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economics

Scale Free economies (long)

This was a paper I wrote in grad school in my macroeconomics class. I think the topic of alternative ideas about the macroeconomy and its relationship with the micro level things is especially relevant these days.

The Economy as a Scale Free Network
an Introductory Exploration

Isaac Crawford

        Mainstream macro economic theories have a tendency to work from the top down. They see the aggregate features of an economy as being capable of being directly influenced and for those influences to be predictable. This belief continues despite the fact that all of the mainstream economic theories seem to work at some times and not others. Most of these theories ignore the vast number of transactions that occur in the economy and instead concentrate on aggregate quantities as if they were actual. physical items. It is assumed that parameters such as interest rate, level of unemployment, inflation, and money supply exist and by adjusting them, the entire economy can be controlled.

        If we step away from the world of mainstream macro models and take a look at the actual economy, a very different picture emerges. Instead of seeing a handful of measures, we see a very complicated structure with millions upon millions of participants. Transactions occur all the time, and they are connected by a chain of events through time. The economy is actually a very dynamic, ever changing thing, quite unlike the models of most mainstream macro theorists.

        But if the economy is so complicated and the regular mainstream ideas fall short, how are we to make any sense of the economy? If we cannot rely on the tried and not so true macro indicators, what can we use to analyze the economy? This paper is an introductory sketch of a different way to look at the economy and the ramifications of that way of looking at it. This sketch, by necessity, simply provides an overview of potential research ideas. It is beyond the scope of this paper to delve deeply into any particular aspect of the macro economy. Instead, it is hoped that it can spark discussions into the possibilities that it raises.

        Instead of looking from the top down like most macro economists do, looking from the bottom up will give us a very different view of the economy. We start with the actors in the economy, the hundreds of millions of consumers that interact every day. They interact with each other directly and through firms. If we imagine that each consumer and firm is independent, and that every transaction is a connection between them, a network framework emerges.

        Networks are fairly well understood and used extensively in other sciences. How networks operate depend on the nodes and the connections between those nodes. If every firm and every consumer is a node, then the flows of goods, services, and money are the connections between them. Why put firms and consumers on equal footing? The real question is why not. From a perspective far enough back, there is little to differentiate a firm from a consumer. It’s true that the quantity of money, goods and services will be larger with the average firm as compared to the average consumer, but that disparity is taken care of by the number of connections. If we look at firms absent of the quantities of goods, services, and money involved, they appear to be like any other consumer.

        Under most macro theories, “The Government” is a monolithic creature that is separate from, and quite independent of the rest of the economy. From a network standpoint, the various agencies and departments of the government are no different than any other node in the network (The Federal Reserve Bank being a notable exception. It will be dealt with later on.). “The Government” is reduced to many different nodes participating in the economy producing and consuming goods and services like any other node.

        There are four obvious characteristics of networks that are of concern in the economy, connectedness, the quantity of goods, services and money that flows along a particular connection, how nodes and connections change with time, and the speed at which those things move through the network. There are undoubtedly more characteristics that can be derived from this type of framework, but these four are basic and powerful. They lead to some interesting conclusions about the economy that would be very difficult to come to with a more traditional outlook.

        The connections between nodes represent the flows of goods, services, and money that are exchanged between them. In many other sciences, nodes are limited in the amount of “stuff” they can pass or distribute. Internet hubs, electrical grids, and various biological models are examples of this. “Starvation” is a much more serious threat to an economic node than overloading. It is difficult to imagine a node taking in too much money. Along the same lines, a node cannot send out too much money, if it doesn’t have any (whether on hand or by credit) it simply cannot send it out. Goods and services are self regulating, if the node does not want or need the good or service, it simply does not purchase them. Nodes with very few connections or none at all are the ones that are in trouble. If it is not receiving money, or is unable to work, or is simply not wanted or needed, the node may fail. True failure will probably be limited to firms, or perhaps the death of a consumer. A person that is alive will consume something, even if they do not work for it.

        How nodes are connected is a vital property of any network. A first guess might be that the nodes in the economy are connected at random. After all, there are so many of them, and the connections are so complicated that we cannot imagine them in their entirety. A more accurate view is that there is a randomness to the entire thing, but there are definitely some nodes that are connected more than others. Firms in particular will be, on average, connected to many more nodes on a regular basis than the “average” consumer. A reasonable hypothesis is that the economy resembles (or perhaps is) a “scale free” network. There is a particular form a scale free network adheres to (Albert and Barabasi 1999), but there is little hope to confirm this with something as complicated as the entire economy. The economy does fit with the central idea of a scale free network, that is that some nodes are more connected than others and so play a greater role in distribution than other nodes.

        This structure has some interesting qualities. Like a randomly distributed network, scale free networks are very robust when it comes to dealing with random failures or attacks on nodes. It would take quite a few random failures at once in order for the failure to propagate throughout the entire network. In addition, both scale free and random networks have relatively few “jumps” from one side of the network to the other. Unlike a random network, scale free networks have more potential problems with directed attacks on, or failures of highly loaded nodes (Motter 2004). A failure of a highly loaded node can lead to a cascading failure throughout the entire network as the failed node takes many other nodes with it. In addition, it is possible for there to be a rash of nodes, either willingly or unwillingly, that disconnect from the network, or at least minimize their connections. An easy example of this would be bank failures and subsequent panics. As people pull their money out of banks they fail, leading other people to worry about their money, etc. Technology advances could also trigger this sort of reaction in the firms specializing in the older technology.

        The more highly loaded or connected the node is, the more potential it has for propagating effects throughout the economy. Since any particular node is relatively close to just about any other one, nodes that are heavily loaded affect other nodes more quickly than less connected ones. If we compare the fallout of Citibank suddenly failing with a landscaper going out of business, it is easy to see which will have the bigger impact.

        Is there a node that is the most connected? Yes there is, the Treasury department. Through the IRS, the Treasury department is directly connected to every other legal node in the entire network. It collects taxes from consumers and firms and distributes them to the various agencies and departments of the federal government. While the Fed may connect directly to several thousand nodes, hundreds of millions of nodes are directly connected to the treasury, no other node comes close to this level.

        This would seem to back up Keynesian economists’ claims that fiscal policy has a much greater impact than monetary policy. When fiscal policy is enacted, the treasury could, in theory, directly effect every consumer and firm practically instantaneously without having to go through any other node. Fiscal policy also has the ability to work through the other agencies and departments of the federal government through the treasury in order to disperse money into the economy, or to target specific parts of the economy.

        Does this mean that the Fed is less powerful than the treasury department? Maybe. The reason that it is ambiguous is because even though the Treasury has many more connections, the volume of money across any given connection with the Fed is probably much higher. The amount of money or goods that flows through each connection has obvious significance to the nodes involved. There may be many more nodes involved than just the original pair, whatever good that has been exchanged could lead to other exchanges with other nodes. If money flows from a firm to an employee, that employee will turn around and distribute that money across many different nodes. The more money he receives, the more he will distribute. In the case of the Fed, such large sums of money are involved, it cannot help but send ripples through the economy.

        How do those ripples propagate? What effects do they have? We have all seen the table top apparatus of clacking metal balls. One on the end is lifted up and allowed to swing back and strike the others. What happens next depends on the arrangement of the other balls. If they are in a tight arrangement, with no space between them, the force of the swinging ball is transferred through the entire stack and the ball on the other end is thrust outward, only to swing back and strike the balls again. This continues until the force is completely dissipated. On the other hand, if the balls have some space between them, or are not lined up properly, the force of the swinging ball is dissipated by the others clacking together resulting in a very small amount of movement before stasis sets in.

        Now imagine nodes of the economy as money flows through them acting in the same way. A primary difference is that a node doesn’t have to hit just one other node, it could hit all of its connected nodes with equal force, sending them off to hit their nodes etc. Trying to imagine a node like Citibank or JP Morgan “swinging” towards all of its connected nodes can lead to quite a headache. The important thing to understand is that these nodes push or pull through any or all of their nodes at the same time. Different parts of the economy will have different levels of “tightness”, resulting in some money effects going across many nodes while others stop with just a single hop, or connection.

        What does this tightness represent? An active economy is inevitably more healthy than a sluggish one. It may be better to look at tightness more as a symptom than a cause. It shows the willingness to spend money on the part of nodes. Why they choose to spend or not spend could be attributed to any number of things. When nodes choose not to complete transactions, connections are lost. If this behavior exists in large parts of the network, or among large numbers of once highly loaded nodes drop connections, a recession may be the result. The speed at which money flows through the network can be seen as a good measure of how the economy is doing.

        Various micro economic theories can be brought to bear on whether or not the economy has the ability to keep itself moving absent any interference from government. In the real world, the Fed plays a role in how money is moved inside the economy. While the treasury is primarily used to redistribute money, the Fed will actually inject more into the economy or take some out. Unlike a Monetarist or even Keynesian viewpoint, it is not clear what will actually happen when the Fed decides to act. Injecting money into the economy will set some things into motion, but it is not clear how quickly it will spread, how far it will spread, or if it does impact the network in a systematic way. Clearly, whatever impact the Fed will have is based completely on how the different nodes react to the actions of the Fed. There isn’t any reason to expect them to act the same way every time. Indeed, there isn’t any reason to expect the money to flow along the same nodes and connections every time, so how could the reaction be the same every time?

        The fact that the network changes over time is one the one hand perplexing, but it is also one of its greatest strengths. Being faced with several hundred million nodes that change the number of connections and the volume transferred across them by the minute will cause many economists to throw up their hands. It is impossible to ever get a complete view of the economy, even a split second snap shot of it. This implies that any static model of the economy, network based or not, will be missing a fundamental aspect of the real thing. It is this changeability that results in robustness. Any sort of rigidity would also be an area of weakness. If nodes were connected by a set pattern of connections and other nodes (as they might be in a controlled economy), any disruption in them would be disastrous. Curiously, there are two rigidities present in the network, the Federal reserve Bank and the Treasury department. While it is unlikely that anything will happen to them, it should be noted that they represent a weakness in the network. The rigidity plus the enormous connectivity present in the Treasury points to a potential disaster if something should happen to it. As it stands, the economy is a very adaptable, ever changing network that is very robust because of it.

        Since the economy is constantly changing and modeling it will be a tremendous challenge, what is the point of looking at it from a scale free network perspective? Why bother with such a complicated idea when simpler models are available? The easy answer is that the simpler models simply do not reflect the true nature of the economy and very often are incorrect. The more complex and fruitful answer is that by taking the economy as a whole from a scale free perspective, we are able to see things in a new light that would be hopelessly obscured with other models. By having a radically different viewpoint it is possible to see relationships and causal chains that the other models simply don’t have room for.

        For instance, it is possible to bring all sorts of network methodologies into analysis of the macro economy. In analog audio circuitry (among many other analog circuits), part of the signal at the output is sent back to the input. The signal is summed and this creates a feedback loop. This so called “negative feedback” circuitry is used to reduce various types of distortions and to control wild oscillations that can occur when the signal is amplified. Is the IRS performing in a similar capacity? By removing a certain percentage of money from each node and putting it back into the economy in a different place, is the economy being prevented from experiencing wildly fluctuating money flows? The IRS is in a much better position to do this than the Fed because of its direct access to all other nodes. If there is the possibility of oscillations, is the network inherently unstable, or does the Fed cause the waves by injecting money into the system? Could the economy be “tuned” by the IRS using predetermined rules based on the “tightness” of the nodes? Could an alternative system accomplish the same thing? While many economists would argue that the IRS needs to have less impact and not more in the economy, the fact that it has direct access to every participant in the network means that it should be looked at carefully. In addition, since it is, by far, the most heavily loaded node extreme caution should be taken when attempting to “reform” it. From the perspective of the more traditional macro theories, the IRS is just “The Government” and no different from any other agency.

        New insights into the connections and relationships of the economy can be explored using topological transformations. If the network, or parts of the network, can be visualized in a physical way, the rearranging of the nodes while keeping the links intact could prove to be an enlightening exercise. Imagine a visual representation of the IRS and its attendant nodes. In three dimensional space, it will look like a complete jumble, with far too many nodes to make any sense out of it. If we instead arrange the nodes by money going into or out of the Treasury, a very different picture arises. The entire economy will be seen feeding into a single node, and then several thousand connections will be on the other side representing the rest of the government agencies. This paints a vivid picture and makes the relationship between the Treasury department and the rest of the economy clearer. Similar transformations can be used to examine various firms, or even certain markets for goods. This technique could prove to be invaluable in figuring out macro consequences of micro phenomena.

        Another potential line of inquiry has to do with the relative “tightness” or “looseness” of the nodes. How quickly do they respond to money flows, and how much do they pass it through. There would undoubtedly be varying levels of these parameters in different parts of the network. Research into how geographical, institutional, or business sector dynamics can affect those groups of nodes’ transmissive qualities could help explain the way money propagates through the network. The velocity of transactions between groups of nodes can be studied to determine their relative health.

        There are some potential problems with moving to a network based view of the economy. New measures would have to be devised to make sense of how the network works. Measures such as GDP, inflation, and money supply wouldn’t be very useful if they were applied to a scale free model. Issues such as average transaction value, average connectivity, and node responsiveness would have more applications. A metric for determining how quickly money propagates through the system could also be of use.

        One of the strengths of the more traditional models is their ability to predict macro events. If Y is done to parameter X through channel Z, then certain results can be expected. The models work very well internally, and it gives policy makers some choices when trying to make decisions. The predictive accuracy of a scale free model is not a known quantity. If the economy is as complicated as thought, trying to work with it could end up giving us the same answer every time, “It depends”.

        To be fair, the traditional models have a sketchy history of usefulness. Some of them appear to be accurate and useful for a time and then they become less so. The fact that they do seem to work some of the time points to the possibility that they may actually capture, in a simpler fashion, some truth that a network model cannot. A possibility that should not be overlooked is that perhaps a network based model could be used to determine which conventional macro theory is most appropriate. It is possible that the insight of the internal workings of the economy can point us to a more accurate way of aggregating data for a particular macro theory.

        If this is the case, macro economics would be split between models based on aggregate data and models dealing with the internal working of the macro economy. Instead of replacing conventional macro theories, network based approaches would serve as the bridge between micro and macro theorists. Closing the chasm between these fields could result in a much more comprehensive understanding of the macro economy.

        A scale free based view of the macro economy is a potentially useful way of organizing thoughts while trying to wrap one’s mind around such a complicated topic. It has the potential for answering many questions that are left behind by traditional models while at the same time opening up new avenues of research. The potential for a micro and macro economic synthesis is an exciting one, and if it comes to pass will certainly be a defining moment in economic history. Emergent macro theories are in their infancy right now, but the potential for new understanding is enormous. With any luck that potential will be realized.

References
Barabasi and Albert. Emergence of Scaling in Random Networks. Science October 1999: 509-512.

Motter, Adilson. Cascade Control and Defense in Complex Networks. Physical Review Letters August 27, 2004: letter 93.

Snowdon, Brian, Howard Vane, and Peter Wynarczyk. 1995. A Modern Guide to Macroeconomics, an Introduction to Competing Schools of Thought.

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