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?

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  • $\begingroup$ Moderation looks at effect modifiers. That is variables for which the causal effect is heterogeneous in subgroups defined by the variables. (Possible) Effect modifiers are variables that come before the treatment intervention and are studied to assess subgroup treatment effects. Mediator variables, on the other hand, come after the treatment and are causally affected by the treatment. Looking at (possible) mediators is useful to see what mechanism actually makes the treatment effective. $\endgroup$
    – user327671
    Commented Aug 30, 2021 at 0:03
  • $\begingroup$ For instance, raised antibody levels caused by a vaccine intervention are considered to be (close to) the actual mechanism that prevents viral infection. If antibody levels perfectly mediate the vaccine efficacy then two different vaccines with the same antibody response should have the same vaccine efficacy. This is useful because you can then approve different vaccines faster by looking at the immune-response generated. If a perfect mediator is found then there is less need for new multibillion dollar clinical vaccine trials every time someone makes a new vaccine. $\endgroup$
    – user327671
    Commented Aug 30, 2021 at 0:04

1 Answer 1


Mediation and moderation are two unrelated concepts that can but do not always occur together.

Mediation occurs when the effect of one variable on another passes through a third variable, e.g., $A \rightarrow M \rightarrow Y$. $M$ is a mediator of the relationship between $A$ and $Y$. $A$ may also have a direct effect on $Y$ or other indirect effects through other mediators.

Moderation occurs when the effect of one variable varies across levels of another variable, e.g., $E[Y^1-Y^0|X=1] \ne E[Y^1-Y^0|X=2]$. $X$ is a moderator of the effect of the treatment on $Y$.

Moderation can occur without mediation when the moderator and the treatment do not cause each other, such as in a randomized experiment where both the treatment and moderator are randomized. There is no mediator because neither variable is caused by the other, but there could be moderation if the effect of the treatment varies across levels of the moderator.


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