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Unconditional Quantile Treatment Effects under Endogeneity

  • Frölich, Markus

    ()

    (University of Mannheim)

  • Melly, Blaise

    ()

    (Brown University)

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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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 3288.

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Length: 83 pages
Date of creation: Jan 2008
Date of revision:
Publication status: published in: Journal of Business & Economic Statistics, 2013, [Online First]
Handle: RePEc:iza:izadps:dp3288
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  1. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, 09.
  2. 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).
  3. Frölich, Markus, 2002. "Nonparametric IV Estimation of Local Average Treatment Effects with Covariates," IZA Discussion Papers 588, Institute for the Study of Labor (IZA).
  4. 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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