Consider the following dummy-variable regression model for the annual salary of engineers on the basis of race.

Here, is annual salary, is years of training/education after the job, is years of experience, and = 1 if the engineer is white and = 0 if the engineer is non-white.

(a) Write down the equation of expected (fitted) salary for both white and non-white engineers.

(b) State the condition under which non-white engineers will not start with a higher salary than white.

(c) Assume that non-white engineers start with higher salary than white engineers. Write down the model that will allow you to investigate whether or not the gap in salary increases or decreases with the increase in years of education and experience.

(d) Write down the condition under which the gap in salary will not decrease with the increase in years of experience. Write down the condition under which the white engineers will catch up with the increase in years of training/education.