Detecting Identification Failure in Moment Condition Models
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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.
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