Identification and Inference with Invalid Instruments

TL;DR

This paper reviews methods for identifying and making inferences using invalid instrumental variables in causal analysis, covering linear, non-linear, and heteroskedastic models, with an empirical case study.

Contribution

It provides a comprehensive review of identification and inference techniques for invalid instruments across different models, highlighting practical challenges and solutions.

Findings

Methods perform variably depending on the violation type.

Empirical analysis demonstrates differences in causal estimates.

Some approaches remain robust despite instrument invalidity.

Abstract

Instrumental variables (IVs) are widely used to study the causal effect of an exposure on an outcome in the presence of unmeasured confounding. IVs require an instrument, a variable that is (A1) associated with the exposure, (A2) has no direct effect on the outcome except through the exposure, and (A3) is not related to unmeasured confounders. Unfortunately, finding variables that satisfy conditions (A2) or (A3) can be challenging in practice. This paper reviews works where instruments may not satisfy conditions (A2) or (A3), which we refer to as invalid instruments. We review identification and inference under different violations of (A2) or (A3), specifically under linear models, non-linear models, and heteroskedatic models. We conclude with an empirical comparison of various methods by re-analyzing the effect of body mass index on systolic blood pressure from the UK Biobank.