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arXiv · 2607.21481

Identification and Robust Inference for Multiple Treatments with Possibly Invalid Instruments

Ziwei Mei·Qingliang Fan·Zijian Guo
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Abstract

The instrumental variable (IV) method is widely used to infer causal effects in observational studies with unmeasured confounding, but invalid instruments can compromise both population identification and finite-sample inference. This paper studies linear IV models with multiple endogenous treatments and possibly invalid instruments. Identification of multiple effects is more delicate than in the single-treatment setting because a single instrument no longer identifies a single candidate effect; instead, each relevant instrument defines a hyperplane in the multidimensional effect space. For identification of multiple treatment effects, we introduce generalized plurality and majority rules which require a sufficiently large number of IVs to be valid. For inference, data-dependent instrument selection may fail to separate certain invalid IVs from valid ones, leading to undercoverage of confidence intervals when these invalid instruments are mistakenly selected as valid. We propose a sampling confidence interval for each treatment effect, which is robust to IV selection errors. We establish asymptotic coverage and parametric-rate length of our sampling confidence interval under regularity conditions and illustrate this method in Monte Carlo simulations and a Mendelian randomization application.

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Ziwei Mei, Qingliang Fan, Zijian Guo. 2026-07-23. Identification and Robust Inference for Multiple Treatments with Possibly Invalid Instruments. https://arxiv.org/abs/2607.21481

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