree with a word in it.

I think that this might be a more generic problem, though? For instance, how is a transversality condition any different? What mechanism prevents deviations from it?

Or UIP, which I just taught today. The "right" response of exchange rates to a change in monetary policy requires not only that actors know the true long-run level of the exchange rate, but that they also know the date on which the actual exchange rate will return to that level.

[JW Mason]

I'm inclined to think it's a general problem with intertemporal optimization.

[notsneaky]

Oy, UIP. That's not even intertemporal optimization, that's supposed to be just arbitrage. So it's supposed to be true under weaker conditions.

But suppose that the foreign interest rate is higher than the home interest rate. And suppose that everyone expects the exchange rate to stay constant. So everyone invests in the higher nominal asset, the foreign one. Interest rates are exogenous (fixed by CBs or whatever, and that's the assumption of the empirical tests of the UIP). So everyone demands the foreign asset, so everyone demands the foreign currency. Except maybe for some import/export traders, which we take as given. Demand for foreign currency is really high, as a result current exchange rate is... well, whatever, as long as it's not zero or infinite.

Next period? Well, the same damn thing happens. With no change in the liquidity in the market, or the number of those import/export traders), or the expectations (which we've assumed) the demand for foreign currency is exactly the same. And nominal interest rates and supply of currency are still exogenously picked by the CBs. So... the next period exchange rate is same as last period's. Which means that the expectations formed in the previous period are model-consistent, i.e. rational. But UIP doesn't hold, since R(home)

If you set this up as an intertemporal max model, you get the standard arbitrage UIP condition. But deriving it also involves dividing through by the % change in expected exchange rate - i.e. potentially zero. Which means there's another equilibrium where UIP doesn't hold as I just described.

It is similar.

[Nick Rowe]

JW: THANKS!

It's not a problem with transversality conditions for the *individual* agent. Starting at full employment, if an individual agent halves his c(t) for all t, with all other agents keeping theirs constant, his income path stays constant, and he simply accumulates "bonds" forever and ever. His euler equation is still satisfied, but he is not maximising his lifetime utility. He could increase his consumption again, and increase his utility in every period forever.

But if every agent expects every other agent to halve his consumption, he expects his income to halve for all periods, so he will have to halve his consumption too, otherwise he would go deeper and deeper into debt, until he hits his borrowing limit, and would have to cut his consumption then by more than half, which violates the euler.

notsneaky: Dunno. My guess is they still assume full employment in the limit, otherwise the solution is indeterminate, and they wouldn't be able to program matlab? But I'm too old to answer that question. Except I know the answer is: they cheat.

sjysync: "Intuitively what it means is if you halve consumption then you also drastically reduce labor supply. The marginal utility of additional consumption is then much higher than the marginal disutility of additional work. You're no longer in an equilibrium since the assumption of these models is that labor supply and labor demand match -- this is one of the much more problematic areas in my view."

They typically assume perfectly flexible wages and slowly adjusting prices. So real wages are lower when output and employment are below the natural rate. The labour market always clears, because W/P falls to make it clear, but it's not "full employment" in any meaningful sense. I am talking about a situation in which the demand for output is too low, so output is too low, so the derived demand for labour to produce that output is too low, so employment is too low, even though the labour market clears.

It's simpler to ignore all that, and just assume self-employed hairdressers, so W=P and C=Y=L.

[Kevin Donoghue]

On the question of who knew what and when, I think Frank Hahn was aware of this scam in 1986. Try Googling the sentence "On rational expectations, Leijonhufvud has a number of good things to say." (Include the quotemarks.) It should take you to some very apt remarks in Individual Forecasting and Aggregate Outcomes: 'Rational Expectations' Examined. In case that doesn't work I've emailed an extract to Nick.

[Sjysnyc]

So my aside about the issue of labor markets in the NK model wasn't particularly useful -- indeed it was a distraction. I was expressing my skepticism about the usefulness of the NK/DSGE blend in general, and specifically about their labor market modeling assumptions as being the worst part.

But that's not particularly relevant to the discussion at hand. Which I take as to whether there is a meaningful trend/equilibrium/full employment that the model comes back to because of equilibriating forces within the model. In the terms you were asking: is consumption halving for everyone an equilibrium?

There I think the answer is no. There isn't just a optimization over consumption but over labor supply -- and as you note in your response to me the model assumes that the agent can work as much as he wants at the prevailing wage. And in the case where you halve consumption the agent would want to work substantially more. There is lurking somewhere in the depths of the model a first order condition with respect to labor supply as well. With a diminishing returns to labor production function around too. It's just when reducing it to the 3 variable system that gets swept under the table. That's why there is a equilibrium to which it makes sense to talk about returning to as time goes to infinity.

Or think about it in terms of the individual agents you were talking about with JW. Suppose one halves her consumption and expects everyone else to do the same. Then, at the prevailing wage she has an incentive to increase her hours of work. And by the assumptions of the model she can do so without affecting wages. She can consume more, but because she is also working more will not violate the transversality condition. But then, so does everyone else. And that gets you back to an equilibrium with what they call full employment.

[mickeyman]

Don't overlook multiple equilibria. http://www.worldcomplex.blogspot.ca/2012/02/unemployment.html

There's no reason to suppose that an equilibrium point should be anywhere near full employment. More likely the employment situation tailors itself to the number of jobs available. If millions of new jobs were suddenly created somewhow, I think we would find the candidates to fill them, even if that number were much greater than the number of officially unemployed people.

Even when the labour force participation rate falls back to 1950s levels, after a suitable period of time, unemployment will officially be back to historical levels, as so many will be dropped from the list.

[jep]

If you look at unemployment since the dawn of time, can you really say it has typically been low? Can you say that,for example, a typical peasant in Leicestershire in 1290 was fully employed? Or in 1620? Why did so many agricultural workers leave Europe in the 19th century? Was it simply because land was available in America, Australia and Africa or perhaps because they would have been underemployed if they stayed in Europe?

Perhaps the wondrous succession of positive technology shocks from the mid 18th century forward has masked some of system instability? Or perhaps the system is so changed that it is completely different an not comparable to what previously existed?

Can you assume that we will always be on the saddle point express train to equilibrium?

The DSGE framework sets up a great benchmark -- but it needs to be tested against a variety of data sets and time periods -- without imposing paradigmatic assumptions (either way) in the testing process.

[stearm]

"Because for most of history, we haven't had fiscal policy being done by sensible governments that understood this model"

For most of history, monetary policy was set up by emperors and kings. Emperors and kings had a tendency to spend more than they could, to start endless wars, to finance their debt through seignorage or simply through violence. It worked sometimes, when it didn't work, it was Zimbabwe all along.

It's been a long way, but we ended up in the other extreme: central banks are independent and debt financing is a no-go policy, governments are run by people who see Keynes as a communist and, at the same time, they have been kidnapped by financial markets. The positive thing is that, if you are not in currency area with the Germans, a financial collapse could be stopped. Things can't go Zimbabwe, but what we see is an irreversible economic and social decline.

[stearm]

To Mickeyman:

Interesting observation. If you read the classics, structural unemployment was indeed impossible for a reason: starvation or, more in general, demographic change caused by economic factors. The classics thought that the economic system was in a long-run equilibrium because unemployed people would simply die and/or their sons and daughter dies. Read Chantillon for example. But why did they get unemployed before the Industrial Revolution?

Not because they could not find a job in the labour market, but because they could not sell enough of their product in order to survive. Up to the late 18th century and well into the 19th, 99% of the population was composed of small capital/land owners. Hence, the classics were thinking to the system equilibrating mechanism as affecting the number of producers, surely not wage workers.

The huge transformation came when people were convinced to accept wage jobs. Read Polanyi, for example. People were either convinced or forced by legislation to supply their labour to whom owned big capital equipment (machineries). But this move involved huge risks.

If you have your peace of land and/or your small capital equipment, you starve if you can't sell enough of your products for a very long period of time. But, even in time of crisis, you still produce something, you have probably a small piece of land which gives you at least some food. You can eventually adapt and start to produce something else. Starvation is in theory possible, but a lot of people have the means to survive the crisis, maybe some of the children died for diseases caused by reduced food or worsened material conditions.

But once you sell your workforce in the labour market and you can't find a job, you simply die if there is no social safety nets. Even if real wages are much higher than what people could expect to earn as small capital/land owners, wage workers choose a riskier option even if justified in terms of inter-temporal optimization under the assumption of an infinite time horizon, that is, you can't die whatever you choose!!!!!!!

So, basically, if you want a market economy, you need social safety net and protect workers from starvation in times of crisis. But if you have a social safety net, there is no equilibrating mechanism. Then a huge recession must be fought through expansionary monetary and fiscal policy.

So, not only Keynes was right, but the evolution of society shows that he was right.