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Title: A Bayesian approach for estimating the causal effects using sparse invalid instrumental variables Authors:  Shunsuke Horii - Waseda University (Japan) [presenting]
Abstract: The estimation of the causal effect of a potentially endogenous treatment on some outcome is studied. One of the ways to handle the endogeneity is to use the additional variables called instrumental variables. Instrumental variables are correlated with the endogenous treatment variable, but they do not have direct effects on the outcome. The latter condition is called excludability. It is known that the excludability condition is not testable, and sometimes it may be violated. We employ a Bayesian estimation in models that consider the endogeneity and shrinkage prior to the instrumental variables which may not satisfy the excludability conditions. The assumption that the excludability condition of the instrumental variables may be violated is modeled by assuming horseshoe prior to the regression coefficients on the regression from the instrumental variables to the objective variable. We show that the Bayesian inference algorithm can estimate the target causal effect correctly through simulation experiments.