An integral equation for the identification of causal effects in nonlinear models

2021/05/11 by Wing Hung Wong, Wong, Wing Hung
Chemistry · Mathematics · #Advanced Causal Inference Techniques #FOS: Mathematics #Molecular spectroscopy and chirality #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.2105.05299

arxiv created 2021/05/11 · openalex publication_date 2021/05/11 · arxiv updated 2021/05/13 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

When the causal relationship between X and Y is specified by a structural equation, the causal effect of X on Y is the expected rate of change of Y with respect to changes in X, when all other variables are kept fixed. This causal effect is not identifiable from the distribution of (X,Y). We give conditions under which this causal effect is identified as the solution of an integral equation based on the distributions of (X,Z) and (Y,Z), where Z is an instrumental variable.

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