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Adaptive Elastic Net for Generalized Methods of Moments

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  • Mehmet Caner
  • Hao Helen Zhang

Abstract

Model selection and estimation are crucial parts of econometrics. This article introduces a new technique that can simultaneously estimate and select the model in generalized method of moments (GMM) context. The GMM is particularly powerful for analyzing complex datasets such as longitudinal and panel data, and it has wide applications in econometrics. This article extends the least squares based adaptive elastic net estimator by Zou and Zhang to nonlinear equation systems with endogenous variables. The extension is not trivial and involves a new proof technique due to estimators' lack of closed-form solutions. Compared to Bridge-GMM by Caner, we allow for the number of parameters to diverge to infinity as well as collinearity among a large number of variables; also, the redundant parameters are set to zero via a data-dependent technique. This method has the oracle property, meaning that we can estimate nonzero parameters with their standard limit and the redundant parameters are dropped from the equations simultaneously. Numerical examples are used to illustrate the performance of the new method.

Suggested Citation

  • Mehmet Caner & Hao Helen Zhang, 2014. "Adaptive Elastic Net for Generalized Methods of Moments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 30-47, January.
    • Handle: RePEc:taf:jnlbes:v:32:y:2014:i:1:p:30-47
    DOI: 10.1080/07350015.2013.836104
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    Citations

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    Cited by:

    1. Tomohiro Ando & Naoya Sueishi, 2019. "On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator," Econometrics, MDPI, vol. 7(1), pages 1-14, March.
    2. Creel, Michael & Kristensen, Dennis, 2015. "ABC of SV: Limited information likelihood inference in stochastic volatility jump-diffusion models," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 85-108.
    3. Caner, Mehmet & Kock, Anders Bredahl, 2018. "Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso," Journal of Econometrics, Elsevier, vol. 203(1), pages 143-168.
    4. de Paula, Aureo & Rasul, Imran & Souza, Pedro, 2018. "Identifying Network Ties from Panel Data: Theory and an Application to Tax Competition," CEPR Discussion Papers 12792, C.E.P.R. Discussion Papers.
    5. Liqian Cai & Arnab Bhattacharjee & Roger Calantone & Taps Maiti, 2019. "Variable Selection with Spatially Autoregressive Errors: A Generalized Moments LASSO Estimator," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 146-200, September.
    6. Zhentao Shi, 2016. "Estimation of Sparse Structural Parameters with Many Endogenous Variables," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1582-1608, December.
    7. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    8. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val & Christian Hansen, 2013. "Program evaluation with high-dimensional data," CeMMAP working papers CWP77/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Ã ureo de Paula & Imran Rasul & Pedro Souza, 2018. "Recovering Social Networks from Panel Data: Identification, Simulations and an Application," Working Papers 2018-013, Human Capital and Economic Opportunity Working Group.
    10. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    11. Anders Bredahl Kock & Haihan Tang, 2014. "Inference in High-dimensional Dynamic Panel Data Models," CREATES Research Papers 2014-58, Department of Economics and Business Economics, Aarhus University.
    12. Ulrike Schneider, 2016. "Confidence Sets Based on Thresholding Estimators in High-Dimensional Gaussian Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1412-1455, December.
    13. Konstantinidi, Antri & Kourtellos, Andros & Sun, Yiguo, 2023. "Social threshold regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 2057-2081.
    14. Kyle Bagwell & Robert W. Staiger & Ali Yurukoglu, 2021. "Quantitative Analysis of Multiparty Tariff Negotiations," Econometrica, Econometric Society, vol. 89(4), pages 1595-1631, July.
    15. Hao Hao & Tae-Hwy Lee, 2023. "Boosting GMM with Many Instruments When Some Are Invalid or Irrelevant," Working Papers 202309, University of California at Riverside, Department of Economics.
    16. Dakyung Seong, 2022. "Binary response model with many weak instruments," Papers 2201.04811, arXiv.org, revised Jun 2024.
    17. Keith Knight, 2016. "The Penalized Analytic Center Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1471-1484, December.
    18. Patacchini, Eleonora & Hsieh, Chih-Sheng & Lin, Xu, 2019. "Social Interaction Methods," CEPR Discussion Papers 14141, C.E.P.R. Discussion Papers.
    19. Ando, Tomohiro & Sueishi, Naoya, 2019. "Regularization parameter selection for penalized empirical likelihood estimator," Economics Letters, Elsevier, vol. 178(C), pages 1-4.

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