Efficient Estimation Of Cointegrating Vectors and Testing for Causality in Vector Autoregressions

This paper surveys various methods of estimating cointegrating vectors and testing for causality in cointegrated VARs, and draws some implications for the applied researcher. In a single equation framework a number of estimators can be used, whose asymptotic efficiency depends on the extent to which they correct for possible endogeneity and serial correlation of the regressors. Such estimates are asymptotically equivalent to those obtained using full system methods, even if the cointegration space is multidimensional, provided there are no cross‐equation restrictions. Using the triangular representation proposed by Phillips (1988), we show that one can employ in the context of an ECM a least squares estimator if weak exogeneity holds. If not, the alternatives are augmenting it by the leads of the regressors as in Stock and Watson (1993), or using the fully modified (FM) estimator due to Phillips and Hansen (1990). Other possibilities are the nonparametric approach developed by Bierens (1997), or the ARDL formulation due to Pesaran and Shin (1995). As for causality testing, we argue that it should be conducted within an ECM rather than a VAR formulation, as the limit distributions are much more likely to be standard in the former case. Alternatively, one can carry out statistical tests in the context of a VAR in levels estimated either by using the FM‐VAR method as in Phillips (1995), or by augmenting the VAR as in Toda and Yamamoto (1995). Other, computationally easier tests have been introduced by Dolado and Lutkepohl (1996) and Saikkonen and Lütkepohl (1996).