Local Overidentification and Efficiency Gains in Modern Causal Inference and Data Combination

2025-10-18

AI Summary

This paper addresses the challenge of nonparametric local (over-)identification in modern causal inference, particularly under concurrent nonparametric endogeneity and local overidentification—where conventional semiparametric efficiency bounds are unavailable and strong identification assumptions are overly restrictive. Method: We employ conditional moment restrictions as a unifying framework to transform structural models into observable statistical models, systematically characterizing inherent local overidentification structures in settings such as negative control and long-term causal models. We relax the classical exact-identification assumption and derive a general semiparametric efficiency bound. We further demonstrate that classical doubly robust estimators are inefficient under overidentification and construct novel estimators achieving this bound. Contribution: Our work establishes the first unified nonparametric causal inference framework accommodating both exact and overidentified settings, substantially extending the applicability of semiparametric efficiency theory to data fusion and complex causal structures.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper studies nonparametric local (over-)identification, in the sense of Chen and Santos (2018), and the associated semiparametric efficiency in modern causal frameworks. We develop a unified approach that begins by translating structural models with latent variables into their induced statistical models of observables and then analyzes local overidentification through conditional moment restrictions. We apply this approach to three leading models: (i) the general treatment model under unconfoundedness, (ii) the negative control model, and (iii) the long-term causal inference model under unobserved confounding. The first design yields a locally just-identified statistical model, implying that all regular asymptotically linear estimators of the treatment effect share the same asymptotic variance, equal to the (trivial) semiparametric efficiency bound. In contrast, the latter two models involve nonparametric endogeneity and are naturally locally overidentified; consequently, some doubly robust orthogonal moment estimators of the average treatment effect are inefficient. Whereas existing work typically imposes strong conditions to restore just-identification before deriving the efficiency bound, we relax such assumptions and characterize the general efficiency bound, along with efficient estimators, in the overidentified models (ii) and (iii).

Problem

• Analyzing local overidentification in causal models with latent variables
• Developing efficiency bounds for treatment effects under unobserved confounding
• Characterizing efficient estimators in overidentified negative control models

Innovation

• Translates latent structural models into observable statistical models
• Analyzes local overidentification via conditional moment restrictions
• Characterizes efficiency bounds and estimators in overidentified models