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Estimation of treatment effects under endogenous heteroskedasticity

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  • Abrevaya, Jason
  • Xu, Haiqing

Abstract

This paper considers a treatment effect model in which individual treatment effect may be heterogeneous, even among observationally identical individuals. Specifically, by extending the classical instrumental-variables (IV) model with an endogenous binary treatment, the heteroskedasticity of the error disturbance is allowed to vary with the treatment variable so that the treatment generates both mean and variance effect on the outcome. In this endogenous heteroskedasticity IV (EHIV) model, the standard IV estimator can be inconsistent for the average treatment effect (ATE) and lead to incorrect inference. After nonparametric identification is established, closed-form estimators are provided under the linear EHIV specification for the mean and variance treatment effect, as well as the average treatment effect on the treated (ATT). Asymptotic properties of the estimators are derived. We use Monte Carlo experiments to investigate the performance of the proposed approach and then consider an empirical application regarding the effect of fertility on female labor supply. Our findings demonstrate the importance of accounting for endogenous heteroskedasticity.

Suggested Citation

  • Abrevaya, Jason & Xu, Haiqing, 2023. "Estimation of treatment effects under endogenous heteroskedasticity," Journal of Econometrics, Elsevier, vol. 234(2), pages 451-478.
    • Handle: RePEc:eee:econom:v:234:y:2023:i:2:p:451-478
    DOI: 10.1016/j.jeconom.2021.01.011
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    1. Rosenzweig, Mark R & Wolpin, Kenneth I, 1980. "Life-Cycle Labor Supply and Fertility: Causal Inferences from Household Models," Journal of Political Economy, University of Chicago Press, vol. 88(2), pages 328-348, April.
    2. Wan, Yuanyuan & Xu, Haiqing, 2015. "Inference in semiparametric binary response models with interval data," Journal of Econometrics, Elsevier, vol. 184(2), pages 347-360.
    3. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    4. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    5. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    6. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    7. 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.
    8. Eric Maurin & Julie Moschion, 2009. "The Social Multiplier and Labor Market Participation of Mothers," American Economic Journal: Applied Economics, American Economic Association, vol. 1(1), pages 251-272, January.
    9. Stacey H. Chen & Shakeeb Khan, 2014. "Semi‐Parametric Estimation Of Program Impacts On Dispersion Of Potential Wages," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(6), pages 901-919, September.
    10. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    11. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    12. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(3), pages 560-586, June.
    13. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, September.
    14. 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.
    15. Rosenzweig, Mark R & Wolpin, Kenneth I, 1980. "Testing the Quantity-Quality Fertility Model: The Use of Twins as a Natural Experiment," Econometrica, Econometric Society, vol. 48(1), pages 227-240, January.
    16. James J. Heckman & Vytlacil, Edward J., 2007. "Econometric Evaluation of Social Programs, Part I: Causal Models, Structural Models and Econometric Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 70, Elsevier.
    17. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    18. Qian Feng & Quang Vuong & Haiqing Xu, 2020. "Estimation of Heterogeneous Individual Treatment Effects With Endogenous Treatments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 231-240, January.
    19. Bronars, Stephen G & Grogger, Jeff, 1994. "The Economic Consequences of Unwed Motherhood: Using Twin Births as a Natural Experiment," American Economic Review, American Economic Association, vol. 84(5), pages 1141-1156, December.
    20. 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.
    21. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    22. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    23. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    24. Victor Chernozhukov & Christian Hansen, 2004. "The Effects of 401(K) Participation on the Wealth Distribution: An Instrumental Quantile Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 735-751, August.
    25. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    26. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
    27. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
    28. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
    29. 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.
    30. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    31. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
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