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Exact computation of GMM estimators for instrumental variable quantile regression models

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  • Le‐Yu Chen
  • Sokbae Lee

Abstract

We show that the generalized method of moments (GMM) estimation problem in instrumental variable quantile regression (IVQR) models can be equivalently formulated as a mixed‐integer quadratic programming problem. This enables exact computation of the GMM estimators for the IVQR models. We illustrate the usefulness of our algorithm via Monte Carlo experiments and an application to demand for fish.

Suggested Citation

  • Le‐Yu Chen & Sokbae Lee, 2018. "Exact computation of GMM estimators for instrumental variable quantile regression models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 553-567, June.
    • Handle: RePEc:wly:japmet:v:33:y:2018:i:4:p:553-567
    DOI: 10.1002/jae.2619
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    Cited by:

    1. Javier Alejo & Antonio F Galvao & Gabriel Montes-Rojas, 2023. "A first-stage representation for instrumental variables quantile regression," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 350-377.
    2. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    3. Grigory Franguridi & Bulat Gafarov & Kaspar Wuthrich, 2020. "Bias correction for quantile regression estimators," Papers 2011.03073, arXiv.org, revised Feb 2025.
    4. Fusejima, Koki, 2024. "Identification of multi-valued treatment effects with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 238(1).
    5. Jau-er Chen & Chien-Hsun Huang & Jia-Jyun Tien, 2021. "Debiased/Double Machine Learning for Instrumental Variable Quantile Regressions," Econometrics, MDPI, vol. 9(2), pages 1-18, April.
    6. David Kang & Seojeong Lee, 2025. "Misspecification-Robust Asymptotic and Bootstrap Inference for Nonsmooth GMM," Working Papers 423284005, Lancaster University Management School, Economics Department.
    7. Grigory Franguridi & Bulat Gafarov & Kaspar Wüthrich, 2021. "Conditional Quantile Estimators: A Small Sample Theory," CESifo Working Paper Series 9046, CESifo.
    8. Yinchu Zhu, 2018. "Learning non-smooth models: instrumental variable quantile regressions and related problems," Papers 1805.06855, arXiv.org, revised Sep 2019.
    9. Xin Liu, 2024. "Averaging Estimation for Instrumental Variables Quantile Regression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(5), pages 1290-1312, October.
    10. Hjertstrand, Per & Swofford, James L. & Whitney, Gerald A., 2023. "Testing for Weak Separability and Utility Maximization with Incomplete Adjustment," Journal of Economic Dynamics and Control, Elsevier, vol. 152(C).
    11. Youngki Shin & Zvezdomir Todorov, 2021. "Exact computation of maximum rank correlation estimator," The Econometrics Journal, Royal Economic Society, vol. 24(3), pages 589-607.
    12. Canepa, Alessandra & de la O. González, María & Skinner, Frank S., 2020. "Hedge fund strategies: A non-parametric analysis," International Review of Financial Analysis, Elsevier, vol. 67(C).
    13. Nahid Farnaz, 2023. "Does Financial Development Relieve or Exacerbate Income Inequality? A Quantile Regression Approach," Economics Discussion Paper Series 2311, Economics, The University of Manchester.
    14. Wüthrich, Kaspar, 2019. "A closed-form estimator for quantile treatment effects with endogeneity," Journal of Econometrics, Elsevier, vol. 210(2), pages 219-235.
    15. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    16. Franguridi, Grigory & Gafarov, Bulat & Wüthrich, Kaspar, 2025. "Bias correction for quantile regression estimators," Journal of Econometrics, Elsevier, vol. 251(C).
    17. Kaspar Wüthrich, 2020. "A Comparison of Two Quantile Models With Endogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 443-456, April.
    18. Koki Fusejima, 2020. "Identification of multi-valued treatment effects with unobserved heterogeneity," Papers 2010.04385, arXiv.org, revised Apr 2023.
    19. Kazi Musa & Marijn Janssen & Jamaliah Said & Nor Balkish Zakaria & Naila Erum, 2025. "The Impact of Public Debt and Quality of Governance on Economic Growth in High-Income Countries," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 16(1), pages 2817-2843, March.
    20. Machado, José A.F. & Santos Silva, J.M.C., 2019. "Quantiles via moments," Journal of Econometrics, Elsevier, vol. 213(1), pages 145-173.
    21. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    22. He, Xuming & Pan, Xiaoou & Tan, Kean Ming & Zhou, Wen-Xin, 2023. "Smoothed quantile regression with large-scale inference," Journal of Econometrics, Elsevier, vol. 232(2), pages 367-388.
    23. Bin Xu & Boqiang Lin, 2021. "Large fluctuations of China's commodity prices: Main sources and heterogeneous effects," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 2074-2089, April.

    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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