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Estimation and Inference for Distribution Functions and Quantile Functions in Endogenous Treatment Effect Models

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Abstract

We propose a new monotonizing method to obtain estimators for the distribution functions of potential outcomes among the group of compliers in an endogenous treatment effect model that are monotonically increasing and bounded between zero and one. Corresponding quantile function estimators are obtain by applying the inverse map to the CDF estimators. We show that both these estimators converge weakly to zero mean Gaussian processes. A simulation method is proposed to approximate the limiting processes for uniform inference. A Monte Carlo simulation and an application addressing the effect of fertility on family income illustrate the usefulness of the results. JEL Classification: C21, C26

Suggested Citation

  • Yu-Chin Hsu & Robert P. Lieli & Tsung-Chih Lai, 2015. "Estimation and Inference for Distribution Functions and Quantile Functions in Endogenous Treatment Effect Models," IEAS Working Paper : academic research 15-A003, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    • Handle: RePEc:sin:wpaper:15-a003
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    Cited by:

    1. Blaise Melly und Kaspar W thrich, 2016. "Local quantile treatment effects," Diskussionsschriften dp1605, Universitaet Bern, Departement Volkswirtschaft.
    2. Victor Chernozhukov & Iván Fernández-Val & Blaise Melly & Kaspar Wüthrich, 2020. "Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 123-137, January.
    3. Huber Martin & Wüthrich Kaspar, 2019. "Local Average and Quantile Treatment Effects Under Endogeneity: A Review," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-27, January.
    4. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    5. Wüthrich, Kaspar, 2019. "A closed-form estimator for quantile treatment effects with endogeneity," Journal of Econometrics, Elsevier, vol. 210(2), pages 219-235.

    More about this item

    Keywords

    distribution function; quantile function; treatment effects; instrumental variables; inverse probability weighted estimator;
    All these keywords.

    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

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