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Identifying Marginal Treatment Effects in the Presence of Sample Selection

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  • Bartalotti, Otávio
  • Kedagni, Desire
  • Possebom, Vitor
Abstract
This article presents identification results for the marginal treatment effect (MTE) when there is sample selection. We show that the MTE is partially identified for individuals who are always observed regardless of treatment, and we derive sharp bounds on this parameter under four sets of assumptions. The first identification result combines the standard MTE assumptions without any restrictions to the sample selection mechanism. The second result imposes monotonicity of the sample selection variable with respect to the treatment, considerably shrinking the identified set. Third, we incorporate a stochastic dominance assumption which tightens the lower bound for the MTE. Finally, we provide a set of conditions that allows point identification for completeness. Our analysis extends to discrete instruments and distributional MTE. All the results rely on a mixture reformulation of the problem where the mixture weights are identified. We therefore extend the Lee (2009) trimming procedure to the MTE context. We propose some preliminary estimators for the bounds derived, provide a numerical example and simulations that corroborate the bounds feasibility and usefulness as an empirical tool. In future drafts, we plan to highlight the practical relevance of the results by analyzing the impacts of managed health care options on health outcomes and expenditures, following Deb, Munkin, and Trivedi (2006).

Suggested Citation

  • Bartalotti, Otávio & Kedagni, Desire & Possebom, Vitor, 2019. "Identifying Marginal Treatment Effects in the Presence of Sample Selection," ISU General Staff Papers 201909150700001080, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genstf:201909150700001080
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    Cited by:

    1. Gayani Rathnayake & Akanksha Negi & Otavio Bartalotti & Xueyan Zhao, 2024. "Difference-in-Differences with Sample Selection," Papers 2411.09221, arXiv.org.
    2. Xiaolin Sun & Xueyan Zhao & D. S. Poskitt, 2024. "Partially Identified Heterogeneous Treatment Effect with Selection: An Application to Gender Gaps," Papers 2410.01159, arXiv.org, revised Oct 2024.
    3. Phillip Heiler, 2022. "Heterogeneous Treatment Effect Bounds under Sample Selection with an Application to the Effects of Social Media on Political Polarization," Papers 2209.04329, arXiv.org, revised Jul 2024.
    4. Bartalotti, Otávio & Kédagni, Désiré & Possebom, Vitor, 2023. "Identifying marginal treatment effects in the presence of sample selection," Journal of Econometrics, Elsevier, vol. 234(2), pages 565-584.
    5. Rui Wang, 2023. "Point Identification of LATE with Two Imperfect Instruments," Papers 2303.13795, arXiv.org.

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    JEL classification:

    • 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
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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