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Efficiency bounds for moment condition models with mixed identification strength

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  • Dovonon, Prosper
  • Atchadé, Yves F.
  • Doko Tchatoka, Firmin

Abstract

Moment condition models with mixed identification strength are models that are point identified but with estimating moment functions that are allowed to drift to 0 uniformly over the parameter space. Even though identification fails in the limit, depending on how slow the moment functions vanish, consistent estimation is possible. Existing estimators such as the generalized method of moment (GMM) estimator exhibit a pattern of nonstandard or even heterogeneous rate of convergence that materializes by some parameter directions being estimated at a slower rate than others. This paper derives asymptotic semiparametric efficiency bounds for regular estimators of parameters of these models. We show that GMM estimators are regular and that the so-called two-step GMM estimator – using the inverse of estimating function’s variance as weighting matrix – is semiparametrically efficient as it reaches the minimum variance attainable by regular estimators. This estimator is also asymptotically minimax efficient with respect to a large family of loss functions. Monte Carlo simulations are provided that confirm these results.

Suggested Citation

  • Dovonon, Prosper & Atchadé, Yves F. & Doko Tchatoka, Firmin, 2025. "Efficiency bounds for moment condition models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 248(C).
    • Handle: RePEc:eee:econom:v:248:y:2025:i:c:s0304407624000691
    DOI: 10.1016/j.jeconom.2024.105723
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    More about this item

    Keywords

    Generalized method of moments; Mixed identification strength; Weak identification; Efficiency bounds; Semiparametric models;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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