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PreprintCC BY 4.0arXiv

Efficient GMM and Weighting Matrix under Misspecification

  • Byunghoon Kang
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Abstract

This paper develops efficient GMM estimation under misspecified moment conditions. The influence function of the standard GMM estimator under misspecification depends on both the moment conditions and their Jacobian, motivating a new class of estimators based on augmented, recentered moment conditions. Standard GMM is a special case and generally suboptimal. By optimally weighting the augmented system, we obtain a misspecification-efficient (ME) estimator with the smallest asymptotic variance for the same GMM estimand. In linear models, its asymptotic variance takes the textbook form (G'W*G)−1, where W* is the inverse variance of the residualized moments after projection on the Jacobian G. We propose a feasible bootstrap estimator, which is a misspecification-robust and efficient version of the Hall and Horowitz (1996) bootstrap GMM estimator. Finally, we establish uniform local asymptotic minimax bounds over a class of weighting matrices. We illustrate the proposed methods in simulation and two empirical examples.

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Cite

BibTeXRIS
BibTeX
@misc{kang2026efficient,
  title = {{Efficient GMM and Weighting Matrix under Misspecification}},
  author = {Byunghoon Kang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.04961},
  eprint = {2605.04961},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.04961},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Efficient GMM and Weighting Matrix under Misspecification
AU  - Byunghoon Kang
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2605.04961
UR  - https://arxiv.org/abs/2605.04961
AB  - This paper develops efficient GMM estimation under misspecified moment conditions. The influence function of the standard GMM estimator under misspecification depends on both the moment conditions and their Jacobian, motivating a new class of estimators based on augmented, recentered moment conditions. Standard GMM is a special case and generally suboptimal. By optimally weighting the augmented system, we obtain a misspecification-efficient (ME) estimator with the smallest asymptotic variance for the same GMM estimand. In linear models, its asymptotic variance takes the textbook form (G'W^*G)^−1, where W^* is the inverse variance of the residualized moments after projection on the Jacobian G. We propose a feasible bootstrap estimator, which is a misspecification-robust and efficient version of the Hall and Horowitz (1996) bootstrap GMM estimator. Finally, we establish uniform local asymptotic minimax bounds over a class of weighting matrices. We illustrate the proposed methods in simulation and two empirical examples.
ER  -