Co-integration rank determination in partial systems using information criteria

We investigate the asymptotic and finite sample properties of the most widely used information criteria for co-integration rank determination in ‘partial’ systems, i.e. in co-integrated Vector Autoregressive (VAR) models where a sub-set of variables of interest is modeled conditional on another sub-set of variables. The asymptotic properties of the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC) and the Hannan-Quinn Information Criterion (HQC) are established, and consistency of BIC and HQC is proved. No- tably, consistency of BIC and HQC is robust to violations of the hypothesis of weak exogeneity of the conditioning variables with respect to the co-integration parameters. More precisely, BIC and HQC recover the true co-integration rank from the partial system analysis also when the conditional model does not convey all information about the co-integration parameters. This result opens up interesting possibilities for practitioners who can determine the co-integration rank in partial systems without being concerned with the weak exogeneity of the conditioning variables. A Monte Carlo experiment which considers large systems as data generating process shows that BIC and HQC applied in partial systems perform reasonably well in small samples and comparatively better than ‘traditional’ approaches for co-integration rank determination. We further show the usefulness of our approach and the benefits of the conditional system anal- ysis to co-integration rank determination with two empirical illustrations, both based on the estimation of VAR systems on U.S. quarterly data. Overall, our analysis clearly shows that the gains of combining information criteria with partial systems analysis are indisputable.