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Identification of heterogeneous treatment effects as a function of potential untreated outcome under the nonignorable assignment condition

Author

Listed:
  • Takahiro Hoshino

    (Department of Economics, Keio University)

  • Keisuke Takahata

    (Graduate of School of Economics, Keio University)

Abstract

We provide sufficient conditions for the identification of hetero- geneous treatment effects (HTE), in which the missing mechanism is nonignorable, when the information on the marginal distribution of untreated outcome is available. It is also shown that, under such a situ- ation, the same result holds for the identification of average treatment effects (ATE). Exposing certain additivity on the regression function of the assignment probability, we reduce the identication of HTE to the uniqueness of a solution of some integral equation, and discuss it borrowing the idea from the literature on statistical inverse prob- lems. Our result contributes to theoretical understandings in causal inference with heterogeneity and also the relaxation of the conditional independence assumption in statistical data fusion or statistical data combination.

Suggested Citation

  • Takahiro Hoshino & Keisuke Takahata, 2018. "Identification of heterogeneous treatment effects as a function of potential untreated outcome under the nonignorable assignment condition," Keio-IES Discussion Paper Series 2018-005, Institute for Economics Studies, Keio University.
    • Handle: RePEc:keo:dpaper:2018-005
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    References listed on IDEAS

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    More about this item

    Keywords

    nonignorable missing; causal inference; identifiability;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods

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