# Dummy variable interaction

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?

Thank-you!

• – landroni May 3 '15 at 17:03

## 1 Answer

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.)

• So the dummy variable interaction is subdividing the group of private school students into male and female? – ajohnrobertson May 17 '14 at 14:21