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Estimation and inference for the counterfactual distribution and quantile functions in continuous treatment models

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  • Ai, Chunrong
  • Linton, Oliver
  • Zhang, Zheng

Abstract

Donald and Hsu (2014) studied the estimation and inference for the counterfactual distribution and quantile functions in a binary treatment model. We extend their work to the continuous treatment model. Specifically, we propose a weighted regression estimator for the counterfactual distribution but we estimate the weighting function from a covariate balancing equation by maximizing a globally concave criterion function. We estimate the quantile function by inverting the estimated counterfactual distribution. To test the distributional effect, we consider the (uniform) confidence bands, the sup and L2 distance, and the Mann–Whitney test. We also consider the stochastic dominance test for the distributional effect and the L2 test for constant quantiles. A simulation study reveals that our tests exhibit a satisfactory finite-sample performance, and an application shows their practical value.

Suggested Citation

  • Ai, Chunrong & Linton, Oliver & Zhang, Zheng, 2022. "Estimation and inference for the counterfactual distribution and quantile functions in continuous treatment models," Journal of Econometrics, Elsevier, vol. 228(1), pages 39-61.
    • Handle: RePEc:eee:econom:v:228:y:2022:i:1:p:39-61
    DOI: 10.1016/j.jeconom.2020.12.009
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    3. Yu-Chin Hsu & Martin Huber & Yu-Min Yen, 2023. "Doubly Robust Estimation of Direct and Indirect Quantile Treatment Effects with Machine Learning," Papers 2307.01049, arXiv.org.

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    More about this item

    Keywords

    Continuous treatment; Counterfactual distribution; Hypothesis testing; Quantile function;
    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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