Before revision:  Together, these results imply that the eigenvalues of the quasi-Jacobian can detect potential local and global identification failures . Furthermore, the quasi-Jacobian is informative about the span of the identification failure. This information permits two-step identification robust subvector inference without any a priori knowledge of the underlying identification structure.
After revision:  Together, these results imply that the eigenvalues of the quasi-Jacobian can detect potential local and global identification failures and the directions in which identification fails. Building on these results, a simple test procedure with chi-squared data-driven critical values is introduced. It yields uniformly valid subvector inferences under strong, semi-strong, and weak identification without a priori knowledge of the underlying identification structure.