On the Testability of Causal Models with Latent and Instrumental Variables

TL;DR

This paper develops a general formula to test the validity of causal models with latent and instrumental variables, enabling researchers to determine if such models can explain observed data or if variables are truly instrumental.

Contribution

It introduces a new formula for testing instrumental variables in causal models with unmeasured factors, advancing causal inference methods.

Findings

Derived a general formula for instrumental variable constraints

Provided a method to test model compatibility with observed data

Enhanced tools for causal inference with latent variables

Abstract

Certain causal models involving unmeasured variables induce no independence constraints among the observed variables but imply, nevertheless, inequality contraints on the observed distribution. This paper derives a general formula for such instrumental variables, that is, exogenous variables that directly affect some variables but not all. With the help of this formula, it is possible to test whether a model involving instrumental variables may account for the data, or, conversely, whether a given variables can be deemed instrumental.