Author : Ki-Ho Kim(Bank of Korea)

Responses to shocks of endogenous variables and those to shocks of exogenous variables are mixed when rotation matrices are used for the sign restriction in VARX model. The mixing of responses to incompatible shocks may result in erroneous identifications when employing sign restrictions in the context of VARX frameworks.

The order in which Givens rotation matrices are multiplied introduces an additional degrees of freedom, a consequence of the non-abelian nature of matrix multiplication. This paper elucidates that the multiplicative order of Givens matrices significantly affects the identification of structural shocks, particularly in settings where sign restrictions are imposed within VARX models that incorporate exogenous variables.

To address these identification challenges, we propose a dual methodology: a systematic ordering of Givens rotation matrices combined with zero restrictions on these appropriately ordered matrices. Both approaches are essential for the accurate identification of structural shocks within VARX models. We designate the ordered Givens matrices as Properly Ordered Givens (POG) matrices and refer to the zero-restricted POG matrices as Zero-Restricted Properly Ordered Givens (ZPOG) matrices.

As a case study, this paper investigates the impact of inflation expectations on the pass-through effect of the Consumer Price Index (CPI) through a counterfactual analysis. The estimation results indicate that the inflation expectations channel amplifies the response of the CPI to shocks originating in the oil market.

Measures of inflation expectations serve as a key signal of the credibility of central bank policies. Consequently, it is imperative for monetary authorities to actively monitor and stabilize inflation expectations to mitigate the potential amplifying effects associated with inflation expectations, thereby enhancing the credibility of their monetary policy.