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Estimation and Inference for Distribution Functions and Quantile Functions in Treatment Effect Models

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Abstract

We propose inverse probability weighted estimators for the distribution functions of the potential outcomes of a binary treatment under the unconfoundedness assumption. We also apply the inverse mapping on the distribution functions to obtain the quantile functions. We show that the proposed estimators converge weakly to zero mean Gaussian processes. A simulation method based on the multiplier central limit theorem is proposed to approximate these limiting Gaussian processes. The estimators in the treated subpopulation are shown to share the same properties. To demonstrate the usefulness of our results, we construct Kolmogorov-Smirnov type tests for stochastic dominance relations between the distributions of potential outcomes. We examine the finite sample properties of our tests in a set of Monte-Carlo simulations and use our tests in an empirical example which shows that a job training program had a positive effect on incomes.

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Bibliographic Info

Paper provided by Institute of Economics, Academia Sinica, Taipei, Taiwan in its series IEAS Working Paper : academic research with number 12-A016.

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Length: 43 pages
Date of creation: Dec 2012
Date of revision:
Handle: RePEc:sin:wpaper:12-a016

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Keywords: Hypothesis testing; stochastic dominance; treatment effects; propensity score;

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Cited by:
  1. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.

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