I am having some difficulty attempting to interpret an interaction between two categorical/dummy variables. For example, lets say there is an interaction term between an individual's gender and her race.
sex=1 if male & race=1 if white
There is an interaction term between sex and race
Let's say this is the regression model:
wage = 𝛽0 + 𝛽1*educ + 𝛽2*sex + 𝛽3*race + 𝛽4*(sex*race) + e
How would you interpret 𝛽4 in this model? I presume it would be that if an individual is male and white, his wage will increase by 𝛽4. 𝛽2 would be if an individual is male, his wage will increase by 𝛽2+𝛽4*race and 𝛽3 would be if an individual is white, then his wage will increase by 𝛽3+𝛽4*white. Is this a correct interpretation? If not, please help me understand any flaws in my intuition. I appreciate the help, thank you.