Empirical likelihood-based model selection criteria for moment condition models

In this note we propose model selection criteria (MSC) for unconditional moment models using empirical likelihood (EL) statistics in the construction of the MSC The use of EL-statistics in lieu of the more common J-statistics leads to a much more transparent interpretation of the MSC by providing a closer analogy with MSC in standard parametric likelihood models and underlying the common likelihood- (or information-) based underlying model selection procedures for bothe parametric as well as semi-parametric models.