Identification and Debiased Learning of Causal Effects with General Instrumental Variables

Instrumental variable methods are fundamental to causal inference when treatment assignment is confounded by unobserved variables. In this article, we develop a general nonparametric causal framework for identification and learning with multi-categorical or continuous instrumental variables. Specifically, the mean potential outcomes and the average treatment effect can be identified via a regular weighting function derived from the proposed framework. Leveraging semiparametric theory, we derive efficient influence functions and construct two consistent, asymptotically normal estimators via debiased machine learning. The first estimator uses a prespecified weighting function, while the second estimator selects the optimal weighting function adaptively. Extensions to longitudinal data, dynamic treatment regimes, and multiplicative instrumental variables are further developed. We demonstrate the proposed method by employing simulation studies and analyzing real data from the Job Training Partnership Act program.

💡 Research Summary

This paper develops a comprehensive non‑parametric causal inference framework for settings where the instrument variable (IV) is multi‑categorical or continuous, extending the reach of IV methods beyond the traditional binary‑IV, monotonicity‑based approaches. The authors introduce the concept of a regular weighting function (RWF), a bounded function π(Z, L) whose conditional covariance with the treatment indicator I{A = a} is uniformly bounded away from zero. This definition simultaneously captures the classic IV relevance and positivity requirements, and under a “strong IV relevance” assumption (Assumption 2.5) the existence of an RWF is shown to be equivalent to the non‑degeneracy of the conditional treatment probability Pr(A = a | Z, L).

To achieve identification, the paper formulates a non‑parametric IV equation E