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Inference on individual treatment effects in nonseparable triangular models

Author

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  • Ma, Jun
  • Marmer, Vadim
  • Yu, Zhengfei

Abstract

In nonseparable triangular models with a binary endogenous treatment and a binary instrumental variable, Vuong and Xu (2017) established identification results for individual treatment effects (ITEs) under the rank invariance assumption. Using their approach, Feng et al. (2019) proposed a uniformly consistent kernel estimator for the density of the ITE that utilizes estimated ITEs. In this paper, we establish the asymptotic normality of the density estimator of Feng et al. (2019) and show that the ITE estimation errors have a non-negligible effect on the asymptotic distribution of the estimator. We propose asymptotically valid standard errors that account for ITEs estimation, as well as a bias correction. Furthermore, we develop uniform confidence bands for the density of the ITE using the jackknife multiplier or nonparametric bootstrap critical values.

Suggested Citation

  • Ma, Jun & Marmer, Vadim & Yu, Zhengfei, 2023. "Inference on individual treatment effects in nonseparable triangular models," Journal of Econometrics, Elsevier, vol. 235(2), pages 2096-2124.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:2096-2124
    DOI: 10.1016/j.jeconom.2023.02.011
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    More about this item

    Keywords

    Individual treatment effects; Nonparametric triangular models; Two-step nonparametric estimation; Bootstrap; Uniform confidence bands; Labor supply and family size;
    All these keywords.

    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
    • 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
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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