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Deflationary spirals reinforce the power of people with money. This triggers a power and wealth acquisition spiral that quickly leads to problems for people with no power and money. They rebel. It is the rebellion that squelches the deflationary spiral. Sometimes the powers that be notice that this will happen ahead of time and squelch the spiral first. Or they start a war as a distraction, which triggers inflation.

Nick, You lost me half way through. You seemed to assume that the public's expectations about the structure of the economy were very different from the actual structure of the economy. Is that right? If so, what motivated that assumption? Isn't it more reasonable to assume that the public's expectations are consistent with the model?

You also assume the central bank permanently cuts the real interest rate. How do they do that?

I assume the last question in your post is purely rhetorical.

George assumes that policymakers would respond if this happened in a way that could return the economy to a stable path. It requires an immediate and substantial drop in the interest rate, as the Fed did, and if that's not enough, fiscal policy intervention.

see here:

http://economistsview.typepad.com/economistsview/2009/08/deep-recession-calls-for-healthy-dose-of-fiscal-stimulation.html

(It's the July 09 paper with Seppoo that addresses this).

@Sumner "You seemed to assume that the public's expectations about the structure of the economy were very different from the actual structure of the economy. Is that right? If so, what motivated that assumption?"

Perhaps the agents have rational expectations but are initially very uncertain about the true structure of the economy. As they acquire observations about their income and other economic variables, their model of the economy converges to the "true" model through Bayesian inference or an approximate version thereof. The agents' behavior would be fully rational, but the practical effect would most likely be intermediate between crude adaptive expectations and full knowledge of the "true" model of the economy.

Jim: there's money, there's bonds, and there's wealth. All different. And in a New Keynesian model, if a deflationary spiral gets going, *can8 they stop it?

Scott: "You seemed to assume that the public's expectations about the structure of the economy were very different from the actual structure of the economy. Is that right?"

I assumed that the public didn't have a clue about the structure of the economy. I assumed they acted rather like atheoretical econometricians who do VAR style forecasting. Only simpler. In a stationary stochastic equilibrium, VAR econometricians may eventually converge to full-blown RE, of course. But if a policy is new, or if any exogenous shock is new, I don't think it's safe to assume strict RE. Even if there are sophisticated agents, I would want to assume some proportion are unsophisticated VAR extrapolators, and define RE as what happens in the limit as that proportion goes to zero. That way you can see if the RE equilibrium path is stable.

"You also assume the central bank permanently cuts the real interest rate. How do they do that?".

Well, any NK model assumes the central bank can set the nominal rate, and by responding quickly enough to expected inflation can set the real rate (absent the zero lower bound). So an NK model ought to be able to tell me what happens if they cut the real rate permanently. If the answer is "the economy eventually explodes, so they had better not", that's OK. That's an answer. I just wanted a simple thought-experiment, to see what the IS curve looked like. I ignored the Phillips Curve.

Mark: George is the (one of the few) exception I had in mind when I kept saying "almost all New Keynesians..". But it is precisely *because* George can say what would happen if monetary policy were chosen arbitrarily, and possibly stupidly, that George can actually say what sensible monetary policy ought to do.

anon: Yep. A more sophisticated version of my answer to Scott. Except, it might not converge. Because their learning about the structure of the economy will sometimes (and will in this model) change the structure of the economy.

Mark: To continue. As I understand it, George has two "nasty" feedback loops in his model:

1. falling output - falling inflation - falling expected inflation - rising real interest rate - falling demand - falling output.

2. falling output - falling expected future income - falling demand - falling output.

I already had my head around the first. It was the second feedback loop, and how it fitted in with the New Keynesian Euler equation IS curve, that I hadn't got my head around. Then I realised it was the same thing that had been puzzling me in that old post of mine, on why I couldn't make sense of New Kynesian macro.

@Nick: One problem with any account of "nasty feedback loops" is that the expectation of a rational agents should be free of predictable bias. So if agents are smart enough to realize that a feedback loop is occurring, their expectations should take this into account, perhaps by jumping to a fixed point. This feature is hard to model, but it makes the "true" behavior much closer to ratexps.

The second feedback loop thus is quite self-limiting, because agents probably know that output is affected by both permanent technological shocks and "demand recessions" which resolve themselves in the long run due to flexible prices, etc. Eventually, the agents should realize that they are probably in a demand recession and their expected future income should stop falling. And the first feedback loop can be addressed by unconventional monetary policy, at least in isolation.

anon: (By the way, since your comments are good, and since I hope you will hang around here commenting, would you like to give yourself a real fake name, so we can distinguish you from all the other anons?)

How quickly will they realise a feedback loop is occurring? And will they all realise it at once? My preference would be to give some fraction of the agents that insight. And I think that, in this case, the results would be qualitatively similar to my results. It would just happen more quickly. (Notice I didn't really say how long my "day" is; it could be a day, or week, or month, or hour.) But in my experiment, if the central bank sets the real interest rate too low permanently, output rises without limit (at least, there's no limit inherent in the IS curve, though there will be one inherent in the AS or Phillips Curve). And if it sets too high a real interest rate permanently, output falls without limit.

In other words, the New Keynesian IS curve, with any reasonable assumption of learning from experience, will give you a Wicksell-like process, only instead of the price level rising/falling without limit, it's real output that rises/falls without limit. If some agents catch on to the model they are living in, all that does is speed up the process.

Nick and anon, I don't have any problem with models where people don't have a clue as to what is going on (the world is complex), as long as the modeller is equally clueless. Where I have trouble is when the modeller is some sort of omniscient God, who all by themself knows more about the structure of the economy than the collective wisdom of 300,000,000 people (or even 30,000,000 Canadians, who are collectively only an epsilon less smart than us 300,000,000 Americans -- just kidding.)

Seriously, you can't say "the model says consumption rises each year, but the people expect it to fall." At least that makes no sense to me. Or at least you can't say that unless you think you are smarter than the consensus.

Now here's what I think you could do. You could say "I just created this toy model, and I don't have a shred of evidence it is true. But if it is true, people would make bad forecasts, as I assume they run VARs to predict the future, and in my model VARs gives bad predictions." I have no problem with people inventing these sorts of toy models, as long as they don't assume they have policy implications. I'm with Bennett McCallum on this---any model used for policy purposes must assume expectations that are consistent with the model. Otherwise the Lucas Critique will eventually come back and bite you. It's only a matter of time.

Hope I don't sound too dogmatic--I fell as passionate about this as you do about raising rates to stop deflation.

@Sumner: "I don't have any problem with models where people don't have a clue as to what is going on (the world is complex), as long as the modeller is equally clueless."

It's easy to respond to this critique. The modeller could say: "Hey, I'm clueless about how the economy actually works. My agents are also clueless, but this is how they will behave if the economy looks like X".

We do something similar every time we assume that the economy incurs an "unanticipated negative shock". In any stochastic model, agents must have subjective expectations about the probability of negative shocks. But in the actual model, the shock occurs with certainty! Does this make such models unsuitable for policy purposes?

Scott: remember my old post about efficient markets and the Biz Skool student and the econ dept student? The Biz Skool student wanted to open a hot dog stall, and the econ student said "don't be silly, if it were profitable it would already exist"?

Maybe, when it comes to building economic models, the economist is now an entrepreneur, just like the Biz Skool student is with the hot dog stall.

Or, following up on anon's comment, maybe *I* know it's an exogenous shock to monetary policy (because I assumed it is), but the agents in the model don't know whether it's an exogenous shock or a sensible response by the central bank to a fall in the natural rate.

Wow.

It's as if you are taking Hayek seriously.

Reasonable assumptions about "agent" learner?

Check.

Changing interest rates change relative consumption (and inter alia investment) choices at different points in time, and expectations or consumption.

Check.

All agents always have an imperfect and ever changing understanding of the changing time/coordinationstructure of the economy-- no one can have a God's eye view of the economy the way an economic model builder does.

Check.

Great stuff.

anon -- I think the model you describe is unsuitable for policy purposes in a narrow respect: to the extent the policy rec implicitly assumes the modeler can predict the shock any better than the agents in the model.

In the simplified version of the model in this post the modeler can predict future consumption better than the agents, who are instead perpetually surprised. This seems fundamentally different than an exogenous shock where it is certain within the particular model but still surprises both the modeler and the agents ex ante. This is still a potential issue when the learning rules get more complex, like Bayesian convergence. As long as the imposed rule leads to predictable outcomes ex ante to the modeler but not the agents, something seems amiss. Sunspots allow the modeler to shock himself, but this is not so when he knows agents' learning process but agents do not. If you consider that agents' learning mechanisms might change unpredictably (changing outcomes in the process and rendering them no more predictable to the modeler than they are to the agents), then you are okay but the value of the models becomes a question mark.

Nick -- isn't you hot dog stall (I remember your post, I think it was a hamburger stall) defense just a generic dismissal of the Lucas critique? The problem with the economist entrepreneur is that he doesn't get to open his hot dog stand in a dark, unpopulated nook of a frictional world, he has to open one outside Yankee stadium and assume the profits don't get competed away in the near future.

On your second point, if you know by assumption the shock is exogenous, don't you have to concede that whatever you learn from this model is totally contingent on this unsupported assumption? And to the extent that the modeler can actually know whether the shock is really exogenous, the agents should know that too.

Nick, I must apologize. I was moving outside the kind of model you seem to be looking at. I was thinking about the history of the 18th and 19th centuries. There was a bit of a cycle there. Deflation was endemic, since people with money had all the power. The period was punctuated by wars which triggered inflation.

More fundamentally I was thinking about the idea that things that cannot continue forever, don't. Something breaks.

Greg: now you mention it, it does have a rather more Austrian flavour about the story. More emphasis on the *process* by which individual agents' plans and beliefs are or are not made mutually consistent.

You missed one Austrian bit though (funnily enough, it was the only thing I had thought of as being Austrian while writing the post). Since there is no (imaginary omniscient omnipotent) central planner, or even futures market, that could reveal to agents that their current plans for spending 20 years in the future, and their expectations of income 20 years in the future, might be mutually inconsistent, it is a very bad idea to assume that they are consistent. Yet standard NK under rational expectations makes exactly this assumption.

Check.

How do you explain that the growth in the capital stock appears positively correlated (sic) with the real-rate?

Nick, two things.

First this: "All the above analysis gets missed if you assume the economy just jumps to a rational expectations equilibrium path that converges to the long-run equilibrium. And yet that's what nearly all New Keynesians do. Even those who assume the economy is currently stuck in a liquidity trap nearly all assume it gets out of it eventually, and that people in the model know it will get out of it eventually. God only knows why it should. And why people in the model should think it should. Some deus ex machina? Where do they expect the cavalry to come from?"

I don't think that's what Woodford and Eggertson did (can'r really remember). Don't they say that switching to a price level target and setting it high enough is what breaks the trap? There is no assumption that the trap can't last forever if the CB does nothing, there is an assumption that the CB never does nothing, always does the right thing and all agents know this.

Secondly, suppose that the economy is an endowment economy with a constant consumption endowment. All agents know it's a constant conumption endowment, then they don't/can't respond to real rate changes with changes in consumption *in equilibrium*.

In such an economy the CB actually can't control the *equilibrium* real rate, the only way to maintain equilibrium in response to a change in the nominal rate is to have everyone co-ordinate their expectations on higher inflation (either by today's prices falling or expected future prices rising or some combination).

In the constant endowment economy the CB only controls the nominal rate and uses it to control inflation.

The point here is that, to the extent that your previous post was about what happens in equilibrium I still think it's wrong. As I was saying back then, the structure of the labour market in the canonical model implies no unemployment, thus output is always maintained at the full employment level and so the supply side makes the economy look just like an constant endowment economy.

This also means in this post you shouldn't say:

"And here's a paradox: the permanent cut in the real interest rate causes people to plan higher initial consumption and a delining path of consumption thereafter. But it causes higher initial actual consumption and a rising path of actual consumption thereafter."

That's not possible because productive capacity can't support that rising path of consumption and everyone understands this! What happens instead is of course that inflation expectations adjust to bring the real rate back to it's natural level.

The point though is that because people understand all this, in equilibrium they are correct to expect this constant long-run income and consumption and *in equilibrium* it happens, confirming their expectations! There is no logical inconsistency *in equilirium*!

All that said, I do think in *this* post you are correct! But I think you can be a bit more precise, the issue here is how do inflation expectations, especially expected future price levels, co-ordinate on exactly the right value? And what happens if they don't?

As far as I can see, the answer to the qestion: 'what happens if they don't?' is that everything goes to hell in exactly the manner you've described. Furthermore, they way the expectational co-ordination is supposed to be accomplished is by everyone knowing the CB reaction function for off equilibrium outcomes that is supposed to enforce the equilbrium.

But if things blow up out of equilibrium then how do they come by this knowledge? I guess this is where the NK people get the idea that CB communication with the public is really, really important:)

The conclusion then is that I agree that the equilibrium of these models is entirely unstable with respect to any expectational error on the part of agents or the CB and out of equilibrium everything blows up.

Nick, in your answer to Scott you say:

"Well, any NK model assumes the central bank can set the nominal rate, and by responding quickly enough to expected inflation can set the real rate (absent the zero lower bound). So an NK model ought to be able to tell me what happens if they cut the real rate permanently."

But the point here is that the model says the CB can set the real rate in any given period but NOT permanently, the model says quite spcificly that no mattter what they do the CB can not set the real rate below the natural rate forever.

But furthermore, the deeper point is that the ability of the CB to set the real rate in any period entirely derives from their promised good behaviour. They have this ability at all *because* they promise not to do anything stupid like trying to cut it permanently.

I think your thought experiment is inconsistent, not the model.

The Biz Skool student wanted to open a hot dog stall, and the econ student said "don't be silly, if it were profitable it would already exist"?

It’s one of the great might-have-beens of the history of economics. When Fama, Lucas and the others started pushing the whole notion of efficient markets and rational expectations, some journal editor ought to have said: “Guys, if these papers were worth publishing, somebody would already have published them.”

We don't buy the groceries we currently plan to consume 20 years from now in today's futures markets. Keynes said that was the underlying problem. New Keynesians just ignore him, and assume it away.

Yes, that's why we say that the "New" stands for "no effing way" – in other words, NK cannot claim to be descended from Keynes. But who cares, really? Everyone agrees that Keynes was right about some things and wrong about others. We just can't agree about which things. I think of NK as a response to the challenge posed by Lucas & Co., the idea being to show that even with RE, somewhat Keynesian problems can arise as long as prices are less than perfectly flexible.

You have to assume that agents believe the economy will return to full employment and act in such a way as to ensure that outcome. Not because it must be true, but because that's one of the rules of the RE game. This is about the way the economics profession likes to argue. It's not about the way the world works.

And BTW Nick, you shouldn't say your critiquing just NK models here. Your critique would apply about a billion times worse to RBC models.

After all, suppose an RBC economy with flexible prices being the only mechansim to ensure full employment had an off equilibrium outcome where consumption fell today because consumption tomorrow was expected to be low?

The only mechansim to get back to equilibrium is that prices today fall *relative* to tomorrow (so basically the real rate falls because inflation is expected). But if, like your thought experiment, this just causes people to revise down their expectation of the future price level then things blow up in the just the same way.

Let's agree that in both cases we are in a constant endowment economy so in both cases (NK and RBC) this is an off-equilibrium outcome (it's not equilibrium because C < Y). The thought experiment you're doing applies to all models with Euler equations in them, meaning all models with any equilibrium foundation at all.

So how do the agents in an RBC model learn that their long-run consumption is stable under currently falling prices?

Greg: yep. And maybe, if I added investment to the model, it would get even closer. But too hard for me to think about, at the moment.

Jon: suppose most shocks are to investment demand, which shifts the natural rate, and most of the time central banks get it roughly right, and so most of the time the actual real rate follows the natural rate. In other words, fluctuations in the actual real rate due to deviations from the natural rate are smaller than fluctuations in the real rate due to fluctuations in investment demand? I think that would get the result of a positive correlation between investment and the real rate. And it sounds roughly plausible.

Adam: "I don't think that's what Woodford and Eggertson did (can'r really remember). Don't they say that switching to a price level target and setting it high enough is what breaks the trap? There is no assumption that the trap can't last forever if the CB does nothing, there is an assumption that the CB never does nothing, always does the right thing and all agents know this."

IIRC, their models show that if the central bank does the right thing (e.g. promises to hold interest rates too low for too long), the economy breaks out of the liquidity trap sooner than it otherwise would. But it still breaks out of the trap eventually even if they do the wrong thing (stick to standard inflation targeting after it breaks out of the trap).

"Secondly, suppose that the economy is an endowment economy with a constant consumption endowment. All agents know it's a constant conumption endowment, then they don't/can't respond to real rate changes with changes in consumption *in equilibrium*."

Suppose each agent has a constant daily endowment of a perishable consumption good, but they cannot consume it themselves, and must sell it for money. (Haircutting services, with a reverse-L-shaped labour supply curve). And each one has monopoly power over his variety of good. We can (under certain assumptions about preferences, and Dixit-Stiglitz won't do it) get a long-run equilibrium in which Price exceeds MC=0, and in which there is unemployment. (This is my own 1987 model). And with sticky prices an increase in AD will cause Y=C to increase, and unemployment to fall. (Y can only increase so far, till you hit full-employment).

More generally, with the Blanchard-Kiyotaki model, the labour supply curve isn't reverse-L, and so the macro-MC curve slopes up. In long-run equilibrium, (which is now consistent with Dixit-Stiglitz preferences), P exceeds MC. With sticky P, an increase in AD can cause Y to rise, (again up to the point where MC=P).

That's what I had at the back of my mind. And it is the standard NK model.

" As I was saying back then, the structure of the labour market in the canonical model implies no unemployment, thus output is always maintained at the full employment level and so the supply side makes the economy look just like an constant endowment economy."

There's no *un*employment in the canonical model, but the labour supply curve slopes up, so employment can increase above "full employment". It's not reverse-L, and that is what makes it very different from an endowment economy. In a pure endowment economy version, there is zero opportunity cost to selling your endowment. So it's a reverse-L.

" But I think you can be a bit more precise, the issue here is how do inflation expectations, especially expected future price levels, co-ordinate on exactly the right value? And what happens if they don't?"

Yep. But I think there are 2 issues. Repeat what you have just said (which is one issue) with "real growth" replacing "inflation", and "income" replacing "price". That's the second issue, and the one I was exploring here.

Adam: "I think your thought experiment is inconsistent, not the model."

I'm still thinking about this. I chose a permanent cut just because it was simplest. I could have done a temporary cut instead, which we know they can do. But I could also answer you by saying "Yes, *we* (the modellers) know the bank can't do this. But do agents in the model? They might think the natural rate has fallen, so the bank can do this. They just really don't know if the bank can do it or not, since they don't know the natural rate".

Kevin: "It’s one of the great might-have-beens of the history of economics. When Fama, Lucas and the others started pushing the whole notion of efficient markets and rational expectations, some journal editor ought to have said: “Guys, if these papers were worth publishing, somebody would already have published them.”"

LOL!

"You have to assume that agents believe the economy will return to full employment and act in such a way as to ensure that outcome. Not because it must be true, but because that's one of the rules of the RE game. This is about the way the economics profession likes to argue."

It's not so much that we *like* to argue that way. It's that it's conceptually tricky to argue any other way, with RE.

Adam: "And BTW Nick, you shouldn't say your critiquing just NK models here. Your critique would apply about a billion times worse to RBC models."

Agreed. (Except the "billion" maybe). But I can get more of a rise out of NK by saying they are like RBC! RBC would just shrug, if I argued in reverse. My main point (well, it was the main point in my old post), is that NK is nowhere near as close to OK as the NK think it is. The (most) NK don't really understand what they are doing with their own NK models.

Nick,

I think we're converging on agreement here. Let's forget the NK v RBC distinction. This is a bit of a side comment but the posturing that tends to go on in the blogosphere drives me up the wall. RBC has real frictions, standard NK has nominal frictions, well reality has both. Neither has any exclusive claim on anything so let's not act like these are mutually exclusive. And anyway, NK models with capital and involuntary unemployment have real frictions as well.

The point of the last paragraph is that in school I never, not once, learned a model without an Euler equation. What you're getting at applies to any model with an Euler equation and it really is just what Rajiv Sethi would say, you need to study the stability of the equilibrium.

On the other hand, Evans in the video from Thoma says that the NK equilbrium is stable under adaptive learning. It's the deflationary one that's unstable. So aren't the NK ok just focusing on the equilibrium? Doesn't that imply that NK models do in fact make sense?

Isn't it the RBC models that might not make any sense?

Nick and anon, Fine. But you can't draw any policy implications from these models. If we learned one thing in the 1970s, it is that it is dangerous to say that "we will do X because we think it will accomplish Y, even thought it will only succeed in accomplishing Y if the public does not in fact understand that doing X will accomplish Y.

As I've said many times, I don't like the term "rational expectations" as it implies something very different from what ratex models actually assume. They assume consistent expectations, expectations that are consistent with the structure of the model. I can't even imagine doing modeling any other way. Again, it's very possible that the public doesn't know the precise effect of something like removing IOR or another $450 billion in QE. And that learning will occur. But then I don't know the precise effect of either of those things. And I will learn if and when they are done.

Nick, The perfectly competitive model assumes that as demand grows new firms will enter an industry. Someone has to be the new firm, so it's not clear that your friend's intention to open the hot dog firm actually conflicts with perfect competition models that assume zero long run profits. It seems to me that a better analogy (to make your point) is the question of why Wall Street firms bother doing fundamental analysis. The interesting question (to me) is whether that violates the EMH in some way. I don't think so, but then I have a fairly elastic definition of the EMH.

Regarding Adam's point; My hunch is that I objected to the real interest rate pegging assumption for the same reason I objected to the expectations assumptions--it seemed to violate ratex. So I think I agree with Adam.

A couple of things... First inflation is consistently lower than the target of the Fed... second the model forms two steady states... We look to be near the steady state on the verge of deflation... so irregardless of Fed targeting, the inflation rate stays low.

you have to keep in mind a couple of things...
1) there is a limit to lowering interest rates and this creates a warp in the normal expression of the IS curve that becomes positive...
2) according to the Taylor rule, nominal interest rates should be negative 5 now (-5)... so as they stall near zero, they form another steady state...
3) prices and wages are sticky...
4) capacity utilization is stalling out at around 78%, still below a level to initiate investment and inflation...
5) lower inflation raises the real interest rate and subsequently lowers consumption...

If you can raise inflation expectations out into the future, thereby decreasing the real interest rate, consumption will increase to get out of the unintended steady state... and start moving back to the targeted steady state...
Paul Krugman wrote about this in the 90´s...

The deflationary trap was reached in Japan... and continues in spite of persistent expectations over time that inflation will return!

Adam: "The point of the last paragraph is that in school I never, not once, learned a model without an Euler equation. What you're getting at applies to any model with an Euler equation and it really is just what Rajiv Sethi would say, you need to study the stability of the equilibrium."

Good point. Agreed.

Scott: "Nick and anon, Fine. But you can't draw any policy implications from these models."

I'm still thinking this through. Suppose you had a model that said that under policy regime A, you could end up in a nasty equilibrium, if people in the model didn't know you were heading there. Now you could validly argue that if "people" didn't know they were heading there, neither would the policymaker, and so the policymaker couldn't do anything about it. OK. But we would still be interested in the model for telling us that. And one policy conclusion we might draw would be to avoid policy regime A. One conclusion you might draw, for example, is that if targeting a nominal interest rate lead to the risk of this sort of outcome, it would be better for the central bank to adopt, say, NGDP targeting! There's policy actions, and there's the policy regime.

The "learning" in this model could be interpreted as compatible with RE, where the agents didn't know the natural rate of output, the natural rate of interest, etc., and are learning these parameters. To explore that fully might take a more sophisticated model. But it would be an open question to ask whether they would succeed in learning the true parameters.

Edward: yep, but I wanted to set aside expected inflation here, in order to concentrate on the IS curve, which is a relation between real output and the real interest rate.

I was confused by Scott's claimed rational-expectations problem in Nick's characterization of NK arguments, so I think I've worked it out below. The argument, as I understand it, is:

1. A lower real interest rate pulls demand forward from the future to now. That is, it causes people to spend more today and believe they'll have to spend less in the future. The expectation is the part that violates RE, so I'll come back to this.
2. Increased spending today raises income today.
3. Tomorrow, people have more income to play with, so instead of spending less tomorrow as they expect today that they'll have to, they spend more, but still expect to spend less the next day.
4. Income increases again tomorrow, increasing spending the next day again. Goto 3.

But, under RE, the model needs to anticipate the "surprise" that shows up in step 2. So say in step 1 that people expect to be able to spend more in the future, rather than having to spend less. That causes them to spend even more today, and then actually decrease their spending tomorrow.

So a permanent shift to lower real interest rates, under rational expectations, should cause a one-time spike in demand and then demand should go back to normal as people deal with their new higher debt. And, because the demand goes back to normal in future periods, the one-time spike shouldn't be all that big. Is that right?

Jeffrey: No, that's not quite right.

Let's take the simplest possible NK model, where there's no foreigners, government, or firms, so there's only households, who consume current output. And keep it really simple by assuming all households are identical. So there is never any borrowing, lending, or debt. Households might *plan* on consuming more than their income in this period, and borrowing to finance it, and so going into debt, but they never *actually* do that. Because if they consume more than they expect their income to be, they are surprised to find their income comes in higher than they expect. Their income comes from other people's consumption, so if all are identical, each finds his income is always equal to his consumption.

The normal way of solving the model is to assume that their expected (distant) future income is pinned down at "full employment" income. And that their planned (distant) future consumption is also pinned down at the same level. So if today's interest rate falls, this can only affect their planned current consumption. It cannot affect their planned (distant) future consumption, or expected (distant) future income.

Nick writes: "I think that would get the result of a positive correlation between investment and the real rate. And it sounds roughly plausible."

Yes, that is a plausible narrative.

But what would you argue against this: http://mises.org/daily/1596

The claim here is that when the real-rate falls (in the market) that individuals observe that real-rate with respect to their own time-preferences and defer real-saving of first order goods.

So in net, the capital stock declines in real terms even as the pool of higher order goods increases.

The lack of first-order goods drives up the price-level.

Indeed, the inflationary process itself is proof that the growth in first-order goods that emerges as a consequence of having more higher-order goods is necessarily does not compensate the increased propensity to consume.

Ergo, the capital stock on the net declines.

Nick: 2Yep. But I think there are 2 issues. Repeat what you have just said (which is one issue) with "real growth" replacing "inflation", and "income" replacing "price". That's the second issue, and the one I was exploring here."

No, this is the point I've been trying to make since the last time we had this argument. Neither income nor expected income growth can explode with rational agents, there is some upper bound on how output due to physical and technonlogical constraints.

And since agents all know that income can't explode you can eliminate the paths that have real explosions and work back from the distant future to pin down behaviour today. That's just transversality conditions, no real explosion and no income left unspent.

Jon: I skimmed the mises.org post. Here's the difference between their thought experiment and mine: they assume that output does not expand when demand increases; I assume it does. I'm assuming that Price is greater than MC initially, and price is sticky, and that firms are willing to expand sales if demand increases. Suppose I made the opposite assumption. P=MC, and if demand increases, firms ration sales. Then, in my model, consumption and income can't increase, which short-circuits my positive feedback loop on the first day. If I had both consumption and investment, then they can't both increase. It would depend if consumers or investors get to the shops first!

Adam: The transversality condition applies to the plans an individual consumer makes now about the path of his present and future consumption, based on his current expectations of the path of his present and future income. Correct?

In my story, the individual always expects (by assumption) that his future income will be the same as his current income. He expects a flat income path. Based on that, he plans either a flat, or rising, or falling, consumption path (depending on the interest rate) which has the same present value as his expected income path.

So I don't think that violates any transversality condition.

If the actual real rate of interest is set below the natural rate, each individual will plan for a declining consumption path, which starts from a point higher than current income, so that both have the same PV.

So at the end of the first "day", each is surprised to find his income higher than he expected, and equal to his consumption. So he revises his expected income path upward accordingly, but it's still flat. And he revises his planned consumption path upward accordingly, but it still slopes down. Then we repeat.

The problem with standard NK treatments is that they don't conceptually distinguish the planned individual expenditure path from the expected individual income path.

"So at the end of the first "day", each is surprised to find his income higher than he expected, and equal to his consumption. So he revises his expected income path upward accordingly, but it's still flat. And he revises his planned consumption path upward accordingly, but it still slopes down. Then we repeat."

You can't keep repeating indefinitely because at some point the surprises stop, real income can't go higher. Instead we just get inflation. Inflation can explode, real income can't.

But in the ratex equilibrium nobody is "surprised" in the first place. Everyone already knows that real income can't explode so don't expect it to.

Adam: "You can't keep repeating indefinitely because at some point the surprises stop, real income can't go higher."

Yep.

"But in the ratex equilibrium nobody is "surprised" in the first place. Everyone already knows that real income can't explode so don't expect it to."

Nobody in my story expects income to explode (upwards) either. They expect it to stay constant.

(Though if I ran my story in reverse, and asked what happens if the bank *raises* the real rate, I think income would (slowly) implode to zero, given homothetic preferences, even holding expected inflation constant. They keep on getting a downside surprise on income, by the same percentage each time (given homotheticity), and so income asymptotes to zero.)

What I would like to do would be to think about what happens to my thought experiment, in the limit, as we increase the proportion of agents who know the model from zero (my story) towards one. I think it's just the same as my story, except that things happen very quickly. I think what happens *in* the limit is not what happens *at* the limit.

Then you could ask: what happens if the rational agents know the model, but don't know the parameters, like the natural rates of interest and output, and those parameters are stochastic. I think they would behave very much like my stupid agents, who just have static expectations. Not exactly alike, but similar. They would be learning, based on what happens.

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