For binary instrumental variable models, there seems to be a long-standing gap between two set of bounds on the average treatment effect: the stronger Balke–Pearl ("sharp") bounds versus the weaker Robins-Manski ("natural") bounds. In the literature, the Balke–Pearl bounds are typically derived under stronger assumptions, i.e., either individual exclusion or joint exogeneity, which are untestable cross-world statements, while the natural bounds only require testable assumptions. In this talk, I show that the stronger bounds are in fact justified by the existence of a latent confounder. In fact, the Balke-Pearl bounds are sharp under latent confounding and stochastic exclusion. The "secret sauce" that closes this gap is a set of CHSH-type inequalities that generalized Bell's (1964) inequality.

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