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Select the valid and relevant moments: An information-based LASSO for GMM with many moments

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  • Cheng, Xu
  • Liao, Zhipeng

Abstract

This paper studies the selection of valid and relevant moments for the generalized method of moments (GMM) estimation. For applications with many candidate moments, our asymptotic analysis accommodates 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 distinguished from the invalid or irrelevant ones; (ii) all desired moments are selected in one step instead of in a stepwise manner; (iii) the parameters of interest are automatically estimated with all selected moments as opposed to a post-selection estimation. The new method performs moment selection and efficient estimation simultaneously 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. We develop asymptotic results for the high-dimensional GMM shrinkage estimator, allowing for non-smooth sample moments and weakly dependent observations. For practical implementation, this one-step procedure is computationally attractive.

Suggested Citation

  • Cheng, Xu & Liao, Zhipeng, 2015. "Select the valid and relevant moments: An information-based LASSO for GMM with many moments," Journal of Econometrics, Elsevier, vol. 186(2), pages 443-464.
  • Handle: RePEc:eee:econom:v:186:y:2015:i:2:p:443-464
    DOI: 10.1016/j.jeconom.2015.02.019
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    Citations

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    Cited by:

    1. Xu Cheng & Zhipeng Liao, 2011. "Select the Valid and Relevant Moments: An Information-Based LASSO for GMM with Many Moments, Second Version," PIER Working Paper Archive 13-062, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 21 Oct 2013.
    2. Frank Windmeijer & Helmut Farbmacher & Neil Davies & George Davey Smith, 2016. "On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments," Bristol Economics Discussion Papers 16/674, Department of Economics, University of Bristol, UK, revised 08 Aug 2017.
    3. Ning Xu & Jian Hong & Timothy C. G. Fisher, 2016. "Model selection consistency from the perspective of generalization ability and VC theory with an application to Lasso," Papers 1606.00142, arXiv.org.
    4. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso," Journal of Econometrics, Elsevier, vol. 191(1), pages 86-109.
    5. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    6. He, Yinghua, 2012. "Gaming the Boston School Choice Mechanism in Beijing," TSE Working Papers 12-345, Toulouse School of Economics (TSE).
    7. Timothy B. Armstrong & Michal Koles'ar, 2018. "Sensitivity Analysis using Approximate Moment Condition Models," Papers 1808.07387, arXiv.org, revised Nov 2018.
    8. Prosper Donovon & Alastair R. Hall, 2015. "GMM and Indirect Inference: An appraisal of their connections and new results on their properties under second order identification," The School of Economics Discussion Paper Series 1505, Economics, The University of Manchester.
    9. P.A.V.B. Swamy & George S. Tavlas & Stephen G. Hall, 2015. "On the Interpretation of Instrumental Variables in the Presence of Specification Errors," Econometrics, MDPI, Open Access Journal, vol. 3(1), pages 1-10, January.
    10. Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.
    11. repec:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-017-0782-7 is not listed on IDEAS

    More about this item

    Keywords

    Adaptive penalty; GMM; Many moments; Moment selection; Oracle properties; Shrinkage estimation;

    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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