PERMANENT-TRANSITORY DECOMPOSITIONS UNDER WEAK EXOGENEITY

This note shows that the orthogonal shocks obtained by imposing a recursive structure on the contemporaneous impacts of the errors in a vector-error correction model ~VECM! are related to the orthogonal permanent-transitory shocks in a Gonzalo and Ng ~2001, Journal of Economic Dynamics and Control 25, 1527– 1546! decomposition provided some of the variables in the system are weakly exogenous+ Specifically, when there are as many weakly exogenous variables as common trends and the weakly exogenous variables are ordered first, the orthogonal shocks obtained directly from the VECM constitute a permanent-transitory decomposition, and the permanent shocks are identical to those in the Gonzalo and Ng decomposition+