Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach
This addresses a critical issue in causal inference for fields like economics and epidemiology where measurement errors are common, offering a novel solution to a previously understudied problem.
The paper tackles the problem of estimating causal effects when the treatment variable is corrupted by measurement error and there is unobserved confounding, proposing a nonparametric instrumental variable estimator. The method, MEKIV, empirically improves over baselines and shows robustness to variations in error strength and distributions.
We propose a kernel-based nonparametric estimator for the causal effect when the cause is corrupted by error. We do so by generalizing estimation in the instrumental variable setting. Despite significant work on regression with measurement error, additionally handling unobserved confounding in the continuous setting is non-trivial: we have seen little prior work. As a by-product of our investigation, we clarify a connection between mean embeddings and characteristic functions, and how learning one simultaneously allows one to learn the other. This opens the way for kernel method research to leverage existing results in characteristic function estimation. Finally, we empirically show that our proposed method, MEKIV, improves over baselines and is robust under changes in the strength of measurement error and to the type of error distributions.