A Simple Test for Identification in GMM under Conditional Moment Restrictions
This paper proposes a simple, fairly general, test for global identiﬁcation of unconditional moment restrictions implied from point-identiﬁed conditional moment restrictions. The test is based on the Hausdorﬀ distance between an estimator that is consistent even under global identiﬁcation failure of the unconditional moment restrictions, and an estimator of the identiﬁed set of the unconditional moment restrictions. The proposed test has a chi-squared limiting distribution and is also able to detect weak identiﬁcation alternatives. Some Monte Carlo experiments show that the proposed test has competitive ﬁnite sample properties already for moderate sample sizes.
Bravo, Francesco; Escanciano, Juan Carlos; and Otsu, Taisuke, "A Simple Test for Identification in GMM under Conditional Moment Restrictions" (2011). Cowles Foundation Discussion Papers. 2133.