Unconditional Quantile Treatment Effects under Endogeneity
This paper develops IV estimators for unconditional quantile treatment effects (QTE) when the treatment selection is endogenous. In contrast to conditional QTE, i.e. the effects conditional on a large number of covariates X, the unconditional QTE summarize the effects of a treatment for the entire population. They are usually of most interest in policy evaluations because the results can easily be conveyed and summarized. Last but not least, unconditional QTE can be estimated at √n rate without any parametric assumption, which is obviously impossible for conditional QTE (unless all X are discrete). In this paper we extend the identification of unconditional QTE to endogenous treatments. Identification is based on a monotonicity assumption in the treatment choice equation and is achieved without any functional form restriction. Several types of estimators are proposed: regression, propensity score and weighting estimators. Root n consistency, asymptotic normality and attainment of the semiparametric efficiency bound are shown for our weighting estimator, which is extremely simple to implement. We also show that including covariates in the estimation is not only necessary for consistency when the instrumental variable is itself confounded but also for efficiency when the instrument is valid unconditionally. Monte Carlo simulations and two empirical applications illustrate the use of the proposed estimators.
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- Frölich, Markus, 2006.
"A Note on Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables,"
IZA Discussion Papers
2126, Institute for the Study of Labor (IZA).
- Markus Frölich, 2006. "A Note on Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables," University of St. Gallen Department of Economics working paper series 2006 2006-11, Department of Economics, University of St. Gallen.
- 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.
- Andrew Chesher, 2005.
"Nonparametric Identification under Discrete Variation,"
Econometric Society, vol. 73(5), pages 1525-1550, 09.
- Andrew Chesher, 2003. "Nonparametric identification under discrete variation," CeMMAP working papers CWP19/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- 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.
- Frolich, Markus, 2007. "Nonparametric IV estimation of local average treatment effects with covariates," Journal of Econometrics, Elsevier, vol. 139(1), pages 35-75, July.
- Frölich, Markus, 2002. "Nonparametric IV Estimation of Local Average Treatment Effects with Covariates," IZA Discussion Papers 588, Institute for the Study of Labor (IZA).
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