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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.

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Bibliographic Info

Paper provided by Department of Economics, Central European University in its series CEU Working Papers with number 2012_16.

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Date of creation: 20 Jul 2012
Date of revision: 20 Jul 2012
Handle: RePEc:ceu:econwp:2012_16

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  1. Markus Froelich, 2002. "Nonparametric IV estimation of local average treatment effects with covariates," University of St. Gallen Department of Economics working paper series 2002 2002-19, Department of Economics, University of St. Gallen.
  2. 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.
  3. 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.
  4. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
  5. 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.
  6. Matias D. Cattaneo, 2010. "multi-valued treatment effects," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
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