Overidentificatietesten

Overidentificatietesten, in the context of econometrics and statistics, refers to a class of hypothesis tests used to determine whether a model is too restricted. Specifically, it is employed when a model has more restrictions imposed on it than are necessary to achieve point identification. A model is point-identified if a unique parameter vector can be estimated from the data. Overidentifying restrictions are additional constraints that, if correct, should hold true for the data but are not essential for the model to be uniquely estimated.

The core idea behind overidentificatietesten is to compare the fit of a more restricted (and thus potentially misspecified) model with a less restricted (and potentially more appropriate) model. If the overidentifying restrictions are valid, the estimations from both models should be similar, or the restricted model should not suffer a significant loss in fit compared to the unrestricted one. Conversely, if the restrictions are not valid, the restricted model will exhibit a poorer fit, and the test will reject the null hypothesis that the overidentifying restrictions hold.

These tests are commonly used in instrumental variables (IV) estimation. In IV models, the validity of the instruments is crucial. If there are more instruments than are needed to identify the parameters, these extra instruments can be used to form overidentifying restrictions. Tests like the Sargan test or the Hansen J test are examples of overidentificatietesten in this context. They assess whether the instruments are uncorrelated with the error term in the structural equation, which is a key assumption for the validity of the IV estimator. A rejection of the null hypothesis suggests that the instruments are likely endogenous or otherwise invalid.