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Identification strength with a large number of moments

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  • Hyojin Han
  • Eric Renault

Abstract

This paper studies how identification is affected in GMM estimation as the number of moment conditions increases. We develop a general asymptotic theory extending the set up of Chao and Swanson and Antoine and Renault to the case where moment conditions have heterogeneous identification strengths and the number of them may diverge to infinity with the sample size. We also allow the models to be locally misspecified and examine how the asymptotic theory is affected by the degree of misspecification. The theory encompasses many cases including GMM models with many moments (Han and Phillips), partially linear models, and local GMM via kernel smoothing with a large number of conditional moment restrictions. We provide an understanding of the benefits of a large number of moments that compensate the weakness of individual moments by explicitly showing how an increasing number of moments improves the rate of convergence in GMM.

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  • Hyojin Han & Eric Renault, 2020. "Identification strength with a large number of moments," Econometric Reviews, Taylor & Francis Journals, vol. 39(7), pages 691-714, August.
    • Handle: RePEc:taf:emetrv:v:39:y:2020:i:7:p:691-714
    DOI: 10.1080/07474938.2020.1771903
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    Cited by:

    1. Antoine, Bertille & Renault, Eric, 2024. "GMM with Nearly-Weak Identification," Econometrics and Statistics, Elsevier, vol. 30(C), pages 36-59.
    2. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    3. Dakyung Seong, 2022. "Binary response model with many weak instruments," Papers 2201.04811, arXiv.org, revised Jun 2024.

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