Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models

TLDR

Such a scenario is common in observational studies and in randomized experiments with imperfect compliance. The article aims to assess the distributional effects of a treatment using instrumental variable methods and a bootstrap procedure to test hypotheses such as equality of distributions and stochastic dominance. The authors compare counterfactual cumulative distribution functions, estimate them with instrumental variable techniques, and use a bootstrap procedure to test distributional hypotheses, applying the method to veteran status effects on civilian earnings. The analysis finds that Vietnam‑era military service has a negative impact concentrated in the lower tail of civilian earnings, yet first‑order stochastic dominance cannot be rejected.

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.