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Suppose I have a model with an interaction between two dummy variables

$$ \begin{equation} wage = \beta_0 + \beta_1 male+ \beta_2 white + \beta_3 educ + \beta_4 (male* white) + \epsilon \end{equation} $$

and that the coefficient for $ \beta_4 $ is significant.

Am I able to say that the impact of being white is significantly conditioned by gender (i.e. that the coefficient for white is different across men and women)? In the case of a continuous moderator, I would plot the conditional effect of the independent variable for different values of the moderator and see whether this effect is statistically different from zero. Should I do something similar also in this case? Thanks a lot.

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  • $\begingroup$ When variable interactions like this start being important, consider a Structural Equation Modeling (SEM) approach. Interaction terms will get the job done, but with less clarity/interpretability. $\endgroup$
    – Mox
    Feb 7, 2023 at 18:35

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You can say both the impact of being white is significantly conditioned by gender and equally the impact of gender is significantly conditioned by being white. You can plot the distribution of $wage$ in each of the four subgroups, for instance using box-and-whisker plots, violin plot, and even scatter plots. See for example Figure R9 here: https://wellcomeopenresearch.org/articles/4-63

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