Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models

Abstract

This article considers the problem of assessing the distributional consequences of a treatment on some outcome variable of interest when treatment intake is (possibly) nonrandomized, but there is a binaryinstrument available for the researcher. Such a 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. This article shows 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 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 during the Vietnam era that appears to be concentrated on the lower tail of the distribution of earnings. First-order stochastic dominance cannot be rejected by the data.

KEY WORDS:

• Compliers
• Empirical processes
• Kolmogorov–Smirnov test
• Stochastic dominance