Long-Run Economic Relationships

"This book is about a subject for which the technical term is cointegration. What it means in everyday language is variables that are tied together in the long run, that are related in some way. For example, you might think that consumption and income are tied together in the long run. If income takes a big left-turn at some point in the data, consumption ought to take a big left-turn in the data as well. One thing they got the Nobel prize for is how, within our models, we can tie these two variables together in a way that makes sense. It sounds easy, but it’s actually a very hard econometric problem. The other thing they got their Nobel prize for was something called ARCH, or autoregressive conditional heteroskedasticity models. What that means is that for, say, income over time, we can measure the variance of income – how variable it is. There is some mean of income over time that follows some trend, and the variation around that trend is the variance. They showed us how to write down economic models that track that variance through time. So, for example it can tell us what’s causing the variance of a financial asset to change. The variance of a financial asset would be how risky it is. If you’re looking at a financial asset, the mean would be the expected return on the asset and the variance is its risk profile. These tools that they developed within this ARCH framework were then used – Engle says inappropriately – to do what were called value-at-risk calculations, prior to the crisis. When you hear about all these financial firms, looking at their portfolio and doing risk assessments, at the heart of what they were doing was these models that Engle and Granger built, the models that allowed us to estimate a time series of variances and see how that variance, or risk profile, changes over time. Yes, and Engle would say that the reason why that happened is that they weren’t using his models correctly. In some sense he’s just protecting himself. The important point here is that at the heart of all the risk analysis for the financial industry was their models. Prior to the crash, and even after the crash, if you wanted to know how risky the portfolio that Bear Stearns was holding was, you would use those techniques. The book is more about the first topic I mentioned, cointegration, though the other stuff is in there as well. Cointegration is important because it allows us to do a better job of looking at things like causality between variables. They showed that if you have variables that are tied together over time, then the standard tools and techniques that were in use at that time would be wrong. It would be inappropriate to use them, you have to use a completely different estimation technique. They showed us how to do tests to find out if you have this problem of a long-run relationship in your data, and if you have this problem how to fix it within the models. That was an important step forward, because we learned that these relationships are all over the place. We had probably been estimating our models wrong up to that time. And ARCH models themselves are useful, there’s no need to throw them out, but we do need to be congnizant of their limitations. The crisis wouldn’t have changed anyone’s view of cointegration. I think the value of the ARCH models might have been questioned a bit more than they were at the time, because they didn’t signal the risks in advance like we expected them to."