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Counterfactual mapping and individual treatment effects in nonseparable models with binary endogeneity

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  • Quang Vuong
  • Haiqing Xu

Abstract

This paper establishes nonparametric identification of individual treatment effects in a nonseparable model with a binary endogenous regressor. The outcome variable may be continuous, discrete, or a mixture of both, while the instrumental variable can take binary values. First, we study the case where the model includes a selection equation for the binary endogenous regressor. We establish point identification of the individual treatment effects and the structural function when the latter is continuous and strictly monotone in the latent variable. The key to our results is the identification of a so‐called counterfactual mapping that links each outcome of the dependent variable with its counterfactual. Second, we extend our identification argument when there is no selection equation. Last, we generalize our identification results to the case where the outcome variable has a probability mass in its distribution such as when the outcome variable is censored or binary.

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  • Quang Vuong & Haiqing Xu, 2017. "Counterfactual mapping and individual treatment effects in nonseparable models with binary endogeneity," Quantitative Economics, Econometric Society, vol. 8(2), pages 589-610, July.
    • Handle: RePEc:wly:quante:v:8:y:2017:i:2:p:589-610
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    Cited by:

    1. Gu, Jiaying & Russell, Thomas M., 2023. "Partial identification in nonseparable binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 528-562.
    2. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    3. Shakeeb Khan & Arnaud Maurel & Yichong Zhang, 2023. "Informational Content of Factor Structures in Simultaneous Binary Response Models," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 385-410, Emerald Group Publishing Limited.
    4. Ma, Jun & Marmer, Vadim & Yu, Zhengfei, 2023. "Inference on individual treatment effects in nonseparable triangular models," Journal of Econometrics, Elsevier, vol. 235(2), pages 2096-2124.
    5. 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.
    6. Brice Romuald Gueyap Kounga, 2023. "Nonparametric Regression with Dyadic Data," Papers 2310.12825, arXiv.org.
    7. Huber Martin & Wüthrich Kaspar, 2019. "Local Average and Quantile Treatment Effects Under Endogeneity: A Review," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-27, January.
    8. Wüthrich, Kaspar, 2019. "A closed-form estimator for quantile treatment effects with endogeneity," Journal of Econometrics, Elsevier, vol. 210(2), pages 219-235.
    9. Kaspar Wüthrich, 2020. "A Comparison of Two Quantile Models With Endogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 443-456, April.
    10. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    11. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Dummy Endogenous Variables in Weakly Separable Multiple Index Models without Monotonicity," Boston College Working Papers in Economics 996, Boston College Department of Economics.
    12. Koki Fusejima, 2020. "Identification of multi-valued treatment effects with unobserved heterogeneity," Papers 2010.04385, arXiv.org, revised Apr 2023.
    13. Takuya Ishihara, 2020. "Panel Data Quantile Regression for Treatment Effect Models," Papers 2001.04324, arXiv.org, revised Nov 2021.
    14. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Identification and Estimation of Weakly Separable Models Without Monotonicity," Papers 2003.04337, arXiv.org, revised Apr 2020.
    15. Christopher Adjaho & Timothy Christensen, 2022. "Externally Valid Policy Choice," Papers 2205.05561, arXiv.org, revised Jul 2023.
    16. Abrevaya, Jason & Xu, Haiqing, 2023. "Estimation of treatment effects under endogenous heteroskedasticity," Journal of Econometrics, Elsevier, vol. 234(2), pages 451-478.
    17. Junlong Feng, 2019. "Matching Points: Supplementing Instruments with Covariates in Triangular Models," Papers 1904.01159, arXiv.org, revised Jul 2020.
    18. Sungwon Lee, 2024. "Partial identification and inference for conditional distributions of treatment effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 107-127, January.

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