CASE STUDY 2: CAUSALITY IN THE ENERGY/GDP RELATIONSHIP
One of the most important questions about the environment-economy relationship regards the strength of the linkage between economic growth and energy use. With a few exceptions, most analyses ignore the effect of energy quality in the assessment
of this relationship. One statistical approach to address this question is Granger causality and/or cointegration analysis. Granger causality tests whether (i) one variable in a relation can be meaningfully described as a dependent variable and the other variable as an independent variable, (ii) the relation is bidirectional, or (iii) no meaningful relation exists. This is usually done by testing whether lagged values of one of the variables add significant explanatory power to a model that already includes lagged values of the dependent variable and perhaps also lagged values of other variables.
Although Granger causality can be applied to both stationary and integrated time series (time series that follow a random walk), cointegration applies only to linear models of integrated time series. The irregular trend in integrated series is known as a stochastic trend, as opposed to a simple linear deterministic time trend. Time series of GDP and energy use are usually integrated. Cointegration analysis aims to uncover causal relations among variables by determining if the stochastic trends in a group of variables are shared by the series so that the total number of unique trends is less than the number of variables. It can also be used to test if there are residual stochastic trends that are not shared by any other variables. This may be an indication that important variables have been omitted from the regression model or that the variable with the residual trend does not have long-term interactions with the other variables.
Either of these conclusions could be true should there be no cointegration. The presence of cointegration can also be interpreted as the presence of a longterm equilibrium relationship between the variables in question. The parameters of an estimated cointegrating relation are called the cointegrating vector. In multivariate models, there may be more than one such cointegrating vector.