🤖 AI Summary
This study addresses the quantification of omitted variable bias in nonlinear instrumental variable (IV) estimation by extending sensitivity analysis to nonlinear IV frameworks, encompassing local average treatment effects (LATE), LATE for treated individuals (LATT), and partially linear IV models (PLIVM). The authors derive bias decompositions, construct partial identification bounds, and develop computable bias bounds alongside robust inference procedures that adjust confidence intervals accordingly. Integrating double machine learning (DML), the approach accommodates flexible control for high-dimensional covariates. Application to the JTPA experiment reveals that estimated program effects for women remain robustly significant, whereas those for men are sensitive to potential omitted variables; first-stage compliance rate estimates are stable, but intent-to-treat and treatment effect estimates exhibit greater fragility.
📝 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.