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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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    File URL: https://www.econ.sinica.edu.tw/~econ/pdfPaper/12-A016.pdf
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    as
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    More about this item

    Keywords

    Hypothesis testing; stochastic dominance; treatment effects; propensity score;
    All these keywords.

    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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