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Estimating Conditional Average Treatment Effects

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  • Jason Abrevaya
  • Yu-Chin Hsu
  • Robert P. Lieli

Abstract

We consider a functional parameter called the conditional average treatment effect (CATE), designed to capture heterogeneity of a treatment effect across subpopulations when the unconfoundedness assumption applies. In contrast to quantile regressions, the subpopulations of interest are defined in terms of the possible values of a set of continuous covariates rather than the quantiles of the potential outcome distributions. We show that the CATE parameter is nonparametrically identified under the unconfoundedness assumption and propose inverse probability weighted estimators for it. Under regularity conditions, some of which are standard and some of which are new in the literature, we show (pointwise) consistency and asymptotic normality of a fully nonparametric and a semiparametric estimator. We apply our methods to estimate the average effect of a firsttime mother's smoking during pregnancy on the baby's birth weight as a function of per capita income in the mother's zip code. For nonwhite mothers, the average effect of smoking is predicted to become stronger (more negative) as a function of income.

Suggested Citation

  • Jason Abrevaya & Yu-Chin Hsu & Robert P. Lieli, 2012. "Estimating Conditional Average Treatment Effects," CEU Working Papers 2012_16, Department of Economics, Central European University, revised 20 Jul 2012.
  • Handle: RePEc:ceu:econwp:2012_16
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    References listed on IDEAS

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    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, December.
    2. Stephen G. Donald & Yu-Chin Hsu & Robert P. Lieli, 2014. "Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 395-415, July.
    3. Abrevaya, Jason & Dahl, Christian M, 2008. "The Effects of Birth Inputs on Birthweight," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 379-397.
    4. Jason Abrevaya, 2006. "Estimating the effect of smoking on birth outcomes using a matched panel data approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 489-519.
    5. Frolich, Markus, 2007. "Nonparametric IV estimation of local average treatment effects with covariates," Journal of Econometrics, Elsevier, vol. 139(1), pages 35-75, July.
    6. Stephen G. Donald & Yu-Chin Hsu & Robert P. Lieli, 2012. "Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT," IEAS Working Paper : academic research 12-A017, Institute of Economics, Academia Sinica, Taipei, Taiwan, revised Jan 2014.
    7. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    8. Matias D. Cattaneo, 2010. "multi-valued treatment effects," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
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    Cited by:

    1. Sheila M. Olmstead & Hilary Sigman, 2015. "Damming the Commons: An Empirical Analysis of International Cooperation and Conflict in Dam Location," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 2(4), pages 497-526.
    2. repec:eee:pubeco:v:152:y:2017:i:c:p:13-33 is not listed on IDEAS
    3. Richard H. Spady & Sami Stouli, 2016. "Dual Regression," Bristol Economics Discussion Papers 16/669, Department of Economics, University of Bristol, UK.
    4. Kazuo Mino, 2016. "Fiscal Policy in a Growing Economy with Financial Frictions and Firm Heterogeneity," The Japanese Economic Review, Japanese Economic Association, pages 3-30.
    5. Sokbae Lee & Ryo Okui & Yoon-Jae Whang, 2016. "Doubly robust uniform confidence band for the conditional average treatment effect function," CeMMAP working papers CWP03/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Roberton C. Williams III & Hal Gordon & Dallas Burtraw & Jared C. Carbone & Richard D. Morgenstern, 2015. "The Initial Incidence of a Carbon Tax Across Income Groups," National Tax Journal, National Tax Association, pages 195-214.

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