Suppose we are interested in the effect of gender on income and estimate a model that includes a dummy variable for men. If we instead estimate a model that includes a dummy variable for women,
A) The coefficient on the dummy variables will be exactly the same.
B) The coefficient on the dummy variables will differ across models, but the estimated difference of means between men and women will not change.
C) The fit of the model will change.
D) We will get different answers when testing a null hypothesis that there is no gender effect.

Question

Quizplus · Accepted Answer

The coefficient on the dummy variables will differ across models since the reference category changes, but the estimated difference of means between men and women will still be captured by the coefficients on the dummy variables. This means that the effect of gender on income will still be estimated, but the interpretation of the coefficients will change. The fit of the model may or may not change, depending on the data and the specific model specifications. We will not get different answers when testing a null hypothesis that there is no gender effect, since the null hypothesis will be the same in both models.

Suppose We Are Interested in the Effect of Gender on Income