In this section we will study the problem of gender-wagediscrimination. It is often argued that women are paid less thanequally qualified men to do the same job. This is also true inacademia. The University of Calgary administrators are trying todetermine the gender earnings gap in order to `compensate' womenwho are underpaid. In the empirical analyses that follow, thefollowing variables are defined as:

Y - Log earnings

F - female indicator

Age - age of individual

Assoc - indicator for Associate Professor Rank

Full - indicator for Full Professor Rank

Ï´_f- faculty/college indicators (e.g., SocialScience, Engineering, Business...)

Ï´_d- department indicators (e.g., economics,history...)

1. Consider the following:

E[Y_i|F_i = 1] -E[Y_i|F_i = 0]

Do you think that this identified thecausal effect of being a woman on wage? Explain.

1. Consider the following regression equation:

Y_i = β₀ + αF_i +ε_i                                                                                                                   (1)

What variation in the data is beingused to identify the male-female difference in earnings?

1. Consider the following augmented regression:

Y_i = β₀ +αF_i + βAge_i +ε_i                                                                                                       (2)

How does adding age to the regressionchange the source of variation used in identifying the male-

female wage differential?

If female professors are, on average,younger than male professors, how would you expect the estimate ofα to change from equation (1)?

1. Consider the following augmented regression:

Y_i = β₀ +αF_i + βAge_i + γ₁Assoc_i+ γ₁Full_i +ε_{i                                                                                                             Â} (3)

Now what variation in the data is usedto identify the male-female difference in earnings? How would theestimate of α change relative to equation (1) if females areover-represented in the assistant professor rank?

1. Consider the following augmented regression:

Y_i = β₀ +αF_i + βAge_i + γ₁Assoc_i+ γ₁Full_i + Ï´_f +ε_i                                                                   (4)

Now what variation in the data is usedto identify the male-female difference in earnings? How would theestimate of α change relative to question 2 if females areover-represented in the higher paying faculties/colleges? What isthe difference between running this regression and runningregression 3 separately for each faculty/college?

1. Discuss whether or not you would want to interact thedepartment (or Assoc and Full) indicators with the femaleindicator. What other interactions might be important? Whatproblems might you run into if you try to include too manyinteractions?

1. Suppose the regression in question e suggested that women wereunderpaid relative to men. Discuss a few things that might be “leftout\" of this regression that you would ideally want to controlfor.