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.