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Estimations of the Local Conditional Tail Average Treatment Effect

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  • Le-Yu Chen
  • Yu-Min Yen

Abstract

The conditional tail average treatment effect (CTATE) is defined as a difference between the conditional tail expectations of potential outcomes, which can capture heterogeneity and deliver aggregated local information on treatment effects over different quantile levels and is closely related to the notion of second-order stochastic dominance and the Lorenz curve. These properties render it a valuable tool for policy evaluation. In this paper, we study estimation of the CTATE locally for a group of compliers (local CTATE or LCTATE) under the two-sided noncompliance framework. We consider a semiparametric treatment effect framework under endogeneity for the LCTATE estimation using a newly introduced class of consistent loss functions jointly for the conditional tail expectation and quantile. We establish the asymptotic theory of our proposed LCTATE estimator and provide an efficient algorithm for its implementation. We then apply the method to evaluate the effects of participating in programs under the Job Training Partnership Act in the US.

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  • Le-Yu Chen & Yu-Min Yen, 2021. "Estimations of the Local Conditional Tail Average Treatment Effect," Papers 2109.08793, arXiv.org, revised May 2024.
    • Handle: RePEc:arx:papers:2109.08793
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    References listed on IDEAS

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    1. Markus Frölich & Martin Huber, 2017. "Direct and indirect treatment effects–causal chains and mediation analysis with instrumental variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1645-1666, November.
    2. Hans Fricke & Markus Frölich & Martin Huber & Michael Lechner, 2020. "Endogeneity and non‐response bias in treatment evaluation – nonparametric identification of causal effects by instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(5), pages 481-504, August.
    3. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    4. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    5. Markus Frölich & Blaise Melly, 2013. "Unconditional Quantile Treatment Effects Under Endogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 346-357, July.
    6. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 487-535.
    7. Bo Wei & Limin Peng & Mei‐Jie Zhang & Jason P. Fine, 2021. "Estimation of causal quantile effects with a binary instrumental variable and censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 559-578, July.
    8. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    9. Yi-Ting Chen & Yu-Chin Hsu & Hung-Jen Wang, 2020. "A Stochastic Frontier Model with Endogenous Treatment Status and Mediator," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 243-256, April.
    10. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    11. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    12. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    13. 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.
    14. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    15. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    16. Meng, Xiaochun & Taylor, James W., 2020. "Estimating Value-at-Risk and Expected Shortfall using the intraday low and range data," European Journal of Operational Research, Elsevier, vol. 280(1), pages 191-202.
    17. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2007. "Inference approaches for instrumental variable quantile regression," Economics Letters, Elsevier, vol. 95(2), pages 272-277, May.
    18. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, October.
    19. James W. Taylor, 2019. "Forecasting Value at Risk and Expected Shortfall Using a Semiparametric Approach Based on the Asymmetric Laplace Distribution," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 121-133, January.
    20. Jonathan B. Hill, 2015. "Expected Shortfall Estimation and Gaussian Inference for Infinite Variance Time Series," Journal of Financial Econometrics, Oxford University Press, vol. 13(1), pages 1-44.
    21. Linton, Oliver & Xiao, Zhijie, 2013. "Estimation Of And Inference About The Expected Shortfall For Time Series With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 29(4), pages 771-807, August.
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    Cited by:

    1. Wei, Bo & Tan, Kean Ming & He, Xuming, 2024. "Estimation of complier expected shortfall treatment effects with a binary instrumental variable," Journal of Econometrics, Elsevier, vol. 238(2).

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