I've encountered lots of causal inference terms and jargons (under the Neyman-Rubin potential outcome framework), and I had a question regarding mediator and moderator.
Is it the case that moderation / moderators (interaction terms) necessarily implies unobserved causal mediation?
For example, both gender and race can have impact on income. In this case, if we have a (significant) multiplicative interaction term for gender and race into the regression model (i.e., gender moderates the impact of race, or vice versa), does it implies that there exists unobserved causal mediation (i.e., indirect effects) and we are trying to use this interaction as a proxy for that?
Causal Inference: Ignorability and Collider
Causal Inference: Selection Bias and Endogeneity