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Distribution and Quantile Structural Functions in Treatment Effect Models: Application to Smoking Effects on Wages

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Abstract

This paper examines the distribution structural functions (DSFs) and quantile structural functions (QSFs) in a semiparametric treatment effect model. The DSF and QSF are defined as the distribution function and quantile function of the counterfactural outcome when covariates are exogenously switched to a fixed value, while the unobserved heterogeneity of the whole population remains unchanged. We show that the DSFs and QSFs are identified under the unconfoundedness assumption, and then propose inverse probability weighted estimators which are n^{-1/2}-consistent and converge weakly to mean zero Gaussian processes. A simulation approach is also proposed to approximate the limiting processes. Finally, we apply the results to construct uniform confidence bands for the structural quantile treatment effect of smoking on wage, and find that smoking does not impose any wage penalty on male workers with low unobserved heterogeneity. JEL Classification: C14, C31, I19

Suggested Citation

  • Yu-Chin Hsu & Kamhon Kan & Tsung-Chih Lai, 2015. "Distribution and Quantile Structural Functions in Treatment Effect Models: Application to Smoking Effects on Wages," IEAS Working Paper : academic research 15-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan, revised Apr 2016.
    • Handle: RePEc:sin:wpaper:15-a001
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    File URL: https://www.econ.sinica.edu.tw/~econ/pdfPaper/15-A001.pdf
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    Cited by:

    1. Maasoumi, Esfandiar & Wang, Le, 2017. "What can we learn about the racial gap in the presence of sample selection?," Journal of Econometrics, Elsevier, vol. 199(2), pages 117-130.

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    Keywords

    distribution structural function; semiparametric models; smoking; treatment effects; quantile structural function; wages;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • I19 - Health, Education, and Welfare - - Health - - - Other

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