Nonparametric Inference with an Instrument under a Separable Binary Treatment Choice Model

Thomas M. Menino Convention & Exhibition Center 

Instrumental variable (IV) methods are widely used to infer causal effects in the presence of unmeasured confounding. In this paper, we propose nonparametric inference with an IV under a separable binary treatment choice model, which posits that the odds of the probability of taking the treatment, conditional on the instrument and the treatment-free potential outcome, factor into separable components for each variable. Our approach employs a new variationally independent parameterization based on nuisance functions defined directly from the observed data. This parameterization, coupled with a novel fixed-point argument, enables the use of modern machine learning methods for estimation. We characterize the semiparametric efficiency bound for any smooth functional of the treatment-free potential outcome among the treated and construct a corresponding semiparametric efficient estimator without imposing any unnecessary restriction on nuisance functions. We also describe a generative model and derive empirically falsifiable implications to help assess our assumptions. Our approach extends to nonlinear effects, population-level effects, and nonignorable missing data settings.

Causal Inference

Instrumental Variable

Missing Data

Odds Ratio

Semiparametric Efficiency 

Section on Statistics in Epidemiology