The Natural Value of Treatment and Its Importance for Causal Inference

The natural treatment value (NTV) is the value a treatment takes when it is not altered by an intervention. This observable random variable is foundational to statistical causal inference. On the one hand, identification hinges on our substantive knowledge about the NTV. On the other hand, the NTV is a defining feature of canonical estimands, like the average treatment effect in the treated, local average treatment effects, and natural effects in mediation analysis. In this article, we argue why an explicit and formal consideration of the NTV is important in statistics and related fields, and describe its role in guiding statistical analysis, formulating identification conditions, falsifying assumptions, and relating different estimands. We also review a growing literature studying estimands explicitly defined by the NTV. This allows us to highlight a subtle, often-overlooked identification issue that challenges the study of dynamic regimes that depend on the NTV. Finally, we illustrate how NTV parameters are often motivated by pragmatic concerns, and we consider the practical relevance of some of these estimands.