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

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Abstract

We propose inverse probability weighted estimators for the distribution functions of the potential outcomes of a binary treatment under the unconfoundedness assumption. We also apply the inverse mapping on the distribution functions to obtain the quantile functions. We show that the proposed estimators converge weakly to zero mean Gaussian processes. A simulation method based on the multiplier central limit theorem is proposed to approximate these limiting Gaussian processes. The estimators in the treated subpopulation are shown to share the same properties. To demonstrate the usefulness of our results, we construct Kolmogorov-Smirnov type tests for stochastic dominance relations between the distributions of potential outcomes. We examine the finite sample properties of our tests in a set of Monte-Carlo simulations and use our tests in an empirical example which shows that a job training program had a positive effect on incomes.

Suggested Citation

  • Stephen G. Donald & Yu-Chin Hsu, 2012. "Estimation and Inference for Distribution Functions and Quantile Functions in Treatment Effect Models," IEAS Working Paper : academic research 12-A016, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  • Handle: RePEc:sin:wpaper:12-a016
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    Citations

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    Cited by:

    1. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    2. Ying-Ying Lee, 2015. "Efficient propensity score regression estimators of multi-valued treatment effects for the treated," Economics Series Working Papers 738, University of Oxford, Department of Economics.
    3. Victor Chernozhukov & Ivan Fernandez-Val & Blaise Melly & Kaspar Wüthrich, 2016. "Generic inference on quantile and quantile effect functions for discrete outcomes," CeMMAP working papers CWP35/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. García, A., 2016. "Oaxaca-Blinder Type Counterfactual Decomposition Methods for Duration Outcomes," DOCUMENTOS DE TRABAJO 014186, UNIVERSIDAD DEL ROSARIO.
    5. Brantly Callaway & Tong Li, 2017. "Quantile Treatment Effects in Difference in Differences Models with Panel Data," DETU Working Papers 1701, Department of Economics, Temple University.
    6. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.

    More about this item

    Keywords

    Hypothesis testing; stochastic dominance; treatment effects; propensity score;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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