Wednesday, April 3, 2013

Causal Relationships and the Crash of 2008

It has become a dominant meme, especially among conservatives, that "giving out subprime loans like candy was the cause of the economic crash of 2008". This is true under only the most naive definition of the word "cause". The naive definition is "A happened then B happened and there was obviously a relationship between the two therefore A caused B". A much better definition to use is "A caused B if and only if A happened then B happened and if A had not happened then, holding all other things equal, B would not have happened". When the second definition is applied to the cause of the Great Recession it becomes doubtful that the subprime mortgage crisis was a large part of the cause. The larger part of the cause was a systemic mistake in the risk models used by investment banks. What follows is an argument supporting that conclusion. The logic is not mine originally although the summary of it and presentation are.

To examine the cause of the Great Recession requires knowledge of "derivatives" and other related financial instruments. Investments are priced based on how risky they are. Risky ones are cheap while safe ones are expensive. When packaging bundled financial instruments from smaller ones, the banks and the credit bureaus have to compute the risk associated with the package product. Prior to 2008 they almost uniformly used a naive Bayesian model to compute this. Specifically, they assumed that the risk involved with the package is equal to the product of the risks involved with each individual item in the package. This computation is only accurate if the failure/success of the individual items are independent identically distributed values. This independence assumption is, however, patently NOT sound when similar types of products are all put together into one big package (e.g. bundles of mortgages). The assumption says that the failure of two mortgages are not related. This ignores the fact that it is possible for some external event to cause many mortgages to go into default simultaneously.

For the sake of argument, assume that the risk of each mortgage going into default was assessed as roughly 5%. If the risk of default for any particular mortgage is independent from the default of other mortgages then a package with 100 mortgages has a risk of being a losing investment of less than .0001%. If, however, the risk of one mortgage defaulting is closely related to whether or not other mortgages go into default (e.g. the defaults share a common cause) then the risk of the package is closer to the 5% risk associated with each individual mortgage. The packaged mortgage instruments were priced based on the .0001% risk. This caused the banks to invest HEAVILY in them. These are not, however, the only things being packaged this way. The banks were (and to a lesser extent still are) packaging all kinds of financial instruments together using the same incorrect risk model. The credit agencies endorse the risk model of the banks because the financial incentives for them are based on the number of ratings they give rather than the success of their previous ratings. The banks have incentives to use the faulty model because 5% is still a small chance of failure and so long as their customers THINK the risk is .0001% they're making money hand over fist. The problems associated with this incorrect risk model compound when it is recursively applied to packages of packages.

Immediately after the housing bubble popped the banks began reassessing their risk models. Similar instruments packaging other financial products which had not yet seen problems were sold and bought at more rational prices and those products never caused any problems. They caused no problems despite the fact that the bottom fell out of some of those markets after the housing bubble popped. The reason they caused no problems was because the pricing and risk models had been correctly updated BECAUSE of the crash. If, however, there had never been a housing bubble the OTHER incorrectly priced packaged instruments that later went bust WOULD have had a very similar impact. Therefore event B, the Great Recession, would've probably still happened in the absence of event A, the subprime mortgage crisis. However, if the pricing model used by the banks had been accurate to begin with then event B probably would NOT have happened even in the presence of event A. This line of reasoning leads to the conclusion that the risk model used for pricing financial instruments was a larger cause of the 2008 crash than was the subprime mortgage crisis. However, this line of reasoning is probabilistic in nature and it is because of the probabilistic uncertainty involved that I said the subprime mortgage crisis was a partial cause of the recession.

The great pity though is that even with the argument broken down that way using language that many people can easily understand it is no where near as pithy or understandable as the dominant causal explanations. As I mentioned in the intro, conservatives have a tendency to say: "liberals forced banks to give out loans to poor people like candy and the crash was caused by that irresponsibility". This post was largely a critique of that idea but the liberal explanation fares no better. The most common liberal explanation is: "greedy and evil wall street cronies took advantage of the lack of regulation to steal billions of dollars from the American people through exploiting the poor and back room deals". That's not true either though. Even if every banker and trader had the heart of the kindliest of generous grandmothers the crash would still have happened if those kind generous bankers were using a mathematically incorrect risk model. The crash didn't happen because of the greed of the poor OR the greed of the wealthy. It happened because there are systemic incentives in place that reward people for using bad math.

No comments:

Post a Comment