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A Comparison of two Quantile Models with Endogeneity

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  • Kaspar W thrich

Abstract

This paper analyzes estimators based on the instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2004, 2005, 2006) under the local quantile treatment effects (LQTE) framework (Abadie et al., 2002). I show that the quantile treatment effect (QTE) estimators in the IVQR model are equivalent to LQTE for the compliers at transformed quantile levels. This transformation adjusts for differences between the subpopulation-specific potential outcome distributions that are identified in the LQTE model. Moreover, the IVQR estimator of the average treatment effect (ATE) corresponds to a convex combination of the local average treatment effect (LATE) and a weighted average of LQTE for the compliers. I extend the analysis to more general setups that allow for partial failures of the LQTE assumptions, non-binary instruments, and covariates. The results are illustrated with two empirical applications.

Suggested Citation

  • Kaspar W thrich, 2014. "A Comparison of two Quantile Models with Endogeneity," Diskussionsschriften dp1408, Universitaet Bern, Departement Volkswirtschaft.
    • Handle: RePEc:ube:dpvwib:dp1408
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    Cited by:

    1. Xu, Xiu & Wang, Weining & Shin, Yongcheol, 2020. "Dynamic Spatial Network Quantile Autoregression," IRTG 1792 Discussion Papers 2020-024, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    2. Grigory Franguridi & Bulat Gafarov & Kaspar Wuthrich, 2020. "Bias correction for quantile regression estimators," Papers 2011.03073, arXiv.org, revised Feb 2025.
    3. Grigory Franguridi & Bulat Gafarov & Kaspar Wüthrich, 2021. "Conditional Quantile Estimators: A Small Sample Theory," CESifo Working Paper Series 9046, CESifo.
    4. Jad Beyhum & Jean-Pierre Florens & Ingrid Keilegom, 2023. "A nonparametric instrumental approach to confounding in competing risks models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 709-734, October.
    5. Kaspar W thrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.
    6. de Castro, Luciano & Cundy, Lance D. & Galvao, Antonio F. & Westenberger, Rafael, 2023. "A dynamic quantile model for distinguishing intertemporal substitution from risk aversion," European Economic Review, Elsevier, vol. 159(C).
    7. David Powell, 2020. "Quantile Treatment Effects in the Presence of Covariates," The Review of Economics and Statistics, MIT Press, vol. 102(5), pages 994-1005, December.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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

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