Detecting identification failure in moment condition models

This paper develops an approach to detect identification failure in moment condition models. This is achieved by introducing a quasi-Jacobian matrix computed as the slope of a linear approximation of the moments on an estimate of the identified set. It is asymptotically singular when local and/or global identification fails, and equivalent to the usual Jacobian matrix which has full rank when the model is globally and locally identified. Building on this property, a simple test with chi-squared critical values is introduced to conduct subvector inferences allowing for strong, semi-strong, and weak identification without a priori knowledge about the underlying identification structure. Monte-Carlo simulations and an empirical application to the Long-Run Risks model illustrate the results.