Testing for Cobreaking and Super exogeneity in the Presence of Deterministic Shifts

We introduce a reduced rank technique for testing for common deterministic shifts. The reduced rank approach is analysed also in the context of super exogenity and an alternative test for super-exogeneity is proposed. One important advantage of this approach is that departing from the unrestricted model we depart from a more general model that does not impose a priori which are the target and the policy variables. This could be useful in case in which there did not existed an exact knowledge about a classification between target and instrument nor about their relationship. Monte Carlo simulations are implemented to investigate the power of this technique.