Identification and Identifiability of non-linear IV/GMM Estimators

Abstract

In this article, the identi¯cation of instrumental variables and generalised method of moment (GMM) estimators is discussed. It is common that representations of such models are derived from the solution to linear quadratic optimisation problems. Here, it is shown that even though the rank condition on the Jacobian and the instrument set is valid, that the transversality condition may not be satis¯ed by the estimated model. Further, acceptance of the transversality condition does occur when identi ¯cation fails or the forward model vanishes. As a result the parameters of such models irrespective of any correction for serial correlation may not be identi¯ed in a fundamental sense. This suggests that either forward looking models should be estimated directly or more complex non-linear restrictions should be imposed.