3
$\begingroup$

If I regress wages on education and the dummy variable gender using a linear conditional expectation function (wage = a + b(education) + c(gender)), how can I test that the slope b is the same for both males and females? i.e. the returns to education are the same?

Intuitively, I was thinking that one could conduct simple linear regressions of wage on education for males and females separately and then do a two-sample hypothesis test for whether the slope estimates are significantly different. Would this introduce issues with the omitted variable gender? Thank you.

$\endgroup$
3
$\begingroup$

Estimate the model $$W_i=a_1+a_2E_i+a_3G_i+a_4E_iG_i+\epsilon_i,$$ where $W,E,G$ denote wage, education, and an indicator for gender (e.g. 1 if male, 0 if female), respectively. The term $EG$ is an interaction term obtained by multiplying the gender dummy by education. A simple t-test of the hypothesis $H_0: a_4=0$ will tell you if the effects of additional education on wage are significantly different for different genders.

$\endgroup$
  • 1
    $\begingroup$ I see what you're doing but wouldn't using the same model without the interaction term and testing for $a3 = 0$ test the same thing ? Thanks for insight. $\endgroup$ – mark leeds Mar 18 at 3:45
  • 1
    $\begingroup$ Good question. $a3$ and $a4$ are actually addressing different effects. In particular, $a_3$ is an intercept shifter for different genders, while $a_4$ is a slope shifter with respect to education level. So testing $a_3=0$ is testing whether, all else equal, wages are significantly different across genders. On the other hand, testing $a_4=0$ is testing, all else equal, whether an extra year of education has a significantly different impact on wages across genders. $\endgroup$ – dlnB Mar 18 at 3:48
  • $\begingroup$ gotcha. it's an intercept test. but I wonder if the intercept coefficient should be in there when testing for different slopes because the intercept inclusion could maybe "effect" the slope effect ? Just a thought. Thanks for great explanation. $\endgroup$ – mark leeds Mar 18 at 18:31
  • $\begingroup$ Whether or not one should include the dummy $G_i$ should be motivated by institutional knowledge of the dataset. In particular, if you have a reason to believe that men earn more than women (or vice versa) independent from the effects of education, one should include $G_i$. $\endgroup$ – dlnB Mar 18 at 18:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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