Applying PageRank
http://www.nature.com/srep/2012/120802/srep00541/pdf/srep00541.pdf
The recent financial crisis imparted in certain European statistics professors a strange desire to model major U.S. financial institutions and their interdependencies as a network. The goal of creating this model was to figure out if there is a critical mass of institutions upon which the entire financial system depends–i.e., if there truly are any institutions that are ‘too big to fail’ and as such must be supported by the U.S. government in hard times in order to avoid systemic collapse. The paper continues on with a good amount of math, which I will not repeat here as it is outside the scope of the course. The conclusions they draw are, however, quite interesting. Using a derivative of PageRank, which was called DebtRank, in which the nodes are financial institutions, the edges are dependencies, and the ranks are the fraction of the total economic value of the network held by that institution. They ran two calculations–one on data from before the crisis and one on data from during the height of the crisis. They found that before the crisis, most of the 22 top institutions had a fairly low DebtRank–i.e., though they were large institutions, they did not have a significant hold over the financial system as a whole. Additionally, all of these institutions had similar DebtRanks. During the height of the crisis, however, though the variance in DebtRanks was around the same, the average DebtRank overall was far, far higher–most were over 0.5. What this means is that during the financial crisis, the majority of these 22 institutions could each influence the majority of the financial system. ‘Too big to fail’ indeed.
For me, the most interesting part of this article as it relates to class is its use of a cool algorithm to analyse data to support a qualitative concept that a lot of people have been throwing around when talking about the financial crisis. (I study computer science, so all of the more algorithmic or computer science-related aspects of this course are what tend to catch my interest.) Computer science does tend to be a lot about adapting old tricks to fit new situations, which is exactly what this article discussed. On that note, it is also worth pointing out that DebtRank could be used to analyse the importance of nodes in pretty much any network–for example, if you are a social psychologist, the relative popularity of catty middle school girls. Really, the possibilities are endless.
–blox