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Identifying Marginal Treatment Effects in the Presence of Sample Selection

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  • Bartalotti, Otávio

    (Monash University)

  • Kédagni, Désiré

    (Iowa State University)

  • Possebom, Vítor Augusto

    (Sao Paulo School of Economics)

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 derive uniformly sharp bounds on this parameter under three increasingly restrictive sets of assumptions. The first result imposes standard MTE assumptions with an unrestricted sample selection mechanism. The second set of conditions imposes monotonicity of the sample selection variable with respect to treatment, considerably shrinking the identified set. Finally, we incorporate a stochastic dominance assumption which tightens the lower bound for the MTE. Our analysis extends to discrete instruments. The results rely on a mixture reformulation of the problem where the mixture weights are identified, extending Lee's (2009) trimming procedure to the MTE context. We propose estimators for the bounds derived and use data made available by Deb, Munkin, and Trivedi (2006) to empirically illustrate the usefulness of our approach.

Suggested Citation

  • Bartalotti, Otávio & Kédagni, Désiré & Possebom, Vítor Augusto, 2021. "Identifying Marginal Treatment Effects in the Presence of Sample Selection," IZA Discussion Papers 14428, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp14428
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    Cited by:

    1. 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.
    2. Rui Wang, 2023. "Point Identification of LATE with Two Imperfect Instruments," Papers 2303.13795, arXiv.org.
    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.

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    More about this item

    Keywords

    sample selection; instrumental variable; marginal treatment eect; partial identication; principal stratication; program evaluation; mixture models;
    All these keywords.

    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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