Using negative controls to identify causal effects with invalid instrumental variables

TL;DR

The paper addresses causal effect identification when instrumental variables may violate core IV assumptions by leveraging reference populations and negative controls under a parallel-trends–like stability condition. It develops a comprehensive semiparametric efficiency framework and a quadruple-robust, cross-fitting estimator for the average treatment effect on the treated, with NSM and NEM variants to enable identification and estimation. Identification relies on a reference population to correct bias and on either no-effect-modification or no-selection-modification to transport effects, while negative controls provide additional bias-reduction mechanisms. Empirical evaluation via simulations and a Life Span Study demonstrates robustness to model misspecification and illustrates the practical utility of these methods when traditional IV assumptions fail.

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.

Figures (1)

• Figure 1: Possible DAG with a reference population

Theorems & Definitions (25)

• Proposition 2.0.1
• Remark
• Remark
• Remark
• Theorem 2.1
• Theorem 3.1
• Definition 1
• Example 1
• Theorem 3.2
• Theorem A.1