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 cointegrated Vector Autoregressive (VAR) models in which 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 the consistency of the BIC and HQC is proved. Notably, the consistency of the BIC and HQC is robust to violations of the hypothesis of weak exogeneity of the conditioning variables with respect to the cointegration parameters. This result opens up interesting possibilities from practitioners who can determine the co-integration rank in partial systems without being concerned with the hypothesis of weak exogeneity of the conditioning variables. A Monte Carlo experiment which uses a dynamic macro model as data generating process shows that the BIC and the HQC 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 by investigating the co-integration implications of a dynamic monetary business cycle model estimated on U.S. quarterly data. Overall, our analysis clearly shows that the gains of combining information criteria with partial systems analysis are indisputable.