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Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments

Author

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  • Xu Cheng

    (Department of Economics, University of Pennsylvania)

  • Zhipeng Liao

    (Department of Economics, University of California Los Angeles)

Abstract

This paper considers the selection of valid and relevant moments for the generalized method of moments (GMM) estimation. For applications with many candidate moments, our asymptotic analysis ccommodates a diverging number of moments as the sample size increases. The proposed procedure achieves three objectives in one-step: (i) the valid and relevant moments are selected simultaneously rather than sequentially; (ii) all desired moments are selected together instead of in a stepwise manner; (iii) the parameter of interest is automatically estimated with all selected moments as opposed to a post-selection estimation. The new moment selection method is achieved via an information-based adaptive GMM shrinkage estimation, where an appropriate penalty is attached to the standard GMM criterion to link moment selection to shrinkage estimation. The penalty is designed to signal both moment validity and relevance for consistent moment selection and efficient estimation. The asymptotic analysis allows for non -smooth sample moments and weakly dependent observations, making it generally applicable. For practical implementation, this one-step procedure is computationally attractive.

Suggested Citation

  • Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:12-045
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    Cited by:

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    2. Creel, Michael & Kristensen, Dennis, 2016. "On selection of statistics for approximate Bayesian computing (or the method of simulated moments)," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 99-114.
    3. Federico A. Bugni & Mehmet Caner & Anders Bredahl Kock & Soumendra Lahiri, 2016. "Inference in partially identified models with many moment inequalities using Lasso," CREATES Research Papers 2016-12, Department of Economics and Business Economics, Aarhus University.
    4. Xu Cheng & Zhipeng Liao & Ruoyao Shi, 2013. "Uniform Asymptotic Risk of Averaging GMM Estimator Robust to Misspecification, Second Version," PIER Working Paper Archive 15-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 25 Mar 2015.
    5. Caner, Mehmet & Fan, Qingliang, 2015. "Hybrid generalized empirical likelihood estimators: Instrument selection with adaptive lasso," Journal of Econometrics, Elsevier, vol. 187(1), pages 256-274.
    6. Mehmet Caner & Esfandiar Maasoumi & Juan Andrés Riquelme, 2016. "Moment and IV Selection Approaches: A Comparative Simulation Study," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1562-1581, December.

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    More about this item

    Keywords

    Adaptive Penalty; GMM; Many Moments; Moment Selection; Oracle Properties; Shrinkage Estimation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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