Using negative controls to identify causal effects with invalid instrumental variables

TL;DR

This paper introduces a method to identify causal effects using negative controls to relax traditional instrumental variable assumptions, enabling valid inference even with invalid instruments.

Contribution

It develops a semiparametric efficiency framework and a robust estimator leveraging negative controls to address violations of instrumental variable assumptions.

Findings

Estimator is multiply robust and locally efficient.

Simulation studies demonstrate estimator performance.

Application to Life Span Study illustrates practical utility.

Abstract

Many proposals for the identification of causal effects require an instrumental variable that satisfies strong, untestable unconfoundedness and exclusion restriction assumptions. In this paper, we show how one can potentially identify causal effects under violations of these assumptions by harnessing a negative control population or outcome. This strategy allows one to leverage sub-populations for whom the exposure is degenerate, and requires that the instrument-outcome association satisfies a certain parallel trend condition. We develop the semiparametric efficiency theory for a general instrumental variable model, and obtain a multiply robust, locally efficient estimator of the average treatment effect in the treated. The utility of the estimators is demonstrated in simulation studies and an analysis of the Life Span Study.