Variance-based difference between graphical identification conditions of causal effects in linear structural equation models

In the context of statistical causal inference using linear structural equation models, researchers in the field of artificial intelligence and statistical science have developed several identification conditions for evaluating causal effects. However, there are some scenarios where several identification conditions can be applied simultaneously to estimate causal effects. To enhance estimation accuracy, we focus on five key identification conditions: the back-door criterion, the front-door criterion, the front-door-like criterion, the conditional instrumental variable condition, and the effect restoration condition. We then compare these five identification conditions in terms of estimation accuracy (asymptotic variance) and conclude that, in some cases, the qualitative comparison of estimation accuracy among these identification conditions can be directly assessed from the graphical structure, even before statistical data are collected.