Covariate-assisted bounds on causal effects with instrumental variables

Area of Science:

• Causal inference
• Econometrics
• Biostatistics

Background:

• Instrumental variables (IVs) are crucial for estimating causal effects when unmeasured confounding exists.
• Traditional IV methods often require strong, untestable assumptions for identifying average treatment effects (ATE).
• Existing bounds on ATE are valuable but have limitations in complex observational and trial settings.

Purpose of the Study:

• To extend the utility of instrumental variable bounds for average treatment effects (ATE) in observational studies with baseline confounders.
• To adapt IV bounds for randomized trials incorporating measured baseline covariates.
• To develop novel statistical methods for efficiently estimating these bounds.

Main Methods:

• Demonstrated the applicability of Balke and Pearl's tight bounds in observational settings with IV confounders and in randomized trials with covariates.
• Proposed influence function-based estimators under a novel margin condition to achieve parametric convergence rates.
• Developed estimators for smooth approximations of the nonsmooth ATE bounds and extended methods to continuous outcomes.

Main Results:

• The proposed methods provide robust bounds on the average treatment effect (ATE) in more complex, real-world scenarios.
• Influence function-based estimators demonstrated the potential for parametric convergence rates with flexible nuisance function modeling.
• Simulations explored finite sample properties, and an application to higher education's effect on wages illustrated practical utility.

Conclusions:

• The study successfully extends instrumental variable bounding techniques to broader observational and trial data settings.
• Novel estimation strategies offer improved efficiency for nonsmooth functional bounds in causal inference.
• The findings provide valuable tools for estimating causal effects in the presence of unmeasured confounding and covariates.