Primary Submission Category: Instrumental Variables
Covariate-Assisted Nonparametric Bounds of Causal Effects with Instrumental Variables
Authors: Alexander Levis, Matteo Bonvini, Zhenghao Zeng, Luke Keele, Edward Kennedy,
Presenting Author: Alexander Levis*
When the effect of an exposure of interest is confounded by unmeasured factors, an instrumental variable (IV) can be used to identify and estimate certain causal contrasts. Identification of the marginal average treatment effect (ATE) from IVs typically relies on strong untestable structural assumptions. When one is unwilling to assert such structural assumptions, IVs can nonetheless be used to construct bounds on the ATE. Famously, linear programming techniques were employed to prove tight bounds on the ATE for a binary outcome, in a randomized trial with noncompliance and no covariate information. We demonstrate how these bounds remain useful in observational settings with baseline confounders of the IV, as well as randomized trials with measured baseline covariates. The resulting lower and upper bounds on the ATE are non-smooth functionals, and thus standard nonparametric efficiency theory is not immediately applicable. To remedy this, we propose (1) estimators of smooth approximations of these bounds, and (2) under a novel margin condition, influence function-based estimators of the ATE bounds that can attain parametric convergence rates when nuisance functions are modeled flexibly. We propose extensions to continuous outcomes, and finally, illustrate the proposed estimators in a randomized experiment studying the effects of influenza vaccination encouragement on flu-related hospital visits.