Quantifying Omitted Variable Bias in Nonlinear Instrumental Variable Estimators

Abstract

We develop a framework for quantifying omitted variable bias (OVB) in nonlinear instrumental variable (IV) estimators, including the local average treatment effect (LATE), the LATE for the treated (LATT), and the partially linear IV model (PLIVM). Extending sensitivity analysis beyond linear settings, we derive bias decompositions, establish partial identification bounds, and construct OVB-adjusted confidence intervals. We estimate OVB bounds and conduct inference using double machine learning (DML), allowing flexible control for high-dimensional covariates. An application to the U.S. Job Training Partnership Act (JTPA) experiment shows that, at conventional significance levels, first-stage compliance estimates are robust to omitted variables, whereas intention-to-treat and treatment effects are more sensitive. Program impacts are robust and significant for females but fragile for males.