Testing the null of identification in GMM

This paper proposes a new test of the null hypothesis that a generalized method of moments model is identified. The test can detect local or global underidentification, and underidentification in some or all directions. The idea of the test is to compare the volume of two confidence sets - one that is robust to lack of identification and one that is not. Under the null hypothesis the relative volume of these two sets is Op(1), but under the alternative, the robust confidence set has infinite relative volume.