Average Treatment Effect with Continuous Instrumental Variables

Music City Center 

The instrumental variable (IV) approach is a widely used method for estimating the average treatment effect (ATE) in the presence of unmeasured confounders. Existing methods for continuous IVs often rely on structural equation modeling, which imposes strong parametric assumptions and can yield biased estimates, particularly for binary outcomes. In this work, we propose a novel nonparametric identification strategy for the ATE using a continuous IV under the potential outcome framework, leveraging the conditional weighted average derivative effect. For estimation, we assume a partial linear model for the IV-treatment relationship. Under this model, we develop a bounded, locally efficient, and multiply robust estimator that extends the properties of semiparametric efficient estimators for binary IVs to continuous IVs. Notably, our estimator remains consistent even if the partial linear model is misspecified. Simulation results demonstrate that our proposed multiply robust estimator is unbiased and robust to model misspecification. Finally, we apply the proposed estimators to estimate the causal effect of obesity on the two-year mortality rate of non-small cell lung cancer patients.

Average Treatment Effect

Continuous Instrumental Variable

Semiparametric Efficiency 

Biometrics Section