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Abstract: This paper develops an approach to detect identification failures in a large class of moment conditions models. This is achieved by using a quasi-Jacobian matrix which is asymptotically singular under higher-order local identification as well as weak and 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 rescaling, 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 robust subvector inference without any a priori knowledge of the underlying identification structure. Monte-Carlo results illustrate power improvements over projection based inference.
Additionally, new results on the concentration of quasi-Bayesian posteriors over identified sets are given. Empirical applications illustrate the approach in practice.