Nonparametric Inference with an Instrumental Variable under a Separable Binary Treatment Choice Model

2026-02-02

AI Summary

This study addresses nonparametric inference on treatment effects in separable binary treatment selection models under unobserved confounding. By introducing a perturbation-independent parametrization directly defined by observed data and combining instrumental variables with a fixed-point argument, the authors construct a semiparametrically efficient estimator that avoids imposing unnecessary restrictions on the nuisance functions. The approach flexibly accommodates nonlinear effects, average treatment effects over the full population, and non-randomly missing data, while allowing modern machine learning methods to estimate nuisance components. Theoretical analysis establishes efficiency bounds and validates the underlying generative model, and both simulations and an empirical application to the Job Corps data demonstrate that the method yields efficient and robust estimation of smooth functionals, along with testable identification assumptions.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationIntelligent Robots: State EstimationReasoning under Uncertainty: Graphical Models

Application Category

User Modeling, Personalization and Recommendation: Fairness-aware retrieval and rankingGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsEconomics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Instrumental variable (IV) methods are widely used to infer treatment effects in the presence of unmeasured confounding. In this paper, we study 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. While nonparametric identification of smooth functionals of the treatment-free potential outcome among the treated, such as the average treatment effect on the treated, has been established under this model, corresponding nonparametric efficient estimation has proven elusive due to variationally dependent nuisance parameters defined in terms of counterfactual quantities. To address this challenge, we introduce 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 nuisance function 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. Furthermore, we describe a straightforward generative model justifying our identifying assumptions and characterize empirically falsifiable implications of the framework to evaluate our assumptions in practical settings. Our approach seamlessly extends to nonlinear treatment effects, population-level effects, and nonignorable missing data settings. We illustrate our methods through simulation studies and an application to the Job Corps study.

Problem

• instrumental variable
• nonparametric inference
• treatment effect
• nuisance parameters
• semiparametric efficiency

Innovation

• nonparametric inference
• instrumental variable
• variationally independent parameterization
• semiparametric efficiency
• machine learning