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Estimation and inference for distribution functions and quantile functions in treatment effect models. (English) Zbl 1293.62070

Summary: We propose inverse probability weighted estimators for the distribution functions of the potential outcomes under the unconfoundedness assumption and apply the inverse mapping to obtain the quantile functions. We show that these estimators converge weakly to zero mean Gaussian processes. A simulation method is proposed to approximate these limiting processes. Based on these results, we construct tests for stochastic dominance relations between the potential outcomes. Monte-Carlo simulations are conducted to examine the finite sample properties of our tests. We apply our test in an empirical example and find that a job training program had a positive effect on incomes.

MSC:

62G05 Nonparametric estimation
62G10 Nonparametric hypothesis testing
62G30 Order statistics; empirical distribution functions
62G20 Asymptotic properties of nonparametric inference
62P20 Applications of statistics to economics
91B82 Statistical methods; economic indices and measures
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