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Assessing the Approximate Validity of Moment Restrictions

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  • Lavergne, Pascal

Abstract

We propose a new theoretical framework to assess the approximate validity of overidentifying moment restrictions. Their validity is evaluated by the divergence between the true probability measure and the closest measure that imposes the moment restrictions of interest. The divergence can be chosen as any of the Cressie-Read family. The considered alternative hypothesis states that the divergence is smaller than some user-chosen tolerance. Tests are constructed based on the minimum empirical divergence that attain the local semiparametric power envelope of invariant tests. We show how the tolerance can be chosen by reformulating the hypothesis under test as a set of admissible misspecifications. Two empirical applications illustrate the practical usefulness of the new tests for providing evidence on the potential extent of misspecification.

Suggested Citation

  • Lavergne, Pascal, 2015. "Assessing the Approximate Validity of Moment Restrictions," TSE Working Papers 15-562, Toulouse School of Economics (TSE), revised May 2020.
    • Handle: RePEc:tse:wpaper:29157
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    References listed on IDEAS

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    Keywords

    Hypothesis testing; Semiparametric models;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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