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Decentralization estimators for instrumental variable quantile regression models

Author

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  • Hiroaki Kaido

    (Institute for Fiscal Studies and Boston University)

  • Kaspar Wüthrich

    (Institute for Fiscal Studies and UCSD)

Abstract

The instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2005) is a popular tool for estimating causal quantile effects with endogenous covariates. However, estimation is complicated by the non-smoothness and non-convexity of the IVQR GMM objective function. This paper shows that the IVQR estimation problem can be decomposed into a set of conventional quantile regression sub-problems which are convex and can be solved efficiently. This reformulation leads to new identification results and to fast, easy to implement, and tuning-free estimators that do not require the availability of high-level "black box" optimization routines.

Suggested Citation

  • Hiroaki Kaido & Kaspar Wüthrich, 2019. "Decentralization estimators for instrumental variable quantile regression models," CeMMAP working papers CWP42/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:42/19
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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. Grigory Franguridi & Bulat Gafarov & Kaspar Wuthrich, 2020. "Bias correction for quantile regression estimators," Papers 2011.03073, arXiv.org, revised Feb 2025.
    3. Fusejima, Koki, 2024. "Identification of multi-valued treatment effects with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 238(1).
    4. David Kang & Seojeong Lee, 2025. "Misspecification-Robust Asymptotic and Bootstrap Inference for Nonsmooth GMM," Working Papers 423284005, Lancaster University Management School, Economics Department.
    5. Undral Byambadalai & Tomu Hirata & Tatsushi Oka & Shota Yasui, 2025. "Beyond the Average: Distributional Causal Inference under Imperfect Compliance," Papers 2509.15594, arXiv.org, revised Oct 2025.
    6. Grigory Franguridi & Bulat Gafarov & Kaspar Wüthrich, 2021. "Conditional Quantile Estimators: A Small Sample Theory," CESifo Working Paper Series 9046, CESifo.
    7. Franguridi, Grigory & Gafarov, Bulat & Wüthrich, Kaspar, 2025. "Bias correction for quantile regression estimators," Journal of Econometrics, Elsevier, vol. 251(C).
    8. Koki Fusejima, 2020. "Identification of multi-valued treatment effects with unobserved heterogeneity," Papers 2010.04385, arXiv.org, revised Apr 2023.
    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. Wenjie Wang & Yichong Zhang, 2024. "Gradient Wild Bootstrap for Instrumental Variable Quantile Regressions with Weak and Few Clusters," Papers 2408.10686, arXiv.org.
    11. Lorenzo Tedesco & Jad Beyhum & Ingrid Van Keilegom, 2023. "Instrumental variable estimation of the proportional hazards model by presmoothing," Papers 2309.02183, arXiv.org.
    12. Wenjie Wang & Yichong Zhang, 2021. "Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters," Papers 2108.13707, arXiv.org, revised Jan 2024.
    13. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    14. 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.

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