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This paper considers the problem of assessing the distributional consequences of a treatment on some outcome variable of interest when treatment intake is (possibly) non-randomized but there is a binary instrument available for the researcher. Such scenario is common in observational studies and in randomized experiments with imperfect compliance. One possible approach to this problem is to compare the counterfactual cumulative distribution functions of the outcome with and without the treatment. Here, it is shown how to estimate these distributions using instrumental variable methods and a simple bootstrap procedure is proposed to test distributional hypotheses, such as equality of distributions, first-order stochastic dominance and second order stochastic dominance. These tests and estimators are applied to the study of the effects of veteran status on the distribution of civilian earnings. The results show a negative effect of military service in Vietnam that appears to be concentrated on the lower tail of the distribution of earnings. First order stochastic dominance cannot be rejected by the data.

Bootstrap Tests for the Effect of a Treatment on the Distribution of an Outcome Variable