Identifying asymmetric, multi-period Euler equations estimated by non-linear IV/GMM

In this article, the identi...cation of instrumental variables and generalized method of moment (GMM) estimators with multi-period perceptions is discussed. The state space representation delivers a conventional ...rst order condition that is solved for expectations when the Generalized Bézout Theorem holds. Here, it is shown that although weak instruments may be enough to identify the parameters of a linearized version of the Quasi-Reduced Form (Q-RF), their existence is not su¢cient for the identi...cation of the structural model. Necessary and su¢cient conditions for local identi...cation of the Quasi-Structural Form (Q-SF) derive from the product of the data moments and the Jacobian. Satisfaction of the moment condition alone is only necessary for local and global identi...cation of the Q-SF parameters. While the conditions necessary and su¢cient for local identi...cation of the Q-SF parameters are only necessary to identify the expectational model that satis...es the regular solution. If the conditions required for the decomposition associated with the Generalized Bézout Theorem are not satis...ed, then limited information estimates of the Q-SF are not consistent with the full solution. The Structural Form (SF) is not identi...ed in the fundamental sense that the Q-SF parameters are not based on a forward looking expectational model. This suggests that expectations are derived from a forward looking model or survey data used to replace estimated expectations.