The very short run

Most macroeconomists make a distinction between the short run (sticky prices) and the long run (flexible prices). I want to talk about the very short run. We mostly ignore the very short run, and I don't think we should. Because the very short run probably isn't really that short.

Old Keynesians used to talk about the very short run. So did Old Monetarists. New Keynesians maybe won't even know what I'm talking about.

When Old Keynesians were talking about the successive rounds of the multiplier process, they were talking about the very short run.

When Old Monetarists were talking about how the monetary hot potato gets passed from person to person, they were talking about the very short run.

You can agree or disagree with the Old Keynesian or Old Monetarist analysis of the very short run, but at least they did have an analysis. They talked about the very short run. New Keynesians don't. Something important in the parental DNAs got left behind and forgotten when the Old Keynesians and Old Monetarists made their New Keynesian baby.

I find Hayek's language the best language to use when talking about the very short run. My plans depend on my expectations, and my expectations include what I expect others to do, and what others will do depends on their plans, which in turn depend on their expectations. Each individual's plans and expectations are assumed to be internally consistent, because each individual is rational and can add and subtract, so nobody plans to do something which he expects to be impossible. But that doesn't mean that all individuals' plans and expectations are mutually consistent in aggregate. Two people may both be planning to get up early and grab the prize first, because each expects the other to get up later than him. They can't both be right.

The very short run is about plans and expectations that are mutually inconsistent in aggregate. When Old Keynesians talk about the successive rounds of the multiplier process, they are talking about plans and expectations that are mutually inconsistent in aggregate. When Old Monetarists talk about the monetary hot potato process, they are talking about plans and expectations that are mutually inconsistent in aggregate. And both were talking about the same thing, even though each emphasised one aspect and ignored the aspect the other emphasised.

Old Keynesians talked about planned purchases and expected sales of newly-produced goods, and ignored the distinction between money and other non-newly-produced goods. Old Monetarists talked about planned expenditures and expected receipts of money, and ignored the distinction between newly-produced and other non-money goods.

The very short run is a disequilibrium process. Not merely a non-market clearing disequilibrium, but a disequilibrium between expectations of others' plans and those plans themselves. Others aren't planning to do what we expect them to do, but we don't know this, so we keep on being surprised, and wish we had planned to do something different.

Let's start in short run equilibrium. There's a consistency between plans and expectations in aggregate. But it's a recession, with excess supply. The representative agent would like to sell more than he expects to sell. But the representative agent is also planning to buy the same amount that he expects to sell to others. So he is sad, but not surprised, when he can't sell as much as he would like to sell.

Now let me tell the Old Keynesian story.

For some reason each individual plans to increase his spending on newly-produced goods by $100 per period. But what he doesn't know is that every individual is planning to do the same thing. The representative agent doesn't know that he is a representative agent. Why should he? So he plans to buy more newly-produced goods but doesn't expect to sell more newly-produced goods. Individuals' plans and expectations are now mutually inconsistent in aggregate. We are now in the very short run. The representative agent is surprised to discover that he is selling $100 more newly-produced goods per period than he expected to sell.

What happens next? The Old Keynesian story normally assumes that the representative agent immediately revises his expected sales of newly-produced goods by $100 per period, and then immediately revises his plans to purchase an additional $60 (or whatever) per period. And so on.

Now if he does revise his expectations immediately, and also revises his plans immediately, and implements those revised plans immediately, then the very short run will last only a very short time. We jump immediately to the new short run equilibrium where plans and expectations are once again mutually consistent. But that isn't very likely. It's much more likely he will think that his $100 unexpectedly increased sales was a temporary fluke, at least in part. Because at the individual agent level, there will be slow days and fast days for sales. It's only when he sees that increased $100 sales persist day after day that he will slowly revise upwards his expected sales.

The Old Keynesian multiplier process is indeed a process, that takes time. It would only happen instantly if every individual knew what every other individual was planning to do, and adjusted his own plans and expectations instantly to make them consistent with other individuals' plans and expectations. Hayek would insist, correctly, that that wouldn't be a very plausible assumption.

Now let me tell the Old Monetarist story.

For some reason each individual finds his stock of money is greater than he wishes to hold, and plans to increase his spending on all goods (not just newly-produced goods) by $100 per period in order to get rid of that excess supply of money. But what he doesn't know is that every individual is planning to do the same thing. The representative agent doesn't know that he is a representative agent. Why should he? So he plans to buy more goods but doesn't expect to sell more goods. Individuals' plans and expectations are now mutually inconsistent in aggregate. We are now in the very short run. The representative agent is surprised to discover that he is selling $100 more goods per period than he expected to sell.

(The perceptive reader will notice that I just copied and pasted everything past the first sentence in that paragraph from the same paragraph in the Old Keynesian story. I just deleted the words "newly-produced".)

What happens next? The representative agent's stock of money is right back where it started. He bought $100 more goods, but also sold $100 more goods. What happens next depends on whether and how quickly he revises his expectations. If he thinks the extra $100 in unexpected sales was just a temporary fluke, the second period is the same as the first. He failed to get rid of any money, and still wants to get rid of it. But eventually, if the higher flow of sales continues period after period, he will revise upwards his expected flow of sales, and will also revise upwards his desired stock of money and his planned flow of purchases.

The Old Monetarist hot potato process is indeed a process, that takes time. It would only happen instantly if every individual knew what every other individual was planning to do, and adjusted his own plans and expectations instantly to make them consistent with other individuals' plans and expectations. Hayek would insist, correctly, that that wouldn't be a very plausible assumption.

(And the perceptive reader will notice that I just copied and pasted that paragraph too, simply changing "Old Keynesian multiplier process" into "Old Monetarist hot potato process".)

The very short run is a process that will be observed in real time. It does not happen in meta-time, coordinated by some non-Walrasian version of the Walrasian auctioneer who ensures individuals' plans and expectations are always mutually consistent in aggregate so that nobody is ever surprised by what other people do and wishes he had done something different.

How long will it take for the very short run process to play out? Dunno. It depends. It depends on whether individuals' sales are smooth from day to day or lumpy and fluctuating. It depends on how well-informed individuals are about what is happening in aggregate. If the initial change in individuals' plans is caused by some policy change, then it matters how the monetary or fiscal authority communicates that policy change. There's a signal-processing problem underlying all this, that Bayesians could probably have fun with. Is it just day-to-day noise, or will my sales stay higher?

Old Keynesians and Old Monetarists had something important to say about the very short run. Their New Keynesian children seem mostly to have forgotten it. They are embarrassed when the old folks mutter about income-expenditure multipliers and monetary hot potatoes. And the two old folks don't seem to realise they are talking about the same thing in different ways. Time to educate the kids, by making them sit down and listen to the old story. But maybe the old story needs updating too.

Comments

[Simon van Norden]

Am I right in thinking that the "very short run" has no place in a rational expectations model with a representative agent? Such agents have no awareness of the co-ordination of expectations.

[Nick Rowe]

Simon: BINGO! Yes.

[Nick Rowe]

My way of saying it is that the representative agent cannot be assumed to know he is the representative agent. And in a representative agent model with RE it is almost automatic to assume that the representative agent knows he is the representative agent. He knows that if he changes his plans and expectations, others must also be changing their plans and expectations at the same time in the same way. If he is planning to buy $100 more goods per period, he automatically knows he will be selling $100 more goods per period.

[JW Mason]

This is an excellent post.

I've been reading a lot of Leijonhufvud lately, and one big point he makes is that what you are calling the very short run process does not necessarily converge -- or rather, where it converges to you get to, depends on the details of the very short run adjustment process. This is because the "income signals" sent by the process can conflict with the price signals that would get you to equilibrium. I.e. if there is a fall in demand for good X, producers of X should lower prices, relative prices of non-X goods rise, and production of non-X goods also eventually rises. But to the extent that expenditure is also responding to income, producers X reduce their purchases, which sends the "wrong" signal to producers of non-X goods -- that they should reduce, not increase, output. This, for Leijonhufvud, is how you can have both high or low unemployment equilibria with the same "fundamentals" and without any price stickiness.

He makes a couple other points that are important here.

First, the role of current income in this process is not just to change expectations of future or "permanent" income, and so desired expenditure; in a world of imperfect credit markets, income also finances expenditure. The unit that sells less than expected may change its beliefs about how much it will sell in the future, albeit not all at once, as you say; but it will *also* have to increase borrowing or run down assets to maintain its current level of expenditure, which may be costly or even impossible.

Second, it is useful to think of a "corridor" of stability, within which the very-short term adjustment process works smoothly (i.e. converges quickly to the "right" short-term equilibrium), outside of which it does not. A small shock to demand doesn't change people's expectations much, and doesn't exhaust many agents financial capacity to buffer expenditure, so the income-expenditure link doesn't really operate, and price adjustments dominate. But a shock that is big enough to destabilize income expectations and/or exhaust many units' financial reserves, then you start getting income adjustments instead and can end up in an inflationary or deflationary spiral. (Or at least a recession or inflationary boom.)

In any case, I think you hit the two key points here. First, that we can't be sure there is a strict Marshallian hierarchy between the market day (i.e. your very short term, I guess), the short term, and the long term -- processes that are shorter logically may not turn out to be shorter in chronological time. And second, that this is critically a story about (initially) inconsistent expectations, so you cannot model it with a representative agent.

[JW Mason]

(When I said "without any price stickiness" that's not quite correct. What I mean is that it's enough that prices don't adjust infinitely faster than expenditure. I suppose for some people less than infinitely quickly adjusting prices are by definition sticky.)

[Mike Sproul]

Nick:

I could have saved you a lot of cutting and pasting. Start with the sentence: "For some reason each individual finds his stock of money is greater than he wishes to hold...". Then add "so the money refluxes to its issuer, and nothing else happens".

[Jeremy Fox]

There are at least loose analogies here to ecology, and perhaps quite close analogies. For instance, consider an animal that moves from one place to another, foraging for food. There are different types and amounts of food in different places. And the animal has perfect information about the distribution of food, and it can act on that information instantly and at no cost so as to maximize its fitness (usually indexed as expected rate of energy intake). In this very simple model, I *think* each animal is like a representative agent, that knows it's a representative agent. If you have a bunch of such animals, you can prove that, in equilibrium, they'll be distributed across patches according to what ecologists call an "ideal free distribution". This just means that the animals are distributed so that everybody has the same fitness and no animal can improve its fitness by changing locations (e.g., because food-rich patches have lots of animals and food-poor patches have few, so that every individual animal ends up with the same food intake rate).

But of course, that simple situation isn't very realistic. Animals don't really have perfect information, it takes time for them to act on the information they do have (e.g., it takes time to move from place to place), etc. The recently-retired Peter Abrams is one prominent ecological theoretician who's modeled more realistic situations. One key finding is that more realistic situations often have very different, and non-equilibrium, dynamics. For instance, you can end up with situations where all the animals pile into one patch, only to discover that everybody else did the same thing and so now they're all starving, so they all leave, etc. Which I *think* is at least a bit like Nick's individually-rational but mutually-inconsistent plans. For one example of Abrams' work, see Abrams 2007 American Naturalist: http://www.jstor.org/stable/10.1086/512688.

[Jeremy Fox]

And I see that just now, Paul Krugman has a post up linking to an old speech of his in which he compares the practice of economics and evolutionary biolog: http://web.mit.edu/krugman/www/evolute.html.

It's a very nice speech, Krugman certainly knows evolutionary biology much better than the average outsider. (I'm intrigued to learn that he accidentally hit on the "replicator equation" in his own work!) Although if he looked at the leading edge of evolutionary biology today I think he'd find that it looks somewhat less like neoclassical economics than it used to, and is more concerned with persistent nonequilibrium dynamics. Not that I'd criticize Krugman at all for not being aware of that. Krugman knows the field of evolutionary biology about as well as an outsider can, I think, but there's a limit to what even a very smart outsider can learn by reading, or reading about, the most famous people in a field (here, Gould, Dawkins, Hamilton, Maynard Smith, etc.) I often wonder about the extent to which my outsider's view of macroeconomics is distorted by reading only blogs by people like Krugman, Thoma, deLong--and Nick!

And on a totally irrelevant note, the bit where he disses Stephen Jay Gould is spot on. I haven't encountered many other prominent people from outside evolutionary biology who saw Gould's serious limitations so clearly...

Apologies for thread hijacking, this started out as a relevant comment and then drifted off as I started chatting about how interesting I found that old speech of Krugman's to be... ;-)

[Josh]

Nick,

Coordination failures are not inconsistent with RatEx. However, the characteristics that matter for coordination failures are often lacking in mainstream models.

[JW Mason]

Coordination failures are not inconsistent with RatEx.

The kind of coordination failures you can describe using rational expectations are very narrow, and in particular exclude the *dynamic* adjustment Nick is describing here.

[wh10]

Nick, in the past, you have referred to the very short run as macroeconomically uninteresting. How does that reconcile with this post?

[JCE]

what i don't get is why these processes are though of as occurring only in the very short run. it would seem to me that this ort of coordination on a large scale would take quite a while

[Min]

"The representative agent doesn't know that he is a representative agent. Why should he?"

Because he is not stupid? I mean, her social environment is full of people just like her, economically. You'd think she would notice. ;)

[JW Mason]

it would seem to me that this ort of coordination on a large scale would take quite a while

Yes, that is Nick's point. That's why he says "the very short run probably isn't really that short" right at the start of the post.

Again, this is Leijonhufvud's central argument in "Keynes and the Keynesians" and elsewhere. If you don't have an auctioneer, you will get out of equilibrium trades, which means you may not ever reach equilibrium even if prices are flexible and people respond to price signals correctly. This is why we need models of the economy that link current income to current expenditure, rather than of intertemporal optimization.

[Min]

"Let's start in short run equilibrium. There's a consistency between plans and expectations in aggregate. But it's a recession, with excess supply. . . .

"Now let me tell the Old Monetarist story.

"For some reason each individual finds his stock of money is greater than he wishes to hold"

Tilt! If there is an excess supply of everything except money, how can everyone find herself with excess money?

[Nick Rowe]

JW: Thanks! Yep, this stuff is Leijonhufvudian.

I can't make my mind up about the stability/convergence stuff. My guess is that it depends massively on monetary policy, especially how monetary policy is communicated. (One can think of monetary policies which would make it very unlikely the process would ever converge). Thinking about this sort of coordination problem reinforces my view that the "concrete steps" way of thinking about monetary policy is very misguided. If the central bank *tells* people that it wants the economy to coordinate on (say) a level of NGDP 5% higher than it is now, and it will adjust the instruments contingent on NGDP, then the agents in my story won't be hunting around in the dark trying to figure out what everyone else is planning and expecting.

I basically agree with most of what you say, except perhaps this bit: "And second, that this is critically a story about (initially) inconsistent expectations, so you cannot model it with a representative agent."

I'm not 100% sure about that. My stories above are actually told from the P.O.V. of a representative agent. But the key is: he doesn't know that he is the representative agent. E.g. suppose there are aggregate shocks to demand and individual-specific shocks to demand. The representative agent doesn't know if his experience of increased sales is representative.

Mike: funny you say that. I was thinking that you would say that, and slowly constructing a new post in response. There are a thousand places I could spend an excess supply of money; the bank is only 1 out of that 1,000. Maybe one of the other 999 would give me a better deal than the bank? Maybe the bank deliberately gives me a worse deal, to deliberately create a hot potato?

Jeremy: "Which I *think* is at least a bit like Nick's individually-rational but mutually-inconsistent plans."

I think it is too. But yours is more like the negative feedback world of microeconomics with scarce resources. There's a positive feedback process going on in my two stories. If all the deer stick together, it's harder for a wolf to catch any one individual deer. The more they eat the more they cr*p, and the more grass there is to eat,....something like that. But yes, very much the same basic idea.

"I often wonder about the extent to which my outsider's view of macroeconomics is distorted by reading only blogs by people like Krugman, Thoma, deLong--and Nick!"

It will be a bit distorted. More lefty, and more Keynesian than the mean (I am possibly more Keynesian than the mean). But not massively so.

Josh and JW: my initial response is to agree with Josh. Then I though maybe JW was right. Then I thought about very complicated Nash games, that in principle can model almost anything, even if it would be very hard. Dunno.

wh10: well, I think you are referring to my past post where I defined the "very short run" **in that context** as 6 weeks. Because the Bank of Canada only adjusts the overnight rate target every 6 weeks (though it can move more quickly if it needs to, and when people expect it to move in future because new information arrives the expectation of a future move has the same effect as an actual move). The whole short run/long run distinction is always context-specific.

JCE: "what i don't get is why these processes are though of as occurring only in the very short run. it would seem to me that this ort of coordination on a large scale would take quite a while"

Maybe "the very short run" means "quite a while". ;-)

Min: "Because he is not stupid? I mean, her social environment is full of people just like her, economically. You'd think she would notice. ;)"

You are teasing, I hope!

"If there is an excess supply of everything except money, how can everyone find herself with excess money?"

There *was* an excess supply of everything except money. Then something changed. Now there is an excess supply of money *conditional on excepted sales of goods*.

[Ritwik]

Nick

There might be a couple of valid reasons why models of the very short run have fallen out of favour.

First, there is presumably no correlation between the a priori definition (period in which prices are sticky) and the length of time for which the multiplier process is supposed to continue. It is central to the argument, but it has been assumed, rather than rigorously shown.

Second, there is an alternative, and perhaps more satisfying, definition of the short run and long run - change in stocks, esp. capital stocks. Capital stock changes may be more instantaneous than price revisions, indeed, they probably accompany the process of multiplier/ hot potato. Yet, the process of multiplier/potato has very little to say about them, or to include them in its description. The analysis freezes the capital stock, but the process does violence o this assumption. To my understanding, Jim Tobin was only one of the Neo-clasicals who tried to grapple with these issues head on.

Process type analysis is necessarily quasi-linear and systems-theoretic. Comparative statics and Walrasian simultaniety leave very little room for such analysis. The Old Keynesians and the Old monetarists understood the relevance of the short run, but were expressing themselves through an analytical framework that was ill-suited to describe processes. So they resorted to hand-waving and verbose text, and were called out on that.

In the spirit of invoking the relevance of Leijonhufvud to all this I again recommend this paper :

http://www.econ.ucla.edu/workingpapers/wp186.pdf

Beginning pg 16, he tries to re-construct the Keynesian/ Monetarist process that IS/LM was trying to capture through a series of quasi-linear changes, which repeat cumulatively.

As an aside, your 'representative agent does not know that he is representative' is basically the same intuition as Lucas '72, right? I can't imagine why he would think that there could be different types of agents unless he had seen in the past that there were indeed different types of agents. In other words, adaptive expectations and heterogeneous actors were critical to the Lucas '72 story and are incompatible with Rat-ex/ representative agent, which is perhaps one reason why the New Classical band-wagon moved on so quickly from that model.

[Jeremy Fox]

Nick: "But yours is more like the negative feedback world of microeconomics with scarce resources. There's a positive feedback process going on in my two stories."

True, but it doesn't have to be that way. For instance, I believe some of Abrams' work considers patch selection under predation risk as well as competition, where predation is modeled in such a way that you can get positive feedback loops from safety-in-numbers-type effects. Good to know that I'm not too far off base in my comment.

Yes, I know the macroeconomists I read are mostly lefties, or at least 'small-c' technocratic conservatives. I'll follow up on that with you via email, don't want to derail the thread any more.

[K]

Nick,

"The representative agent doesn't know that he is a representative agent. Why should he?"

If there are people with different expectations, then barring complete markets, you wont get an equilibrium (or a dynamic) that's the same as you would get with some single representative agent. What do you mean by "representative agent?" Do you mean a single representative of all agents, and if so, how is that meaningful? There is *no* model with a single representative agent that will give the real dynamics.

There are people who do models with multiple agents with different priors, information, preferences, etc. Those are multiple agent models. I think you are really confusing things by describing such a model as a single "representative agent with MPD disorder" model.

The way I see it, each group of similar agents can be replaced by a representative with some resource endowments. What is important is the process of each of those agents discovering:

1) the "parameters" of the exogenous dynamics and
2) the beliefs/expectations of the other representatives.

Then there is the issue of whether the updating of the beliefs of each representative is rational or not.

"It's only when he sees that increased $100 sales persist day after day that he will slowly revise upwards his expected sales."

If he is rational, then his expectation is supposed to be a Martingale. If his "expectation" is trending upwards in a statistically significant way, then it's not a probability weighted sum of tomorrows possible expectations. That's possible, but it is not consistent with the standard neo-classical view of rationality. So this part of your story, at the root, is not about old vs new Keynesianism/Monetarism. It's about adaptive vs rational expectations, or about expectations *conditioned* on different information sets. Rational expectations may be martingales conditioned on the observer's information set, but not on a fuller or complete information set.

[Ritwik]

K

Exactly! Leijonhufvud also makes the point that adaptive expectations and process change type expectations depend fundamentally on heterogeneous agents acting on different information sets. It's not just about tastes.

[Nick Rowe]

Suppose there were 4 types of shock, in a 2x2 matrix: individual-specific vs aggregate; temporary vs permanent. Assume rational expectations, and that people know the distribution of shocks across the 4 types. Now suppose an aggregate permanent shock hits. How long would it take individuals to figure out that it was an aggregate permanent shock?

Yes, in one sense this is like Lucas '72 signal processing. But that misses the temporary/permanent distinction (which, IIRC, Brunner and Meltzer talked about??). But you can accept that Lucas was onto something with the idea that distinguishing signal from noise is important for macro, without necessarily buying the rest of his model as is.

[Mike Sproul]

Nick:

New gold, freshly dug out of the ground, will not reflux to the ground. It is an asset to the gold miner, but it creates no liability. The gold will do what you call the hot potato and gold will lose value. (But I don't like that hot potato idea. It's much better to just say the supply curve of gold shifts to the right and that's why its value falls.)

New money, either in the form of paper or computer blips, shows up on the liability side of its issuer's balance sheet, and is matched by the issuer's new liabilities. That new money clearly can reflux to its issuer. You at least have to recognize the difference between new gold and new paper money when you tell your hot potato stories.

Sure, there are thousands of things the new money can be spent on, but you have to assume crazy things for that to happen. Are we supposed to think that some consumer, with no desire for more cash, goes down to the bank anyway and borrows $100 of cash and then spends it on goods? If he didn't want that cash and it got lent to him anyway, why wouldn't he just return it to the bank? or not borrow it in the first place?

[Nick Rowe]

Mike: "Are we supposed to think that some consumer, with no desire for more cash, goes down to the bank anyway and borrows $100 of cash and then spends it on goods?"

YES! That's nearly always why we borrow cash from the bank. Not to keep it under the mattress, but to spend it.

[W. Peden]

Mike Sproul,

"If he didn't want that cash and it got lent to him anyway, why wouldn't he just return it to the bank?"

?!

[Nick Rowe]

W Peden (and Mike): if we were talking about renting any other good apart from the medium of exchange, it would make perfect sense.

"Why would I rent a fridge/car/house/whatever, if i didn't plan on using it? And if I did accidentally rent a fridge, and found I didn't want it, I would return it to the rental company."

[rsj]

"Why would I rent a fridge/car/house/whatever, if i didn't plan on using it? And if I did accidentally rent a fridge, and found I didn't want it, I would return it to the rental company."

Why, yes.

[Determinant]

Great post Nick, it gets to exactly what I have been arguing about second-degree differential equations and transitory responses, though in different words.

Put simply, we live in an economy with savings and investment, which form a mutual storage/reactive pair relative to consumption. A complete description of this system, in principle, must be at least a second-order differential equation, it must have counterparts to acceleration, velocity and position in physics.

When we talk about second-order differential, we know the response equation has two parts, the transitory and the forced. Think y(t) = y[trans](t)+y[forced](t). At different times, the forced response or the transitory response will matter more.

To my mind, economics has developed the unproductive habit of neglecting either the transitory or the forced response in order to have simple, linear models. Savings and investment through time make it impossible to generate a self-consistent model of this behaviour with a simple linear equation. It's just plain more complex than that, though there are methods to minimize this and make that complexity easy to deal with.

Economics has this endless circular argument "it's short (transitory)" "No, it's long (forced)". It never ends. They're both incomplete.

You've realized this Nick through the problems it generates with your models.

[Min]

Moi: "If there is an excess supply of everything except money, how can everyone find herself with excess money?"

Nick: "There *was* an excess supply of everything except money. Then something changed. Now there is an excess supply of money *conditional on excepted sales of goods*."

This is a kind of recurrent problem I have with some of your posts. You state that something causes certain sweeping changes to the economy. Fine, I suppose, as an intellectual exercise, but how relevant are its conclusions to the real world? Furthermore, I have trouble thinking that such strong shocks would have such focused effects.

I am not saying that everything has to be realistic. After all, studying unrealistic but possible economies has value. But I would like more coherent stories. :)

[Mike Sproul]

Nick and W. Peden:

Apparently I didn't phrase that bank loan/reflux story very well. Seems I caused nothing but confusion. I'll try again.

Compare newly-mined gold to newly-minted gold coins. We all seem OK with the idea that newly-mined gold can't reflux to the ground, so when new gold is mined, gold loses value.

But it's different for coins. If people want more coins, they bring gold to the mint and have it stamped into coins. If they have too many coins, they melt the coins and the coins 'reflux' back to bullion. Newly-minted coins do not do the hot potato. If, for some crazy reason, a mint takes it upon itself to make a 'forced issue' of more coins even though people already have all the coins they want, then those coins will be melted as fast as they are minted. The minting will not change the value of gold relative to other goods, nor will it change the value of coins relative to other goods. It makes no sense to say that those coins could have been spent on thousands of things, rather than being melted.

Now make one change: The mint, rather than issuing a 1 oz. coin every time someone brings in 1 oz of gold, starts issuing paper certificates for 1 oz every time someone brings in stuff worth 1 oz. of gold. My key point, which I hope is clearer this time, is that the law of reflux works exactly the same for paper as it does for coins, and that paper money does not do the hot potato any more than coins do.

[rsj]

I agree with Mike Sproul. Wow.

[Arin D]

One way of marrying the "short short run" with "something more long term than short short run" is to postulate the dynamic adjustment itself as an equilibrating condition. That can allow for not just exactly determined systems (such as K supply conditions and K demand conditions) but also for over-determined systems, which turns out to be fairly interesting in thinking about Keynesian systems, taking into account disequilibrium adjustments across multiple markets. To this day, I think the best formal treatment of this is by Steve Marglin in an unpublished manuscript ... http://www.economics.harvard.edu/pub/hier/2000/HIER1907.pdf

[JoeMac]

Nick,

I guess this is a silly question, but why would any individual ever accept money if he did not want it? The mere fact that he accepted the cash as wages from his employer or from a sale to customers, by definition means he has as much money as he wants. It seems to me that it is impossible for an individual to NOT have his money balances be satiated.... the mere fact that an individual accepts the cash means he always has as much money as he wants. If people accept cash in the first place, then there can be no hot potato effect.

I just realized that this means we are always in a permanent liquidity trap with infinite money demand.....

[Christiaan Hofman]

It seems to me that the very short run is also where a crisis happens. That is, the Minsky moment is a pure very short run issue. No wonder economists were unprepared for 2008.

[Nick Rowe]

Determinant: Thanks! I think I follow that, more or less. But you need to remember though: in one respect you are getting a very warped perspective on economics from the blogosphere, and especially from me. Blogs don't use math much, because most readers don't understand it. And I'm very bad at math, for an economist. There is a lot of economics that is expressed in those there differential equations, of who-knows-what order. But you have picked about the worst possible economist to discuss it with.

I have to use the old trick of math-challenged economists: I divide time up into "runs", so I can talk about things one process at a time, letting one process end before I let another one begin. Even though I know they will all be happening at once. This is my cross-eyed bear. But I get by.

JoeMac: "I guess this is a silly question, but why would any individual ever accept money if he did not want it?"

That's the "silly" question that gets right to the root of it. So I'm going to take it first.

In Auutralia once, I was trying to sell my car. A guy offered me opals in exchange for it. I have absolutely no use for opals. I do not want any opals. So I refused his offer. Now, you might say: "Hang on Nick, if he had offered you a large enough quantity of high enough quality opals, wouldn't it have been rational to have accepted his offer? You could have sold the opals, even if you didn't want any opals yourself, provided someone else out there did want opals?". And if I had in fact been sure that his opals were as valuable as he said they were, and that I could in fact easily have sold them for the price he said they were worth, I would have accepted his offer, and then sold the opals to someone else. But I thought "If these opals really are as valuable and easily sold as he says they are, why doesn't *he* sell them, and then pay me dollars for the car?"

Money, if we are talking about a "pure" money rather than a commodity money like cows, which also have a non-monetary use, is exactly like those opals were to me, only it's like that for everyone. Nobody ever wants it. We only ever accept it because we think we can get rid of it by passing it on to someone else. It's just there is always a delay before we find the right opportunity to pass it on to someone else. And it's a lot easier for nearly all people to figure out what they can get by passing a bunch of dollars on to someone else than by passing a bunch of opals on to someone else. I would have had to sell the opals to a specialist opal dealer, probably. Everyone is a dollar dealer. So it's much easier to pass dollars on to someone else than to pass opals on to someone else. Even though some people actually want opals and nobody wants dollars.

In one sense there is no (stock) demand for (a pure) money. In another sense there is a (stock) demand for money, because it is costly for us to pass it on immediately to someone else (infinite velocity). The demand for a dealer's inventory is not like other demands.

The demand for money is not like the demand for other goods. I can get rid of money anywhere, equally easily, not just at the bank. But in aggregate we can only get rid of money at the bank, on the terms the bank offers, and we can often get better terms by passing it onto someone else. And a monetary hot potato is precisely when the bank offers us worse terms than everyone else.

I should do a post on this particular topic, so lets not discuss it further here, but wait for that post.

[Nick Rowe]

Arin: I have skimmed the Steve Marglin paper. I'm afraid I do not like it. The whole paper could have been made much simpler and explained much more clearly. But if he had done that, the results would not be very interesting.

He simply assumes that the central bank can set the real rate of interest, and that it sets it too high. So of course the system is "over-determined" for real variables, and "under-determined" in nominal variables. In simple language, there's high unemployment, and prices and wages and money supply fall without limit. He doesn't need all that math for that.

And that paper is all short run. There's no very short run analysis (in the sense I'm talking about here).

[Nick Rowe]

Christiaan: "It seems to me that the very short run is also where a crisis happens."

I think I might agree with that, setting aside the question of Minsky and predictability. If there is no guidance from the central bank about what equilibrium to coordinate on, it might not be surprising if the very short run process (like I have discussed above, only in reverse, because people plan to spend less rather than more) does not converge to anything nice.

[W. Peden]

Mike Sproul,

"If they have too many coins, they melt the coins and the coins 'reflux' back to bullion."

This is a restatement of the offending sentence: if I have more coins than I want to keep, it's probably because I want to spend them e.g. if I get a student loan, I don't keep that in a bank account, but spend it on my education.

I know that Nick Rowe wants to suspend this discussion until his next post, but I do want to make it clear that your rephrasing doesn't remove what monetarists consider untenable in your argument.

[vimothy]

I agree with Mike Sproul. Wow.

Even though Mike Sproul's ideas are generally distinct from Chartalism (e.g., role of taxes, etc), there's some obvious overlap, so I'm surprised that you're surprised.

[Ritwik]

Nick

Say you increase your purchases rather than refluxing back the 'excess' money that you have come into. Why would you want to model it as a 'medium of exchange' effect rather than as a wealth effect?

(There's the added question of how you came into that unexpected money in the first place, but let's leave that be)

In your Australia car example, the car and the opals both existed anyway. Nothing new was to be produced. You are both less happy than you would have been otherwise, but this is not a recession.

[Rajiv Sethi]

Nick, this is a very nice post. But I would add that we are always in the very short run. Financial crises and major asset revaluations are responses to the discovery that plans have been mutually inconsistent to a high degree for a long while. They cannot be understood (in my opinion) as equilibrium phenomena, or simply as responses to exogenous shocks. Nobody has yet found an exogenous shock large enough to account for the 1987 crash for instance. Mason's point above, that one can't take convergence for granted, especially global convergence, is spot on.

One would have expected the learning literature to address this but most learning models themselves adopt a representative agent framework so we have a decision-theoretic approach to learning and all the interactions that can cause instability are assumed away. No surprise then that most learning models satisfy convergence to RE. I think these are all really interesting questions, and have tried to discuss them from time to time on my blog. It's nice to see you address them here. I always enjoy your posts.

[Mike Sproul]

W. Peden:

I say that unwanted money will reflux to its issuer (and not do the hot potato), and Nick says it will be spent on goods (and do the hot potato). At first, it seems like there's no way to say for sure which of these two things will happen, and so Nick and I, as usual, reach a stalemate and my coin story looks to you like a "restatement of the offending sentence".

I don't think so. Full-bodied coins cannot do the hot potato, because if they did, excessive minting of coins would cause a 1 oz gold coin to lose value, so that the 1 oz coin will buy the same groceries as 0.99 oz. of gold bullion. Every coin holder faces the choice of spending his coin on .99 oz worth of groceries, or melting the coin to get 1 full oz of bullion, which will buy 1 oz of groceries. Everyone will choose to melt (not spend) until the value of the 1 oz coin returns to 1 oz.

I don't see how anyone could argue against the above paragraph, but you guys would probably say that even if it's true of coins, it's not true of modern paper money. But if you think of the example of a mint, the validity of the Reflux view becomes clearer. Suppose that the mint, rather than stamping 1 oz. of gold into coins, takes the 1 oz. of gold from the customer and puts the 1 oz. in its vault, while giving the customer a 1 oz. paper receipt. Does anything important change? No, it doesn't. If people want more paper money they will bring more gold to the mint. If they have too much paper money then the paper will reflux to the mint as people take out their gold. Reflux works the same as it did for coins.

One last step: The mint starts issuing paper money to anyone who brings miscellaneous stuff worth 1 oz to the mint. The mint keeps the stuff in its vault, just like it did with the gold. There's still no important difference. If people want more paper money they will bring more stuff to the mint. If they have too much paper money they will return their paper money to the mint and get their stuff back. Reflux still works exactly the same.

[rsj]

W. Peden,

if I have more coins than I want to keep, it's probably because I want to spend them e.g. if I get a student loan, I don't keep that in a bank account, but spend it on my education.

That is not true at all. Our target deposit ratio is continuously changing, requiring adjustments. Same for our target debt ratio.

Tomorrow, due to a change of preferences or expectations or whatever, we can all decide we have too many deposits, and as a result we can all decrease how many deposits we hold by selling deposits back to the bank and buying bank bonds in their place.

It is this freedom that allows us to say that we are always able to maintain the quantity of deposits that we want, which is a separate statement from saying that we never get into a situation in which we want to adjust that quantity. We just don't adjust that property by madly going on a shopping spree for goods, we push the deposits back onto the banking system and replace them with bonds. Only when our total wealth is more than what we want do we go on the shopping spree and reduce it in real terms.

Again, loans and deposits do not move one for one with deposits because bank loans are backed by more than just deposits, they can be backed by bank bonds and bank equity. There is no iron relationship that forces a bank to make an adjustment on its asset side when the composition of its liabilities changes. Therefore how many deposits households hold has nothing to do with how much they want to borrow.

It could well be the case that they decide they want to borrow less but keep their deposits unchanged. No intervention by the CB is necessary to effect this change.

Similarly, if the CB were to attempt to create more deposits than households want, it would fail. It would find that for every dollar of deposits created, that dollar would be refluxed back onto the banks, so that the in effect the CB is conducting asset swaps with the banking system.

That has repercussions for interest rates (they go down up until the zero bound) and premia charged to borrowers (they go up) but the quantity of deposits held by the non-financial sector remains whatever quantity is demanded.

[rsj]

Vimothy,

Yes, I was focusing too much on differences rather than commonalities.

[Ritwik]

Rajiv

But if we're always in the very short run and disequilbrium, then what is the use of focusing on the equilibrium states between the start and the end of the processes that Nick describes? Nick laments that the new guys don't even understand the process, but I'd argue that the old guys were not that clever in describing it anyway. The 'disequilibrium' part of the process was assumed, pushed to the background and described inn words, and the equilibrium states at the beginning and end were modelled and formally expounded upon.

And no one seemed to quite know the answers of - what happens when the prices finally change? What happens when the capital stock changes?

Agree with you about non-convergence, though note that it is not Nick's point. He is comfortable enough with a representative agent and ratex, his signal processing issues are aggregate vs individual and temporary vs permanent. His representative agent is just terribly bad at parsing the monetary authority's signals and that's how the authority has power, and once it has this power it can make the agent do whatever it wishes.

Nick's mental model is somewhere half-way between IS/LM and Lucas gen I, the model that Friedman perhaps had but never wrote.

[Nick Rowe]

Rajiv: Thanks! (And it's especially nice to hear that from someone whose judgement on this sort of area I really respect.)

"One would have expected the learning literature to address this but most learning models themselves adopt a representative agent framework so we have a decision-theoretic approach to learning and all the interactions that can cause instability are assumed away."

After I had posted this I really wondered about whether the learning literature maybe did address it. And I'm just not up to date enough on the learning literature to really know. (Hmmm, am I at all up to date with any literature, nowadays??) So it was good to see you answer that question.

Guys: OK, I won't try to discourage you from arguing about the Law of Reflux, since you are clearly so keen to discuss it. I'm nearly finished my post on money opals and cars (at least, I think I am).

BTW, as I say in my new post, Mike Sproul makes an excellent foil for this question, just because he believes the Law of Reflux in such a clear and hardline way. (I'm staking out an equally hardline position on the other extreme). But nearly all economists believe some sort of soft form of the Law of Reflux. So it's not really surprising, as vimothy notes, that rsj (or, for that matter, anyone who leans towards "money is endogenous/demand-determined") would agree with Mike on this question (and totally disagree with everything else). MMT+perfectly flexible prices=Mike is only slightly over-simplified!

[Nick Rowe]

Ritwik: "Say you increase your purchases rather than refluxing back the 'excess' money that you have come into. Why would you want to model it as a 'medium of exchange' effect rather than as a wealth effect?"

1. Because "inside money" (strictly speaking, money produced by a competitive zero-profit banking system) is not net wealth, and:

2. Because even though "outside money" (central bank money, or strictly speaking money produced by someone earning monopoly profits by issuing money) is net wealth, the wealth effect is almost always (unless we are talking about massive increases in the money growth rate) is too small to matter much. For example, the Bank of Canada normally (before the recession) earned about $2 billion per year.

[Ritwik]

Nick

If inside money is not net wealth, then your unexpected increase in money has to be either :

1) necessarily outside, or
2) necessarily matched by an unexpected decrease somewhere, or
3) the result of a decision by some economic actor in the economy to change the pattern of his wealth holding from money to non-money. A reduction is money demand.

In 2, the mechanism you'd want to argue for is marginal propensities and heterogeneity, not hot potato.
In 3, the 'mechanism' is not needed because the economic decision preceeds and causes the phenomenon of extra money. This decision is better modelled as a wealth portfolio choice.
In 1, we're back to the question of how much control a monetary authority has, and through what 'mechanisms'. For one, I'd argue that realised seigniorage profits have very little to do with net wealth. However, even if you were to argue that, this is only an argument against the 'helicopter' view of money and for the 'control the real interest rate' view.

Where does one need the hot potato in all of this? What does the hot potato explain that portfolio choice doesn't?

[Nick Rowe]

Ritwik: If inside money is not net wealth, then your unexpected increase in money has to be either : 1 [] 2 [] 3[] "

Why? You lost me there.

[Ritwik]

Nick

Why not? What is the 'source' of your unexpected increase in money?

[K]

Nick,

I totally agree that learning is a critical missing bit in ratex. And there is in fact a significant and growing literature on Bayesian updating of (perfectly rational) subjective expectations (I recently linked here to Weitzman's paper on subjective expectations and the premium puzzles, which points to profound philosophical problems with even simple models with ratex). Priors matter, except in absurdly trivial models, so agents are necessarily heterogeneous.

But I'm confused by your description of your representative agent. Rather than "a" representative agent, why do you not just say that there are multiple agents with different priors, different information, etc? This is not a representative agent economy.

[123]

Nick: "the wealth effect is almost always (unless we are talking about massive increases in the money growth rate) is too small to matter much. For example, the Bank of Canada normally (before the recession) earned about $2 billion per year."

I disagree. The rate to discount these profits is very low, both because the cost of capital is very low, and as profit increases during depressions, you have negative risk premium. Your views on the irredeamability of central bank money, and views on the wealth effect contradict each other.

[W. Peden]

rsj,

What if there are alternatives to bank deposits other than bank bonds, like student loans?

"we are always able to maintain the quantity of deposits that we want"

That's the heart of the matter, perhaps: as far as I can tell, you and Mike Sproul (and Nicholas Kaldor) are saying that money is always in equilibrium, whereas monetarists and Keynes saw monetary disequilibrium and equilibriating processes as the core topic of macroeconomics.

[Nick Rowe]

Ritwik: Suppose there's an increased demand for bank loans. Or an increased supply of bank loans. I give the bank my IOU, and the bank gives me its IOU. No net wealth is created. But the bank's IOU is money, so money is created.

K: But I'm confused by your description of your representative agent. Rather than "a" representative agent, why do you not just say that there are multiple agents with different priors, different information, etc? This is not a representative agent economy."

Even if there are lots of different agents, with different priors, and different information, it may (or may not) be possible to talk about what is happening in aggregate in terms of some fictional representative agent who is like the average, but who doesn't realise that he is the average. If it is possible to do this, it would only be possible under special assumptions (e.g. everything is linear). If it is possible to do this, it would be nice to do it that way. Easier for our intuition. My guess is that it is possible.

123: I'm not sure. Currency/GDP ratio in Canada is about 5%. Suppose the BoC did a one-shot helicopter doubling of the money supply. At existing prices and incomes, that would be an increase in wealth equal to 5% of one year's GDP. Total wealth is (say) 20 times annual GDP?? A 100% increase in the money supply, but only a 0.25% increase in wealth?

BTW, if I'm wrong on this, then the old Pigou effect, which everyone says theoretically exists but is too small in practice to bother about, is very important.

W Peden: "as far as I can tell, you and Mike Sproul (and Nicholas Kaldor) are saying that money is always in equilibrium, whereas monetarists and Keynes saw monetary disequilibrium and equilibriating processes as the core topic of macroeconomics."

My guess is that's roughly right. Weird bedfellows! I wonder where the Austrians belong? My guess is in with me and monetary disequilibrium theorists across the old monetarist/keynesian spectrum. I don't think it's an accident that I had to use Hayek's language to talk about this properly. I find it impossible not to talk like Hayek when I'm talking about this topic.

Where's Greg Ransom when you need him, and when I'm saying something very nice about Hayek??

[Ritwik]

Nick

The bank's IOU has a smaller haircut than my IOU, which is why it circulates as money. Presumably, there's some economic reason convenient to do this type of transaction. Net wealth has been created. The bank is just monetizing this wealth.

[123]

Nick, I roughly estimate the pre-crisis market value of BoC's equity at approx. 15% of GDP ( 5% currency that will never be redeemed, 5% option value due to additional balance sheet expansion during depressions, 5% is the NPV of the future seigniorage from base money that will be regularly issued in the future). In December 2008 probability of depression was much higher than in 2007, so the option value could have easilly tripled. This 10% GDP boost of the BoC's equity value looks quantitatively important in the context of TSX index losses that were roughly 50% of GDP from stockmarket top to bottom. And the process is non-linear - further losses in TSX generate progressively larger increases in BoC's equity value. So Pigou effect stabilizes the expected AD.

In a pure gold coin standard where coins are widely distributed every person has the opportunity to exploit the Pigou effect. With central banks, it is the responsibility of the central banks to share the gains in central bank's equity value. Basically bernanke has underestimated the Pigou effect in late 2008, he could have helped much more.

[W. Peden]

Nick Rowe,

It gets weirder: Keynes's version of the liquidity trap doesn't make any sense in contemporary Post-Keynesian theory and I doubt it makes much sense in most New Keynesian models either, because Keynes regards broad money as exogenous and causally significant, while Post-Keynesianism regards broad money as always (?) endogenously determined and a lot of New Keynesian models seem almost designed to neutralise money from having any importance whatsoever. I seem to remember that Kaldor felt the need to correct Keynes on this point in "The Scourge of Monetarism" (a title that Kaldor obviously awarded to himself, not Keynes).

[Edmund]

Nick,

Are you familiar with the El Farol Bar Problem? Your post reminded me of it. I suppose it's a bit of game theory - W. Brian Arthur from the Santa Fe Institute came up with it. From his paper "Complexity and the Economy":

"The conventional approach asks what forecasting model (or expectations) in a particular problem, if given and shared by all agents, would be consistent with—would be on average validated by—the actual time series this forecasting model would in part generate. This “rational expectations” approach is valid. But it assumes that agents can somehow deduce in advance what model will work, and that everyone “knows” that everyone knows to use this model (the common knowledge assumption.) What happens when forecasting models are not obvious and must be formed individually by agents who are not privy to the expectations of others?

Consider as an example my El Farol Bar Problem [10]. One hundred people must decide independently each week whether to show up at their favorite bar (El Farol in Santa Fe). The rule is that if a person predicts that more that 60 (say) will attend, he will avoid the crowds and stay home; if he predicts fewer than 60 he will go. Of interest are how the bar-goers each week might predict the numbers showing up, and the resulting dynamics of the numbers attending. Notice two features of this problem. Our agents will quickly realize that predictions of how many will attend depend on others’ predictions of how many attend (because that determines their attendance). But others’ predictions in turn depend on their predictions of others’ predictions. Deductively there is an infinite regress. No “correct” expectational model can be assumed to be common knowledge, and from the agents’ viewpoint, the problem is ill-defined. (This is true for most expectational problems, not just for this example.) Second, and diabolically, any commonalty of expectations gets broken up: If all use an expectational model that predicts few will go, all will go, invalidating that model. Similarly, if all believe most will go, nobody will go, invalidating that belief. Expectations will be forced to differ.

In 1993 I modeled this situation by assuming that as the agents visit the bar, they act inductively—they act as statisticians, each starting with a variety of subjectively chosen expectational models or forecasting hypotheses. Each week they act on their currently most accurate model (call this their active predictor). Thus agents’ beliefs or hypotheses compete for use in an ecology these beliefs create. Computer simulation (Fig. 1) showed that the mean attendance quickly converges to 60. In fact, the predictors self-organize into an equilibrium “ecology” in which of the active predictors 40% on average are forecasting above 60, 60% below 60. This emergent ecology is organic in nature. For, while the population of active predictors splits into this 60/40 average ratio, it keeps changing in membership forever.

Why do the predictors self-organize so that 60 emerges as average attendance and forecasts split into a 60/40 ratio? Well, suppose 70% of predictors forecasted above 60 for a longish time, then on average only 30 people would show up. But this would validate predictors that forecasted close to 30, restoring the “ecological” balance among predictions. The 40%–60% “natural” combination becomes an emergent structure. The Bar Problem is a miniature expectational economy, with complex dynamics."