PERMANENT-TRANSITORY DECOMPOSITIONS UNDER WEAK EXOGENEITY
证明，在向量误差修正模型中，当弱外生变量个数等于共同趋势数且排序靠前时，递归正交冲击可直接构成永久-暂时分解，且永久冲击与Gonzalo和Ng分解一致。
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.We are grateful to the co-editor Paolo Paruolo and an anonymous referee for useful comments, which have helped to improve the content and exposition of this note. Financial support from the Australian Research Council is gratefully acknowledged.