Latent variable justifies the stronger instrumental variable bounds

          @misc{ pirsa_PIRSA:23040120,
            doi = {10.48660/23040120},
            url = {https://pirsa.org/23040120},
            author = {Guo, Richard },
            keywords = {Quantum Foundations},
            language = {en},
            title = {Latent variable justifies the stronger instrumental variable bounds},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {apr},
            note = {PIRSA:23040120 see, \url{https://pirsa.org}}
          }
          

Abstract

For binary instrumental variable models, there seems to be a long-standing gap between two sets 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 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 generalize Bell's (1964) inequality.