Tests for Violations of Moment Conditions

This paper presents optimal tests for violations of the moment conditions in the GMM framework. New tests are presented for the validity of the overidentifying restrictions. The usefulness of these tests is highlighted by a simple AR(1) example with instability in the moment conditions. For this example, the J test in Hansen (1982) does not reject the overidentifying restrictions but the rejection by a parameter stability test incorrectly suggests a time varying parameter model. The new tests correctly show the instability in the moment conditions and would direct the researcher to consider alternative moment conditions.