Assessing Sensitivity to IV Exclusion and Exogeneity without First Stage Monotonicity

TL;DR

This paper introduces new sensitivity analysis methods for IV assumptions that do not rely on monotonicity, accommodating heterogeneity and providing computational tools for empirical research.

Contribution

It develops identified sets for potential outcomes under broad relaxations of exclusion and exogeneity, with practical estimation techniques.

Findings

Derived identified sets as solutions to linear programs.

Provided estimation methods for infinite-dimensional linear programs.

Applied methods to peer effects in movie viewership with weather as an instrument.

Abstract

Exclusion and exogeneity are core assumptions in instrumental variable (IV) analyses, but their empirical validity is often debated. This paper develops new sensitivity analyses for these assumptions. Our results accommodate arbitrary heterogeneity in treatment effects and do not impose any monotonicity requirements on the first stage. Specifically, we derive identified sets for the marginal distributions of potential outcomes and their functionals, like average treatment effects, under a broad class of nonparametric relaxations of the exclusion and exogeneity assumptions. These identified sets are characterized as solutions to linear programs and have desirable theoretical properties. We explain how to estimate these solutions using computationally tractable methods even when the linear program is infinite-dimensional. We illustrate these methods with an empirical application to peer effects in movie viewership, using weather as a potentially imperfect instrument.