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Heterogeneous treatment effects with mismeasured endogenous treatment

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  • Takuya Ura

Abstract

This paper studies the identifying power of an instrumental variable in the nonparametric heterogeneous treatment effect framework when a binary treatment is mismeasured and endogenous. Using a binary instrumental variable, I characterize the sharp identified set for the local average treatment effect under the exclusion restriction of an instrument and the deterministic monotonicity of the true treatment in the instrument. Even allowing for general measurement error (e.g., the measurement error is endogenous), it is still possible to obtain finite bounds on the local average treatment effect. Notably, the Wald estimand is an upper bound on the local average treatment effect, but it is not the sharp bound in general. I also provide a confidence interval for the local average treatment effect with uniformly asymptotically valid size control. Furthermore, I demonstrate that the identification strategy of this paper offers a new use of repeated measurements for tightening the identified set.

Suggested Citation

  • Takuya Ura, 2018. "Heterogeneous treatment effects with mismeasured endogenous treatment," Quantitative Economics, Econometric Society, vol. 9(3), pages 1335-1370, November.
    • Handle: RePEc:wly:quante:v:9:y:2018:i:3:p:1335-1370
    DOI: 10.3982/QE886
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    Citations

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    Cited by:

    1. Nguimkeu, Pierre & Denteh, Augustine & Tchernis, Rusty, 2019. "On the estimation of treatment effects with endogenous misreporting," Journal of Econometrics, Elsevier, vol. 208(2), pages 487-506.
    2. Francis J. DiTraglia & Camilo Garcia-Jimeno, 2020. "Identifying the effect of a mis-classified, binary, endogenous regressor," Papers 2011.07272, arXiv.org.
    3. Vira Semenova & Matt Goldman & Victor Chernozhukov & Matt Taddy, 2023. "Inference on heterogeneous treatment effects in high‐dimensional dynamic panels under weak dependence," Quantitative Economics, Econometric Society, vol. 14(2), pages 471-510, May.
    4. Santiago Acerenza & Kyunghoon Ban & D'esir'e K'edagni, 2021. "Marginal Treatment Effects with a Misclassified Treatment," Papers 2105.00358, arXiv.org, revised Apr 2023.
    5. Kruse, Herman & Myhre, Andreas, 2021. "Early Retirement Provision for Elderly Displaced Workers," MPRA Paper 118689, University Library of Munich, Germany, revised 21 Sep 2023.
    6. DiTraglia, Francis J. & García-Jimeno, Camilo, 2019. "Identifying the effect of a mis-classified, binary, endogenous regressor," Journal of Econometrics, Elsevier, vol. 209(2), pages 376-390.
    7. Lina Zhang & David T. Frazier & Don S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Monash Econometrics and Business Statistics Working Papers 34/20, Monash University, Department of Econometrics and Business Statistics.
    8. Augustine Denteh & D'esir'e K'edagni, 2022. "Misclassification in Difference-in-differences Models," Papers 2207.11890, arXiv.org, revised Jul 2022.
    9. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2022. "Identification Of Regression Models With A Misclassified And Endogenous Binary Regressor," Econometric Theory, Cambridge University Press, vol. 38(6), pages 1117-1139, December.
    10. Kruse, Herman & Myhre, Andreas, 2021. "Early Retirement Provision for Elderly Displaced Workers," MPRA Paper 109431, University Library of Munich, Germany.
    11. Vitor Possebom, 2021. "Crime and Mismeasured Punishment: Marginal Treatment Effect with Misclassification," Papers 2106.00536, arXiv.org, revised Jul 2023.
    12. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.

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