A fully stochastic potential outcome model proves that the IV estimand identifies the degree-of-compliance-weighted average treatment effect (DATE) without assuming deterministic parallel universes.
Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics
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Never Too LATE: A Fully Stochastic Update to the Potential Outcome Framework
A fully stochastic potential outcome model proves that the IV estimand identifies the degree-of-compliance-weighted average treatment effect (DATE) without assuming deterministic parallel universes.