Nonparametric Estimation of Local Treatment Effects with Continuous Instruments

2025-04-03

AI Summary

Local average treatment effects (LATE) under continuous instrumental variables (IVs) rely heavily on strong parametric assumptions—often unverifiable and limiting practical applicability. Method: We propose the first nonparametric LATE generalization framework, introducing the “Maximum Complier-Class Average Effect” (MACAE) as a newly identifiable target. Under monotonicity, we extend LATE identification to continuous IVs; construct a doubly robust nonparametric estimator free of functional-form assumptions; and derive its optimal convergence rate and asymptotic normality, explicitly characterizing how nuisance function estimation impacts inference with continuous IVs. Results: Simulations demonstrate substantial improvements in bias, variance, and robustness over existing parametric approaches. The framework provides ready-to-use solutions for data-driven bandwidth selection and asymptotic variance estimation, enabling principled inference for continuous-IV settings without restrictive modeling assumptions.

Technology Category

• Machine Learning: Causal Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Causality

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Instrumental variable methods are widely used to address unmeasured confounding, yet much of the existing literature has focused on the canonical binary instrument setting. Extensions to continuous instruments often impose strong parametric assumptions for identification and estimation, which can be difficult to justify and may limit their applicability in complex real-world settings. In this work, we develop theory and methods for nonparametric estimation of treatment effects with a continuous instrumental variable. We introduce a new estimand that, under a monotonicity assumption, quantifies the treatment effect among the maximal complier class, generalizing the local average treatment effect framework to continuous instruments. Considering this estimand and the local instrumental variable curve, we draw connections to the dose-response function and its derivative, and propose doubly robust estimation methods. We establish convergence rates and conditions for asymptotic normality, providing valuable insights into the role of nuisance function estimation when the instrument is continuous. Additionally, we present practical procedures for bandwidth selection and variance estimation. Through extensive simulations, we demonstrate the advantages of the proposed nonparametric estimators.

Problem

• Nonparametric estimation of treatment effects with continuous instruments
• Generalizing local average treatment effect to continuous settings
• Addressing limitations of parametric assumptions in instrumental variable methods

Innovation

• Nonparametric estimation with continuous instrumental variables
• Doubly robust estimation methods for treatment effects
• Bandwidth selection and variance estimation procedures