Valid Instrumental Variables Selection Methods using Auxiliary Variable and Constructing Efficient Estimator
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In observational studies, we are usually interested in estimating causal effects between treatments and outcomes. When some covariates are not observed, an unbiased estimator usually cannot be obtained. In this paper, we focus on instrumental variable (IV) methods. By using IVs, an unbiased estimator for causal effects can be estimated even if there exists some unmeasured covariates. Constructing a linear combination of IVs solves weak IV problems, however, there are risks estimating biased causal effects by including some invalid IVs. In this paper, we use Negative Control Outcomes as auxiliary variables to select valid IVs. By using NCOs, there are no necessity to specify not only the set of valid IVs but also invalid one in advance: this point is different from previous methods. We prove that the estimated causal effects has the same asymptotic variance as the estimator using Generalized Method of Moments that has the semiparametric efficiency. Also, we confirm properties of our method and previous methods through simulations.
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