Generalized method of moments specification testing

This paper analyzes the asymptotic power properties of specification tests which are based on a finite set of moment conditions. It shows that any such test may fail against general misspecification that causes estimator inconsistency. The mutual asymptotic equivalence of maximal degree of freedom tests is shown and the form of optimal tests against specific forms of misspecification is derived. Applications to testing for exogeneity of a set of instrumental variables are presented.