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Nonparametric Tests of Conditional Treatment Effects

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  • Sokbae Lee

    (University College London)

  • Yoon-Jae Whang

    (Seoul National University)

Abstract

We develop a general class of nonparametric tests for treatment effects conditional on covariates. We consider a wide spectrum of null and alternative hypotheses regarding conditional treatment effects, including (i) the null hypothesis of the conditional stochastic dominance between treatment and control groups; (ii) the null hypothesis that the conditional average treatment effect is positive for each value of covariates; and (iii) the null hypothesis of no distributional (or average) treatment effect conditional on covariates against a one-sided (or two-sided) alternative hypothesis. The test statistics are based on L_{1}-type functionals of uniformly consistent nonparametric kernel estimators of conditional expectations that characterize the null hypotheses. Using the Poissionization technique of Gine et al. (2003), we show that suitably studentized versions of our test statistics are asymptotically standard normal under the null hypotheses and also show that the proposed nonparametric tests are consistent against general fixed alternatives. Furthermore, it turns out that our tests have non-negligible powers against some local alternatives that are n^{-1/2} different from the null hypotheses, where n is the sample size. We provide a more powerful test for the case when the null hypothesis may be binding only on a strict subset of the support and also consider an extension to testing for quantile treatment effects. We illustrate the usefulness of our tests by applying them to data from a randomized, job training program (LaLonde (1986)) and by carrying out Monte Carlo experiments based on this dataset.

Suggested Citation

  • Sokbae Lee & Yoon-Jae Whang, 2009. "Nonparametric Tests of Conditional Treatment Effects," Cowles Foundation Discussion Papers 1740, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1740
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Taoufik Bouezmarni & Jeroen V.K. Rombouts & Abderrahim Taamouti, 2011. "Nonparametric Copula-Based Test for Conditional Independence with Applications to Granger Causality," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 275-287, October.
    2. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2013. "Testing functional inequalities," Journal of Econometrics, Elsevier, vol. 172(1), pages 14-32.
    3. Donald, Stephen G. & Hsu, Yu-Chin, 2014. "Estimation and inference for distribution functions and quantile functions in treatment effect models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 383-397.
    4. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    5. Chen, Le-Yu & Szroeter, Jerzy, 2014. "Testing multiple inequality hypotheses: A smoothed indicator approach," Journal of Econometrics, Elsevier, vol. 178(P3), pages 678-693.
    6. David M. Kaplan & Matt Goldman, 2013. "Comparing distributions by multiple testing across quantiles," Working Papers 13-19, Department of Economics, University of Missouri, revised Feb 2018.
    7. Sung Jae Jun & Yoonseok Lee & Youngki Shin, 2016. "Treatment Effects With Unobserved Heterogeneity: A Set Identification Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 302-311, April.
    8. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
    9. beare, brendan & shi, xiaoxia, 2015. "An improved bootstrap test of density ratio ordering," MPRA Paper 74772, University Library of Munich, Germany.
    10. Fan, Yanqin & Park, Sang Soo, 2014. "Nonparametric inference for counterfactual means: Bias-correction, confidence sets, and weak IV," Journal of Econometrics, Elsevier, vol. 178(P1), pages 45-56.

    More about this item

    Keywords

    Average treatment effect; Conditional stochastic dominance; Poissionization; Programme evaluation;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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

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