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Preprints, Working Papers, ... Year : 2023

The difference between structural counterfactuals and potential outcomes

Lucas de Lara

Abstract

Most of the literature on causality considers the structural framework of Pearl and the potential-outcome framework of Neyman and Rubin to be formally equivalent, and therefore interchangeably uses the do-notation and the potential-outcome subscript notation to write counterfactual outcomes. In this paper, we superimpose the two causal frameworks to prove that structural counterfactual outcomes and potential outcomes do not coincide in general---not even in law. More precisely, we express the law of the potential outcomes in terms of the latent structural causal model under the fundamental assumptions of causal inference. This enables us to precisely identify when counterfactual inference is or is not equivalent between approaches, and to clarify the meaning of each kind of counterfactuals.
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Dates and versions

hal-04203003 , version 1 (11-09-2023)
hal-04203003 , version 2 (06-10-2023)
hal-04203003 , version 3 (17-03-2024)

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Lucas de Lara. The difference between structural counterfactuals and potential outcomes. 2023. ⟨hal-04203003v1⟩
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