Modified Hausman tests for inefficient estimators

Widely-used estimators such as the generalized method of moments (GMM) and quasi-maximum likelihood (QML) are not efficient in general. This study shows how the Hausman specification test may easily be corrected to be used with inefficient estimators. It introduces a related test that has better power, and it points out the relationship to the GMM criterion test of specification of overidentified models. A brief simulation illustrates the results.