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.