Wednesday, April 18, 2012

Surplus-Lag Granger Causality Testing

My previous posts (here, here, and especially here) on Granger causality testing have attracted more interest than I anticipated. One of the things that I've discussed at some length is the "surplus-lag" approach that can be used when the data are possibly non-stationary and possibly cointegrated. In particular I've talked about the Toda and Yamamoto (1995) procedure, but there are alternatives such as those introduced by Dolado anLütkepohl  (1996) and Saikkonen and Lütkepohl (1996).

These modifications to the standard approach to testing for Granger (non-) causality are needed to ensure that the Wald test statistic has its usual chi-square asymptotic null distribution. You can't just test in the usual way unless the data are stationary. In fact, the "surplus lag" approach has advantages even beyond those that we knew about already.

In a really nice upcoming article in Journal of Econometrics, Bauer and Maynard (2012) provide results that :
"demonstrate that the surplus-lag causality test applies, without adjustment, to a considerably wider range of processes. This argues for its usefulness as a robust complement to tests that are more powerful in more restrictive settings".
The earlier Working Paper version of the paper can be found here.

The paper's abstract reads as follows:
"Previous literature has introduced causality tests with conventional limiting distributions in I(0)/I(1) vector autoregressive (VAR) models with unknown integration orders, based on an additional surplus lag in the specification of the estimated equation, which is not included in the tests. By extending this surplus lag approach to an infinite order VARX framework, we show that it can provide a highly persistence-robust Granger causality test that accommodates i.a stationary, nonstationary, local-to-unity, long-memory, and certain (unmodelled) structural break processes in the forcing variables within the context of a single χ2 null limiting distribution."
If you're seriously interested in testing for Granger non-causality, then the Bauer and Maynard paper is a must-read item.

References

Bauer, D. and A. Maynard, 2012. Persistence-robust surplus-lag Granger causality testing. Journal of Econometrics, in press.

Dolado, J. and H. Lütkepohl, 1996. Making Wald tests work for cointegrated VAR systems. Econometric Reviews, 15, 369–38.

Saikkonen, P. and H. Lütkepohl, 1996. Infinite-order cointegrated vector autoregressive processes. Econometric Theory, 12, 814–844.

Toda, H. Y. and T. Yamamoto, 1995. Statistical inferences in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66, 225-250.