The hub and spoke model of money -- a rejoinder to Arnold Kling

The textbooks say that money serves as: store of value; medium of account; and medium of exchange. Arnold Kling seems to miss the importance of the fact that money is a medium of exchange. Worse, he misunderstands me, thinking that I am one of those economists who makes a big deal of money's role as a store of value. I don't. I'm a medium of exchange nut. Worse still, he claims Clower and Leijonhufvud as intellectual ancestors, on his side of the debate aginst me! Clower especially emphasised the role of money as medium of exchange, and Leihonhufvud followed suit. They are my ancestors, not Arnold's!

The good that serves as medium of exchange in a monetary exchange economy is like the city that serves as the hub of a hub and spoke model of airlines. If Peoria is a spoke, and Peoria is closed, nobody can fly to or from Peoria. If Atlanta is the hub, and Atlanta is closed, nobody can fly anywhere. Money is like Atlanta; every other good is like Peoria.

Let's tighten the analogy a little. Suppose all flights are round trip return flights, from A to B and back to A again. And airlines insist that there must be an equal number of passengers on the two legs of a round trip. If 100 people want to fly from A to B, but only 60 people want to fly from B to A, then the airline uses a 60-seater airplane for the round trip and only allows 60 people to fly from A to B. No empty seats allowed. This is how exchange works. You can't trade A for B unless you find a partner willing to trade B for A. In this case there's an excess demand of 40 seats from A to B.

If there are n-1 spokes, with the nth city being the hub, each of the n-1 spokes has a unique excess demand (or supply). But the nth city has n-1 excess demands.

Suppose we start in equilibrium, with balanced flights. Then 10 new people decide they want to take a one-way trip to Atlanta, to live there. (Or 10 fewer people who had previously been planning to leave Atlanta decide to stay there after all.) That initial excess demand for seats to Atlanta screws up the whole system, affecting people who had merely wanted to fly between Peoria and Washington. If I can't fly from Peoria to Washington, because I can't find a seat on Peoria to Atlanta, then you can't fly from Washington to Peoria. Under a point to point model (barter exchange) our Peoria/Washington flight would balance, even if Atlanta was unbalanced.

That's the vision of monetary exchange I got from reading Clower. So I was surprised to see Arnold Kling cite Clower and Leijonhufvud, when arguing for his vision against mine.

Arnold puts forward a "re-calculation" theory of recessions. When there is a shock to relative demands or supplies of goods, it takes time for the economy to re-calculate the new efficient allocation of resources.

The way a market economy re-calculates is by changing prices in response to excess demands, and by people responding to those changed prices. In a monetary exchange economy, the prices will be money prices, and the excess demands will be those of a monetary exchange economy, where money has n-1 excess demands and all the other goods have just 1 excess demand. You can't try to understand how a monetary exchange economy re-calculates by ignoring the central role of money as medium of exchange. It would be like trying to understand why air traffic gets gridlocked in bad weather while assuming a point-to-point model. "Peoria and Washington are both open, so why can't people fly from Peoria to Washington?". Because Atlanta is closed, that's why.

Sure, the structural unemployment that follows a relative demand or supply shock may be part of the problem in many recessions. And if you see excess supply in some markets, and excess demand in others, that's probably the main part of the problem. But that doesn't seem much like what's happening now.

If you see passengers waiting in Peoria, Washington, Las Vegas, etc., etc., then check what's happening in Atlanta.

Arnold writes:

"Rowe, like many economists, has a very hard time imagining anything other than a frictionless economy with instant movement to general equilibrium. In that (mythical) economy, a shift in demand between industries cannot possible lead to unemployment. In order to explain unemployment, these economists posit a shift in demand toward a non-produced good, and they leap on money as an example.

I am explicitly attacking this tradition, which I associate with Keynes, of making a big deal of money as a store of value. In this view, as long as the supply and demand for money are in balance, there can be no unemployment. In my view, the supply and demand for money could be in balance, but if the supply and demand for different forms of capital (houses vs. small businesses) is out of whack, there can be unemployment."

Nope. Not me. Not guilty.

First, if prices adjusted to clear markets instantly, without frictions, my view of excess demands for money would be nonsense. And it is only the frictions of transactions costs that explain why people use a hub and spoke system like monetary exchange anyway.

Second, a shift in demand (or supply) between industries can and will cause structural unemployment (the LRAS curve shifts left temporarily). No doubt that's part of the current recession. But I don't think it's the major part.

Third, and most importantly, I don't make a big deal of money being a store of value. Land (and lots of other goods) is a store of value, and a non-produced one at that. But an excess demand for land cannot cause an excess supply of everything else (yes, I am contradicting Walras' Law). An excess demand for the medium of exchange, however, will cause an excess supply of everything else.

Arnold also writes:

"Inflation rates are very sticky. A major change in the trend inflation rate requires a regime change, which changes people's expectations. That process of changing expectations takes years."

Yep. Absolutely. (Indeed, the major thing wrong with the Calvo model of price adjustment used by New Keynesians is that it has price level inertia but not inflation inertia.) And this stickiness of the price level and rate of inflation is why changes in the level and growth rate of the demand or supply of money can have large real effects. I don't just agree with Arnold here; I have to agree with Arnold here. My theory of monetary disequilibrium wouldn't make sense otherwise.

Comments

[Mike Sproul]

Nick:

Even if the medium of exchange function creates a demand for money, and even if you accept supply and demand as a relevant framework for money, that model of money becomes useless when the supply of money is horizontal (which it is). Monetary theorists need to go back to the drawing board and ask why they ever believed that money could have value without backing. If such a thing were true, there should be some bank somewhere that holds no assets as backing for its money. There is no such bank, and there never has been.

[Mattyoung]

Metaphors are a pain because of the constant translation. But I can work with this metaphor.

Prices had nothing to do with the organization of air travel, originally. The idea of hub and spoke was designed and implemented without regard to ticket prices, or ticket prices were calculated as an afterthought to make sure the system was competitive.

Hub and spoke resulted because it was the simple method to keep passenger flow the most constant with the least number of flight exchanges. Once the hub and spoke system was installed, planners knew ticket prices would adjust properly because there was a critical mass of passengers for whom the small delay was a small discomfort to pay for inventory smoothness.

Money, as a medium of exchange, played a minor role in the calculation.

Another metaphor to consider is the software industry in which the transaction costs of money are too high to use. Software projects across companies are agreements written in terms of software modules, functions or lines of code. This happens in both closed and open software systems.

[fourthtimeanon]

"But an excess demand for land cannot cause an excess supply of everything else (yes, I am contradicting Walras' Law."

would you mind illustrating this briefly again; I still don't get it; thanks

[Nick Rowe]

Mike: the supply of money is horizontal in the SR as a function of the rate of interest; it is not horizontal in the SR as a function of the price of money. Big difference.

"Monetary theorists need to go back to the drawing board and ask why they ever believed that money could have value without backing." ! "...back to the drawing board.."?! What do you think monetary theorists have been doing all these years? They have been putting forward theories of why people want to use money, and why they want to hold a stock of money. If you can explain why people use money, and demand a stock of it, you have a demand function. Add a supply function, and voila!

It is the backing theorists who need to go back to the drawing board, and ask whether "backing" would be relevant to a firm that could issue shares, promising a negative 2% real rate of return (on average), and where the interest on the proceeds from issuing new shares would all be paid out to some third party, rather than the shareholders.

What is your estimate of the Present Value of the dividends plus share buybacks of the corporation known as the Bank of Canada? Because mine is negative (unless I use a negative real interest rate in the PV formula).

To answer your question: the Bank of Canada has no backing. It just pretends it does. The "backing" it claims to own is really owned by the government, since the government gets all the interest from the backing (net of admin costs). Bernie Madoff wouldn't have needed backing either, if he could borrow at minus 2% real, and he could have stayed in business forever!

Ah, you devil! You enticed me right off topic!

Matt: I thought of continuing the metaphor, to take prices into account, but the metaphor just gets stretched too far. They aren't ticket prices. The relative price of good A to good B is like the allowed ratio between passengers flying A to B to passengers flying the reverse. The metaphor is no longer helpful (to me) at this point.

[Nick Rowe]

fourthtimeanon: I'm glad someone has picked up on the one really controversial thing I said in that post!

Suppose every individual is initially planning to buy $100 worth of land financed by net sales of $100 worth of other goods. So far Walras Law is fine. Now suppose the price of land relative to other goods is fixed, so the price of land cannot rise to eliminate the excess demand. (Fix all prices, if you like, to keep it simple). You can't buy land without someone else selling, and since everybody wants to buy, and nobody wants to sell, people can actually buy $0 worth of land. Realising they can only buy $0 of land, they revise their plans, and scrap the idea of selling $100 worth of other goods to finance the purchase of land. They would be violating their budget constraints if they planned to sell $100 worth of other goods to buy $0 worth of land.

Unless, of course, they try to sell money to buy land. Which is what one does of course when you try to buy land, in a monetary exchange economy! You offer the landowner $100 cash.

[RebelEconomist]

I think I understand your logic Nick - in a nutshell, expected falling asset prices increase the demand for money as a safe asset (so money's role as a store of value does matter), and, because money is also the medium of transaction, people can attempt to get more of it by buying less, which, given sticky prices, causes a recession. But what evidence is there that people actually choose to try to obtain more money by buying less newly produced goods. It seems more natural that people would choose to try to switch between money and other assets instead.

If so, it seems to me that the policy prescription would be to do nothing to facilitate the adjustment of the relative prices of money and assets - ie allow the bust to proceed unchecked - with any public money spent on mitigating the consequences and repairing any disruption that remains after adjustment.

[septizoniom]

you are one of the best writers about economic issues in the blogosphere. bravo!

[Nick Rowe]

Rebel: *Something* (it could be expected falls in asset prices) causes the demand for money to increase. People can try to get more money by buying less newly-produced goods, or by trying to sell other assets. But they cannot in fact sell other assets (because everyone else is trying to sell too). So this doesn't work, and they are back to buying less newly-produced goods. Now, the prices of those other assets will of course fall, if they are flexible. But this doesn't change the story. Either other asset prices are flexible, and fall until people don't want to sell them, or they are fixed, and there's an excess supply (ABCP), and people can't sell them. Same results either way. Other assets are just a side-effect, not part of the main channel of causation.

septizonion: thanks!

[Nick Rowe]

Rebel: on whether money's role as store of value matters. I just find it so hard to think about a medium of exchange that is not also a store of value. So I can't think of a clear thought experiment to separate the two.

[JP Koning]

Nick, I've read one or two of Clower's papers. How is your thinking influenced by him? Am I wrong in reading the idea of the Clower constraint into your writing - that all transactions must have money on one side? This would explain your hub & spoke model, which effectively prevents any trading between spokes (barter) or alternative hubs, like credit. In what other ways is Clower an influence? Interesting exchange between you and Kling, though I agree that he misread you.

[RebelEconomist]

Nick,

What the something is matters, and I think that it is overwhelmingly likely that the something was falling asset prices, beginning with ABCP and progressing to term bank deposits etc. Now, if that is true, then this demand for money is a demand relative to asset prices (ie like Keynes' speculative demand for money), and if asset prices are allowed to fall freely, that relative demand can be readily accommodated by a fall in asset prices. As I say, I can appreciate your logic for the money / newly-produced g&s relationship but I would have expected that relationship to be relatively insensitive and therefore less disturbed. It is not enough to say that the mechanism logically works; it is also necessary to consider how important it is.

[Nick Rowe]

JP: This post is especially influenced by Clower. "Money buys goods, and goods buy money, but goods do not buy goods". n-1 markets, with money appearing on one side of each of them. Pure Clower. And the idea of constrained vs notional demand follows from Clower and Patinkin. Those are the two ways I was influenced by Clower.

I am ambivalent on the Clower constraint though. I see what he was trying to do (I think), but it did more than he was trying to do with it. It set V=1, and moreover the length of the period wasn't a real calendar length, but just an arbitrary length (chosen by StatsCan?). So it took the choice element out of Velocity, and money demand.

[JP Koning]

Thanks Nick. I found this post
http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/04/says-law-and-monetary-policy.html
which did a good job explaining constrained vs notional demand.

I think I accidentally assumed "Money buys goods, and goods buy money, but goods do not buy goods" was the Clower constraint, but it seems not to be.

[Ritwik]

Nick: I think both you and Arnold can claim to the intellectual successors of Clower and Leijonhufvud, and so can post-Keynesians like David Colander and Steve Keen. All post-Walrasians can claim descent from Clower and Leijonhufvud.

Your theory is one of monetary disequilibrium - in your view a barter economy will not have a recession and hence there is no 'real disequilibrium' without money. Arnold's theory is one of real disequilibrium and neutral money. The Minsky-style post-Keynesian view is also of real disequilibrium, but it is a disequilibrium brought about not by a structural shift (Arnold) but by over-leveraging. In this view, money IS privileged but only because money is debt and debt is privileged. Thus, there could be a recession in a barter economy as long as there is lending and borrowing (This is more or less what fourthtimeanon was arguing on some of your previous posts).

[Nick Rowe]

JP. Yes. The Clower constraint was an attempt to put that quote into math, but it didn't quite work.

Ritwik: You might be right. Clower and Leijonhufvud had lots of kids, some of whom don't know all their siblings?

[kharris]

Setting aside economic implications for a moment, I think it's interesting, and funny at times, how we very clever people can be so dense. The example here is Kling wanting Nick to be saying things that he is decidedly not saying, because it allows Kling to make an argument that he wants to make. We have all seen this countless times. Rather than absorbing what the other side is saying, even in its most superficial implications, a disputant assigns the other side an argument based on a stray word or phrase.

I don't have in mind forcing a straw man on the other side, because that presumes a certain malice aforethought. What I see is such an overwhelming focus on the world being in a particular way. At the slightest opportunity, the other side is assigned that mistake, so that one can rush happily into the explanation that one has ready and waiting.

Nick didn't see the world as frictionless. Who does these days? But Kling really wanted to whip out the accusation of frictionless thinking, so he assigned that view to Nick. It takes real disregard for the other guy's argument to make that sort of error, but it happens a lot.