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

Abstract

In this article, the identification of instrumental variables and generalized method of moment (GMM) estimators with multi-period perceptions is discussed. The state space representation delivers a conventional first 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 sufficient for the identification of the structural model. Necessary and sufficient conditions for local identification 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 identification of the Q-SF parameters. While the conditions necessary and sufficient for local identification of the Q-SF parameters are only necessary to identify the expectational model that satisfies the regular solution. If the conditions required for the decomposition associated with the Generalized Bézout Theorem are not satisfied, then limited information estimates of the Q-SF are not consistent with the full solution. The Structural Form (SF) is not identified 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.