Model Equivalence Tests for Overidentifying Restrictions

I propose a new theoretical framework to assess the approximate validity of overidentifying moment restrictions. Their approximate validity is evaluated by the divergence between the true probability measure and the closest measure that imposes the moment restrictions of interest. The divergence can be chosen as any of the Cressie-Read family. The considered alternative hypothesis states that the divergence is smaller than some user-chosen tolerance. Model equivalence tests are constructed for this hypothesis based on the minimum empirical divergence. These tests attains the local semiparametric power envelope of invariant tests. Three empirical applications illustrate their practical usefulness for providing evidence on the potential extent of misspecification.