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?



1 Answer 1


Let's say that $\beta_1>0, \beta_2<0, \beta_3>0$.
$\beta_1$ says that wage is higher for men.
$\beta_2$ says that wage is lower for people (irrespective of gender) from private schools.
$\beta_3$ says that wage is higher for men from private schools (but lower for women from private schools, when $male_i=0$; even lower than for women from public schools.)

  • $\begingroup$ So the dummy variable interaction is subdividing the group of private school students into male and female? $\endgroup$ Commented May 17, 2014 at 14:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.