Breakdown Analysis for Instrumental Variables with Binary Outcomes

TL;DR

This paper develops methods to assess the robustness of instrumental variable estimates with binary outcomes when the key independence assumption may be violated, providing bounds and breakdown values for treatment effects.

Contribution

It introduces nonparametric estimators for bounds and breakdown values in IV models with binary outcomes, addressing violations of the independence assumption.

Findings

The bounds are $ oot{N}$-consistent and nonparametric.

Empirical analysis shows sensitivity of results to independence violations.

Provides tools for robustness assessment in observational IV studies.

Abstract

This paper studies the partial identification of treatment effects in Instrumental Variables (IV) settings with binary outcomes under violations of independence. I derive the identified sets for the treatment parameters of interest in the setting, as well as breakdown values for conclusions regarding the true treatment effects. I derive $\sqrt{N}$-consistent nonparametric estimators for the bounds of treatment effects and for breakdown values. These results can be used to assess the robustness of empirical conclusions obtained under the assumption that the instrument is independent from potential quantities, which is a pervasive concern in studies that use IV methods with observational data. In the empirical application, I show that the conclusions regarding the effects of family size on female unemployment using same-sex siblings as the instrument are highly sensitive to violations of independence.