To Investigate Whether or Not There Is Discrimination Against a Sub-Group

To investigate whether or not there is discrimination against a sub-group of individuals, you regress the log of earnings on determining variables, such as education, work experience, etc., and a binary variable which takes on the value of one for individuals in that sub-group and is zero otherwise. You consider two possible specifications. First you run two separate regressions, one for the observations that include the sub-group and one for the others. Second, you run a single regression, but allow for a binary variable to appear in the regression. Your professor suggests that the second equation is better for the task at hand, as long as you allow for a shift in both the intercept and the slopes. Explain her reasoning.