Constructing valid instrumental variables in generalized linear causal models from directed acyclic graphs

TL;DR

This paper develops a formal framework for constructing and testing valid instrumental variables within generalized linear causal models, addressing the challenge of unobserved confounders and imperfect instruments.

Contribution

It provides a formal validity condition for instruments in generalized linear models, enabling construction and testing of valid instruments and assessing bias when instruments are imperfect.

Findings

Validity condition for instruments in generalized linear models

Method for constructing valid instruments using DAGs

Bias estimation for imperfect instruments with bootstrapping

Abstract

Unlike other techniques of causality inference, the use of valid instrumental variables can deal with unobserved sources of both variable errors, variable omissions, and sampling bias, and still arrive at consistent estimates of average treatment effects. The only problem is to find the valid instruments. Using the definition of Pearl (2009) of valid instrumental variables, a formal condition for validity can be stated for variables in generalized linear causal models. The condition can be applied in two different ways: As a tool for constructing valid instruments, or as a foundation for testing whether an instrument is valid. When perfectly valid instruments are not found, the squared bias of the IV-estimator induced by an imperfectly valid instrument -- estimated with bootstrapping -- can be added to its empirical variance in a mean-square-error-like reliability measure.