Jonathan L. Rubin, J.D., Ph.D.
Robert F. Engle and Clive W. J. Granger, two econometricians who did most of their work together while at UC San Diego, were awarded the Nobel Prize on October 8, 2003 for their research on the statistical analysis of economic time series. Both made important contributions on their own, but their most influential work by far is contained in a short and elegant paper they published together in 1987. Their paper changed the way statisticians perform almost all regression analysis.
Until the late 1980's, regression analysis was the standard approach to estimating the statistical relationship between variables. The technique developed by Engle and Granger turned the econometric world on its head, by, among other things, explaining why the standard approach was usually wrong.
Their technique, known as cointegration, has been described as a method of uncovering long-run relationships between variables that are concealed by the noise of short-term fluctuations. An engineer might look at this as disentangling the “signal” from the “noise.” An economist could consider it a way of distinguishing between a random fluctuation and a correction back to an equilibrium level. A statistician would regard it as a way of doing regression analysis on non-stationary (i.e., stochastically trending) variables that gives statistically sound results.
A moment’s reflection is all that is needed to realize the significance of such a technique. Consider the movement of one point in the price of a given stock. That one point move might be the beginning of a trend, or it might be a temporary fluctuation that will evaporate on the next trading day. Or it might be a little of both. Any investor would like to know how much of each is represented by that one-point move.
The technique works like this. Ordinary regression analysis weighs the statistical significance of a change in the level of one variable against the change in the level of another. Alternatively, one could measure the effect of the difference of one variable from one period to another on the difference of another variable from one period to another. The level of a variable is its absolute position, while the difference is a measurement of how much the quantity has changed in one period. The first type of regression looks at the entire history of one variable and compares it to the entire history of the other. The second type of regression, looks only at the short-term change in the variable and compares it to the short-term change in the other. Cointegration does both at the same time by splitting up the movement of each variable into a long-run and short-term direction, and performing separate statistical inference on each effect.
In a cointegrated system, the researcher gets two types of estimates in a single equation. One gives the coefficients for the long-run, or equilibrium, relationship between the variables (if there is one), and the other gives the coefficients for the short-term, or noise effects, between the variables.
The ability to perform inference on the potential long-run relationships between economic variables has many applications. In antitrust analysis, the technique could be used to determine market definition by analyzing the extent to which two price series from different geographical locations move together over time. Since prices are usually non-stationary variables, ordinary regression will not be statistically valid. But a cointegration analysis of the two price series can reveal whether they share a common long-run stochastic trend. If so, there is statistical evidence that there is one market; if not, the markets can be considered separate.
Because regression analysis is such an important econometric tool, and because so many variables are non-stationary, cointegration is likely to find its way into the courtroom soon. Cointegration offers a way of explaining why the regression results presented by your opposing expert are not statistically valid, and a way for your expert to present statistical relationships that can withstand methodological attack.
Congratulations to Professors Engle and Granger for their tremendous contribution and for a Nobel Prize well-deserved.