The Equivalence of Causality Detection in VAR and VECM Modeling with Applications to Exchange Rates

Vector error-correction models (VECM) are increasingly being used to capture dynamic relationships between financial variables. Estimation and interpretation of such models can be enhanced if zero restrictions are allowed in the coefficient matrices. Specifically, in tests of indirect causality and/or Granger non-causality in a VECM, the efficiency of the causality detection is crucially dependent upon finding zero coefficient entries where the true structure does indeed include zero entries. Such a VECM is referred to as a zero-non-zero (ZNZ) patterned VECM and includes full-order models. Recent advances have shown how ZNZ patterns can be explicitly recognized in a VECM and used to provide an effective means of detecting Granger-causality, Granger non-causality and indirect causality. This paper develops a general approach and framework for I(d) integrated systems.We show that causality detection in an I(d) system can be discovered identically from the ZNZ patterned VECM’s or the equivalent VAR models.