Financial Crisis Contagion in Financial Networks

What an incredibly interesting and timely study.

A new study by Raja Kali and Javier Reyes, economics professors in the Sam M. Walton College of Business at the University of Arkansas, reveals that integration in the global financial network is a double-edged sword. On one hand, being well connected to the network can make a country more vulnerable to systemic shocks. However, this same connectedness also is associated with an increased ability to dissipate economic shocks to the system. Kali and Reyes reached these conclusions by studying how international financial crises travel though the network of global trading relationships.

You can find a pre-print copy of the paper from Kali's website here. It's too bad they didn't drum up some visualizations of the network detailing their findings. Network visualizations are at the same time extremely useful for getting an idea of the structure of a network and extremely cool.

I haven't read the paper in-depth yet, so if anyone does, please let me know your opinion on it! The goal of this study is understand how financial crises are transmitted. In this increasingly integrated financial world, economists have a great interest but a poor understanding of how this happens.

They used a measure that I'm not familiar with. Aside from degree centrality - the preschooler's centrality - they use a measure called 'node importance.' Node importance is supposed to be a measure of how much other nodes rely on the subject node for their integration into the network. Through some quick Google searches I haven't been able to find a precise mathematical definition of how this is measured.

Oh well - this still looks like a cool study particularly because it relates qualities and behavior of nodes to their position in the network structure instead of just a survey of the features of the network.

See America in it's roads

This is pretty amazing... The only feature in this map of the United States is roads as black lines at a constant width (meaning interstates are the same size as small rural roads).

No other features were added, the fact that you see mountains and lakes is because roads conform to those features.



Click the image to see the source page with some close-up detail of certain areas.

I find it fascinating how political boundaries of counties show some stark differences in the road density.

Too much love, not enough violence

Game theory can provide some very interesting predictions. Here are two examples that claim that 'coward' agents can disrupt a peaceful society of xenophobic warriors, and another that claims a surfeit of altruism can be bad for cooperations.

The first paper, "Emergence and Collapse of Peace with Friend Selection Strategies", examines cooperation among agents with different 'friend selection strategies' (FSS). There are several kinds of strategies, there's an agent that attacks everything it sees, there's an agent that leaves other agents alone unless they attack one of their friends, then there's an agent who won't attack anyone even if someone attacks their friend.

The "best" strategy, it seems, is the us-TFT (TFT stands for tit-for-tat, if you hit me, I'll hit you). The us-TFT agent tends to create strong cooperation among members of the 'us' since they collaboratively defend each other. When the 'society' reaches a critical number of us-CWD (or us-cowards, who won't attack enemies) the cooperation collapses, almost instantaneously. In a way the us-CWD can be seen as a free-rider, being part of the society, but not defending it against attack, and any society can only absorb so many defectors before it collapses.

But this is a very simplistic model. If you read the paper they address the numerous sociological issues with the model, how moralistic groups, or self-identifying groups, or groups with rumor and communication, would probably behave very differently and would handle free-riding or defense very differently. This is the physics equivalent of a sphere in a vacuum.

The next paper comes out of the Santa Fe Institute, a research institute in New Mexico dedicated to the study of complex systems*. The methods in this paper are completely mathematical, involving no simulation at all.

Altruism is helping others at a cost to yourself. It is assumed that the ideal society would consist solely of altruistic members. The members of this theoretical society give to the community as a whole, they provide a public good, meaning that everyone in the society shares the benefit. The hope is that others in the society also provide public goods and the net benefit to each individual is much greater than the cost of providing a good.

But there are free-riders, again, that don't contribute any goods, but still reap the benefits (such is the nature of public goods, like roads or environmental protection or pot-luck dinner). They give each member of the society an option to punish free-riders when they are detected and in return the punisher gets a 'warm-glow' - a good feeling from punishing the person - but punishment comes, just like providing a good, at a cost to the punisher.

They optimize their system for maximum payoff to the society. The math gets nice and heavy and they conclude with this:

Our results suggest that for a community wishing to sustain high levels of cooperation, seeking to enhance unconditional altruism may be counter-productive. But punishment may also be counter-productive. By definition acts of altruism increase the joint surplus of the community; but punishment is often (as in our model) resource-using. Unless or until levels of contribution sufficient to make punishment rare are achieved, the costs associated with punishment of low contributors may more than offset the gains to cooperation that the punishment allows. This is particularly true in a case we have not considered, namely when vendetta-like cycles of punishment and counter punishment are allowed.

What they find is that there is a balance of altruism and punishment within a society. It is not beneficial to exert punishment on individuals until punishment is rare enough, otherwise you are exerting a cost to punish too much. The resulting increase in cooperation does not make up for the cost of punishment.

-- So, there, I thought I'd share some game-theory demonstrating that balance in very important when trying to maintain cooperation between rational** entities.

* I really wish they had a PhD program.
** Even though I disagree with the rational paradigm...

Here comes life from non-life!

Ah - self-organization, the almost-magic.



Fun stuff - I like the video of the fatty acids self organizing into a sphere.

The very interesting part about the artificial life these biologists intend to create (imo, of course) is that it probably doesn't resemble any life that has ever existed on the planet. This would be a unique creation that eventually would take on the attributes of self-replication and metabolism.

But, as discussed in the article, this doesn't mean much about the origin of life on Earth. When they finally create a self-replicating system it would be very good evidence that life could have started from non-living materials at some point in the planet's past. One of the major arguments Creationists have against evolution concerns abiogenesis (even though that's not really a part of evolutionary theory), and I fully expect a 10x more voracious version of the Lenski/Schlafly debacle.

Better than least squares? L1 Linear Regression

Everyone with basic statistics background has certainly seen or used the Ordinary Least Squares method of regression. Everyone would always tell me, you square the error to remove the negative, but this always confused me.

Why not just take the absolute value of the error? That would achieve the same goal right?

Well, Will Dwinnell at this blog has revealed the L1 Regression (or least absolute errors regression) which does exactly that. It optimizes the absolute value of errors instead of the squared error.

So, why do we use least squares when L1 regression is certainly an option? Will tells us: Least-squares makes the calculus behind the fitting process extremely easy!

That's it. Statisticians will give all manner of rationalizations, but the real reason least-squares regression is in vogue, is that it is extremely easy to calculate.

I guess that's a good reason. But the fact is, there are times when you should be using the L1 regression instead of the OLS regression. For instance, in graphic shamlessly taken from Dwinnell's blog, we have some data in which there are a couple outliers. The OLS regression skews, but the L1 regression better matches the actual relationship:



The comments tell us a bit more about when we should use L1 regression, and when OLS would be better.

We would like our regression to be a maximum likelihood estimate (MLE) - that is, we would like the values that the model predicts to represent the value that is most likely to result from the system we are modeling. Makes sense. But in some cases the OLS is closer to the MLE and in other cases the L1 is closer to the MLE.

When the distribution of errors is Gaussian (normal, bell curve, whatever) then the OLS is the best choice. But when the distribution errors are Laplacian, or double exponential, then your best choice is the L1 distribution.

So for those of you who are all haughty and uptight about good statistics (like me), you might want to try this out.

This public service announcement was brought to you by the Poisson Distribution, estimating the duration in time between discrete events since 1838!

Very Cool Class: Blending Network Science and Art

Each of the items in that image illustrate the topic for each week of Burak Arikan's Creative Networking course.

This looks like a really fun class. It is all about the conceptualization and dynamics of networks and then couples that with the aesthetic visualization of networks.

For instance, here's the assignment for week 9:

Exercise Part 1
Create a virus that infects the nodes in your friend’s network. Can your virus diffuse partially or fully, how long does it take? What happens to individual nodes when they are infected? Visualize the spreading activity.

Exercise Part 2
Create a vaccine for the virus in your network, so that the nodes gain immunity. Visualize your network’s healing activity.

Exercise Part 3
Create a new tactic for your virus that can exploit immuned nodes.

It reminds me of a math course for liberal arts and fine arts students at CSU. It had assignments like hypercubes, and drawing or visualizing the growth of a population, etc. It, like this class, wasn't heavy on the math or theory, but more on the conceptualization and dynamics. It's the idea that you can learn something by playing with it.

But - if you ever really want to do anything significant with it, it would help to learn the math, computer science, and theory behind it all. I bet classes like this do a great job in creating interest and motivation to explore the concepts and ideas in network science and other fields.