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Many proposals for the identification of causal effects require aninstrumental variable that satisfies strong, untestable unconfoundedness andexclusion restriction assumptions. In this paper, we show how one canpotentially identify causal effects under violations of these assumptions byharnessing a negative control population or outcome. This strategy allows oneto leverage sub-populations for whom the exposure is degenerate, and requiresthat the instrument-outcome association satisfies a certain parallel trendcondition. We develop the semiparametric efficiency theory for a generalinstrumental variable model, and obtain a multiply robust, locally efficientestimator of the average treatment effect in the treated. The utility of theestimators is demonstrated in simulation studies and an analysis of the LifeSpan Study.

Using negative controls to identify causal effects with invalid instrumental variables