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Limited Monotonicity and the Combined Compliers LATE

Author

Listed:
  • Nadja van ’t Hoff

    (University of Southern Denmark)

  • Arthur Lewbel

    (Boston College)

  • Giovanni Mellace

    (University of Southern Denmark)

Abstract

We consider estimating a local average treatment effect given an endogenous binary treatment and two or more valid binary instruments. We propose a novel limited monotonicity assumption that is generally weaker than alternative monotonicity assumptions considered in the literature, and allows for a great deal of choice heterogeneity. Using this limited monotonicity, we define and identify the Combined Complier Local Average Treatment Effect (CC-LATE), which is arguably a more policy relevant parameter than the weighted average of LATEs identified by Two Stage Least Squares. We apply our results to estimate the effect of learning one’s HIV status on protective behaviors.

Suggested Citation

  • Nadja van ’t Hoff & Arthur Lewbel & Giovanni Mellace, 2023. "Limited Monotonicity and the Combined Compliers LATE," Boston College Working Papers in Economics 1059, Boston College Department of Economics, revised 25 Apr 2024.
    • Handle: RePEc:boc:bocoec:1059
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    References listed on IDEAS

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    1. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    2. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    3. Clément de Chaisemartin, 2017. "Tolerating defiance? Local average treatment effects without monotonicity," Quantitative Economics, Econometric Society, vol. 8(2), pages 367-396, July.
    4. Gordon B. Dahl & Enrico Moretti, 2008. "The Demand for Sons," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(4), pages 1085-1120.
    5. Magne Mogstad & Alexander Torgovitsky & Christopher R. Walters, 2021. "The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables," American Economic Review, American Economic Association, vol. 111(11), pages 3663-3698, November.
    6. Angrist, Joshua D & Evans, William N, 1998. "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size," American Economic Review, American Economic Association, vol. 88(3), pages 450-477, June.
    7. Christian M Dahl & Martin Huber & Giovanni Mellace, 2023. "It is never too LATE: a new look at local average treatment effects with or without defiers," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 378-404.
    8. Mogstad, Magne & Torgovitsky, Alexander & Walters, Christopher R., 2024. "Policy evaluation with multiple instrumental variables," Journal of Econometrics, Elsevier, vol. 243(1).
    9. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    10. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    11. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
    12. Huntington-Klein Nick, 2020. "Instruments with Heterogeneous Effects: Bias, Monotonicity, and Localness," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 182-208, January.
    13. Rebecca L. Thornton, 2008. "The Demand for, and Impact of, Learning HIV Status," American Economic Review, American Economic Association, vol. 98(5), pages 1829-1863, December.
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    Cited by:

    1. Goff, Leonard, 2024. "A vector monotonicity assumption for multiple instruments," Journal of Econometrics, Elsevier, vol. 241(1).

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    More about this item

    Keywords

    Instrumental variable; Local Average Treatment Effect; monotonicity; multiple instruments;
    All these keywords.

    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
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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