Underidentification?

We develop methods for testing the hypothesis that an econometric model is underidentified and inferring the nature of the failed identification. By adopting a generalized-method-of moments perspective, we feature directly the structural relations and we allow for nonlinearity in the econometric specification. We establish the link between a test for overidentification and our proposed test for underidentification. If, after attempting to replicate the structural relation, we find substantial evidence against the overidentifying restrictions of an augmented model, this is evidence against underidentification of the original model.

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