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Efficient semiparametric estimation of quantile treatment effects. (English) Zbl 1201.62043

Summary: This paper develops estimators for quantile treatment effects under the identifying restriction that selection to treatment is based on observable characteristics. Identification is achieved without requiring computation of the conditional quantiles of the potential outcomes. Instead, the identification results for the marginal quantiles lead to an estimation procedure for the quantile treatment effect parameters that has two steps: nonparametric estimation of the propensity score and computation of the difference between the solutions of two separate minimization problems. Root-\(N\) consistency, asymptotic normality, and achievement of the semiparametric efficiency bound are shown for that estimator. A consistent estimation procedure for the variance is also presented. Finally, the method developed is applied to evaluation of a job training program and to a Monte Carlo exercise. Results from empirical applications indicate that the method works relatively well even for a data set with limited overlap between treated and controls in the support of covariates. The Monte Carlo study shows that, for a relatively small sample size, the method produces estimates with good precision and low bias, especially for middle quantiles.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62F10 Point estimation
65C05 Monte Carlo methods

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