Here’s a nice article by Robert Henderson in the science magazine Nautilus which poses the question: “Can topology prevent the next financial crisis?” My short answer: No. A longer answer–which I sketch out below–is that a belief that it can is positively dangerous.
The idea behind applying topology to the financial system is that financial firms are interconnected in a network, and these connections can be represented in a network graph that can be studied. At least theoretically, if you model the network formally, you can learn its properties–e.g., how stable is it? will it survive certain shocks?–and perhaps figure out how to make the network better.
Practically, however, this is an illustration of the maxim that a little bit of knowledge is a dangerous thing.
Most network modeling has focused on counterparty credit connections between financial market participants. This research has attempted to quantify these connections and graph the network, and ascertain how the network responds to certain shocks (e.g., the bankruptcy of a particular node), and how a reconfigured network would respond to these shocks.
There are many problems with this. One major problem–which I’ve been on about for years, and which I am quoted about in the Nautilus piece–is that counterparty credit exposure is only one type of many connections in the financial network: liquidity is another source of interconnection. Furthermore, these network models typically ignore the nature of the connections between nodes. In the real world, nodes can be tightly coupled or loosely coupled. The stability features of tightly and loosely connected networks can be very different even if their topologies are identical.
As a practical example, not only does mandatory clearing change the topology of a network, it also changes the tightness of the coupling through the imposition of rigid variation margining. Tighter coupling can change the probability of the failure of connections, and the circumstances under which these failures occur.
Another problem is that models frequently leave out some participants. As another practical example, network models of derivatives markets include the major derivatives counterparties, and find that netting reduces the likelihood of a cascade of defaults within that network. But netting achieves this by redistributing the losses to other parties who are not explicitly modeled. As a result, the model is incomplete, and gives an incomplete understanding of the full effects of netting.
Thus, any network model is inherently a very partial one, and is therefore likely to be a very poor guide to understanding the network in all its complexity.
The limitations of network models of financial markets remind me of the satirical novel Flatland, where the inhabitants of Pointland, Lineland, and Flatland are flummoxed by higher-dimensional objects. A square finds it impossible to conceptualize a sphere, because he only observes the circular section as it passes through his plane. But in financial markets the problem is much greater because the dimensionality is immense, the objects are not regular and unchanging (like spheres) but irregular and constantly changing on many dimensions and time scales (e.g., nodes enter and exit or combine, nodes can expand or contract, and the connections between them change minute to minute).
This means that although network graphs may help us better understand certain aspects of financial markets, they are laughably limited as a guide to policy aimed at reengineering the network.
But frighteningly, the Nautilus article starts out with a story of Janet Yellen comparing a network graph of the uncleared CDS market (analogized to a tangle of yarn) with a much simpler graph of a hypothetical cleared market. Yellen thought it was self-evident that the simple cleared market was superior:
Yellen took issue with her ball of yarn’s tangles. If the CDS network were reconfigured to a hub-and-spoke shape, Yellen said, it would be safer—and this has been, in fact, one thrust of post-crisis financial regulation. The efficiency and simplicity of Kevin Bacon and Lowe’s Hardware is being imposed on global derivative trading.
God help us.
Rather than rushing to judgment, a la Janet, I would ask: “why did the network form in this way?” I understand perfectly that there is unlikely to be an invisible hand theorem for networks, whereby the independent and self-interested actions of actors results in a Pareto optimal configuration. There are feedbacks and spillovers and non-linearities. As a result, the concavity that drives the welfare theorems is notably absent. An Olympian economist is sure to identify “market failure,” and be mightily displeased.
But still, there is optimizing behavior going on, and connections are formed and nodes enter and exit and grow and shrink in response to profit signals that are likely to reflect costs and benefits, albeit imperfectly. Before rushing in to change the network, I’d like to understand much better why it came to be the way it is.
We have only rudimentary understanding of how network configurations develop. Yes, models that specify simple rules of interaction between nodes can be simulated to produce networks that differ substantially from random networks. These models can generate features like the small world property. But it is a giant leap to go from that, to understanding something as huge, complex, and dynamic as a financial system. This is especially true given that there are adjustment costs that give rise to hysteresis and path-dependence, as well as shocks that give rise to changes.
Further, let’s say that the Olympian economist Yanet Jellen establishes that the existing network is inefficient according to some criterion (not that I would even be able to specify that criterion, but work with me here). What policy could she adopt that would improve the performance of the network, let alone make it optimal?
The very features–feedbacks, spillovers, non-linearities–that can create suboptimality also make it virtually impossible to know how any intervention will affect that network, for better or worse, under the myriad possible states in which that network must operate. Networks are complex and emergent and non-linear. Changes to one part of the network (or changes to the the way that agents who interact to create the network must behave and interact) can have impossible to predict effects throughout the entire network. Small interventions can lead to big changes, but which ones? Who knows? No one can say “if I change X, the network configuration will change to Y.” I would submit that it is impossible even to determine the probability distribution of configurations that arise in response to policy X.
In the language of the Nautilus article, it is delusional to think that simplicity can be “imposed on” a complex system like the financial market. The network has its own emergent logic, which passeth all understanding. The network will respond in a complex way to the command to simplify, and the outcome is unlikely to be the simple one desired by the policymaker.
In natural systems, there are examples where eliminating or adding a single species may have little effect on the network of interactions in the food web. Eliminating one species may just open a niche that is quickly filled by another species that does pretty much the same thing as the species that has disappeared. But eliminating a single species can also lead to a radical change in the food web, and perhaps its complete collapse, due to the very complex interactions between species.
There are similar effects in a financial system. Let’s say that Yanet decides that in the existing network there is too much credit extended between nodes by uncollateralized derivatives contracts: the credit connections could result in cascading failures if one big node goes bankrupt. So she bans such credit. But the credit was performing some function that was individually beneficial for the nodes in the network. Eliminating this one kind of credit creates a niche that other kinds of credit could fill, and profit-motivated agents have the incentive to try to create it, so a substitute fills the vacated niche. The end result: the network doesn’t change much, the amount of credit and its basic features don’t change much, and the performance of the network doesn’t change much.
But it could be that the substitute forms of credit, or the means used to eliminate the disfavored form of credit (e.g., requiring clearing of derivatives), fundamentally change the network in ways that affect its performance, or at least can do so in some states of the world. For example, it make the network more tightly coupled, and therefore more vulnerable to precipitous failure.
The simple fact is that anybody who thinks they know what is going to happen is dangerous, because they are messing with something that is very powerful that they don’t even remotely understand, or understand how it will change in response to meddling.
Hayek famously said “the curious task of economics is to demonstrate to men how little they really know about what they imagine they can design.” Tragically, too many (and arguably a large majority of) economists are the very antithesis of what Hayek says that they should be. They imagine themselves to be designers, and believe they know much more than they really do.
Janet Yellen is just one example, a particularly frightening one given that she has considerable power to implement the designs she imagines. Rather than being the Hayekian economist putting the brake on ham-fisted interventions into poorly understood symptoms, she is far closer to Adam Smith’s “Man of System”:
The man of system, on the contrary, is apt to be very wise in his own conceit; and is often so enamoured with the supposed beauty of his own ideal plan of government, that he cannot suffer the smallest deviation from any part of it. He goes on to establish it completely and in all its parts, without any regard either to the great interests, or to the strong prejudices which may oppose it. He seems to imagine that he can arrange the different members of a great society with as much ease as the hand arranges the different pieces upon a chess-board. He does not consider that the pieces upon the chess-board have no other principle of motion besides that which the hand impresses upon them; but that, in the great chess-board of human society, every single piece has a principle of motion of its own, altogether different from that which the legislature might chuse to impress upon it. If those two principles coincide and act in the same direction, the game of human society will go on easily and harmoniously, and is very likely to be happy and successful. If they are opposite or different, the game will go on miserably, and the society must be at all times in the highest degree of disorder.
When there are Men (or Women!) of System about, and the political system gives them free rein, analytical tools like topology can be positively dangerous. They make some (unjustifiably) wise in their own conceit, and give rise to dreams of Systems that they attempt to implement, when in fact their knowledge is shockingly superficial, and implementing their Systems is likely to create the highest degree of disorder.