Assessing Sensitivity to IV Exclusion and Exogeneity without First Stage Monotonicity

2026-04-08

AI Summary

This study addresses the challenge of conducting instrumental variable analysis when the exclusion restriction and exogeneity assumptions are difficult to verify and the standard first-stage monotonicity condition fails to hold. The authors propose a novel nonparametric sensitivity analysis framework that relaxes these conventional assumptions, enabling identification of sharp bounds on the marginal distributions of potential outcomes and their functionals—such as the average treatment effect—without imposing monotonicity or restricting treatment effect heterogeneity. The resulting identification problem is cast as a linear program with favorable theoretical properties, accompanied by a computationally feasible estimation strategy suitable for infinite-dimensional settings. Empirically, the method is applied to estimate peer effects in movie attendance using weather as an imperfect instrument, demonstrating its practical utility and robustness.

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.

Problem

• instrumental variables
• exclusion restriction
• exogeneity
• sensitivity analysis
• treatment effect heterogeneity

Innovation

• instrumental variables
• sensitivity analysis
• exclusion restriction
• exogeneity
• nonparametric identification