This paper develops an approach to detect identification failures in a large class of moment condition models. This is achieved by introducing a quasi-Jacobian matrix which is asymptotically singular under higher-order local identification as well as weak /set identification; in these settings, standard asymptotics are not valid. Under (semi)-strong identification, where standard asymptotics are valid, this matrix is asymptotically equivalent to the usual Jacobian matrix. After re-scaling, it is thus asymptotically non-singular. 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.  Monte-Carlo simulations and empirical applications illustrate the results.
This paper develops an approach to detect identification failure in a large class of moment condition models. This is achieved by introducing a quasi-Jacobian matrix which is asymptotically singular under weak or set identification, and when local identification fails. In these settings, standard asymptotics are not valid. Under (semi)-strong identification, where standard asymptotics are valid, the quasi-Jacobian is asymptotically equivalent to the usual Jacobian and, after re-scaling, is asymptotically non-singular. Hence, the eigenvalues of the quasi-Jacobian are informative about 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 about the underlying identification structure. It is non-conservative under strong identification. Monte-Carlo simulations and an application to the Long-Run Risks model illustrate the results.
R
failures
failure
R
higher-order local identification as well as weak /set identification; in
weak or set identification, and when local identification fails. In
R
this matrix
the quasi-Jacobian
R
matrix. After
and, after
R
it is thus
is
R
Together, these results imply that
Hence,
R
can detect potential
are informative about
R
. Furthermore, the quasi-Jacobian is informative about the span of the identification failure. This information permits two-step identification robust subvector inference without any
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
R
of
about
A
It is non-conservative under strong identification.
R
empirical applications
an application to the Long-Run Risks model