Consider the following model:
$wage_i = \beta_0 + \beta_1male_i + \beta_2private_i +u_i$
where $male_i=1$ if male; $0$ if female, and $private_i=1$ if private school; $0$ if state school.
The base group is females from state schools.
So when $male_i=1$ and $private_i=1$, the coefficients $\beta_1 + \beta_2$ measure the average wage differential of males from private schools compared to females from state schools.
But now suppose we add an interaction between the two dummy variables into the model so that:
$wage_i = \beta_0 + \beta_1male_i + \beta_2private_i + \beta_3male_iprivate_i+u_i$
So now when $male_i=1$ and $private_i=1$, what do the coefficients $\beta_1 + \beta_2 +\beta_3$ measure?
What is the interaction between these two dummy variables adding to the model?