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A Comparison of two Quantile Models with Endogeneity

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  • Kaspar Wüthrich

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 Wüthrich, 2014. "A Comparison of two Quantile Models with Endogeneity," Diskussionsschriften dp1408, Universitaet Bern, Departement Volkswirtschaft.
  • Handle: RePEc:ube:dpvwib:dp1408
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    2. Grigory Franguridi & Bulat Gafarov & Kaspar Wuthrich, 2020. "Conditional quantile estimators: A small sample theory," Papers 2011.03073, arXiv.org, revised Apr 2021.
    3. Kaspar Wüthrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.
    4. 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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    More about this item

    Keywords

    Endogeneity; instrumental variables; quantile treatment effect; local quantile treatment effect; average treatment effect; local average treatment effect; rank similarity;
    All these keywords.

    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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