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Sharp Bounds on Causal Effects under Sample Selection

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  • Martin Huber
  • Giovanni Mellace

Abstract

type="main" xml:id="obes12056-abs-0001"> In many empirical problems, the evaluation of treatment effects is complicated by sample selection so that the outcome is only observed for a non-random subpopulation. In the absence of instruments and/or tight parametric assumptions, treatment effects are not point identified, but can be bounded under mild restrictions. Previous work on partial identification has primarily focused on the ‘always observed’ (irrespective of the treatment). This article complements those studies by considering further populations, namely the ‘compliers’ (observed only if treated) and the observed population. We derive sharp bounds under various assumptions and provide an empirical application to a school voucher experiment.

Suggested Citation

  • Martin Huber & Giovanni Mellace, 2015. "Sharp Bounds on Causal Effects under Sample Selection," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 129-151, February.
    • Handle: RePEc:bla:obuest:v:77:y:2015:i:1:p:129-151
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    File URL: http://hdl.handle.net/10.1111/obes.2015.77.issue-1
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    Cited by:

    1. Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series 1109, University of St. Gallen, School of Economics and Political Science.
    2. 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.
    3. German Blanco & Xuan Chen & Carlos A. Flores & Alfonso Flores-Lagunes, 2020. "Bounds on Average and Quantile Treatment Effects on Duration Outcomes Under Censoring, Selection, and Noncompliance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 901-920, October.
    4. Phillip Heiler & Asbj{o}rn Kaufmann & Bezirgen Veliyev, 2024. "Treatment Evaluation at the Intensive and Extensive Margins," Papers 2412.11179, arXiv.org.
    5. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    6. Lutz Depenbusch & Pepijn Schreinemachers & Stuart Brown & Ralph Roothaert, 2022. "Impact and distributional effects of a home garden and nutrition intervention in Cambodia," Food Security: The Science, Sociology and Economics of Food Production and Access to Food, Springer;The International Society for Plant Pathology, vol. 14(4), pages 865-881, August.
    7. 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.
    8. Heiler, Phillip, 2024. "Heterogeneous treatment effect bounds under sample selection with an application to the effects of social media on political polarization," Journal of Econometrics, Elsevier, vol. 244(1).
    9. Possebom, Vitor, 2018. "Sharp bounds on the MTE with sample selection," MPRA Paper 89785, University Library of Munich, Germany.
    10. Martin Huber & Giovanni Mellace, 2010. "Sharp IV bounds on average treatment effects under endogeneity and noncompliance," University of St. Gallen Department of Economics working paper series 2010 2010-31, Department of Economics, University of St. Gallen.
    11. Daniel Brüggmann, 2020. "Women’s employment, income and divorce in West Germany: a causal approach," Journal for Labour Market Research, Springer;Institute for Employment Research/ Institut für Arbeitsmarkt- und Berufsforschung (IAB), vol. 54(1), pages 1-22, December.
    12. Martin Huber & Blaise Melly, 2012. "A test of the conditional independence assumption in sample selection models," Working Papers 2012-11, Brown University, Department of Economics.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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