A comparison of some common methods for detecting Granger noncausality

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.