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Exact computation of GMM estimators for instrumental variable quantile regression models

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  • Le-Yu Chen
  • Sokbae (Simon) 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 (Simon) Lee, 2017. "Exact computation of GMM estimators for instrumental variable quantile regression models," CeMMAP working papers 52/17, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:52/17
    DOI: 10.1920/wp.cem.2017.5217
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    15. Chen, Le-Yu & Lee, Sokbae, 2018. "Best subset binary prediction," Journal of Econometrics, Elsevier, vol. 206(1), pages 39-56.
    16. Bilias, Yannis & Florios, Kostas & Skouras, Spyros, 2019. "Exact computation of Censored Least Absolute Deviations estimator," Journal of Econometrics, Elsevier, vol. 212(2), pages 584-606.
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    Cited by:

    1. 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.
    2. Koki Fusejima, 2020. "Identification of multi-valued treatment effects with unobserved heterogeneity," Papers 2010.04385, arXiv.org, revised Apr 2023.
    3. Machado, José A.F. & Santos Silva, J.M.C., 2019. "Quantiles via moments," Journal of Econometrics, Elsevier, vol. 213(1), pages 145-173.
    4. 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.
    5. Yinchu Zhu, 2018. "Learning non-smooth models: instrumental variable quantile regressions and related problems," Papers 1805.06855, arXiv.org, revised Sep 2019.
    6. 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.
    7. Wüthrich, Kaspar, 2019. "A closed-form estimator for quantile treatment effects with endogeneity," Journal of Econometrics, Elsevier, vol. 210(2), pages 219-235.
    8. 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).
    9. 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.
    10. 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.
    11. 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.
    12. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    13. Youngki Shin & Zvezdomir Todorov, 2021. "Exact computation of maximum rank correlation estimator," The Econometrics Journal, Royal Economic Society, vol. 24(3), pages 589-607.
    14. 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).
    15. Grigory Franguridi & Bulat Gafarov & Kaspar Wuthrich, 2020. "Bias correction for quantile regression estimators," Papers 2011.03073, arXiv.org, revised Nov 2024.
    16. Fusejima, Koki, 2024. "Identification of multi-valued treatment effects with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 238(1).
    17. 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.
    18. 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.
    19. Grigory Franguridi & Bulat Gafarov & Kaspar Wüthrich, 2021. "Conditional Quantile Estimators: A Small Sample Theory," CESifo Working Paper Series 9046, CESifo.
    20. 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.

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    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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