A comparison of some common methods for detecting Granger noncausality

Abstract

We compare testing strategies for Granger noncausality in vector autoregressions (VARs) that may or may not have unit roots and cointegration. Sequential testing methods are examined; these test for cointegration and use either a differenced VAR or a vector error correction model (VECM), in which to undertake the main noncausality test. Basically, these strategies attempt to verify the validity of appropriate standard limit theory. We contrast such methods with an augmented lag approach that ensures the limiting χ² null distribution irrespective of the data’s nonstationarity characteristics. Our simulations involve bivariate and trivariate VARs in which we allow for the lag order to be selected by general to specific testing and by model selection criteria. We find that the practice of pretesting for cointegration can result in severe overrejections of the noncausal null, whereas overfitting results in better control of the Type I error probability with often little loss in power.

Keywords:

• Cointegration
• Error correction model
• Lag length selection
• Sequential testing
• Testing for Granger noncausality
• Monte Carlo simulation

Acknowledgements

This research was supported by a grant from the Social Sciences and Humanities Council of Canada for the first author. We benefited greatly from N. Dastoor’s careful reading and suggestions. We thank the reviewers of this paper in addition to J.-M. Dufour, W. Fuller, J. Galbraith, R. Garcia, D. Giles, S. Gordon, L. Khalaf, B. McCabe, N. Roy, P. Siklos, K. Stewart, and participants at several conferences and seminars.

Notes

^†Granger 1, which builds on earlier work of Wiener 2.

^†Saikkonen and Lütkepohl 5 extend this to infinite order cointegrated VARs.

^†The introduction of moving average errors can potentially alter the causality structure. This is unlikely here due to our assumption of uncorrelated errors across equations. Our DGPs under S3 satisfy the noncausality Theorems 3 and 4 of Boudjellaba et al. 35 but these theorems require invertible ARIMA processes, which precludes cointegrating relations. It would seem highly likely that the theorems would extend in this case, but the proofs are as yet unavailable; see Boudjellaba et al. [35, p. 278] for discussion.

^‡The usual tabulated results are available from the first author.