The Long Tailed Network Structure of Trade

 

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.” – Nicholas Rowe

 

In 1999 Albert-Laszlo Barabasi and Reka Albert published a paper in Science that showed the way in which websites connect to each other. They noted some interesting properties in these internet connections which are also found in biological and other networks, but not found in purely randomly connected networks. They report a “high degree of self-organization characterizing the large scale properties of complex networks.”

This in part is built off the observations by Derek de Solla Price, who famously showed in 1976 that a small minority of academic works get cited vastly more often than all others, creating a long tailed distribution. Nicely put in his introduction, what Price highlighted and tried to formalized is that “in many diverse social phenomena… success seems to breed success.”

Barabasi and Albert give two necessary requirements for “success” to be self reinforcing within a network: “(i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected.” This method of organization, which has come to be known as preferential attachment, creates a frequency distribution much different than the standard or “normal” bell curve distribution that we are used to in random samples. The bias toward linking with that which is already linked creates a relationship such that number of nodes with degree k is proportional to 1/k^2. In mathematics this is called a power law distribution or a “scale free” model, because in its idealized mathematical form, the shape of the curve will be identical at any scale you pick.

 

Power Law Distribution vs Normal Distribution

Obviously in the real world, we don’t quite see distributions as perfect as mathematicians can theorize about, but as Price, and later Barabasi and Albert, have shown is that preferential attachment can be found scattered through everyday life in things like the world wide web and citations. One of the most obvious example these days is perhaps the way airlines and delivery companies have set up “hub and spoke” systems. While they may lack some of the evolutionary traits of naturally evolving networks, the end result is the same – only a few ports or “nodes” are highly connected, while the vast majority of nodes have significantly fewer connections. Hub and spoke has become a colloquial term used when discussing the success of companies like Fedex, but at their roots these actually fit quite close to power law distributions.

 

Money as a Hub*

While he didn’t have the fancy terms or the underlying mathematics formalized, I think that Carl Menger actually understood preferential attachment quite well. In On the Origins of Money (1892), Menger argued that when trading goods, patterns emerge where a few goods are highly connected, while the vast majority of goods are not. This process of spontaneous self-organization explains how money can become both a good valued like any other in an economy, but also have some special properties which no other good has.

As indirect exchange is discovered, people will be become willing to accept not only the goods they ultimately want, but also goods which they think will be more likely to be traded in the future. With each transaction traders will look to increase their certainty of future trades. The reason is intuitive, if you don’t have any need for bits of metal you won’t accept them in trade, unless you think they’re easier to trade – i.e. have a bigger market – than whatever goods you currently own. Goods will be sought out with the lowest “bid-ask spread”, or the most liquid good (what Menger called a “saleable” good), in order to best obtain the goods they ultimately desire. 

Under these circumstances, when any one has brought goods not highly saleable to market, the idea uppermost in his mind is to exchange them, not only for such as he happens to be in need of, but, if this cannot be effected directly, for other goods also, which, while he did not want them himself, were nevertheless more saleable than his own

Furthermore, Menger notes that those who are successful at such a strategy of trading for more liquid goods, will be imitated by other market participants who are also looking to minimize costs. With this convergence on demand for liquid goods, there will be a feedback loop – the more acceptable these goods with low bid-ask spreads become, the smaller the spread will be, or the more people willing to accept good X, the easier it becomes to sell good X. In the same way certain papers rise to the top of the citation list, eventually one good will rise to the top of demanded goods in trade, a perfectly liquid good we call money. Hence, a commonly accepted medium comes about as “the spontaneous outcome, the unpremeditated resultant, of particular, individual efforts of the members of a society, who have little by little worked their way to a discrimination of the different degrees of saleableness in commodities”, an insight strikingly similar to Barabasi and Albert’s. 

 

Connectivity of Goods in a Trade Network

Modern trade patterns fulfill Barabasi and Albert’s two requirements for long tailed distribution; new goods are constantly coming to market and being added to the network, and these sell for, or “attach” to, goods which are already well connected in trade. Like Price’s citations, there is a path dependence or a bias, where we end up with the form indirect trade that we see in modern economies. What we call “money” then, is just defined as the good which forms the hub, and all other goods are out on the spokes. In other words, the end result of this preferential attachment mechanism is that money is traded for all goods and all goods are traded for money – money becomes one half of every exchange.

 

The Importance of Transaction Costs

But imagine the feedback-loop which creates the long tailed distribution of indirect trade was nonexistent, such that it didn’t look how I’ve represented it above. If that were the case, we could easily think up an example where the chain of goods being traded becomes longer than two (trade a for b, b for c, c for d…. y for z). This would be what would happen if trade networks look more like a lattice. Absent transaction costs, this could also be an effective way to maximize the gains from trades. When transaction costs become high relative to the potential gain from trade however, this long chained indirect trade system will likely become impossible to execute as the cost of the multiple trips between nodes quickly becomes prohibitively high.

The uncertainty from an unknowable future makes indirect exchange difficult and we can’t assume the exact lattice structure would be known to the traders. Furthermore, because time is scarce, search costs (the time and effort searching for a buyer) at each node matters. If searching for, and bargaining with, potential buyers of a specific good is costly, then the more steps between an initial good and final desired goods, the higher the cost. Two trades can be cheaper than one because it can solve the double coincidence of wants, but three or more trades is always more costly than two in a world with transaction costs.

 

Lattice vs Hub and Spoke Networks

Minimizing trips between nodes is therefore really important to minimize costs. But in a lattice type network, the more nodes (goods) added to the network the larger the average path length between any two nodes becomes. The path length increase has no limit – if the nodes are infinitely increasing then so is the average path length. With hub and spoke style systems, an increase in the total number of nodes will never have an average path length exceeding two. Only with money as a hub can an actor go directly from any good A, to money, to any good B. Therefore, it is not just any form of indirect trade which allows for specialization and increased division of labour, but only indirect trade in a long tailed network structure (i.e. the structure where money is the hub). Money brings the cost of trade down enough to allow it to happen at a much larger scale, and this further helps explain why barter economies cannot grow beyond small communities.

 

The Downside

Although this system is immeasurably beneficial, it creates a special importance and role for money that it does not share with other goods. As was pointed out in the opening quote, because all transactions must go through the hub, if the hub is altered, everything is altered.

All long tailed networks are incredibly robust to random node failure, much more so than randomly distributed networks. If ppe.life goes down, it would definitely be sad, but it will not disrupt the internet in the same way as Google or Facebook going down would. Likewise, disequilibrium in the fishing lure market will be bad for many, but it will not have a large pervasive impact on the overall patterns of trade in the economy. When the vast majority of nodes have low connectivity, a random failure will most probably be within one of these nodes, and the odds of random failure at a hub is increasingly small as the size of the network grows.

Where this robustness is limited is when node “attack” is non-random, or targeted. If hackers wants to disrupt the most internet traffic, they won’t just target websites at random, but target the ones with the most connections. If a highly connected node is disrupted, then the whole network is disrupted via its massive connectivity through the network. If money is disrupted, it makes our whole network of trade distorted. Disequilibrium in the money market effects all the goods markets which money is a part of. The low bid-ask spread which caused a bias towards a single money in the first place is altered. 

The insight that money fits the long tailed models of Price, Barabasi and Albert, I think draws attention to the fact that the pattern of trade we currently have is incredibly vulnerable when money is messed with. In a previous post, I tried to show some of the consequences of a money market in disequilibrium (specifically one with excess demand), and how that affects the economy as a whole. I think the story of “good” and “bad” deflation fits my long tailed hub and spoke story nicely, and could also be reversed to show the consequences of “good” and “bad” inflation.

 

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Note – While I am happy with the depth I’ve explored this and think some of these ideas are unique, I wasn’t the one to come up with the analogy of trade as a hub and spoke network in the first place. To my knowledge, the first one to make this connection explicit was professor Nicholas Rowe (who I quoted in the opening, and who also taught me Micro and Macro back in the day at Carleton). He wrote a blog post about it back in 2009, and more recently discussed the idea on the Macro Musings podcast.

*UPDATE: Since writing this post, I’ve become aware that I made a mistake on where the Hub and Spoke analogy originated. George Selgin actually has been using it at least since 1988. In his book The Theory of Free Banking, professor Selgin states:

One can think of the market as being like a wheel, with money as the hub, prices as the spokes, and other goods as the rim. A change in the relation of one good to the rest is like a tightening or loosening of a single spoke: it has a great effect on one small part of the wheel, but much less effect on the rest of the wheel. A change in the relation of money to other goods is like moving the hub: it has a great effect on all parts of the wheel, because it moves all the spokes at once. Adjust a spoke—a particular price—improperly, and you make one small part of the wheel wobble; adjust the hub—money—improperly, and you bend the whole wheel out of shape.

 

 

4 thoughts on “The Long Tailed Network Structure of Trade

  1. With all due respect to Nick, I think I can claim priority on the analogy in question:

    “One can think of the market as being like a wheel, with money as the hub, prices as
    the spokes, and other goods as the rim. A change in the relation of one good to the rest
    is like a tightening or loosening of a single spoke: it has a great effect on one small
    part of the wheel, but much less effect on the rest of the wheel. A change in the
    relation of money to other goods is like moving the hub: it has a great effect on all
    parts of the wheel, because it moves all the spokes at once. Adjust a spoke—a
    particular price—improperly, and you make one small part of the wheel wobble;
    adjust the hub—money—improperly, and you bend the whole wheel out of shape.”

    The Theory of Free Banking, 1988.

    1. Indeed, my mistake, you have professor Rowe beat by quite a number of years it seems! I’ve added an update at the bottom of the post to note this correction.

  2. Casey: I was reading through it, thinking “why doesn’t he talk about Menger?”. And then you did talk about Menger! Good post!

    So George beat me to it on that metaphor. Damn! Ah well, it’s a good metaphor.

    1. Thanks for taking the time to read the post! I’m glad I could build a little suspense before the big Menger reveal 🙂

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