Testing for Identification in Potentially Misspecified Linear GMM

Abstract

The difference between the population analogs of the traditional Jacobian rank statistic and the J-statistic provides an appropriate identification measure for the pseudo-true values of the continuous updating and two-stage estimators in the misspecified linear generalized method of moments, whilst the population analog of the traditional Jacobian rank statistic alone does not. The sample analog of the identification measure leads to a likelihood ratio no-identification test. We construct a conditional critical value function for the test in the homoskedastic setting which controls the size. Applying the test to empirical asset pricing where misspecification is common, we find that no-identification is often not rejected at the 5% significance level while the Jacobian rank test wrongly signals the opposite.